ANL-79-41 ANL-79-41

PROCEEDINGS OF THE HEAVY ION FUSION WORKSHOP HELD AT ARGONNE NATIONAL LABORATORY SEPTEMBER 19-26, 1978

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ANL-79-41

Argonne National Laboratory 9700 South Cass Avenue Argonne, Illinois 60439

Proceedings of the Heavy Ion Fusion Workshop Held at Argonne National Laboratory September 19-26, 1978

Sponsored by the U.S. Department of Energy Office of Laser Fusion and Division of High Energy and Nuclear Physics

Proceedings Editor R. C. Arnold

Workshop Organizing Committee R, L. Martin {ANL, Chairman), R. Bangerter (LLL), T. Godlove (DOE), W. Herrmannsfeldt (SLAC), D. Keefe (LBL), J. Leiss (NBS), A. Maschke (BNL), L. Teng (FNAL), and D, Tidman (U. Md.)

PREFACE

This workshop was the third in a series of annual workshop meetings on Inertial Fusion Driven by Beams of Heavy Ions at GeV Energies. It was held September 19 through 26, 1978, at Argonne National Laboratory. There were 158 participants, representing U.S. national Laboratories, other government laboratories, universities, and industries; European and Japanese representa­ tives also attended.

The workshop had three primary goals:

1. Critical examination of reference designs for prototype one-mega- joule reactor drivers (previously distributed by ANL, BNL, and LBL), includ­ ing the suitability of heavy-ion demonstration experiments based on these designs, and possible upgrading to a few megajoules.

2. Exchange of information on the progress of heavy ion fusion programs at the participating institutions.

3. Communication of information on heavy ion fusion in order to enhance industry and university support for the civilian heavy ion fusion program, as suggested by a recent U.S. DOE Fusion Review.

At the workshop, four different conceptual driver designs were presented. To accomplish the first goal of the workshop, technical review of these de­ signs was carried out by parallel workshop sessions, examining the areas of ion sources, low-velocity linacs, beam manipulations, beam transport and focussing, plasma effects in the reactor chamber, ionic collision cross sec­ tions, and cost estimation.

The second workshop goal, information exchange, was accomplished through presentations on the first day from each of the principal laboratories cur­ rently funded by DOE (ANL, BNL, LBL, and LLL) for work in heavy ion fusion, and by invited talks and informal discussions in the workshops.

On Monday, September 25, tutorial sessions were held on all aspects of heavy ion fusion, primarily for industrial and university observers, in pur­ suit of the third goal. These tutorial sessions were videotaped for wider distribution, and are now available on loan from Argonne.

In addition to the working review sessions, plenary invited talks were held on the mornings of September 20-22 covering topics of interest to the participants. Some of the texts for those talks were provided by the authors for reproduction here.

The conclusions of the technical review were assembled by a committee of four (L. Teng, Chairman; D. Sutter; D. Judd; and F. Mills). Their report, included in these Proceedings, provides a technical overview of the current status of heavy-ion reactor driver design.

TABLE OF CONTENTS

PREFACE i

I. OVERVIEW vii

II. REVIEWS OF CURRENT LABORATORY PROGRAMS ARGONNE NATIONAL LABORATORY 1 LAWRENCE BERKELEY LABORATORY 31 LAWRENCE LIVERMORE LABORATORY 57

III. INVITED TALKS A PLAN FOR THE DEVELOPMENT AND COMMERCIALIZATION OF INERTIAL CONFINEMENT FUSION T. Willke 61 FOCUSING EXPERIMENTS WITH LIGHT ION DIODES D. J. Johnson 89 HIGH CURRENT LINEAR ION ACCELERATORS FOR INERTIAL FUSION S. Humphries, Jr. 93 DIAGNOSTICS FOR PELLET EXPERIMENTS R. R. Johnson 101 SCALING LAWS FOR INERTIAL CONFINEMENT FUSION K. A. Brueckner 111

IV. REPORTS OF THE WORKSHOPS ATOMIC AND MOLECULAR PHYSICS J, Macek, Chairman 117 COST ANALYSIS AND SYSTEM DESIGN E, K. Freytag, Chairman 121 ION SOURCES D. J. Clark and R. L, Seliger, Chairmen 127 LOW BETA LINACS J, Keane, Chairman 131 BEAM MANIPULATIONS AND BUNCHING T. Khoe, Chairman 139 HIGH CURRENT TRANSPORT AND FINAL FOCUS LENSES A, Garren. Chairman 141 PLASMA EFFECTS W. Thompson, Chairman 147

111 V. REPORT OF THE REFERENCE DESIGN COMMITTEE 1. Teng, Chairman 15^ VI. CONTRIBUTED PAPERS A. ATOMIC AND MOLECULAR CROSS SECTIONS CHARGE CHANGING CROSS SECTIONS FOR Cs"*" + Cs"^ COLLISIONS R. E. Olson 171 ATOMIC CROSS SECTIONS FOR FAST Xe^"*" AND u'^"'' IONS COLLIDING WITH ATOMS AND MOLECULES G. Gillespie, K-T. Cheng, and Y-K. Kim 1'^^ PRELIMINARY ESTIMATE OF HEAVY ION ELECTRON-TRANSFER CROSS SECTIONS S. Sramek, G. Gallup, and J. Macek 183 CHARGE EXCHANGE CROSS SECTIONS FOR THE REACTION Xe+8 + Xe+8 ^ Xe+9 + Xe+7 J. Macek ^^^ LOW-LYING STATES OF (Cs2) G. Das, R. C. Raffenetti, and Y-K. Kim 19^ CHARGE EXCHANGE BETWEEN SINGLY IONIZED HELIUM IONS B. H. Choi, R. T. Poe, and K. T. Tang 201 COST ANALYSIS AND SYSTEMS DESIGN PRELIMINARY SYSTEMS EVALUATION OF HEAVY ION BEAM FUSION DRIVERS 209 T. Kammash and C. R. Drumm ELEMENTS TO BE CONSIDERED IN PLANNING A HEAVY ION FUSION PROGRAM - A SUMMARY 219 I. Bohachevsky ELECTRIC POWER FROM INERTIAL CONFINEMENT FUSION: THE HYLIFE CONCEPT M. Monsler, J. Blink, J. Hovingh, W. Meier, and 225 P. Walker PHASE-SPACE CONSTRAINTS ON SOME HEAVY-ION INERTIAL- FUSION IGNITERS AND EXAMPLE DESIGNS OF 1 MJ RF LINAC SYSTEMS 237 D. Judd HEAVY ION FUSION DEVELOPMENT PLAN A. W. Maschke 249 REMARKS ON HIF DEVELOPMENT AND WEAPONS PROLIFERATION ISSUES R. C. Arnold 255 ION SOURCES NEUTRALIZATION OF POSITIVE PARTICLE BEAMS BY ELECTRON TRAPPING R. M. Mobley, A. A, Irani, J, L. LeMaire, and A. W. Maschke 257

IV NOTE ON XENON TESTS WITH LBL MATS SOURCE R. Mobley 265 A CHARGE SEPARATING SPECTROMETER FOR ANNULAR ION BEAMS W. B. Herrmannsfeldt 267 D. LOW BETA LINACS A MULTI-AMPERE HEAVY ION INJECTOR FOR LINEAR INDUCTION ACCELERATORS USING PERIODIC ELECTROSTATIC FOCUSING W. B. Herrmannsfeldt 273 FACTORS CAUSING LARGE TRANSVERSE EMITTANCE INCREASE IN LINACS USING A HIGH-BRIGHTNESS ION SOURCE J. Staples 287 GABOR LENS THEORY A. A. Irani 291 GABOR LENSES—EXPERIMENTAL RESULTS AT BROOKHAVEN R. M. Mobley 299

E. BEAM MANIPULATIONS AND BUNCHING INSERTION OF SKEW QUADRUPOLES TO EXCHANGE X-X' AND Y-Y' PHASE SPACES D. Neuffer 309 COMBINING BEAMS IN TRANSVERSE SPACE IN A LINEAR SYSTEM M. Foss 313 F. HIGH CURRENT TRANSPORT AND FINAL FOCUS LENSES HIGH CURRENT TRANSPORT OF NON K-V DISTRIBUTIONS I. Haber 317 COMPARISON OF INSTABILITY THEORY WITH SIMULATION RESULTS L. J. Laslett, L. Smith, and I. Haber 321 THE ARGONNE NATIONAL LABORATORY HEAVY ION BEAM TRANSPORT EXPERIMENTS WITH A 2 mA 80 keV Xe+l SOURCE M. Mazarakis, D. Price, and J. Watson 325 GEOMETRIC ABERRATIONS IN FINAL FOCUSSING FOR HEAVY ION FUSION D. Neuffer 333 QUADRUPOLE SYSTEMS FOR FOCUSSING ION BEAMS WITH LARGE MOMENTUM SPREAD J, Steinhoff 345 OCTUPOLE CORRECTION OF THIRD ORDER ABERRATION S. Fenster 355 CORRECTION OF CHROMATIC AND GEOMETRIC ABERRATIONS USING SEXTUPOLES AND OCTUPOLES E. Colton 365 G. PLASMA EFFECTS

FILAMENTATION AND TWO-STREAM INSTABILITIES IN HEAVY ION FUSION TARGET CHAMBERS R. F. Hubbard, D. S. Spicer, and D. A. Tidman 379 DISRUPTION OF GEOMETRIC FOCUS BY SELF-MAGNETIC FIELDS D. Mosher and S. Goldstein 387 FILAMENTATION DURING FINAL TRANSPORT IN A HIGH PRESSURE GAS E. P. Lee 393 BEAM PROPAGATION THROUGH A GASEOUS REACTOR—CLASSICAL TRANSPORT S. S. Yu, H. L. Buchanan, E. P. Lee, and F. W. Chambers "^03 THE BEAM-TARGET INTERACTION IN HEAVY ION FUSION

R. 0. Bangerter ^15

VII. PROGRAM ^21

VIII. LIST OF PARTICIPANTS ^23

VI I. OVERVIEW

OVERVIEW

The four conceptual accelerator designs presented to the workshop partic­ ipants were: a 10 MJ, 200 TW linac-accumulator system with U^^ (BNL); a 1 MJ, 160 TW linac-accumulator system with Hg"'"^ (ANL); a 1 MJ, 160 TW synchrotron- accumulator system with Xe"'"^ (ANL); and a 1 MJ, 160 TW induction linac system with U+4 (LBL). The comments on these designs by the technical working groups, as assembled by the Reference Design Committee, represent an important review of the present status of heavy ion drivers for inertial confinement fusion.

Specific comments were made on each of the conceptual designs and are contained in the report of the Reference Design Committee. General conclu­ sions were as follows:

1. High confidence was expressed in the feasibility of the linac-accumulator systems.

2. Considerably lower confidence was accorded to synchrotron-accumulator systems. This rating is based on the seemingly more complex beam manipu­ lations required, the greater technical difficulty (i.e., the vacuum system), and the possibility of unfavorable charge changing cross sec­ tions. The cost advantage of synchrotron acceleration over linear accel­ eration for this application has also proven to be less than originally anticipated.

3. Induction linacs are attractive because of the simplicity of the required beam manipulations. The acceleration of ions, however, has yet to be demonstrated; and more R&D is required to prove their practicality for this application.

Other working groups contributed information not specifically related to the design concepts. These were groups on atomic and molecular physics, plasma physics, and beam transport.

The Atomic and Molecular Physics Group concluded that the charge exchange cross section for ions with loosely bound electrons, e.g., U"^, could be much more unfavorable than initially anticipated. For ions with no loosely bound electrons (e.g., Cs"*"), the collision ionization cross section (Cs"^I + Cs -"• ^ Cs"*'-'- + Cs*^2 + e) could be more important than charge exchange; theoretical estimation of such cross sections remains difficult.

The Plasma Effects Group concluded that there remains a good possibility that a pressure window around 1 Torr exists for stable propagation through gas in a reactor. Plasma instabilities of various kinds might occur at

Vll pressures outside the window, but the theory needs to be confronted with experiment. It is also clear that propagation in high vacuum (p < 10"^ Torr) is allowed.

Considerable progress has been made in the understanding of the transport of intense beams. The agreement between computer simulation and theory (with the Kapchinski-Vladimersky distribution) for predicting the onset of insta­ bilities is encouraging. It gives confidence to further results of computer simulations (since analytic theory cannot deal with other distributions). However, there does exist a clearly acceptable region of phase advance per cell for transport of intense beams without instabilities.

Chromatic and third order geometric aberrations in the final focus have been investigated and appear to place certain restrictions on the beam. Cor­ rection of these effects with sextupole and octupole magnets is being studied. At worst, avoiding these aberrations might require a larger number of beams on the target.

The Cost Group had a particularly difficult task and found that one week was inadequate to assess the numerous cost saving proposals by the different laboratories and to assure that costing was done on the same basis for the different systems. There was general agreement, however, that 1 MJ driver systems could be built for $400-500 M direct cost and that these figures probably do not represent cost optimized systems. It seems clear that a more detailed cost study is required.

Ronald L. Martin

Vlll II. REVIEWS OF CURRENT LABORATORY PROGRAMS

OVERVIEW OF THE ARGONNE NATIONAL LABORATORY PROGRAM*

Ronald L. Martin Argonne National Laboratory

The heavy ion fusion program at Argonne has two components: design activities and an experimental R&D program. Separate reports on these two activities will be presented. We will make only some general remarks here.

We have presented two reference designs, HEARTHFIRE Reference Concept //2 is a 1 MJ, 160 TW rf linac-accumulator system, a description of which is now available. It had always been our intention to produce such a design since both A, Maschke and I pointed out in our opening addresses at the first workshop in July 1976 the very significant advantages of conventional linac- accumulator systems over synchrotron-accumulator systems in terms of repeti­ tion rate (hence, average beam power) and efficiency. The major drawback at that time appeared to be the relatively high cost of linacs per unit of ion energy. Consequently, we have spent the majority of our design effort inves­ tigating synchrotron acceleration for this application. HEARTHFIRE Reference Concept #3, which was distributed in June of this year, is a description of a 1 MJ, 160 TW synchrotron-accumulator system.

There are many similarities between the two systems. The injector for the synchrotrons, of course, is an rf linac so all of the low energy questions of both systems are nearly identical; and the final beam transport and focus­ sing questions are nearly independent of what type of acceleration is used to arrive at this point. Also, the charge states proposed are similar (Hg"*"° vs. Xe*^8) but for somewhat different reasons.

One of the major uncertainties of synchrotron-accumulator systems has been the charge changing cross sections. Accumulation in much less than 1 sec is difficult if multiple synchrotron pulses are required. Hence, cross sec­ tions of lO"-'- cm^ would lead to unacceptable beam loss. The resolution to this problem, we believe, is in the choice of Xe"^°. This ion has closed shells of principle quantum number 4. It, therefore, should be a very small ion with tightly bound electrons. We estimate that the charge changing cross sections (Including ionization) are an order of magnitude less than those of Xe"*"! and even Xe"*"^ and might be of the order of 10"^^ cm^ in the energy range of interest. Beam loss due to this effect of less than 10% in 1 sec would be expected with this ion. Other ions with the same electronic configuration would be Ba'*'l*^, Cs"*"^, I"^^, and so on to Ag'''^. Xenon appears to be an appro­ priate choice from the point of view of source and accelerator technology

Work supported by the U.S. Department of Energy although very bright cesium sources can be made and iodine is unique in having only a single stable isotope. If lower charge states were desired for syn­ chrotron based systems, it would seem desirable to develop other sources in this series.

For linac-accumulation systems, the charge changing cross sections are of minor importance since accumulation can be done in a few milliseconds. Our earlier work-*- had indicated that a cost advantage was realized in going to lighter ions and higher charge states. The technical difficulty is increased, however, for choices in this direction. In addition, the cost minimum was rather broad so that rational choices depend more on source technology, on the degree of confidence in the beam manipulations required, or other factors, than on cost. For this system, we have chosen mercury ions because they are somewhat heavier than xenon and because we believe the source technology with this ion is quite advanced, Hughes Research Laboratories has built mercury sources as ion thrusters with 90% of the injected mercury atoms appearing in the beam as ions. Mercury is not chemically active and can be prevented from depositing on electrode surfaces (or removed if deposits occur) by maintaining such surfaces at 50-100° C. Thus, a relatively small development program could demonstrate the reliability of a high gradient column transmitting an intense mercury ion beam. Hughes is developing for Argonne 100 mA sources of both xenon and mercury ions. The charge state of eight was chosen for HRC #2 as the highest that we were comfortable with in terms of number of rings and beam lines to transmit the desired power. A lower charge state would increase the confidence level in the credibility of the system and somewhat increase its cost.

The most difficult problem of rapid cycling synchrotrons for this appli­ cation, and one recognized prior to the 1977 workshop at Brookhaven, is the low bunching factor allowed if one wants to maintain a small Ap/p with a high B. In HRC #3 to accelerate with a B of 130 T/sec (60 Hz repetition rate in the synchrotron), the maximum allowed bunching factor is 0.075. As a conse­ quence, the space charge limit per pulse in the synchrotron is correspondingly reduced so that eight synchrotrons, each operating at 60 Hz, are required to accumulate enough ions in 1 sec. The cost advantage initially perceived for synchrotron-accumulator systems is thus reduced. This raises serious ques­ tions of direction: whether the cost advantage for synchrotron-accumulator systems (now projected at little more than $100 M for a 1 MJ driver) justifies the added difficulty, complexity, and greater uncertainty in the result as compared to rf linac-accumulator systems. Our general feeling at this time is that the higher level of confidence of rf linac-accumulator systems overshad­ ows any cost advantage that might remain with rapid cycling synchrotrons. It seems especially clear in view of the many other nonaccelerator related uncer­ tainties of inertial confinement fusion (involving pellets, reactors, tritium handling) that minimizing the cost for the first "proof-of-concept" effort should be a secondary goal. Therefore, we believe the main emphasis of the program should be placed on rf linac systems. This conclusion in no way, of course, impacts Argonne*s R&D program which is focussed on producing a reli­ able front end (source, preaccelerator, low beta linac) common to either rf linac or synchrotron systems.

One should not lose sight of the fact that single pulsing synchrotrons may yet play an important role in the development of heavy ion fusion. Rep­ etition rate and efficiency are not so important in the development and demonstration of the technology, nor in ion-target coupling experiments, as they are in commercial power production. Single pulsing synchrotrons avoid many of the problems referred to above and might represent a significant cost savings for the development program.

R. J. Burke will describe our 1 MJ reference designs in another report. Let me emphasize here that it is essential in both systems to maintain the longitudinal emittance area of the beam at the exit of the linac. This re­ quirement relates to the momentum spread, Ap/p, which can be transported and focussed on the target. Final compression of the beam increases the momentum spread so that dilutions of the longitudinal emittance of the linac beam of a factor of only a few are allowed if one is to have Ap/p on the target <. 3 X 10"-^, which appears to be a maximum value without serious chromatic correc­ tions (dependent, of course, on the size of the target). Therefore, debunch- ing (decreasing Ap/p and increasing the bunch length) at the end of the linac seems essential and is included in both system designs. In addition, in the synchrotron-accumulator system of HRC #3, the preservation of longitudinal emittance was the reason for the complicated (and time consuming) debunching- rebunching operations in stacking rings. Some of these requirements could be alleviated somewhat by achromatic transport lines and chromatic corrections to the final focussing elements. Investigation of chromatic corrections using sextupole magnets, suggested by Brown,3 are being carried out and will be the subject of a paper in these proceedings.^

Another aberration of the final focussing system is the third-order geo­ metrical aberration. The importance of this effect was pointed out by Garren and Neuffer^ and discussed at a meeting held in Berkeley early this summer. The effect is very sensitive to the radius, a, of the beam in the final trip­ let and is proportional to a^. Outstanding questions were where the main contributions of this aberration were coming from and whether a system of octupole magnets could be used to correct the aberration. Work to be reported here^ indicates that the effect is almost entirely due to the fringe fields of the quadrupoles. Calculations with a system including six realizable octupoles indicate that one can nearly eliminate the aberration for a 20 GeV Xe beam with a maximum radius of 30 cm. Space charge forces were not included in this calculation. However, they are not very dominant with beams of such large size in the final focussing system.

J, Watson will give a status report on our experimental program. Our goal is to achieve as high a preaccelerator voltage as we find practical. Space charge limited currents in the initial section of the linac are sensi­ tive to the preaccelerator voltage (since sources of adequate currents are only achieved by extracting singly charged ions). In addition, the resulting higher velocity ions allow a higher initial linac frequency, hence fewer frequency transitions to final, more economic linac structures. Our initial goals are 30 mA of Xe'**-'- at 1.5 MeV and initial linac sections of 12.5 MHz.

References

1. R. Burke, S, Fenster, and S, Grammel, "Systems Analysis of Accelerator and Storage Ring Systems for Inertial Fusion," IEEE Transactions on Nuclear Science, Vol, NS-24, No, 3, p. 996 (June 1977). 2. Tat K. Khoe. Argonne National Laboratory orivar^ . - *-• September 1977. ^' ^^^^^""^ communication.

3. K. Brown. "A Design Procedure for Correcting Second-Order Geometric and Chromatic Aberrations in a Beam Transport System," Report BNL-50769 (1977),

4. E. Colton, "Correction of Chromatic and Geometric Aberrations Using Sex- tupoles and Octupoles," this workshop.

5. A. A. Garren, "Summary of the Working Group on High Current Transport and Final Focus Lenses." this workshop. D. Neuffer, "Geometric Aberrations in the Final Focussing for Heavy Ion Fusion," this workshop.

6. S, Fenster. "Octupole Correction of Third Order Aberration," this work­ shop. ARGONNE NATIONAL LABORATORY (ANL) DESIGN ACTIVITIES^ Robert J, Burke Argonne National Laboratory

Sunnmary

During the past year, Argonne's heavy ion fusion design studies have continued to develop systems based on synchrotrons as well as linac/storage ring systems. Since it is generally recognized that workable Heavy Ion Fusion (HIF) systems can be designed but that such systems may be too costly, the emphasis of our design studies has been to minimize cost. This has in­ volved developing concepts for components, for example, clustered quadrupoles for parallel beam transport lines, but the most important issue has continued to be realization of the cost savings possible with synchrotrons.

Viable synchrotron system designs were worked out at both of the previ­ ous HIF workshops. '^ Both designs used singly charged Ions, however, and needed 2 GV linac injectors. Also, with singly charged ions, the ability to hold beam losses to an acceptable level was uncertain. On the other hand, our cost studies have indicated that multiply stripped ions are advantageous for synchrotron as well as linac systems. These ions also make the expecta­ tion for beam loss more optimistic. The main problem is, of course, the reduced space charge limit; and the approach that we have been taking to this problem is the use of multiple, rapid-cycling synchrotrons that fill storage rings. The complications of these designs, however, are leading to the conclusion that the rapid cycling option is not attractive. This con­ clusion has no bearing, of course, on the prevailing view that synchrotron systems can (a) probably be made to work, albeit wi-th more effort then rf linac systems,(b) have deficiencies as reactor drivers, but (c) may be less expensive than the alternatives. Rather, the results of our work on the rapid cycling option indicate that our design work for synchrotron systems should concentrate on finding ways to minimize the cost of systems which are more similar to the less complicated designs worked out in previous years.

The linac system that we have written up for this workshop contains a novel approach to transverse stacking, which may be the most interesting question about the workability of these systems. The real issue for these systems, however, is well known to be cost minimization, which can be ap­ proached by optimizing the parajneters, finding cost effective design concepts and working on unit costs. Following the first two of these approaches is manifested in our designs by the use of multiply stripped ions, the clustered beam lines, and compressors that handle multiple beams. Unit cost reduction is more difficult to address. In fact, the real gains to be made in unit costs are likely to result from large scale industrial Involvement in pro­ ducing power using HIF, predicting the impact of which will require years of

Work supported by the U.S. Department of Energy. work with annual funding well beyond the present, total HIF budget. Without the benefit of unit cost reduction, our expectation remains that synchrotron systems still have a cost advantage, as long as the efficiency and repetition rate of linac systems are not issues of overriding importance.

The linac system (HEARTHFIRE Reference Concept #2) and the synchrotro^ system (HEARTHFIRE Reference Concept #3) are described in separate reports, ' and the following concentrates on qualitative aspects of the designs. Some of the important design issues are suggested by the parameters given in Table I.

Choice of Ion Parameters

The considerations involved in choosing the ion mass, charge state, and kinetic energy for our HIF systems have included ion source availability and practicality, overall system cost, targetting, and beam losses. The state of ion source technology has held us to using two ions, mercury and xenon, for which sources with the necessary high brightness seem in hand and which pro­ mise a minimum of chemical or other problems likely to depreciate the relia­ bility of the system.

For choice of the charge state and kinetic energy, the issues are not so plain. Cost studies Indicate advantages for higher charge states and kinetic energies because of the reduction of the sizes of linacs and circular machines with higher charge states and the increased storage per circular machine with increased ion kinetic energy. Targetting requirements, however, limit the maximum kinetic energy. For synchrotron systems, which thrive on high kinetic energy, this effectively sets the choice for the kinetic energy at the maximum allowed by targetting. Using maximum range ions with linac systems is not as traceable to one predominating reason. Additional reasons Include the length and strength of final focussing elements, beam losses, and the beam power transport limit, which increases with charge state for a given linac length.

Consideration of beam loss reinforces the selection of multiply charged ions, particularly for synchrotron systems. As is well known, the relatively long time required for a synchrotron system to build up the total beam energy creates a need for an ion that is resistant to beam loss processes; and the sharp drop in t^e cross section for beam-beam charge changing collisions expected for Xe as compared to Xe is the basis for using Xe in the synchrotron system. "^ Using this relatively high charge state reinforces the choice to use the maximum allowed kinetic energy, as this offsets the effect of the higher charge state on the number of particles that can be injected into the synchrotron at the space charge limit.

The especially low beam-loss cross section for Xe also helps explain why xenon is used only for the synchrotron system. While consideration of the range in the target allows a higher kinetic energy to be used with mercury than with xenon, and therefore relaxes the space charge problem somewhat, this gain would be more than offset by the much higher charge state needed for a mercury ion to have as low a cross section as Xe for beam-beam charge changing collisions. On the other hand, the much reduced importance of beam losses for the rapidly charging linac systems leaves them free to make use of the shorter range properties of mercury. To best represent the current view­ point of the design studies, however, it should be noted that the potentially higher practicality of high voltage accelerating columns for xenon compared to mercury could be an overriding factor. Thus, the use of mercury for the linac system is at least not as consequential as is the use of xenon for the synchrotron system.

Transverse Phase Space Considerations

The consequences of using a high charge state ion in a synchrotron system become apparent when the details of injecting, accelerating, mani­ pulating, and eventually targetting the beam are studied. The transverse phase space is typically considered first. Through the linacs of either the synchrotron system (Fig. l) or the linac system (Fig. 2), the objective is to accelerate a beam with a current sufficient to keep the number of turns of transverse injection to a practical number and with a minimal transverse emittance. When this beam is injected into the synchrotrons, it is found that a relatively few turns of injection reach the low space charge limit caused by the high charge state. Thus, at this step, considerable dilution in the transverse phase plane is tolerable, and in fact, needed to maximize the space charge limit. The direct approach is to inject the synchrotrons with a beam whose normalized emittance is equal to the value chosen for final targetting reasons. This requires, however, that all subsequent stacking would have to be in the longitudinal phase space; and this was found to pro­ duce a momentum spread in the beam that was larger than wanted at the final focussing lenses. The approach to this problem was to lower the transverse emittance of the beam injected into the synchrotrons and transversely stack synchrotron pulses in special rings, called rebunchers, until the maximum emittance is reached. The larger values of the relativistic parameters and the bunching factor allow a much higher space charge limit and the rebuncher rings could accommodate more particles per pulse than the synchrotrons with the same normalized emittance. Thus, even though more synchrotron pulses were required, this procedure resulted in less longitudinal stacking in the final storage rings.

The total 36 turn transverse stacking in HRC#3 consists of nine turns into the synchrotrons by two into the rebuncher rings by two into the storage rings. The stacking in the synchrotrons involves both the horizontal and vertical phase planes with the emittances equal in the two planes after load­ ing. Stacking in the rebunchers and storage rings uses only the horizontal plane. The beam is rotated in a solenoid magnet during transfer between the rebunchers and storage rings, and the emittances in the two planes are again equal in the storage rings.

In this scheme, the available dilution in the transverse plane is used up at injection into the synchrotrons and transverse stacking in the rebunch­ ers and storage rings uses a technique with the possibility of low dilution. The principle of this technique, proposed by Khoe in 1971, is to create a separatrix in the transverse phase space in the form of a figure eight sur­ rounding two stable areas so that previously stored beam resides in one and a new pulse can be Injected into the other, as shown in Fig. 3. The two areas are caused to adiabatlcally merge by slowly adjusting the dipole, quadrupole, and octupole magnets used to generate the figure eight.

As shown by the entry in Table I of "none" for multiturn injection in the linac based system, the problems of transverse stacking were further explored for HRC#2. Multiturn injection was avoided by merging beam lines, external to the rings, with septum magnets. The penalty of this technique is the apparent complication, as seen in Fig. 2. However, the reason it was suggested is that it offers the possibility of combining both a small beam loss and a small dilution factor, as is described in the discussion of usin^ the technique to combine the beams from the four rings of the CERN booster.

Proposing this technique underscores the importance and difficulty of many-fold stacking in the transverse plane with both low beam loss and low emittance dilution. The problem is that intense heavy ion beams have a great potential for destroying whatever they strike because of the short range of the ions, and the impact of this destructive power is compounded by the high vacuum requirements. These specificatious for injecting HIF machines are significantly different than those for proton machines, which frequently operate with an injection efficiency of 30% or less to maximize density in phase space. For HIF the question is how much dilution must be accepted to avoid losing even a small percentage of the beam.

It seems possible to accomplish beam combination with septum magnets without loss and with an emittance dilution factor of about 1.4. This is much smaller than the dilution that is apparently necessary to avoid loss during multiturn injection, due to the effect of space charge on the latter. In the synchrotron system (HRC#3), a factor of three was allowed in each plane for injection of only three turns in each plane. For the sixteen turns in each plane of HRC#2, the dilution factor would need to be considerably larger, even if a special ring were used in which the beam would be injected into only one plane and then transferred to the final storage rings, again injecting into only one plane.

The Impetus for using septum magnets to combine beam lines is that, without resorting to higher linac current (which is, however, feasible), the low dilution of the technique is mandatory.

Dilution would be essentially the same whether the stacking ring is small and in circumference and filled and emptied many times during the filling of each storage ring or large in circumference and injected with the total number of particles that can be accommodated in each of the storage rings. The advantage of the latter is that it avoids a number of beam ex­ traction events, but it has the disadvantage of exceeding the ordinary space charge limit. Although it may be possible to exceed the space charge limit for a small number of turns, this is not a simple question. Recognising this, we considered employing a number of stacking rings which together would store all the particles for a single storage ring, but rejected this as without special merit in favor of the conservative, though possibly expensive, approach of merging beam lines. Longitudinal Phase Space As indicated above, we found considerable coupling of the problems of the transverse and longitudinal phase spaces, particularly for the synchrotron system. For these systems, the minimum longitudinal phase space area per pulse is the greater of (l) the sum of the areas of the linac bunches in a length of linac beam equal to the circumference of the synchrotron or (2) the sum of the beam bucket areas required for synchrotron acceleration. In the HRC#3 design, we strained to minimize dilution of the area occupied by the linac bunches. The means that we employed were to substitute some•transverse stacking for some longitudinal stacking after the synchrotrons, debunch the linac beam by a large factor, and carry out adiabatic manipulations in the rebuncher and storage rings.

As expected, the longitudinal phase space was easier to handle for the linac system. Since all stacking could be in transverse space, the momentum spread of the beam at the final focussing lenses could be made substantially less than the prescribed value. The available margin led, in fact, to con­ sideration of substituting some longitudinal stacking as a means of reducing the number of turns of transverse injection; but this was rejected as this approach did not seem needed.

Discussion of Reference Designs

Due to difficult manipulations which seem hard to avoid, the message from the HRC#3 design seems to be that rapid cycling is at best a very hard way around the low space charge limit caused by using multiply stripped ions. The real problems in the manipulations in HRC#3 are in avoiding dilution after Injection into the synchrotron. In the transverse phase space, this requires dilutionless two-turn injection twice, plus other beam handling. Likewise for the longitudinal phase space, the debunching of the linac beam is not extreme, but avoiding dilution through the operations of capture in stationary buckets and acceleration in the synchrotron, debunching and re- bunching twice, and various compression operations would seem to require extreme precision.

Conclusions about the workability of HRC#3, however, should not be applied to synchrotron systems in general, because it seems quite probable that the design choices leading to the complicated beam manipulations can be avoided. On the other hand, the most fundamental problem, beam loss, con­ tinues to appear tractable. Though undeniably difficult, the vacuum required to allow up to a second to accumulate beam seems feasible, and the loss from intrabeam collisions appears to be less of a problem than that resulting from collisions with background gas. Although very important in the context of an on-line power plant, the deficiencies of synchrotrons concerning repetition rate and efficiency do not rule them out for important demonstrations in the inertial fusion program. Therefore, it seems advisable to improve the design of synchrotron systems, especially by taking a design path that avoids some of the prominent pitfalls illustrated by HRC#3, which mostly concern rapid cycling.

The technical problems of the linac system, HRC#2, are less significant. The novelty of the delay lines and delay rings used for transverse stacking may attract question, but their flaw seems, if anything, to be a possible in­ crease in the cost. Combination with septum magnets is certainly a means to minimize both dilution and beam loss, and the most difficult switching pro­ blem, that of the first switch in the delay line network, seems quite tract­ able in view of the small aperture in the switching magnet needed to accommo­ date the beam and the liberal dimensions that may be used to separate the various routes through the delay lines. On the other hand, the bare accommo­ dation of the needed transverse stacking that makes beam combination with septum magnets necessary could be avoided by increasing the multiplicity of the sources. Likewise, the large factor by which the linac beam would be debunched to minimize the final momentum spread invites questions; but the dilution that might be expected is acceptable. Cost remains the important issue; and, while some concepts used in this system may have Increased the cost without sufficient reason (e.g., delay lines and rings), and the savings possible with suggested new concepts (e.g., clustered beam lines) need to be evaluated, rather major efforts are needed to assess the ultimate cost of the components (e.g., rf power, linac structures, superconducting magnets) in the context of major power production using HIF.

Additional Design Activities

Clustering quadrupole magnets wherever parallel beam lines are employed is under consideration because of the cost savings of the magnets themselves and also for other advantages of compactness. An iron yoke is only needed around the entire cluster, and some savings in the cryostats shoiild also be possible. The favored concepts for pellet irradiation currently call for packing beams into a small number of tight bundles, and clustering has an obvious use in this regard. Multiple final beam transport lines may profit from cost reduction; and a very compact cluster could make it possible to accelerate parallel beams in a single structure, which could lead to signifi­ cant cost savings for a linac tree or final compression system.

Pellet irradiation by beams packed into tight clusters also minimizes the number of penetrations of the reactor vessel. A reactor concept that has been conceived in the design studies that shows the virtue of combining all the beams into two clusters, even if the area of the clusters is greater than the sum of the beams it comprises, is shown in Fig. 4. This departure from the falling lithium concept, proposed at Argonne National Laboratory (ANL) in 1974 in connection with an Relativistic Electron Beams (REB) driven reactor was suggested by the fact that accelerator beams normally lie in the horizontal plane. This would require messy penetrations of a falling moderator. As can be seen by inspection of Fig, 4, the flow path of the liquid through the centrifugally positioned blanket can be arranged to provide structural protection from neutrons over all of the solid angle seen by the reacting fuel except that actually occupied by the beam port.

Finally, the design studies have been considering an approach to realiz­ ing high power at the pellet that complements the existing concepts of multiple beams and longitudinal compression. This concept, called telescoping beams, allows separate beam bunches to interpenetrate each other in real space by generating bunches of ions of different species so that their phase spaces are independent. Accelerated and manipulated separately until the final

10 transport, a bunch of higher velocity ions switched into a beamline after a lower velocity species will overtake and penetrate the latter. With different velocities, the requirement is that the charge state and mass of the different species be appropriately selected to equalize their stiffness, the elementary condition for handling the different species in a common beamline. The advantages of this concept can be looked at from either of the complementary points of view that it increases (a) the total volume in phase space or (b) the number of bunches at the designer's disposal. More bunches allow more total phase space, and this means relaxation of the brightness requirements. Whatever one Imagines the limit to be on the number of beams, telescoping allows a number of bunches greater than this limit.

Our earliest cost minimization studies indicated that low cost systems involve a large number of bunches, although we assumed each bunch required a beam line. An example of such systems were linac/storage ring systems operating with high charge state ions. Basically using a high charge state, such systems can easily accommodate a series of charge states. The complication of accelerating different species, as well as the need for a switch in the beam line, must be noted; but the elementary advantage in expanding the usable volume in phase space has the potential to be more important.

References

1. ERDA Summer Study of Heavy Ions for Inertial Fusion, LBL-5543, Claremont Hotel, Oakland/Berkeley, California, July 19-30, 1976.

2. Proceedings of the Heavy Ion Fusion Workshop, October 17-21, 1976, BNL-50769.

3. R. Burke, et al.. Systems Analysis of Accelerator and Storage Ring Systems for Inertial Fusion, IEEE Transactions on Nuclear Science, Vol. NS-24, No. 3, June, 1977, p. 996.

4. R. Arnold, et al., HEARTHFIRE Reference Concept #2 Outline: An RF Linear Accelerator System, September 18, 1978 (distributed at Workshop).

5. R. Arnold, et al., HEARTHFIRE Reference Concept #3'. A Rapid Cycling Synchrotron System, ANL, ARF Division Report ACC-6, June 16, 1978.

6. J. Watson, The ANL Experimental Program, these proceedings,

7. Y,-K. Kim, Atomic Data For Xenon Ions, ANL/IBF Note #60, December 13, 1977. 8. T, K. Khoe and R. J. Lari, Beam Stacking in the Radial Betatron Phase Space, Proceedings of the 8th International Conference on High Energy Accelerators, CERN, 1971, p. 98.

9. J. P. Delahaye, Etude Des Modifications De La Llgne De Transfert BR-PS Pour Assurer La Recombinaison a 10 ou 5 Paquets, CERN Internal Report PS/BR/Note #76-20, June 13, 1976.

11 Table I

PARAMETERS OF TWO REFERENCE DESIGNS

Synchrotron Linac (HRC#3) (HRC#2)

Total Energy 1 MJ 1 MJ

Total Power 100 TW (peak) 160 TW shaped unshaped Time Per Pulse 1 sec SO.Ol se

Ion 20 GeV Xe"^^ 20 GeV Hg

Pellet Radius 0,8 mm 1.1 mm

Port Radius 30 cm 20 cm

Chamber Radius 5 m 5 m

Number of Beams 24 18

Beam Emittance 4.7 cm-mr 4.4 cm-mr

Momentum Spread 0.25^ 0.0355^ Number of Rings 16 18 Number of Synchrotrons

Linac Voltage 550 MV 2500 MV

Multiturn Injection x9x2x2 None Longitudinal Stacking x8 None Linac Debunching xl6 xl07 Debunch/Rebunch twice once Final Compression x65 x73 (in ring) (external)

12 / MJ//oo TW (P/<.)//HZ HEARTHFIRE REFERENCE CONCEPT# SYSTEM CONFIGURAT/ON

4.4 6cV Xe*^ Kl( INJECTION: S TURAIS DM: 550 MV UMC DEBUNCHFR if •SYNCNROTRONS ZHZD

12.5 MHZ secr/OA/s a SOURCES SYNCNROTROi IZ.5 MffZ- aOGeV LOW'£ LINACS

4 REBUNCHER STORAGE RINGS RINGS

/NJECT/ON (HORIZONTAL) 2-TURN Z-n/RN {HORIZONTAL) SOLENOID TV INJECTION ROTATE BEAM 30' WITH )Cd LONGITUDINAL STACKING

24 BEAM - LWE5 TOTAL

Fig. 1 13 rrjr^i^^—-

+3t:

I MJ SYSTEM USING RF LINAC

Fig. 2 Figure 1 Figure 4 = 0. 0 cm = 4 radians = 1.13 (top) e = 0. 0265 cm = 1. 00 = 0. 80 cic:^;:) I -2 £ = 0. 00 (bottom) £ = 0. 33 cm HUB; - 0. 0004 cm -2

Figure 2 Figure 5 = 0. 8858 cm £ = 0. 0265 cm 0 £ 1 = 1.13 .^ = 1.13 £ - 0. 0004 (top) ^ -2 -2 £ ^ 0. 33 cm £ = 0. 0006 / £ = 0. 000883 (bot))

Figure 3 Figure 6 £„ - 0. 1811 cm e ^ 0. 8858 cm = 0.0 (top) £ ^ = 1.13 (top) £ = 0.96815 (midcile) £ = I. 09081 (midcile) = 1.13 (bottom) £ = 0. 00 (bottom) = 0. 0004 cm -2 E, = 0. 000883 cm -2

NOTE: For all figures° , v X. =0.84. i^ z = 0.79, and « 1 - TT, excepI-t Figo. 1.

Fig. 3

15 -PELLET

OUTFLOW WEIR LITHIUM BLANKET DISTRIBUTION ANNULUS ROTATING DRUM PRESSURIZED FEED PLENUM SUPPORT VESSEL

BEARING ROTATING SEAL

HOT LITHIUM EXHAUST-

ROTATION DRIVE TRAIN

COLD LITHIUM INPUT

REACTOR \A/ITH CENTRirUGAL BLANJKEX ANL EXPERIMENTAL PROGRAM^

J. M. Watson Argonne National Laboratory

HEARTHFIRE Injector

Introduction

The primary goal of the HIF experimental program at Argonne National Laboratory (ANL) is to develop an Injector which would satisfy the require­ ments of an accelerator-based power plant. The injector under development consists of a high-intensity heavy ion preaccelerator and low-beta linac. The Injector will be pulsed with instantaneous Xe"*"^ currents up to 100 mA with a normalized emittance of 0.01 mrad cm.

Our experimental program began 14 months ago with the acquisition of a surplus Dynamitron from the Goddard Space Flight Center. This type of parallel-fed voltage multiplier should be an excellent power supply for the preaccelerator. It has high current capability with little stored energy and the use of high-pressure insulating gas greatly reduces the space neces­ sary for very high-voltage operation.

To achieve the current and emittance requirements it was clear that a new source and accelerating column would be needed. Hughes Research Laboratories (HRL) were contracted to develop the source. In their ion- implantation research HRL had already developed a Penning discharge source capable of 4 mA of Ar"*"^ with a normalized emittance of 0.002 mrad cm at 90 keV. We obtained one of these sources for our test stand and it is routinely operated at 80 keV with Z.'y mA of Xe+^ with a normalized emittance of .001 mrad cm. The 100 mA single aperture source has been constructed and is being tested at HRL prior to delivery next month.

A new high-gradient accelerating column is being assembled here now. The high voltage gradient is necessary because of the large space charge forces at current densities up to 15 mA/cm^. The column will be similar to those used on the major proton accelerators except that special protection from ion bombardment of the ceramic walls is provided.

The general layout of the portion of the injector we are constructing and its experimental beam line is shown in Fig. 1. The experimental hall where the Injector is being assembled is shown in Fig. 2. The preaccelerator is within the concrete vault. The control room is on the lower right and the beam line on the lower left. The preaccelerator is followed by an rf buncher and three sections of low-beta linac. These are independently-phased cavities

17 PREACCELERATOR -RECTIFIER STACK

-TERMINAL

-SOURCE

-COLUMN

PAPS 1-PROFILE MONITOR

-Tl-TOROID

-SD 1

-SO 2

2 MeV Xe+'

Figure 1 HEARTHFIRE Injector Layout

18 Fig. 2 Injector Experimental Hall

Fig. 3 1.5 MV Preaccelerator Power Supply

Fig. 4 1.5 MV Preaccelerator Rectifier Stack and Terminal

19 with magnetic focussing quadrupoles between pairs of accelerating gaps. The first unit has two gaps and the second and third units have four gaps each. The buncher and first accelerating structure are nearing completion. The design of the next two units will be finished next month. The experimental area downstream will be used to evaluate component performance by measuring current, charge state, and emittance. Neutralization and transport experi­ ments could also be performed here.

Our approach is to try to operate the preaccelerator at the highest possible voltage in order to simplify the low-beta linac. Our short term goal is to operate at 1.5 MeV. The linac could then start with reasonably sized structures at 12.5 MHz. Higher intrinsic current limits are then possible and the number of frequency transitions and the accompanying losses in the matching sections are reduced. The high preaccelerator voltage may be needed for adequate performance by an injector.

Preaccelerator

High Voltage Power Supply

The high voltage power supply is a modified Radiation Dynamics Incor­ porated 4 MeV Dynamitron which is shown in Figs. 3 and 4. This is a parallel- fed capacitively-coupled voltage multiplier driven by a 110 kW oscillator operating at 105 kHz. We have made extensive modifications to increase the current capability and allow pulsed operation. A new solid-state rectifier stack was installed with two 40-rectifier circuits in a full-wave config­ uration. With adequate oscillator power, the stack is capable of 100 mA operation at 2 MeV. The rf electrodes were also moved closer to the stack to improve the capacitive coupling and they were fitted with new rigid supports to prevent bouncing during pulsed operation. The toroidal transformer turns ratio was reduced to further stiffen the supply and improve the power match to the oscillator. Other mechanical modifications were made such as length­ ening the tank 3 feet and adding a quick-opening flange at the end where the new column will be located (in the original configuration the low-gradient column was inside the rectifier stack).

This summer we extensively tested the capability of this power supply in pulsed and dc operation. These machines had never before been pulsed. We used a variable chilled-water resistor as a current load. With the present small oscillator we are able to ramp the machine from 0.5 MV to 1,5 MV in 7 msec with a stack current of 70 mA. It is capable of 30 mA of dc current at 1.5 MV. The machine conditioned easily with 65 psig of SF^ to voltages as high as 2.7 MV. We found that voltages above the dc-condltioned voltage could be tolerated for high voltage pulses on the order of 100 msec.

The initial operation with the source will attempt 30 mA beam pulses since the oscillator can be ramped during the beam spill so that no voltage sag should occur. By adding a second pass tube with energy storage in par­ allel with the original pass tube, pulses up to 60 mA should have no voltage sag. Well-regulated pulses of 100 mA will probably require a larger oscillator. Such oscillators are available from Radiation Dynamics Inc.

20 This tjrpe of power supply performs very well for pulsed duty up to 2 MV and probably higher. With the new terminal and column the total capacitance is approximately 500 pf, so the damage from a spark is minimal. If adequate gas handling capability is provided, the advantage of a small-sized vessel outweighs the nuisance of an insulating gas. We are installing a system which will allow a turn-around time of less than 2 hours.

Heavy Ion Source

The low-erndttance heavy ion source for our preaccelerator was developed by Hughes Research Laboratories and is described in detail elsewhere in these proceedings,^ It utilizes a low-voltage Penning discharge coupled with a single-aperture Pierce extraction electrode configuration. A schematic drawing of the source is shown in Fig, 5. The 100 mA source is presently undergoing performance tests at HRL. The gas valve is pulsed and the beam is pulsed by modulating the anode. It achieves 100 mA within 10 ysec of turn-on. The optimal operating parameters for 30 mA of Xe"*"^ are now being determined before the source is shipped next month.

Since last September we have been using the 2.5 mA version of this source on our test stand to study the operation of the source and to do transport experiments with 80 keV Xe ^. The smaller source turns on in 3 ysec and has a measured normalized emittance of 0.001 cm mrad. The details of its perfor­ mance are given elsewhere in these proceedings.^

Accelerating Column

The fabrication of the high-gradient accelerating column is nearing completion. It consists of titanium and ceramic rings which are epoxy bonded. An indium 0-ring isolates the bond from the internal vacuum. The details of the design are shown in Fig. 6. The ceramic wall is protected from ion bombardment by- interlocking T-shaped rings which also serve as the voltage tap points for the two intermediate electrodes. The two electrodes are shown tapped for 30 mA Xe"*"^ operation. This is a Pierce geometry through the second intermediate electrode, followed by a constant gradient. The expected trajectories for 30 mA and 100 mA Xe"*"^ operation are shown in F'ig. 7. The 100 mA case represents a current density of 15 mA/cm^ and indicates the beam is becoming divergent in the constant gradient region. The completed shell and a T-shaped ring are shown in Fig. 8.

The Ion source is re-entrant into the terminal end of the column. The ground electrode is also re-entrant and houses a magnetic quadrupole triplet to focus the beam on the linac buncher accelerating gap. These magnets will be completed by November.

Low-Beta linac

Despite severe limitations due to Inadequate funding we are developing the first sections of a low-beta linac which will operate at 12.5 MHz. In order to test several different structures and construction techniques, the first independently-phased cavities are very different in design.

21 MAGNET HOUSING SUPPORT 7549-8 TUBE

MAGNETIC POLE PIECE -FOCUS ELECTRODE

Figure 5. Schematic of ion source and mounting 'Structure

22 High-gradient Accelerating Colu,nn Figure 6 4MkV

Ion trajectories for 30 niA of Xe^

tST iuo EXIT INTERMEDIATE INTERMEDIATE PLANE ELECTRODE ELECTRODE FOCUS ISOOkV ELECTRODE 200 kV 650 kV

Ion trajectories for 100 mA of Xe"^

Fig, 7 Calculated Beam Trajectories in Accelerating Column

24 Figure 8 Accelerating Column Shell and T-Shaped Ring

Figure 9 Helix and Drift Tube of Lumped-Inductor Cavity

25 The first, which will be used as a buncher, is a single drift tube lumped- inductor resonator. The outside shell of the resonator is made of aluminum except for the copper bottom can. The inside inductor and drift tube are made of copper. The inductor is a coil of 2-1/3 turns in a 20 in. diameter. It is shown in Fig. 9-

The first accelerating structure is also a single drift tube resonator which is capacitively-loaded by a plate near the drift tube. It is shown schematically as the first element in Fig. 10, which is our system design up to 4 MeV The capacitively-loaded cavity is made entirely of copper and should require only 10 kW to achieve 100 kV across the accelerating gaps. The outer electrode and frequency-tuning ball are shown m Fig. 11.

The design of the two drum-loaded resonators is nearly complete. They will have two drift tubes per resonator. The drum-shaped capacitor has a wider gap to the outer electrode, so these structures should be capable of higher voltages. The inner and outer electrodes will be copper.

The design of the 12-gap TT/5TT single stub Wlderoe which will accelerate Xe+l from 2 MeV to 4 MeV is underway. If funding is adequate, construction of this unit should begin in a few months.

To excite these cavities, we have constructed a 25 kW 12.5 MHz amplifier and have ordered five more from Instruments for Industry, Inc. These should be delivered in January. Bids have been requested for the 250 kW amplifiers which will be needed for the 12-gap structures.

These cavities will utilize conventional quadrupole magnets for beam focussing. These magnets have been designed and are being fabricated in our shops. These will have a maximum gradient of 46 T/m. This imposes a trans­ port limit near 25 mA of Xe"^^ for these structures. Our superconducting group is presently developing small quadrupoles with a maximum field gradient of 140 T/m. These could be used to significantly upgrade the front end of the low-beta linac.

SO keV Xe"^^ Test Beam

We have set up the 2 mA Xe"^^ HRL ion source to inject into a 4 m long transport line. Most of our operation has been at SO keV. At present, the vacuum capability is in the 10"^ Torr range throughout the line. This will be improved to 10"^ next year. The transport line is shown in Fig. 12. The source is in the high voltage cage to the right. The source and some of its support equipment are shown in Fig. 13. Figure 14 is a photograph of the Xe"*"^ beam as it exits the source. The waist near the source has a 2 mm diameter.

We have used this beam line to study the operation of the source, the problems associated with transporting intense heavy ion beams(2 mA is consid­ erably above the space charge limit), and to investigate the parameters of neutralization. In this rather poor vacuum we have been able to transport and focus 90^ of the beam 4 m from the source. The source has operated very reliably with a normalized emittance of 0.001 mrad cm. We have also pulsed the source via an optical link and measured plasma formation times of 3 usee.

26 n

I 1 DRUM LOAOEO CAVlT?

,.LL.,

A ^ |M| ]il[fL=Jiil( i!|CJ =tS;ouAD';i

euA6

Figure 10 Low-Beta Linac to 4 MeV

Figure 11 Outer Electrode and Tuning Ball of Capacitively Loaded Cavity

27 Figure 12 80 keV 2 mA Xe"^^ Transport Line

Figure 13 2 mA Xe"^^ Source and Support Equipment

Figure 14 2 mA Xe+1 Beam Out of Source at 80 keV

28 Further details of the test beam are presented elsewhere in these proceedings.^

While the higher vacuum system is being assembled a second beam line will be installed to be used to measure Xe"*"^ - Xe"*"^ cross sections up to 80 keV. The second beam will use a collimated duoplasmatron source set up by an ANL- University of Chicago collaboration.

We are also considering lengthening the beam line to study instabilities which may occur in periodic transport lines.

References

1. R. P. Vahrenkamp and R. L. Seliger, "A Heavy Ion Source and DC Pre- Accelerator Design for Ion Beam Fusion," this workshop.

2. M. Mazarakis, D. Price, and J. Watson, "The Argonne National Laboratory Heavy Ion Beam Transport Experiments with 2 mA 80 keV Xe"*"-^ Source," this workshop.

^Work supported by the U. S. Department of Energy

29 30 STATUS REPORT ON THE

LAWRENCE BERKELEY LABORATORY

HEAVY ION FUSION PROGRAM*

PART I. A DESIGN AND COST PROCEDURE FOR HEAVY-ION INDUCTION LINACS A. Faltens, Eo Hoyer, D. Keefe, and L.Jo Laslett Lawrence Berkeley Laboratory (presented by D, Keefe)

1. Introduction and Background

For electrons, the induction linac has been well-established as a high- current {^1 kA) accelerator with high repetition rate, good electrical effi­ ciency and high operational reliability (reference 1 contains an extensive list of references). In such systems the electrons are injected at relativis­ tic speed so that pulse compression by differentially accelerating the head and tail of the beam bunch is not an available option; the beam current, I, and pulse duration T, remain constant along the accelerator. The design pro­ cedure thus becomes one of designing a single accelerating module (appropriate to the chosen I and x) and simply iterating such modules until the final beam particle energy (voltage) has been reached. (This is not to discount the fact that there are many options that must be examined; e.g.,choices in ferromag­ netic material, in stacking cores radially, in insulator configurations, etCo, before arriving at the final design of the single basic unit).

For a non-relativistic (6 < 0,5) heavy ion induction-linac driver, how­ ever, the design procedure is much less transparent^ For instance, the parti­ cle mass and charge can have a range of values - also the final beam voltage, Vf, (kinetic energy/charge-state, q), is a matter of choice since only the product, [IxjVf = Q, is specified for a driver delivering Q megajoules. A novel and most important degree of freedom is available in such a machine - namely, the ability to achieve pulse compression by modest differential accel­ eration (slightly-ramped voltage pulses); this comes at the price - to the designer - of allowing a free choice of beam current over a wide range at any point along the machineo The upper bound on current is set by the transverse space charge limit (equivalent to the so-called Maschke power-limit); on the lower side, while there is no physical bound, in general one finds that a de­ crease in current is accompanied by a decrease in electrical efficiency and an Increase in cost.

*This work was supported by the Office of Laser Fusion and the Office of High Energy and Nuclear Physics of the Dept, of Energy.

31 The essence of our design procedure is to pick a specific total beam rharae FITI one value in a sequence, and examine the differential cost, AC, required to add an increment of voltage AV = 1 MV to the beam at each voltage point, V. along the accelerator. In general, there is a mmmum value of AC/AV at each voltage point, V, which in turn determines the exact design for the accelerating modules, pulsers and magnets at that point; if one seeks for example, a minimum-cost accelerator, the entire design is determined and the cost - except for the injector and final beam manipulation sections - is given by ^ (1) min [IT] [IT] In most cases some departure from the minimum-cost design, particularly at the higher voltage points, is desirable for electrical efficiency reasons and for meeting the final longitudinal requirements. Thus it is important to have detailed information of the nature of the AC/AV variation, i.e., whether it is a broad or narrow stationary minimum or if it is a non-stationary mini­ mum arising from a constraint. See Fig. 1 for an example AC/AV curve.

That, in principle, a stationary minimum for AC/AV exists can be illus­ trated as follows. The volt-second requirements for the cores to add 1 MV is

Volt-Sees = 106^ = lO^IIiLcc (i)-^ (2)

Thus lower core and pulser costs can be achieved by arranging for the highest beam-current; this requires a high density of transport magnets (occupancy fraction, n. approaching unity). The current I attains its maximum value as n ^ 1 but this leaves no space at all for the accelerating cores and the cost to add 1 MV tends to infinity. Conversely, the cost of the magnet system can be lower by operating au low beam-current (i.e., n -^ 0) which in turn, from Eqno 2, implies increa'ed volt-seconds of core and likewise cost. Between these extremes there is an appropriate partition between the space occupied by accelerating cores which leads to a minimum cost. While a stationary minimum exists in principle, there are cases at the low-B end of the accelerator where the stationary point is not accessib!-^ in practice -- usually because of the need to restrict the quadrupole pole-tip field to a manageable value {<_ 4T).

In December 1977, a first Reference Conceptual Design, called IL 4/26, was described for a 1 MJ, 156 TW driver using U"*"^ ions accelerated to 26 GeV (i.e., Vf = 6,5 GV)J2) while we were aware at that time of the general design criteria described above, the detailed cost data required for evaluat­ ing cost-minima were not yet in hand then and the choices of induction-core and magnet configurations at various points along the accelerator were simply a matter of educated guessing. A block-diagram showing some of the parameters in that design is given in Figure 2. The injector (which included the strip­ ping section) provided [IT] = 155 uC and was based upon three stages of pulsed drift-tube acceleration^^^ with solenoid focussing. An appropriate bunching section was designed for the latter part of the accelerator after which the beam was allowed to become large transversely and split with a four-way septum magnet to enter the final four transport lines leading to the target chamber.

32 The points to be emphasized here that influence the interpretation of the partially-complete results that follow are:

- In Reference Design IL 4/26 the injector cost was about 10% of the accelerator system, and the final beam transport also represented about 10% of the cost,

- Because 80% of the cost was identified (for that case) to reside in the induction linac part from the injection voltage (50 MV) to the final voltage, Vf = 6.5 GeV, we decided to concentrate our efforts on refining the design procedure for this major-cost part of the system, and these are the results that are discussed below.

- We believe that the costs of the final transport and focussing systems for most of the parameter ranges to be discussed will indeed be of the order of 10% of the overall system cost, or possibly less.

- We are uncomfortable at this time about stating the scaling law for the injector cost as a function of the beam-charge [IT] delivered. It is certainly less than linear with total charge, since at worst several in­ jectors may always be paralleled in a tree configuration. Undoubtedly the injector cost will increase with increasing [IT] while the induction linac cost will decrease (see below) for reasonable assumptions about the beam emittance. Thus the "10% injector-cost" rule will be violated if we wish to scale too far away from Reference Design IL 4/26, and as yet we cannot furnish a reliable estimate of by how much. The high current injector design presents a fascinating design question, and there is room and need for innovation. Several interesting ideas need pursuing, but up to this date - apart from examining some designs in the spirit of existence proofs - we have felt it more important first to address in a proper way the cost-dominating section of the system,

- Results for costs for the induction linac section given below can be referred to as "80% of cost" values but with the caveat that if one strays too far from the IL 4/26 case of [IT] = 155 uC, the 80% figure becomes unreliable. We feel now that a preferred reference example would be IL 4/19 with [IT] = 210 yC and that more study of the injector is needed before cases with much larger [IT] values can be reliably costedo^^'

2. Cost Procedure

Up to this point we have simplified the problem in studying the "80% - cost figure" by assuming

(i) A suitable injector at V^^j = 50 MV is available (this has been established in detail only for the Reference Design IL 4/26).

(ii) The final rapid-buncher section costs about the same as if it were composed of a pure accelerating section with modest bunching. (In Reference Design IL 4/26 the cost differential was small).

More work is needed on both of these topics before they can be incorporated in detail into a comprehensive cost-estimating program.

33 To address the main part of the Induction Linac system, viz. the "80% part", a computer program (LIACEP) has been developed to sort through the possible engineering options at each voltage point, V, along the machine and to generate the desired cost and design information^

Ue start by specifying an ion species with atomic weight. A, and charge state, q, (so far only Uranium with charge states 1, 2, and 4, and Cs with charge state 1, have been studied). Next, an electrical beam charge [IT] is specified with a sequence to be explored — 30 yC, 60 yC, 90 yC..., etc., ... up to 1000 yCo Then at any voltage point, V, along the accelerator the cost consequences of adding a further 1 MV are examined. The independent variable is chosen to be the current, I, with the magnet occupancy factor, n» for a symmetrical FODO lattice, as a separately set and varied parameter (e.g., n = .5, .33, .17, .10, .05, etc.). In this way a set of curves for each value of n can be generated to display differential cost versus current and so to arrive at a minimum or indicate the cost/benefit ratio of departing from the minimum (see Fig. 1),

At this point we have to identify three distinct classes of information which are key ingredients of the optimization process:

(1) Engineering Design Options and Constraints

(2) Cost data base which can affect the trade-off among design choices

(3) Physics assumptions about (i) the desirable beam emittance determin­ ed by the pellet and transport requirements, or the realizable beam emittance set by the source performance, and; (ii) the transverse space charge limiting current.

These input classes are discussed in sequence belowo At this time the great­ est cost uncertainties seem to arise from the consequences of the physics assumptions.

(1) Essential to this costing routine is the spectrum of engineering options that are examined in the process. To date we have chosen to input the engin­ eering possibilities and constraints listed below. A few of the options. Identified by the asterisk, have not yet been exercised in the program (which is still under development):

A: Accelerating module design based upon an economic choice between iron or ferrite

A: Accelerating module design based upon an economic choice between amorphous ferromagnetics or ferrite^^)

B: A module design with the oil-vacuum interface insulator near the inner radius of the cores (Fig. 3)

B: A module design with the insulator near the outer radius of the cores (Fig. 4)

B: A module design wherein the transport magnets can be re-entrant within the pulsed cores (most appropriate for low-B section)

34 * B: A module design with radial sub-division of the cores(^)

* C: Conventional-conductor/iron quadrupole transport magnets (appro­

priate for test facility but probably not for power-plant)

C: Superconducting quadrupole magnets

D: Constraint that the quadrupole "pole-tip" field does not exceed 4T D: Constraint that the quadrupole bore-radius to length ratio never exceeds 0o25.

D: Constraint that the electrical stress on the insulator never exceeds 10 kV per cm for pulse duration greater than 1 ysec and 10-40 kV per cm for pulse durations of less than 1 ysec.

D: Constraint that the "longitudinal space-charge factor" (LSCF) never exceeds OJ, The LSCF is defined as the ratio of the extra grad­ ient needed to hold together the ends of a beam bunch with 10% tapered ends to the average accelerating gradient. This constraint implies at most an extra 1-2% of overall core volt-seconds in the accelerator if separate longitudinal focussing modules are used.

D: Constraints on the maximum "reasonable" radius of a core and on the maximum weight of an assembled module,

D: Constraint that the maximum beam-pipe bore radius not exceed 0.2 m.

(2) The cost input data are of such complexity that they cannot be discussed in detail in this report. Briefly, their breakdown falls under the following headings:

A. Technical Components

1. Accelerating Modules (cores, insulators, structures, etc) 2. Pulsers 3. Vacuum System 4. Support and Alignment 5. Control Room 6. Computer System 7. Beam monitoring and control 8. Quadrupoles, refrigeration and cryogenic distribution, power supplies, testing, control, support and alignment.

B. Conventional Facilities 1. Site Work 2. Accelerator Housing 3. Control Room Building

35 4. Mechanical Facilities 5. Electrical Facilities 6. Safety

Details of the unit costs based upon manufacturers'quotes, and the inter­ polation or extrapolation formulas based upon projects completed or under construction are documented in internal LBL engineering notes by E. Hoyer. An obvious advantage of having the program, LIACEP, to sort through many cases is that by varying the input cost data we can quickly identify those items or design features to which the overall costs are most sensitive, (3) Until adequate experiments can be carried out for high current heavy-ion beams on achievable beam brightness and on the details of the transverse space- charge limit we shall continue to have uncertainties in specifying these quantities precisely. These uncertainties span actually a rather narrow range but unfortunately can lead to significant cost effects. The first of these arises from the fact that in the final focussing lens the third-order geometric aberrations impose a condition that the entering beam (or beamlet) have an upper limit on emittance. From the work of Garren(^^ and Neuffer(9) we have derived the following approximate expression for this emittance limit in a single plane (x,for example): ^N ^ °-^2 er r//^ (3)

where the superscript, L, refers to the doublet lens, the subscript, N, in­ dicates normalized emittance, and rs is the target spot radius. If we denote by E^ the total normalized emittance of the beam transported through the accelerator then the number of final separate beamlets, Nh, required to meet the target needs can be expressed as

M . ifNWlzifN^ERT _ 2 I ., , ,,,

^^N^HORIZ^^N'VERT where the factor 2/3 arises from the fact that in the y-plane the emittance can be some 50/. larger than the x-plane emittance limit given by Eqn. (3);.^^ this comes about because of the inherent x-y asymmetry of a doublet lens. '^' finn m^nno?c'']^°^ a four-beamlet splitter using current-sheet septum split- an "Pinht hL'?fJ"''*T°^f '' ?^°^" ^" ^'^' ^' "^^is represents One half of beanll?. ^rn^inLc'r^^^ for pellet irradiation, i.e., two clusters of four of arr^nolnn fn^^f directions When one examines the engineering details fL rSnV K I ^ ^""^^l ""^^^^ °^ beamlets in a cluster then it appears that the complexity becomes formidable for Nb much in excess of 20.

J thaf r.n^hp'tni'o^'rn ^^"L^'^^^'^ ' Constraint on the total beam emittance, c^. that can be tolerated in the accelerator and this probably should not exceed 3 x 10-5 ^^j.^n. for the reference 1 MJ design. The studies show that the capital cost decreases and the electrical efficiency increases if a hiaher value of emittance can be tolerated; this comes abourbecluseThe sjace JhaJge

36 T 2/3 limited current is proportional to (el^) ' . This sensitivity of cost and efficiency to the space-charge limited current seems a general feature and it becomes important to have a good understanding of what betatron tune depres­ sion can be safely tolerated in the transport system^ Extensive studies of this question have been carried out by Laslett using computational techniques for a Kapchinskij^Vladimirskij distribution^^^) and by Haber using numerical simulation codes.^'^^ Conclusions have varied somewhat from time to time and a convincing final result is not yet available. Early LIACEP program runs used a tune depression OQ -*- a of 90° -> 36°, later this was revised to 90? 57.5** and still later to 60° ^ 24°. The non K-V case results by Haber^^-^^ suggest that a tune depression 90° -^ 30° may perhaps be tolerable, but no cost study has been made for this case. Such uncertainties in the tune-depression specification are reflected in cost uncertainties of as much as 20%,

The LIACEP program procedure for a particular choice of tune-depression is to pre-set the magnet occupancy factor, n, and calculate magnet length, period length, and magnet pole tip field for a variety of beam currents, and later to cycle through several values of n- Thus in any instance the magnet parameters and the available space for the accelerating modules is derived and the appropriate engineering solutions described earlier can be examined,

3, Results

It must be emphasized that these "80% cost" studies are useful as a de­ sign guide and as a tool for identifying the cost sensitivity to any of the input assumptions and engineering options and costs. Thus the absolute value of the cost figures should be treated with considerable caution and attention focussed on the trends suggested by the data; in our view, reliable costs can be derived only when a particular case is settled upon and an ab initio design carried through in detail for that case. The sample results given here reflect work-in-progress, and inconsistencies in assumptions will be noticed. Fig. 6 shows example results for minimum "80%-cost" designs as a function of charge- state for uranium and an example point for Cs"'"^ The interesting result is that the variation is not large but higher charge states are favored on cost grounds by perhaps 25%. There are physics arguments favoring the lower charge states which correspond to lower kinetic-energy (shorter range) examples, T -5 These examples used a tune depression 90** -»• 57.5** and an emittance e., = 2x10 rad-m.

Fig, 7 shows costs for U (again for the same tune-shift) if the emit­ tance can be permitted to be as high as 4 x 10"5 rad-m, and constant at that value independent of the beam charge [IT]. The minimum for most energies seems broad and in the range [IT] = 200 - 500 yC.

Fig. 8 shows costs for U with different assumptions for tune-shift (60° -^ 24°) and emittanceo The normalized emittance is assumed to be 3 X 10-5 y^ad m ^p to [IT] = 210 yC and to scale as [IT]''^ beyond that point. If the increased beam charge is achieved by increasing the area of the ion source then this square-root law would arise naturallyo The increase of emittance for higher beam charge does not lead to difficulties in the final focus since the target spot radius can also be larger. Note that the curves for fixed joules tend monotonically downward towards higher beam charge; this

37 arises primarily from the corresponding allowed increase in emittance. It must be emphasized again, however, that the cost of the injector will increase as [IT] increases and the overall cost of the accelerator may show a stationary minimum.

Fig. 9 summarizes information for the new reference design IL4/19. Illus­ trated are the theoretical maximum current variation as a function of voltage along the accelerator (close-packed magnets, and tune-shift 60° -»• 24°), the practical maximum current set by the structure constraints discussed earlier, and the way the current would vary for an accelerator that used the minimum- cost solution at each point. Also shown are the ranges of beam-current varia­ tion allowed for costs up to 20% above minimum. The higher the current the higher will be the electrical efficiency so if the latter were to be a prime consideration for the 1 MJ driver it could pay to choose to increase the capi­ tal cost of the last part of the accelerator by some 20%.

TABLE I

+4 Exampl e Parameter Choices for a 1 MJ U Driver

T T [IT] T V R ^B [yC, GeV GV g/cm mm (xlO^) (xlO^) > rad-m rad-m 15C) 26„7 6.67 .78 1.01 .77 3 10 21C) 19.0 4c76 .5 lo26 .69 3 12 30C 13.3 3.33 .33 1.55 .79 3.6 14

50C 8.0 2.0 .17 2.16 .935 4.6 16

lOOC 4.0 1.0 .08 3,15 1.07 6.6 25

Table I shows a variety of parameter options for a 1 MJ driver. The first entry is close to the old Reference Case IL4/26 and the second entry corresponds to the new Reference Case IL4/19. The succeeding entries have advantages in a lowing large pellet radii but realistic injector designs will have to be developed for each before they can be properly evaluated.

We wish to acknowledge the help of Mr. Victor Brady in performing much of the computational work.

38 References and Notes - Part I

1. D. Eccleshall and J.K. Temperly, Transfer of Energy From Charged Trans­ mission Lines with Applications to Pulsed High-Current Accelerators^ J.A.P. 49 (7), July, 1978.

2c Preliminary Cost Figures for an Induction Linac, HIF Staff, HI-FAN-54, 1977.

3.. A. Faltens and D. Keefe, Particle Accelerators 8^, 245 (1978).

4o LBL HIF Staff, Linear Induction Accelerator Conceptual Design, HI-FAN-58, 1978.

5o Amorphous ferromagnetic tape material is under intensive study for low-loss motors and transformers by Allied Chemical (under the trade name METGLAS), G.E,, and several universities. It is made in typical thicknesses of 0.001" - 0.002" and has high resistivity. Extensive descriptions and references can be found in Amorphous Magnetism II. edited by R.A. Levy and R. Hasegawa, Plenum Press, N.Y. and London, 1977.

6o Modules with four-fold and five-fold radial sub-divisions have been studied and are in operation at NBS, see Preliminary Report of Pro­ totype Induction Accelerator Performance, M.A. Wilson, and J.E, Leiss, N,BoS,, Washington, DoC.

7. E. Hoyer, Summary of Induction Linac Cost Factors, Eng, Note M5250, (1978),

8. A. Garren, Final Focusing of the Ion Beams of a Pellet Fusion Reactor by Quadrupole Doublets, Proc. 1976 HIF Workshop, LBL-5543.

9. D. Neuffer, Geometric Aberration in Final Focusing, HI-FAN-36, (1978).

10c Do Neuffer, Unpublished, (1978).

Ho L.J. Laslett, L. Smith, J. Bisognano, Computational Study of a Third- Order Instability Suggested by Computations of Dr, Haber, HI-FAN-43, (1978).

12. I. Haber and A. Maschke, Steady State Transport of High Current Beam in a Focused Channel, NRL-3787, (1978).

13c I. Haber, private communication, October, 1978.

39 400 -1 r ETfl IRDN FERRITE 1/20 fl U 1/10 B U 1/6 C U 1/4 D X 1/3 E Y 1/2 F Z D BEFF>4TES 300 I INRDEOUPTE RPTID X LSCF> .1

200. -

100.

0. 0, 500. 1000 15 SEP ?B K$/nU OS RnPS R = 238.00 Q = 4. ITflU= 210.IRC U = 2SC0.riiJ TB60240 £N= 3.0E-05

Figure 1 EXAMPLE COST CURVE

40 TENTATIVE COST FIGURES FOR EXAMPLE INDUCTION LINAC

26 GiV, U**. IMJ. l56TW(4b«Qmj).(^'2xlO''rodion-mttirs, Bpoi, ,,p'4T.

6500 6500 2000 5500 VOLTS (MV) 40 200 500

FERR, CORE IRON I IRON I f FERRITE CORES NJECT. IRON CORES (BUNCHING) CORES ICORgSfl

30 200 75 PULSE DURATION 4000 SOO 400 (nsoe)

\ 22% M 100% «I00% MAGNET PACKING t%) s50V. 17% 25% FRACTION

1670 2800 855 696 SECTION LENGTH (m) • 60 618 469

U*' SOURCE- HELIUM STRIPPER, U** PULSED DRIFT TUBE- INDUCTION LINAC INJECTOR

Figure 2 XBL 7810-12083 HIGH VOLTAGE FEED FEfiROMAGNETIC CORE -SUPERCONDUCTING OUADflUPOLE

VACUUM PUMPOUT EVERY 6 MODULES

FERROMAGNETIC CORE MODULE - TYPE 2

XBL 789-10717 Figure 3

42 -FERROMAGNETIC HIGH VOLTAGE -SUPERCONDUCTING CORE FEED QUADRUPOLE

FERROMAGNETIC CORE MODULE - TYPE I

Figure 4 XBL 789-IO716

43 ALL ELEMENTS 1-2 m LONG (B <.4T)

SURROUNDING IROM YOKES (NOT SHOWN)

4-WAY SEPTUM RECOMBINER

NEUTRON MAZE

PANOFSKY CURRENT-SHEET QUADS •-DO

CURRENTS 4-WAY SEPTUM SPLITTER

[*- 1 m-*j

Figure 5

SCHEMATIC - 1 BEAM TO 4 BEAM SPLIT AND FOCUS

44 Figure 6

MI^^IMu^^ INDUCTION ACCELERATOR COST

FROM 50MV USING METALLIC GLASS CORES FOR URANIUM & CESIUM FOR 90° - 57.5° PHASE SHIFT, & £,. = 2-0 X 10"^ M-RAD

45 1 ;., : 1 1^ 1 1 —- . •

—•

1 - lOOOuc • :.. 1 2 - 500gc> • ^ ^ innn 3 - 300yc- ~1 Ml 1 j" 4 - 210yc 1 5 - 150uc H -d 6 - 9niir. -I IMJ- x^ i

-^ -•- — 1

!J • ~^-y . .: .'•:. ?^' : L .::; l^n •:. • • /^i> FERRITE

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•

CJ ^ K -— •\ •^^ : ' -^ f L ^ '"'^ -'- r - • ••n (^ , ^ . '9/' " :_ . - — - ! 1 L / y ~ 3 / X "

i • • 1 1 X/T j' L.. 1 :4r / / 1 • • 1 / >' 1 1 1.. / 10 6/ •• i 100 1000

VOLTAGE - (MV)

Figure 7 MINIMUM INDUCTION ACCELERATOR COST FROM 50MV USING METALLIC GLASS

U'^'^, 90° - 57.5° PHASE.SHIFT, & l^^ = 4.0 x 10"VRAD

46 1 ^'^;r-r-^N innn c 1 - 1000 UC. 6.6 X 10 "- 1 u ( i 1 lOMJ-E=- 2 - 500 UC. 4.6 X 10 L 1 i -s 1 y 3 - 300 UC, 3.6 X 10 3MJ— K . , 4 - 210 UC. 3.0 X 10"^- ,— i — -- 5 - 150 UC. 3.0 X 10"^-- -~^ IMJ* ~^-C-\" . . ,„-5 . 6 - yu UC, J.u X lu -J.- A ^* .^ ^y i J ' 1 FERRITE • CORES 1 ^ o 100 x^ I 1 y _ f^ I y A ; 1 / ,-' r y 1 DC ._ J_ .y o 1 / ^"^J^y _J L. I— I / j^ y 1OOKJ- >^> / ... ^:z:. — ^ ~Zyj y — — ] / / /" ^ / -2 - — _.. - ^ —- -- 1 I /// , 3 — 4 b y^ 1 6/ 1 10 IC h u)0 0 innn

Voltage - {MV)

Figure 8 MINIMUM INDUCTION ACCELERATOR COST FROM 50MV USING METALLIC GLASS & FERRITE CORES FOR A = 238, z = +4, 60° - 24° TUNE SHIFT

47 1000

occ

100

10 1000 5000 VOLTAGE - (MV)

Figure 9

ACCELERATOR CURRENT AND P[]l SF

DUgAlJQN FOR REFERENCE T.I ,

CASE 4/19 (IMJ - 100 TIJ)

48 PART II. THEORETICAL ACTIVITIES

(presented by D. Keefe)

Progress this year has been achieved in three major areas:

A. Beam Transport (J. Bisognano, I. Hofmann, L.J<, Laslett, L. Smith)

Further work on instabilities of the ICapchinskij-Vladimirskij (K-V.) distribution has led to revision of the recommended choice of maximum trans­ portable power for design purposes. A significant achievement has been the successful comparison between our theoretical results and the simulation com­ putations by Irving Haber for a particular unstable mode; this comparison gives credence to both the theoretical and simulation work and suggests that the simulation approach can be trusted when applied to more realistic distri­ butions, which cannot be treated analytically.

Bo Final Focussing (Ac Garren, D, Neuffer)

The work of A, Garren^ ^ on the parametrization of a final focusing doublet has been extended to triplets, which are more suitable in certain parameter regimes. The effect of third order geometric and fringing field aberrations in the final lens system has been explored, leading to constraints on the emittance of the individual beams approaching the target. The effect of chromatic aberrations has been studied quantitatively and appears to be somewhat more serious than indicated by the previously used rule of thumb; work has begun on the correction of these aberrations by the use of bending magnets and sextupoles upstream from the final lens system.

Cc Parameter Studies (D. Judd, L. Smith)

In light of the constraints imposed by the final focusing system, the six-dimensional phase space requirements have been re-formulated and used to develop a number of r.f. linac and synchrotron scenarios. As others have found, the synchrotron schemes do not look very attractive, particularly since the trend this year has been toward lower kinetic energy and higher current, whereas the virtue of a synchrotron is rather to provide high kinetic energy at low current.

References

1, A. A. Garren, Report of Summer Study of Heavv Ions for Inertial Fusion, July 19-30, 1976, LBL-5543, p. 102.

49 Part III- THE EXPERIMENTAL PROGRAM ON HEAVY ION FUSION AT LAWRENCE BERKELEY LABORATORY*

S. Abbott, W. Chupp, D. Clark, A. Faltens, E. Hoyer D Keefe, C. Kim, R. Richter, S. Rosenblum, J. Shiloh, J. Staples, E. Zajec Lawrence Berkeley Laboratory

W. Herrmannsfeldt Stanford Linear Accelerator Center

(Presented by C. Kim)

1. Introduction The experimental efforts at LBL have been focused on both the develop­ ment ofalarqe aperture 2 MeV,lACs+l ion beam'J using contact ionization and drift tube techniques as an injector for an induction linac and, also, a 750 kV, 60 mA Xe+1 ion beam2) using multiaperture accel-decel extraction and a Cockcroft-Walton accelerator high gradient column for an r.f. linac source.

2. The One-Ampere Cesium Source

A schematic diagram of the Cs"*" beam experiment is shown in Fig. 1. Neutral Cs atoms, generated either by heating metallic Cs or a (CsCl + Ca) mixture, are sprayed onto a hot iridium plate (anode) of 30 cm dia. which is ,at a temperature of 1200°K-1400°K. The ionization potential of Cs (3.9V) is smaller than the work function of iridium so that most of the Cs atoms are adsorbed on the anode surface as ions. The supply rate of Cs atoms is deter­ mined by the oven temperature and is designed in such a way that there is ~ 1% of a monolayer (ImC) of Cs accumulated on the anode when the extraction voltage pulse is applied to it. The Cs"*"! ion emission rate is determined by the temperature and coverage of the iridium hot plate and is designed to be about 5 times the space charge limited current. In this space-charge limited operation the beam emission is uniform over the surface independent of the non-uniformities of the temperature of the anode and the neutral Cs flux.

The space-charge limited current is lA for the extraction voltage of 500 kV which was applied to the anode. Emission-limited operation occured when the anode temperature was below 1100°K in which case the Cs+l current was independent of the applied voltage pulse and depended only upon the anode temperature.

*This work was supported by the Offices of Laser Fusion and of High Energy and Nuclear Physics of the Dept. of Energy.

50 Cs depletion was observed when the anode temperature was high and the neutral Cs supply was low. In this case all the available Cs ions were used up during the earlier part of the voltage pulse. The space-charge-limited condition was recovered when the oven temperature was increased in this case.

Beam neutralization could increase the current above the classical space charge limit. Our current measurement is not yet accurate enough to estab­ lish this because of the undetermined secondary electron correction. Al­ though the secondary electron effect was measured to be small in our earlier Cs test stand experiment, we are building improved diagnostics to delineate the phenomenon.

Time-of-flight measurements, as shown in Figure 2, proved that virtually all of the beam was composed of Cs''"^ ions. The beam also had orders of mag­ nitude lower intrinsic neutral background pressure compared to any electron- bombardment ionization source. This is as expected since the Saha-Langmuir equation shows that more than 99% of the incident Cs atoms are ionized. The ion beam has a very low thermal velocity equal to the temperature of the anode (0.1 eV). It is thus very bright. Normalized emittance based on the thermal spread is calculated to be ^^ = 0.006 cm-mrad. The final beam emit- tance will be determined by non-source-originated mechanisms such as lens aberrations and scattering by grids.

The source is now operating at a few pC capacity but it can be easily scaled up by increasing the extraction voltage (up to 1 MV) and the area of

HOT IRIDIUM PLATE PlgRCe ,£ueCTKOP& PULSED DRIFT TU&ee»

^RID

iis* • ..--.:,-••..••.'.V^../?I

^2S2SZ^^:SEZ3J N^r^sr^gsS^

J^OC? KV OO KV MARK GENERATORS MARX C&eiUM (GENERATOR

Fig. 1: Schematic diagram of the Cs"*" beam experiment (Drift tube lengths not to scale)

51 the anode. (The contact i onization source is also applicable to uranium.^) Since the uranium ionizati on potential, approximately 6.3 volts, is higher than the work function of any refractory material, the anode needs to be oxidized or flouridated to obtain a higher work function.) The extracted Cs'''^ beam is focused by Pi erce electrodes^) (Fig. 3) and will be further accelerated by a three-sec tion pulsed drift-tube, which is being assembled at the present time. The beam will gain an increment of 500 keV per stage and reach 2 MeV at the end of the drift tubes. Other experiments under con- sideration are: (1) an add ition of accelerating stages using induction linac cavities, and (2) a strong -focusing transport experiment.

Note Added in Proof, January 1979: Since the September workshop, this source has delivered 1.1 amperes of Cs+1 ions at 500 kV. In addition, repetition rate tests up to 1 Hz showed reproducible space-charge-limited current pulses.

4 -

o

L = 81 cm L = 128 cm L'^ 194 cm

^/-Fu^ (cn-kV*'^) Fig. 2: Time of flight measurements of Cs"^^ beam TimP

current pulse. Ls are the distances of the drift space.

XBL 7810-12076

52 Fig, 3: A photograph showing the iridium hot plate, the Pierce electrode, and insulator column of the Cs"*"^ contact ionization source.

3. The 60 mA Xe"^^ Source

The Xe multiaperture source has been described in Ref. 2. The pre­ sent source configuration utilizes an array of 13 holes each 4 mm in dia­ meter symmetrically arranged within a 25 mm diameter circle. Development of this source was carried out in the Bevatron 20 kilovolt test stand.

A beam of 40 mA at 20 kV was transported one meter through a quadrupole triplet and measured with a biased Faraday cup. The measured beam diameter was 38 mm and the emittance was — = -^^ = 0.03 cm mrad. A 50-degree mag- TT TT ^. netic analysis showed the beam to contain 9Q7o Xe charge state. This source was then installed in the 750 kilovolt Cockcroft-Walton accelerator. The 20 kV Xe"*"^ beam was transported one meter through two mag­ netic quadrupole triplets and accelerated to 500 kilovolts through the high gradient column.

53 A beam of 60 mA was measured with an electrically biased Faraday cup. This cup is also provided with a transverse magnetic field. The observed beam diameter was 38 mm.

The plasma arc was operated at 30 V and 50 A and a pulse length of 500 usee. These conditions are the same as on the 20 kilovolt test stand which yielded 90% Xe+1.

A typical beam current pulse is shown in Figure 4.

Our computer calculations show that the two quadrupole triplets can only transport about 1 mA of un-neutralized Xe"*"^. This implies that the initial beam is more than 98% neutralized.

Measurements of emittance and a magnet analysis of the beam are in progress. Following this the beam energy will be increased to 750 kV.

COL £>-/7 CuP )

^ i u HHHllalH •1 i 1 1 Hf^^HBSB• -• S o •-M M -j CM i

i .

100 usec/cm

+1 Fig. 4: 500 kV Xe beam current vs. ti me

54 References

1. Proceedings of the Heavy Ion Fusion Workshop, Brookhaven National Laboratory Report 50769 (1977), p. 88.

2. Reference 1, page 91.

3. J. B. Taylor and I. Langmuir, Phys, Rev. 44^. 423 (1933).

4. M. Hashmi, A. J. Van der Houven van Oordt, Conference on U Isotope Separation, London, March 5-7 (1975).

5. Designed by W. Herrmannsfeldt, SLAC.

55 56 THE LAWRENCE LIVERMORE LABORATORY HEAVY ION FUSION PROGRAM*

R, 0, Bangerter, E. P. Lee, M. J. Monsler, S. S. Yu Lawrence Livermore Laboratory, Livermore, CA 94550

In the large fusion program at Livermore we are actively doing research in most areas of inertial confinement fusion. The areas in which we are funded for research specific to heavy ion fusion are:

I. Target Design II. Energy Conversion Chamber Design

III. Ion Beam Propagation in the Combustion Chamber

Target Design

There are two main thrusts to the target design effort: 1. Development of targets which are optimally suited to heavy ion fusion power production. 2. Fundamental studies of the beam-target interaction.

Target Development

For the accelerator designer, the measure of target development is the input requirements. These requirements have not changed significantly in the last year.^ In particular, input energies > 1 MJ at power levels ^ 100 TW are required for power production. During the past year, progress has been made in target design which increases our confidence in these input requirements.

In some ways it would be advantageous if the input requirement could be significantly lower. Analyses based on idealized target models indicate that targets having energy gains of about 1000 at input energies of 100 kJ are possible. Such targets would only require about 20 TW of power.^ Unfortunately, detailed numerical simulations have so far usually shown much larger input requirements than the idealized models. Furthermore, smaller targets require lower energy ions and smaller focal spot sizes and may not be compatible with reasonable accelerator technology. For power production, smaller targets impose more severe requirements on pulse repetition rate and target fabrication costs, but may ease some energy conversion problems.

Taking all of these things into consideration, we conclude that 1 MJ and 100 TW still represent reasonable minimum requirements for power production. *Work performed under the auspices of the U.S. Dept. of Energy at the Lawrence Livermore Lab. under contract number W-7405-ENG-48.

57 Beam-Target Interaction

Our studies of the beam target interaction have established the following conclusions:

1. The range of heavy ions in matter will not be appreciably longer than we have been assuming. 2, Target preheat will be at an acceptable level.

The conclusion regarding the range of the ions is discussed in a separate paper in this report.

Target preheat increases the energy required to compress the fuel, and if sufficiently severe, can prevent ignition and burn. For ion beams, we have calculated preheat from the following mechanisms:

a. Suprathermal electrons b. X-rays from beam and target c. Charged nuclear reaction products d. Neutrons e. Gamma rays.

Preheat increases with increasing ion energy, but is acceptable for reactor targets up to ion energies in excess of those allowed by the range limit. So far, this conclusion is based on particular target designs. We plan to refine our calculations and extend them to a wider selection of targets in the future.

Energy Conversion Chamber Design

Most of the effort in energy conversion has gone into a conceptual design study of a 1050 MW^ electrical power plant.^ The fusion power is provided by 2700 MJ yield pellets (gain 900) fired at a rate of one Hertz. The concept chosen utilizes a liquid lithium blanket which is injected into a chamber to provide protection between the fusion pellet and structural walls. The blanket consists of a dense array of jets and provides effectively a one-meter thickness of lithium. It is completely re-established between pulses. The blanket attenuates and moderates the neutrons sufficiently to allow the steel structure to last the lifetime of the power plant. The lithium is at a temperature of 500°C, leading to a background vapor pressure in the chamber of 10 to 5 x 10~^ torr. This may be supplemented by the addition of a background noble gas to achieve the required ion beam propagation conditions.

Ion Beam Propagation in the Combustion Chamber

Efforts in ion beam transport theory at Livermore in the past year have been focused on two areas: the filamentation instability and classical beam transport.

58 Filamentation Instability

The filamentation instability is predicted for a very broad range of beam and chamber parameters. At the point of injection the beam has large radius and low transverse velocity spread. The process of collapse into filamentary magnetic pinches causes a considerable increase in velocity spread, with concomitant increase in emittance. Spot size on target is proportional to emittance. Several methods are available to eliminate filamentation. Conceptually, the most straightforward approach is the use of multiple beams, thereby reducing current density of the individual beams and making them "magnetically stiff". Increasing the radius at injection and reducing the ion charge state have the same effect. A second class of cures involves propagation in a self-pinched state with large or small initial radius, and there is also the possibility of propagation in a focusing field created by an auxiliarly electric discharge. A sample calculation of the filamentation instability is given in an appendix by E. P. Lee in this report.

Classical Beam Transport

The classical beam transport calculations follow the evolution of the ion beam together with the beam-generated plasma channel with all instability effects excluded. The size and shape of the ion beams at the target area are determined quantitatively in our transport codes. These studies are prerequisites for a more detailed instability analysis since the growth rates of instabilities depend on the evolving state of the beam and the plasma channels. The feasibility of propagating the beam in a self-pinched state, which is less prone to the filamentation instability is also investigated.

Two sets of transport codes are being developed at LLL. The 1-D codes are relatively fast, and are useful for parameter searches. A 2-D code is also being developed which maps out the detailed radial profiles of the electromagnetic fields and the plasma channels. The models, together with some numerical results from both the 1-D and the 2-D models, are reported in an appendix by S. S. Yu, H. L. Buchanan, E. P. Lee and F. W. Chambers.

REFERENCES

1. Proceedings of the Heavy Ion Fusion Workshop held at Brookhaven National Laboratory, October 17-21, 1977. (Smith, Lyle W., ed.) (Brookhaven National Laboratory, 1978).

2. J. H. Nuckolls, R. 0. Bangerter, J. D. Lindl, W. C, Mead, Y. L. Pan, University of California Lawrence Livermore Laboratory Report UCRL-79373, Rev. 1 (1978).

3. M. Monsler, J. Maniscalco, J, Blink, J, Hovingh, W. Meier and P. Walker, "Electric Power From Laser Fusion: The HYLIFE Concept", LLL Report UCRL-81259, Rev. 1, June 1978.

59 60 III. INVITED TALKS

A PLAN FOR THE DEVELOPMENT AND COMMERCIALIZATION OF INERTIAL CONFINEMENT FUSION

T. Willke, D. Dingee, L. Ault, M. Bampton, W. Bickford, J. Hartman, A. Rockwood, E. Simonen, and V. Teofilo Pacific Northwest Laboratory and T. Frank Los Alamos Scientific Laboratory

Introduction

A national energy policy is emerging to meet the anticipated shortage in worldwide fuel supplies. The immediate concerns are to formulate programs in energy conservation and to expand energy production from traditional supplies (natural gas, oil, coal, and uranium). National energy policy must also be directed toward the development of appropriate inexhaustible energy sources to insure against the exhaustion of conventional fuel supplies. The only known inexhaustible energy sources which can provide insurance against a future energy gap are fusion, solar, and fission breeder reactors. All of these options should be developed as part of a diverse and dynamic energy economy.

This paper describes an engineering development program strategy to take inertial confinement fusion (ICF) from the milestone of scientific feasibility to a point where its commercial viability can be determined. The impetus for this plan is the optimism that inertial confinement fusion can be developed as an economic, safe, and reliable energy source.^"8

The purpose of the planning effort is to design a program plan for the development of inertial confinement fusion technology for commercial applica­ tions. The principal objectives of the planning effort are as follows:

• To define an orderly and rational development program which takes into account technical, schedule, and budgetary goals and con­ straints.

« To identify and define the necessary RD&D tasks to solve the tech­ nological issues from the achievement of scientific feasibility through the commercialization of ICF.

• To establish a framework for setting program priorities in terms of level of effort and cost to the program.

The central thrust of the program plan is the use of ICF technology for commercial electric power and fusion-fission hybrid applications. Potential

61 applications of fusion systems include the direct production of hydrogen and/ or synthetic fuels, process heat, and fission product waste disposal. Efforts are In progress to evaluate these applications. The present and planned programs will permit timely information on which decisions can be made to pursue these opportunities. The program plan considers the full range of technological possibilities, including the full spectrum of potential fusion drivers, as follows: (1) Nd:glass lasers; (2) CO2 lasers; (3) advanced lasers; (4) electron or light ion particle beam accelerators; and (5) heavy ion beam accelerators.

While ICF technology supports both the national security and energy missions of the United States, the program plan addresses only the development of ICF technology for energy applications. While much of the research performed to date has been classified, no classified information was used in the formula­ tion of the program plan. The plan does not examine the needs, priorities, or programs within the currently planned physics research effort. Rather, the plan assumes the achievement of scientific feasibility by 1985 within the physics research program. While the major thrusts of the engineering develop­ ment program are assumed to start after 1985, the possibility of starting certain long lead-time activities in the near term (e.g., systems studies) was considered. No attempt was made to assess the scientific and/or technical feasibility of ICF either on a technical or economic basis. There is confidence that ICF can be developed to meet the technical, economic, and social criteria applied to energy technologies early in the 21st century.

ICF Program Objectives

The overall objectives of the ICF Program are:

1985: to gain an understanding of the nature of laser and particle beam interactions with matter, demonstrate high energy gain from pellet implosions (i.e., scientific feasibility), and realize the initial benefits of significant military applications,

1990: to demonstrate the technical feasibility of sustained power gen­ eration by means of inertial confinement fusion, and to develop and operate dedicated facilities for weapon physics and weapon effects simulation and for materials tests,

2000: to operate a demonstration power plant capable of demonstrating inertial confinement fusion as a safe, environmentally acceptable, and economical energy source for commercialization.

The development of this program plan has been affected by a number of guidelines that reflect national energy needs, the present stage of technology development, the scheduled physics research programs, ultimate user require­ ments, and recognized technological problems and opportunities.

The assumptions upon which this program strategy is based are that the physics research and technology development programs will be predictably suc­ cessful, but that no dramatic, unanticipated breakthroughs in physics or tech­ nology will occur. Nor will there be any serious setbacks from anticipated orderly progress toward solving recognized problems and achieving required milestones. The strategy is conservative (i.e.. low risk) in the sense that

62 all recognized proof-of-principle experiments are included and major facility commitments are not made until preceding experiments have provided the neces­ sary information for determining how to proceed.

The Basic Program Strategy

Analysis of the ICF sequential development strategy and the many strategy options reveals a central theme which can be captured as a generic development strategy. The generic development strategy consists of seven generic facili­ ties, each of which must be interpreted in the context of driver candidates and ICF applications. The generic facilities, along with potential specific interpretations, are as follows:

(1) Systems Integration Facility (SIF)

• Advanced Laser driven • Light particle beam driven • C0« laser driven

(2) Single-pulse Target Facility (SPTF)

• NOVA Upgrade • CO2 laser target facility • Light particle beam target facility • HIDE upgrade (100 TW/IMJ)

(3) Engineering Test Facility (ETF)

• Advanced laser driven • Light particle beam driven • CO2 Laser driven • HIDE upgrade (100 TW/IMJ) • Modification of the SPTF • Hybrid Reactor Experiment

(4) Materials Test Facility (MTF)

(5) Pellet Fabrication Facility (PFF)

(6) Fusion Pilot Plant (FPP)

• Pure fusion

• Fusion-fission hybrid

(7) Prototype Fusion Power Plant (PFPP)

• Pure fusion (Electric Power) • Fusion-fission hybrid The six mainline facilities are sequenced as shown in Figure 1. All of these facilities may not be required, but their basic functions must be served in other facilities or supporting technology development programs.

Gross estimates of the program schedule indicate that the Prototype Fusion Power Plant (PFPP) could be operating shortly after the year 2000. There is

63 ADVANCED LASER MTF

CO2 LASER ^ LIGHT ETF PARTI CL£ 2ooe- BEAM BYPASS ETF 2007 1988- 1995- 2000 1989

HEAVY ION BEAM ODECISION POINT OMILESKM

FIGURE 1. A Generic Strategy for the Development of Inertial Confinement Fusion for Civilian Applications little time variation among the program strategy options that can be selected from the ICF sequential development strategy. Bypassing one of the facility stages does not measurably affect the pace of the program, but it does add to the technical risk. The total development time period could be compressed by three contingencies: (1) a sense of national urgency and a recognized need for ICF technology; (2) spectacular and unanticipated performance in the planned physics research program; and (3) an accelerated technology development effort with emphasis on completing the pulsed systems integration efforts by the time scientific feasibility is demonstrated. An early decision to emphasize fusion-fission hybrids combined with accelerated technology development could produce an operating hybrid plant in the mid 1990*s. Both physics and technology requirements are somewhat relaxed in hybrid applica­ tions. Achievement of pellet gains approaching 100 in NOVA II coupled with resolution of the wavelength coupling issue concerning CO2 lasers would eliminate the need for the Single-Pulse Target Facility (SPTF). If the Engineering Test Facility (ETF) were also eliminated, the PFPP could operate in the mid to late 1990's. But based upon the given assumptions of orderly progress, there is little time advantage in choosing a high risk program strategy option (at this time).

Total program cost, including both capital and operating expenditures, is highly uncertain and will remain uncertain until more is known about progress in the physics programs in the early 1980's. Guided by such infor­ mation, the capital cost of major facilities must be estimated from facility conceptual design studies. Early scoping studies would also help to deter­ mine the probable range of facility costs. Operating costs, including all supporting technology development costs, greatly exceed the total capital cost of facilities under reasonable cost assumptions.

The program strategy as presented here provides for the orderly develop­ ment of all presently conceived driver concepts and power plant applications. The strategy is robust; it is flexible and can be adapted readily to varying performance levels and rates of progress. This plan is not a static blueprint to be followed blindly, but a management tool — part of the evolving process of guiding and directing the development of a promising technology. It will be changed and modified as new insights into the nature of the task evolve.

Development Strategy

The development strategy has been formulated around a set of major facilities, milestones, decision points, and major program activities. These research, development, and demonstration (RD&D) activities have been sequenced in series and in parallel, to provide for an aggressive and timely development of ICF technology for commercial applications.

The strategy must take into account current uncertainty about the problems and opportunities facing the ICF program. Since many of the techno­ logical issues cannot be resolved at any particular point in time, either now or in the future, the strategy is built around a set of decision points and RD&D activities which are sequenced iu time over the period of the pro­ gram. The sequence of activities reflects both program priorities and the need to resolve some issues before others can be clearly defined. For example, the design of a reactor cavity concept depends upon the expected pellet yield, pulse rate of operation, and type of driver. These inputs await developments

65 xmn driver technology, pellet design, and power supply technology. These devel­ opments, in turn, are functions of the current physics experiments and funda­ mental driver research. The logic of these sequences and the correlated uncertainty about relative progress in technology development demand that the program strategy be laid out sequentially from one decision point to the next.

Fusion has a special advantage over other large-scale energy technologies —the capability to build modular experiments to simulate portions of the tech­ nology without the necessity to integrate all of the technologies at each stage in the program. For example, it is possible to achieve high pellet gain in one device and high pulse rate capability in a second device, programs which complement each other and reduce development cost. Only in the demonstration phase is it necessary to Integrate all of the subsystems in one reactor facility.

ICF Program Facilities

Nine generic types of facilities were designed for the development strategy, two of which are combined function facilities. The seven basic facilities are listed in Figure 2 along with their principal functions and a stylized representation which serves to identify each symbolically. The central burst implies D-T pellet microexplosions, pellet injection is shown by the multiple dots within the chamber and useful radiation is illustrated with arrows radiating from the microexploslon to the wall.

Sequential Development Strategy

The sequential development strategy is focused upon the major facilities, major development activities, and the milestones (and decision points) from the currently planned physics program through 1985 to the operation of a prototype fusion plant early in the next century. The strategy is presented schematically by a DELTA chart as shown in Figure 3*. The chart is read from left to right starting on the left with the currently planned physics program through 1985. Toward the right, four development stages are shown, separated by decision points. Each stage is related to a set of optional engineering development facilities.

The first stage emphasizes commercial pellet development, pulsed tech­ nology developments, and the integration of pulsed subsystems. The second * DELTA is an acronym for d_ecision, event, _logic, ^ime arrow, and a.ctivity diagram. Decision points are indicated by "diamonds" and have one or more outcomes as represented by the time arrows. Time is presented implicitly through the sequence of activities chosen. The actual schedule (i.e., time) for any one path through the DELTA chart depends upon the number of activi­ ties performed and the time required for performance. The principal de­ velopment activities are represented by rectangular blocks. Major facility options are presented by darkly outlined activity blocks. To facilitate the interpretation of the strategy, logic AND and OR blocks are indicated. All activities leading to an AND block must be accomplished before proceed­ ing. Only one activity need be accomplished before proceeding beyond an OR block. Multiple time arrows leading out of an AND block indicate the trans­ fer of information to other activities. Multiple time arrows leading out of an OR block indicate that an either/or decision was previously made.

66 • SYSTEMS INTEGRATION FACILITY

DRIVER-PELLET TARGETING

PELLET INJECTION

BEAM TRANSPORT AND GUIDANCE

PELLET TRACK ING AND TARGETING

PULSED POWER SUPPLY DEVELOPMENT SIF PROTOTYPE DRIVER-MODULE TESTING

BEAM PROPAGATION STUDIES

•SINGLE-PULSE TARGET FACILITY

COMMERCIAL PELLET DEVELOPMENT

REACTOR COMPONENT TESTING (LIMITED)

• ENGINEERING TEST FACILITY

REACTOR CAVITY/BLANKET TESTING

REACTOR SYSTEMS QUALIFICATION (NUCLEAR)

• MATERIALS TEST FACILITY

PULSED IRRADIATION EFFECTS

MATERIALS QUALIFICATION

• PELLET FABRICATION FACILITY MTF FABRICATION PROCESS DEVELOPMENT

PROTOTYPE FUEL SYSTEM DEVELOPMENT PFF PELLET PRODUCTION FOR FACILITIES

• FUSION PILOT PLANT

PROTOTYPE PLANT TECHNOLOGY CONFIRMATION

SIGNIFICANT THERMAL POWER (FISSILE FUEL) PRODUCTION PILOT (EXPERIMENTAL HYBRID REACTOR)

•PROTOTYPE FUSION POWER PLANT

PRACTICAL POWER (FISSILE FUEL) PRODUCTION

RELIABLE OPERATION ON UTILITY GRID

EXTRAPOLATABLE POWER COST

MAJOR INDUSTRIAL INVOLVEMENT

(PROTOTYPE HYBRID PLANT)

FIGURE 2. Major ICF Developmental Facilities

67 0^ 00

FIGURE 3. ICF Sequential Development Strategy stage emphasizes the development of reactor cavity concepts and reactor sub­ systems to operate in a pulsed, high pellet yield (nuclear) environment. The third stage is the pilot reactor stage, in which all major reactor subsystems are Integrated for the significant production of thermal energy for pure fusion or fissile fuel production in a hybrid fusion-fission device. The last stage of the engineering development effort is required for integrating the complete fuel system and for upgrading reactor performance to a level which demonstrates the potential for commercial application.

It is assumed that any of the four candidate driver concepts can proceed through the development program to commercialization — advanced lasers, light particle beam accelerators, CO^ laser, or heavy ion beam accelerators. Although driver choices and assessments are indicated in the strategy, no definite decision points for dropping driver candidates are indicated since the criteria for making such decisions cannot be determined at this time. Indeed, the strategy retains the flexibility to carry along alternate driver concepts until near the end of the program. Most of the facilities and activities are not driver specific; most technology developments and driver developments are complementary. New information gained from a facility using a specific driver concept will almost always advance the state-of-the- art as it affects other drivers.

The keystones of the sequential development strategy are the major pro­ gram activities and decision points, the lines of development activities listed as follows: (1) driver development; (2) commercial pellet development; (3) pulsed systems integration; (4) materials qualification; (5) reactor systems qualification in a pulsed nuclear environment; (6) fuel systems development; and (7) reactor systems integration and demonstration. Each of these activities are expected to consume significant financial resources and many will require support in the form of one of the major facilities. The type of facilities chosen, the specific form and structure, and the functions performed will depend upon technical outcomes, program objectives, and assess­ ment of the performance of candidate drivers. These choices are indicated by the decision points which separate one development path from another.

Implicit in the decision points listed below are performance criteria and program assessments: (1) early hybrid reactor assessment? (2) need for a Single Pulse Target Facility? (3) construction of a Systems Integration Facility or High Rate Driver Target Facility? (4) need for reactor systems qualification in a pulsed nuclear environment? (5) type of facility needed for reactor systems qualification? (6) need for a Materials Test Facility? (7) choice of application (pure fusion or fusion-fission hybrid) for the pilot and prototype facilities? and (8) the choice of driver type for each major facility?

ICF Program Logic

It will be necessary to consider whether an immediate thrust toward the hybrid application is to be made in the mid 1980's. If decided in the affirmative, either gas lasers or particle beams may be candidate drivers for this application based on driver technology in existence in 1985. A hybrid thrust will affect the type of reactor systems developed as indicated by systems studies.

69 rn^n,.rr-i.l Pellet Development. If the program is not to be diverted toward the hybrid application in 19^5 and/or the goal of pure fusion is retained, the next logical major facility for experimental development is the Single- Pulse Target Facility (SPTF). The purpose of this facility is to develop commercial pellet designs and to demonstrate their performance. The driver energy per pulse (or power level per pulse) should be large enough to permit optimization of pellet designs for minimum power production costs in the com­ mercial environment. Pellet design optimization should take into account such factors as driver efficiency and pellet gain, adaptability of pellet designs for mass production, pellet production costs, and implications for reactor size and design and thus generating station size, modularity and cost. The most desirable progression of driver size for the remainder of the engineering development program would be that driver energy per pulse would decrease for facilities beyond the SPTF. That is to say, the SPTF driver should be capable of sufficient energy per pulse to provide flexibility for optimization experi­ ments whereas succeeding drivers would be tailored to match the requirements of the optimized pellet design.

The driver choice for the SPTF should be based on the best assessment possible at the time of the driver to be developed for eventual commercializa­ tion. If it is determined that the eventual driver of choice is to be a gas laser and the technology of this laser is sufficiently well developed to per­ mit its use in the SPTF, then it is the obvious choice for this facility. If the eventual driver of choice is a relatively undeveloped, short-wavelength gas laser or a particle beam, the driver for the SPTF might logically be an upgrade of the SHIVA-NOVA Nd:glass laser.

It is assumed that pellet development will continue in the target facili­ ties operating in the mid 1980's in addition to target experiments in the SPTF. Potential modifications to allow for reactor systems qualification on a limited pulsed basis will be discussed later.

Pulsed Systems Integration. One of the supporting technology development pro­ grams that will have begun prior to the mid 1980's but will continue beyond this period and may require significant facility construction is the pulsed systems integration activity. Lumped into this activity are beam transport, power supplies, pellet injection, and driver-pellet targeting development. This activity is expected to require facilities which will be constructed as modular units of increasing complexity and cost. The most important goal is to integrate a driver with a pellet injection system for operation on a repeti­ tive basis. Thus, the facility is called a Systems Integration Facility (SIF). This function will require development of systems for repetitive pellet injec­ tion with reproducable and predictable pellet trajectories, systems for track­ ing the pellets to confirm trajectories, to point the driver beams, and to initiate the driver firing sequence; and systems (i.e,, diagnostics) to monitor the performance of the integrated system. Secondary functions of this activity include beam propagation experiments to determine the effects of different atmospheres on integrated system performance, and ultimately, testing of proto­ type driver modules for successive facilities such as the Fusion Pilot Plant (FPP). Finally, depending on the energy per pulse and other characteristics of prototype driver modules tested in the SIF, this facility could be modified and adapted for materials testing and qualification.

70 The systems integration activity will begin in the late 1970's or early 1980's. Initial experiments will be done with a small (few tens of joules per pulse) single pulse laser with good beam quality. In-flight targeting experiments will be done with this laser using various schemes to inject dummy pellets into a target chamber with a precisely controlled atmosphere. Since any commercial reactor design will require multiple beams, the next step in this activity would include experiments using two small, single-pulse lasers fired simultaneously to intercept a pellet in flight.

The second major phase of the systems integration activity will require at least limited repetitive pulse capability of the driver and pellet injection system. This phase will begin in the mid 1980's and a driver choice different from the first phase can be made. The driver will be selected from among ad­ vanced lasers, C0„ lasers, and REBs. The driver energy per pulse will be several tens of kilojoules per beam, and two or more beams will be provided. If the driver is a gas laser, limited pulse repetition capability (say 10 to 20 pulses in a sequence) could be provided by including a gas blowdown and storage facility. After operation for a sequence of pulses, the lasing gas would be cooled and reprocessed if necessary in preparation for a subsequent period of operation. There is no requirement for fusion yield from pellets in this phase so that dummy pellets can be used.

An additional phase of operation of the SIF can be considered if it is desirable to test a prototype module(s) of the driver for the Fusion Pilot Plant (FPP). This objective could have been satisfied in the previous phase by having provided the total energy per pulse from one beam, which could be approximately the anticipated energy per pulse requirement per driver module for the FPP. There is no requirement, per se, for fusion pellet yields from this phase of operation of the SIF; thus, unless some testing function requir­ ing pellet outputs is adopted for this facility, dummy pellets can be used.

Materials Qualification. Materials studies will be conducted in concert with systems studies prior to the mid 1980*s with some limited materials testing performed in simulated ICF environments. Some testing can be performed in existing fission, weapons, and/or magnetic fusion facilities available in the mid 1980*s, and at that time it will be necessary to consider whether materials testing should be conducted in dedicated ICF facilities. If an early decision is made, the SIF could be designed initially with the capacity for upgrading for materials testing. Because of the extra, though limited, design require­ ments, the facility is called a High Rate Driver Target Facility (HRDTF). The early phases of development would proceed as described above for the SIF.

If the HRDTF is retrofitted with at least one FPP driver module (for pro­ totype tests), the addition of an additional module would provide sufficient driver energy and pellet yield to do materials testing. (Note that the thres­ hold of neutron output needed for accelerated materials testing is '^10^° neu­ trons once per second or a pellet thermonuclear yield of "^100 kJ with a one- per-second repetition rate.) Therefore, the possibility for doing accelerated materials testing at a relatively early date exists. There are, of course, significant requirements for reliability, for relatively long-lived components, for a large and continuous supply of pellets, and for a shielded target chamber with remote handling facilities. The materials testing function would occur approximately simultaneously with construction of the FPP, thus qualified

71 driver components should be available. Accelerated development of pellet mass production facilities, compared to delayed materials testing, would, how­ ever, be required.

The decision to build a Materials Test Facility (MTF) could be deferred until after the SIF is constructed. A separate MTF would resolve potential conflicts between SIF objectives and materials qualification requirements. The decision to design the SIF for possible upgrading for materials testing (i.e., HRDTF) would not significantly add to its cost. Thus, the decision to upgrade the HRDTF or build a separate MTF could be deferred.

Economy of operation for the materials testing program would not be an overriding issue. The driver need not be as efficient as required for commer­ cial operation and neither are pellet production costs dominated by commercial considerations. Since the driver energy per pulse would be considerably smal­ ler than for the FPP, the pellet design would probably be quite different from the commercial design and may be easier to produce.

Reactor Systems Qualification (Nuclear). An ongoing activity that will become increasingly important in the 1980's is the design and development of reactor concepts. A reactor design must have been selected, tested, and qualified prior to design of the FPP in the early 1990's. The major testing requirements to qualify a reactor design include verification of its gross performance fea- Lures during pulsed operation and verification of required component lifetimes and/or replacement procedures. Gross performance can be established with a few successive pulses, whereas long-term materials testing will be required to determine component lifetimes.

Depending on the design of the reactor and on the cavity phenomenology during pulsed operation, gross reactor performance might be reasonably well established using simulated pellet microexplosions, etc., small high explosive charges, exploding wires, etc. However, it eeems unlikely that testing with simulated microexploslon sources alone will qualify the reactor design ade­ quately to ensure the necessary confidence to proceed with construction of the FPP (which may cost three quarters of a billion dollars). Therefore, a facility whose main purpose is to qualify the reactor design for the FPP using fusion pellet microexplosions is included. This facility is called an Engin­ eering Test Facility (ETF) and would include a driver of moderate size and a scaled version of the reactor cavity with such blanket components as necessary to verify gross reactor performance. Pellet yields need only be large enough to produce the reactor cavity and blanket phenomena of importance for assess­ ing essential features of the reactor design. Driver energy per pulse require­ ments will be established by pellet yield requirements and the parametric pellet design investigations that will have been conducted with the SPTF.

Some continuous operation at design pulse repetition frequencies for the FPP will be required for the ETF; however, operation for extended periods will not be necessary. (A desirable goal would be to operate the ETF continuously until equilibrium conditions have been established, a few hundreds of sequential pulses.) Thus, reliable, long-lived driver components will not be a require­ ment for the ETF. The pellet fabrication requirement will also be minimal and pellet production costs will not be of extreme importance.

72 The exact nature of the ETF will depend upon the driver concept which is chosen as the leading candidate for the prototype fusion plant. If the Single- Pulse Target Facility has been constructed, it could possibly be modified for engineering testing of reactor cavity concepts (i.e., the SPTF-ET). The tar­ get chamber would require modification for pellet injection and driver-pellet targeting. A partial or full first wall and blanket would also be required. The driver and associated power supplies would be reconfigured for a few tens or hundred of pulses. (A few tens of pulses are required to test first wall and wall protection concepts; a few hundreds of pulses would be needed to bring the blanket up to thermal equilibrium.) Modification of the SPTF would depend upon reasonable confidence in the leading reactor cavity concept and a decision to deemphasize hybrid applications.

Apart from low confidence in the reactor concepts (and hence the need for qualification in a pulsed nuclear environment), a separate Engineering Test Facility may be required if the SPTF is not built or a decision is made to change driver concepts. For example, if a laser driver was employed in the SPTF but a decision was made to pursue commercial development of light parti­ cle beam drivers following successful testing in the SIF, the ETF would be a logical facility to follow the EBFA II. Following an assessment of the ac­ celerator technology for heavy ion fusion at the 10 to 30 TW/lOO kJ per pulse level, the heavy ion demonstration experiment (HIDE) could be upgraded to the 100 TW/1 MJ per pulse level for target experiments as well as reactor concept testing. In that case, the ETF would perform some of the functions of the Single-Pulse Target Facility.

A decision to emphasize hybrid applications would create the requirement for a Hybrid Reactor Experiment (HRE) to test blanket designs and breeding per­ formance. The decision to build an engineering test facility (i.e, hybrid reactor experiment) would depend upon the assessed requirement for nuclear qualification prior to building a Fusion Pilot Plant (i.e., an Experimental Hybrid Reactor).

Fuel Systems Development. Large quantities of pellets will be required for the high pulse rate nuclear facilities starting with the engineering test facil­ ity (ETF) and materials test facility (MTF) which will operate in the early 1990s time period. Average daily requirements will escalate rapidly from 100 to 10 pellets for each facility as running time and reliability are increased. Pellets for these facilities could be produced offslte in one or more pellet fabrication facilities (PFF), e,g. "pellet factories," since pellet fabrication will not be integrated with the reactor until the construction of the Prototype Fusion plant in the early 2000s.

Increasing pellet production by at least five orders of magnitude, from a few hundreds of pellets per year today to at least 10^ pellets per year in 15 years, is a formidable technological objective. Three functional objectives have been identified:

(1) development of pellet fabrication processes suitable for mass produc­ tion operations;

(2) development of a prototype pellet fabrication subsystem for integra­ tion with commercial reactors; and

73 (3) pellet production to meet the demand for pellets in experimental facilities.

All three functions could possibly be accomplished in one facility. Alter­ natively, the pellet production function could be associated with each of the facilities having high pellet consumption.

The potential difficulties in mass producing large quantities of high quality pellets at an acceptable cost suggest that research on pellet fabrica­ tion should commence even before the achievement of scientific feasibility in the mid 1980s. It is assumed that this technology will be developed in a timely fashion, but there is the possibility that pellet fabrication develop­ ment could slow the pace of the program. Pellet fabrication processes are strongly coupled to commercial pellet development, an activity scheduled for the late 1980s. Construction of a pellet fabrication facility could begin in the early 1990s.

Fuel systems development will be a phased activity over the next twenty years. Assuming commercial pellet development in the late 1980s and mass pro­ duction in the early 1990s, development of fuel handling and processing (exclud­ ing pellet fabrication) techniques will be associated with the Fusion Pilot Plant in the late 1990s. Cavity pumping, debris removal, and tritium recovery will be accomplished in the Engineering Test Facility (ETF). Pellet injection systems will be developed and tested in the Systems Integration Facility (SIF). The complete fuel system, with the exception of on-line pellet fabrication, will be part of the Fusion Pilot Plant (FPP). The Prototype Fusion Plant will have a fully integrated fuel system.

Because of insufficient knowledge at this time in pellet fabrication, it has been included in the sequential development strategy as one or more Pellet Fabrication Facilities coupled to the facilities which have large pellet require­ ments.

Reactor Integration and Demonstration. Following verification of the reactor design in the ETF, the design of the Fusion Pilot Plant (FPP) can be finalized and construction initiated. The main objective of the pilot (FPP) is to demonstrate the performance of a totally integrated system. For pure fusion application, the pilot will demonstrate thermal power production in the regimes of interest for electricity generation. If the fusion-fision hybrid option is chosen, the pilot will be an Experimental Hybrid Reactor (EHR) with the func­ tion of demonstrating the breeding of fissile materials and/or thermal energy.

The FPP (or EHR) will be prototypical of a commercial plant in a functional sense except that the fuel cycle will not be closed and the energy produced need not necessarily be converted to electricity (or reprocessed for recovery of fissile fuel). Tritium will be bred for the fuel cycle and separated from the fertile material. Driver efficiency and pellet gain will be demonstrated at suitable pulse rates for limited periods of time. For electric applications, power-plant quality heat will be produced. Reactor components for the proto­ type plant will be qualified in the appropriate operating regimes.

The Fusion Pilot Plant (FPP) is a significant milestone on the road to demonstrating engineering feasibility. It will be a proof-of-concept facility

74 to demonstrate the reactor or energy-producing part of a commercial plant with all the necessary ICF components. Reliability and energy cost will be of lesser importance.

Once the Fusion Pilot Plant has operated successfully and demonstrated the potential for ICF application, the Prototype Fusion Power Plant (PFPP) will be constructed. The protype could be a Prototype Hybrid Plant (PHP). The proto­ type will contain an integrated fuel cycle, including a pellet factory and a "balance of plant" for converting thermal energy into electricity. The PFPP (PHP) will be prototypical of a commercial plant in terms of function and operating characteristics. It will be scaled down in size and probably not contain production-type components. Operating characteristics, especially relia­ bility and safety, will be more important than economically competitive energy production.

The program strategy has been designed only through the operation of the Prototype Fusion Power Plant. Federal involvement in commercialization will extend beyond this point, but the prototype is expected to be the last facility in which the funding is largely provided by the government. Upgrading to commer­ cial status and the associated funding should be largely industry supported.

Scenarios for Engineering Development

To show how the sequential development strategy can be applied to a variety of situations, several scenarios are presented and their impact on over­ all program schedules examined. The genral range of potential scenarios is explored in the discussion of the "Nominal Risk" Option and the "High Risk, Mini­ mum Time" Option, Until the fundamental physics and engineering problems are better understood, no option is said to be low risk; the minimum time option is considered high risk relative to the nominal risk option.

The figure accompanying each scenario shows the sequence of facilities and the date of operation of the Prototype Fusion Power Plant. The cost for each facility is proportional to the area of the facility symbol. The Prototype Fusion Power Plant (PFPP), being the most costly, is used as a basis.*

Nominal Risk Option

The Nominal Risk Option shown graphically in Figure 4 evolves from an assumption that a major facility is needed to perform each of the major develop­ ment functions. The functions are as follows:

• Commercial pellet development (Single-Pulse Target Facility) • Non-nuclear pulsed systems Integration (Systems Integration Facility) • Reactor systems qualification (Engineering Test Facility) • Materials qualification (Materials Test Facility) • Fuel systems development (Pellet Fabrication Facility) • ICF proof-of-concept (Fusion Pilot Plant) • Power and/or hybrid demonstration (Prototype Fusion Power Plant)

*For example, the Fusion Pilot Plant (FPP) is expected to cost 40 percent as much as the Prototype Fusion Power Plant (PFPP). The area covered by the FPP symbol is 40 percent of the area covered by the PFPP symbol.

75 Nothing is implied about the driver concept ultimately chosen or whether pure fusion and/or fusion-fission hybrid applications are emphasized.

As can be seen from the schematic of the ICF Sequential Development Strat­ egy (Figure 3), the most significant early decisions following the currently planned physics research programs are the assessment of hybrid versus pure fusion applications and the decision to build a new target facility. A decision to emphasize fusion-fission hybrid applications would affect the decision to go ahead with a target facility, but would not necessarily eliminate the need for such a facility. If a target facility is indicated, then it is assumed in this option that it will be a major upgrade of NOVA-II or a completely new facility with Nd:glass, C0„, advanced laser, or particle beam driver.

The next decision in the sequence is the need for a facility to qualify reactor systems and cavity concepts in a pulsed nuclear environment prior to the construction of a pilot fusion reactor. A decision is made to build an ETF and a choice is made among a pure fusion reactor (laser or light particle beam driver), an upgrade of HIDE with a reactor cavity, or a Hybrid Reactor experiment (HRE). The choice of a non-laser driver and/or a hybrid experiment can be made even though the SPTF is laser driven and dedicated to pellet development for pure fusion.

A decision to build a Materials Test Facility (MTF) is made in this same time period based upon theoretical studies and materials tests made in non-ICF- driver facilities. Initial results impact upon the design of the Prototype Fusion Power Plant (PFPP) and materials qualified for commercial fusion plants.

A Fusion Pilot Plant (FPP) ad Prototype Fusion Power Plant (PFPP) are con­ structed in sequence after the ETF. A decision to build hybrid plants instead would change these facilities to an Experimental Hybrid Reactor (EHR) and a Prototype Hybrid Plant (PHP), respectively.

High Risk, Minimum Time Option

There is the possibility that pellet performance greatly exceeding proof of scientific feasibility will be achieved by the currently planned physics program, i.e., pellet performance approaching the requirements for commercial application of ICF technology. If this event is accompanied by successes in -

\

FIGURE 4. Nominal Risk Option

76 either the advanced laser, the CO^ laser, or the particle beam programs and by continued successes in theoretical modeling of driver-pellet physics, then there may be justification for proceeding directly to a Fusion Pilot Plant (FPP). Commercial pellet development would be accomplished using drivers in existence in 1985. A systems integration function and thus a Systems Integration Facility (SIF) would also be required. This option is shown schematically by Figure 5.

The pulsed systems integration activity might be accelerated for this strategy compared to the nominal risk strategy. Initial experiments with low- energy, single pulse systems will be done, but the next phase of this activity would probably require the construction of a one- or two-module prototype of the FPP driver. Thus, prototype testing of the driver of choice would be com­ bined with development and testing of integrated driver-pellet injection systems.

The supporting technology development programs take an added significance for this strategy. The reactor concept to be utilized in the FPP will have to be qualified using simulated pellet micro explosion sources. Materials testing and qualification will be done using steady-state fusion sources (OFE Program) and non-fusion pulsed sources that simulate the damage caused by pulsed fusion sources (e.g., ion beam sources). Operation of the FPP will also contribute materials data for use in designing the PFPP.

The savings in time to the commercialization phase for this strategy com­ pared to lesser risk strategies is probably not significant insofar as market penetration is concerned; however, there could be significant savings in over­ all program costs.

Moderate Risk Option (A Scenario for Heavy Ion Fusion)

The strategy option labeled Moderate Risk Option has the same elements as the Nominal Risk Option with the exception of the single-pulse target facility (SPTF). Figure 6 illustrates the option. Along with the SIF, pilot, and proto­ type, the option includes a materials test facility (MTF) and an Engineering Test Facility (ETF). This option results from a decision near 1985 that a new target facility is not required for commercial pellet development at the 1 MJ pulse energy level. It assumes that existing facilities are adequate for this function; no upgrading of NOVA-II or ANTARES is comtemplated. It has the

^

FIGURE 5. High Risk, Minimum Time Option

77 specific advantage of avoiding funding requrests for a facility (i.e., the SPTF) costing at least twice as much as any previous facility.

At least three contingencies can be envisioned that would support this option. The first possibility is that the fusion-fission hybrid option is emphasized over pure fusion as an early application. An urgent and nationally recognized need for fissile fuel breeding to support the converter reactor economy would be a prerequisite. Adequate performance would have to be demon­ strated in one of the physics research facilities—a combination of driver efficiency and driver-pellet coupling to project adequate fusion energy gain. This potential exists for the EBFA II facility and possibly ANTARES. A second possibility exists that commercially-attractive results could be achieved in NOVA-II with pellet gains approaching 100 or more. Resolution of the wavelength coupling issue in ANTARES or successful performance of an advanced laser would then make the SPTF unnecessary. The third possibility is that heavy ion accelera­ tors could emerge as the leading driver candidate. The SPTF could then be bypassed in favor of the Engineering Test Facility (e.g., an upgrade of HIDE). Both commercial pellet development and reactor systems qualification could be performed in the ETF/HIDE. A heavy ion fusion facility could combine the func­ tions of the SIF, SPTF, and ETF at considerable savings to the program.

The ETF is the next logical facility for the particle beam programs and/or a fusion-fission hybrid program. Each of these programs require technology development and integration around the functions of pulsed nuclear operation, reactor cavity qualification, and blanket development, i.e. the functions of the ETF. The ETF could become either a pulsed reactor following EBFA II, an upgrade of HIDE to the 100 TW/1 MJ per pulse level, or a Hybrid Reactor Experiment (HRE). It is not anticipated that the ETF stage could be bypassed; it is unlikely that funding for a Fusion Pilot Plant can be adequately justified without some pulsed nuclear testing.

Program Schedule and Timing

Based upon the program assumptions, the key date for the start of any major engineering development facilities is 1985. By that date, scientific breakeven (i.e. a pellet gain of one) should be established in one or more of the physics programs, and it is anticipated that scientific feasibility will be established. 1985 is also the date all major driver concepts will be developed to the point

/

^T).

FIGURE 6. Moderate Risk Option

78 where assessments can be made about the potential for further development. The facility schedules for the five strategy options all start in 1984 with facility design and construction starting on the early facilities in 1986.

The Nominal Risk Option has four sequential facility stages with the fol­ lowing dates of operation (see Figure 7): SIF-1988 (first stage); SPTF-1989; ETF-1993 (second stage); MTF-1997; FPP-2000 (third stage); and PFPP-2007 (fourth stage). This date can be significantly reduced only by eliminating one of the facility stages as is done in the High Risk, Minimum Time Option. The High Risk, Minimum Time Option trips five years off the schedule for operation of a Prototype Fusion Power Plant; the projected date of operation is 2002. The schedule is essentially the same as the Nominal Risk Option with PFPP opera­ tion in 2007.

There are three contingencies which could shorten the development time, provided ICF is given greater priority in the energy supply picture. First, scientific breakeven is perceived as a major watershed for fusion, both scienti­ fically and psychologically. If ANTARES performs as planned, scientific break­ even could be demonstrated in 1982 or 1983. Within significantly increased funding, construction of the SIF and SPTF could begin in 1984, two years ear­ lier than anticipated. Provided that the wavelength dependence issue is resolved before ANTARES comes on line, the CO2 laser could probably be devel­ oped more expediently than any other driver concept.

Second, from a technical perspective there is no outstanding reason why pulse rate capability cannot be developed earlier. Power supply development, pulsed lasers, pellet injection, and driver-pellet targeting which are early functions of the SIF could be demonstrated by the time scientific feasibility is achieved. This is not to understate the technological difficulties particu­ larly in power supply development, but the problems do not depend upon driver- pellet physics. Only budget limitations stand in the way.

Third, there is the possibility that fusion-fission hybrid systems could be developed on an accelerated schedule assuming that the required pellet gain regimes are demonstrated in ANTARES, EBFA II, or NOVA. The possibility exists

ANTARES KEY CURRENT NOVA II PLANNED DESIGN EBFA II FACILITIES t 1 CONSTRUCTION, MODIFICATION ADVANCED LASER ^ ^B OPERATION HEAVY ION BEAM NO SPECIFIED TIME LIMIT =1= ---' r- -- - SYSTEMS INTEGRATION FACILITY NOMINAL SINGLE-PULSE TARGET FACILITY RISK ENGINEERING TEST FACILITY I 1 OPTION MATERIALS TEST FACILITY I I FUSION PILOT PLANT PROTOTYPE FUSION POWER PLANT -4 - ^^- HIGH RISK SYSTEM INTEGRATION FACILITY MINIMUM TIME FUSION PILOT PLANT OPTION PROTOTYPE FUSION POWER PLANT

2000

FIGURE 7. Facility Schedules for the Nominal Risk Option and High Risk, Minimum Time Option

79 for a Hybrid Reactor Experiment operating in the late 1980s and a Prototype Hybrid Plant operating before the year 2000. This would require an early deci­ sion to emphasize hybrids over pure fusion plus some acceleration in pulsed technology development.

Implementation of the Development Program

The development program has been divided into seven program areas—fusion theory and experiments, driver technology, reactor technology, materials, fuel cycle, safety and environment, and the special projects office—and an economics and systems analysis function for support of the management of the program. While not equal in magnitude or funding requirements, these areas can be associated with program funding categories and line management functions as they should evolve. The first six program areas define the supporting techno­ logy development and integration functions performed within the Hybcategory of "operating" funds. The last function, the Special Projects Office, is respon­ sible for the management of the design, construction, and operation of the facilities procured under "capital" funds. Each of the program areas are fur­ ther decomposed into subprogram areas as shown in Figure 8.

Fusion Theory and Experiments Program Area

Even with the achievement of scientific feasibility, an aggressive program directed toward a full understanding of the pellet fusion process and the devel­ opment of research tools—computer codes, pellet designs, and diagnostics—will be required. Four lines of research are anticipated in the fusion theory and experiments area, including (1) code development, (2) beam-plasma interactions, (3) target design, and (4) diagnostics. The complex computer codes used to design fusion targets and to model experimental results will be developed and refined throughout the program as knowledge of the basic physics is gained. Target design and target experiments will continue with a shifting focus toward conmiercial pellet design. The work will be closely coupled with driver techno­ logy development, pellet fabrication process development, and cavity design and testing. Improved diagnostics will be needed for both the experimental program and reactor systems development.

Driver Technology Program Area

The main objective of the driver technology area is to provide for the development of at least one driver system, consisting of both the driver and the power supplies, which can be used to produce economical energy gain from the implosion of commercially-produced fusion fuel pellets. The driver develop­ ment program will include all tasks related to the near term development and assessment of alternate driver candidates—lasers, light particle beams, and heavy ion beams—and the ultimate development of a commercial fusion driver. Pulsed power supply development has been designated as a distinct sub-area in order to stress the importance of the power supply systems and to maximize the use of common technology elements. Continuing efforts to develop and evaluate the three categories of ICF drivers places this program area at the core of the ICF program along with the fusion theory and experiments area. The overall fusion performance of the driver candidates will greatly affect the other pro­ gram areas by establishing probable values for the following quantities which relate to commercial plant design and operation: (1) pellet yeild and output

80 ICF 8.0 ENGINEERING ECONOMICS DEVELOPMENT AND SYSTEMS ANALYSIS

I 1.0 2.0 3.0 4.0 6.0 7.0 FUSION DRIVER REACTOR SAFETY SPECIAL THEORY AND MATERIALS TtCHNOLOGY TECHNaOGY AND PROJECTS EXPERIMENTS ENVIRONMENT

1.1 2.1 3.1 4.1 5.1 6.1 7.1 H CODE LASER CAVITY IRRADIATION PELLET SAFETY SPECIAL DEVELOPMENT DRIVERS SYSTEM PERFORMANCE FABRICATION CRITERIA FACILITIES AND ANALYSIS

1.2 2.2 3.2 4.2 TT VACUUM RADIATION PELLET ^ BEAM-PLASMA LIGHT 6.2 7.2 AND DEBRIS EFFECTS HANDLING INTERACTIONS PARTICLE RADIATION l_|S.I.F. PROJECT BEAM COLLECTION STUDIES OFFICE DESIGN CO 5.3 1.3 6.3 3.3 4.3 FUEL TARGET CHEMICAL 2.3 BLANKET NON-NUCLEAR PROCESSING DESIGN AND PHYSICAL HEAVY AND SHIELD REQUIREMENTS ION BEAM HAZARDS DRIVERS 5.4 3.4 4.4 1.4 TRITIUM THERMAL NON-STRUCTURAL HANDLING 6.4 DIAGNOSTICS 2.4 POWER MATERIALS H HYBRID L_l PULSED SYSTEMS SAFETY POWER SUPPLY DEVELOPMENT 3.5 STRUCTURAL SUPPORT SYSTEMS

3.6 3.7 3.8 3.9 3.10 3.11 ELECTRICAL INSTRUMENTATI ON REMOTE HANDLING CONTAINMENT SYSTEM HYBRID POWER AND CONTROL AND MAINTENANCE SYSTEM STUDIES REACTORS SYSTEMS SYSTEMS

FIGURE 8. Work breakdown Structure for the ICF RD&D Program spectra; (2) pellet design; (3) reactor vessel dimensions; (4) reactor chamber environment requirements; and (5) reactor pulse rate requirements.

Reactor Technology Program Area

The objectives of the reactor technology program are (1) to develop reactor subsystems and components for all facilities through the commercializa­ tion phase, (2) to provide integrated and specific systems engineering design studies which would support this development and (3) to study and develop as appropriate alternative applications to pure fusion electric power generation. This program area includes all components and subsystems associated with the reactor cavity and the balance-of-plant with the exception of driver systems and the fuel cycle outside the cavity environment. The number and diversity of reactor subsystems led to the definition of eleven program area divisions, as follows: (1) cavity system; (2) vacuum and debris collection; (3) blanket and shield; (4) thermal power systems; (5) structural support systems; (6) electrical power systems; (7) instrumentation and control systems; (8) remote handling and maintenance; (9) containment system; (10) systems studies; and (11) hybrid reactors. The last sub-area would emphasize blanket development for fusion-fission hybrids, as appropriate. The reactor technology area will relate strongly to every other program area. The actual content will depend heavily upon target physics and driver development activities of the next several years.

Materials Program Area

The functions of the materials area are the identification and the genera­ tion of a materials property data base for experimental facilities, the estab­ lishment of a framework for selection and end-of-llfe testing of materials for commercial reactgrs, and in situ end-of-life testing in the, n'olsed nuclear environment. The analysis and testing programs will culminate in a compre­ hensive data base of properties and failure criteria enveloping expected materials stresses, stress histories, chemistry, fabrication processes, and thermal and irradiation exposure hsitories. Special emphasis will be given to materials needs which are unique to ICF, namely high-rate pulsed irradiation, high cycle fatigue testing of irradiated materials, and development of driver components. Four program divisions are defined: (1) irradiation performance; (2) radiation effects studies; (3) non-nuclear requirements; and (4) non­ structural materials.

Fu^l_ Cycle Program Area

The main function of the fuel cycle area is the development and integration of the technology of the ICF fuel cycle, including some responsibility for commercial pellet development and the engineering of pellet production systems for experimental and intermediate facilities. The fuel cycle scope includes all necessary processes from the recovery of fuel and pellet materials, the management and handling of such materials (including tritium) through pellet fabrication and injection into the reactor cavity. This area will be responsible for the development of processes for producing both experimental and commercial grade pellets. Mass production of pellets will become a function of the special projects office for the Pellet Fabrication Facility once requirements reach the level of several hundred pellets per day. Commercial pellet design will be a joint product of this area and the fusion theory and experiments

82 area. The fuel cycle area will be concerned with the cost and means of pro­ ducing large quantities on an automated basis. Pellet injection and targeting systems will be developed in conjunction with both the driver systems and reactor systems areas. This area has been divided into four subprogram areas, including (1) pellet fabrication, (2) pellet handling, (3) fuel processing, and (4) tritium handling. Many requirements of fuel processing and tritium handling in the ICF program are shared with the magnetic fusion program. Com­ mon problem areas will be investigated jointly, although it is expected that the more mature magnetic fusion program will develop much of the base techno­ logy for tritium breeding, recovery, and handling.

Special Projects Office Program Area

Early in the life of a major ICF facility—those projects included as line items in the capital budget—a special project office will be set up for the management of the final design, construction, and operation. Normally, respon­ sibility will be transferred to the special projects office upon completion of conceptual design studies (Title I) and upon authorization of construction design (Title II). The function of each of these offices is to direct, monitor, and control the work performed for the Office of Laser Fusion so that the project is kept within cost, schedule, and specifications. The program monitor within the Office of Laser Fusion might also serve as the formal program manager or might contract for such services. It is anticipated that the special project offices will be set up for the Systems Integration Facility (SIF) and subsequent facilities. Another office could be set up to manage the smaller developmental (support) facilities.

Safety and Environment Program Area

Like all large energy projects, the ICF program must address safety and environment issues; safe and reliable operation will be the key to public acceptance and successful commercial licensing of facilities. The function of the safety and environment program area is to ensure that all safety and environmental concerns unique to ICF are resolved as an integral part of program development. The scope of this area includes the identification of potential occupational and environmental hazards, the performance of unique safety research related to accident analysis or design standards for input into other program areas, and the development of specific safety systems if required. The divisions within the safety and environment program area are (1) safety criteria and analysis, (2) radiation, (3) chemical and physical hazards, and (4) hybrid safety. An early and comprehensive review of S&E issues will be performed in time for their resolution prior to the construction of the Engineering Test Facility (ETF), the first major ICF facility to operate in a nuclear environment. Before design begins on the pilot or prototype plants, the ICF program should complete an Environmental Development Plan (EDP) and a Generic Environmental Statement (GES). These will document the needed R&D and the impacts expected from a national commitment to this energy source. For all major demonstration projects, a standard series of Environ­ mental Impact Statements as well as Preliminary and Final Safety Analysis Reports will be required.

Economics and Systems Analysis

In addition to the seven program areas defined above, a broad program of economics and systems analysis will be required in support of the management

83 of the ICF program. The main objective of the area is to provide a framework for the guidance and evaluation of the RD&D program. Studies will be performed to establish and assess program goals and milestones on the basis of maximizing the probability of success within a minimum of practical program costs and with an acceptance level of risk consistent with national energy needs and priorities. Technological problems that require special attention or intensive RD&D are highlighted by system studies. These studies allow the performance/ cost tradeoffs to be assessed for alternative system and subsystem designs. System studies performed primarily for reactor technology development will be performed in that program area. Studies required for the effective mangement of the ICF program, such as cost-benefit analyses, user requirements definition and impact analysis, and institutional studies, will fall into this category.

Commercialization

A clear rationale for Federal Government support of research and develop­ ment on new energy technologies has emerged over the last several decades. For new technologies, which have the potential for providing benefits to the nation, especially those technologies whose benefits are too distant for private investment and the costs too great for existing corporate entities, the U.S. underwrites research, development, and demonstation (RD & D) until engineering and commercial feasibility has been demonstrated. Government policy for introducing the fruits of these efforts into the market is not well defined, however. If a new technology is shown to provide benefits to the nation which exceed its costs, both economic and social, then its development can be justified. The development of the technology creates a corollary obli­ gation to provide for its commercialization. This is not the same as forcing a technology into the marketplace, a process called technology push. Rather, development should be managed to meet the needs of the market, including devel­ opment of the market itself. Failure to do so will result in frustration of the commercialization process. Having determined that an emerging technology will provide significant benefits to the nation, it is important that actions be planned to obtain the benefits.

The process of commercialization is essentially a matter of "market devel­ opment" and can, using familiar terms, be either related to "demand pull" or "technology push." This "market development" process parallels the technologi­ cal development process in that both of these processes are striving to reduce uncertainty through the generation of improved information. The process of com­ mercialization has two distinct phases, depending on the existence of a func­ tioning market. In the early stage, labeled market identification, the techno­ logy is not fully developed and thus market transactions are not occurring. However, even at this time a "psuedo market" exists where information concern­ ing economic and technical feasibility is exchanged. The second stage is init­ iated by the introduction of the new technology into the marketplace. Now actual market exchanges involving the technology can occur, with the informa­ tion flow continuing as Inferior products are "weeded out" and surviving products are continually refined. As the process evolves, the level of infor­ mation is increased with a corresponding reduction in uncertainty.

A similar argument has been concerning industrial innovation:

"...there are two sources of ambiguity about the relevance of any particular program of research and development—target uncertainty and technical uncertainty,"9

84 The traditional view is that the reduction of "technical uncertainties" is the principal objective of the R&D program. Today's concern for the rapid development of new technologies has accentuated the notion of target uncer­ tainty. In the earliest stages of development, target uncertainty may include both the vendors and consumers of a technology. The process of commerializa- tion can thus be viewed as the reduction of target uncertainties. One can, of course, employ a broad definition of the target concept for it includes many individual attributes of the ultimate market. Let us then proceed with a more detailed analysis of the commercialization concept.

A Conceptual Model

Recent studies of both successful and unsuccessful attempts at commerciali- ation have demonstrated rather convincingly that a number of requirements must be satisfied before a given technology can penetrate the market. •^*^>^^ First, and most important, there must be a market for the technology. The direct user must recognize a need for the technology, the demand must be large enough to justify its introduction, and the technology must be competitive in terms of both expected cost and risk. Second, the technology must be compatible with the needs of the user. It must not only demonstrate acceptable technical performance, but it must meet the economic, regulatory, and social criteria at the time of its introduction- These two requirements place a special burden on the R&D decision maker to guide the development process so that an accept­ able product is produced. Third, property rights must be clearly established or there will be no incentive to produce the technology even in the face of a strong market demand. Property rights can take the forms of patent protection and an institutional framework that confers rights to produce and make a profit. Fourth and often overlooked, a capacity to produce the technology must be engendered by the transfer of technology to the producing sectors well before the date of commercial introduction. Such transfer of "know-how" is fostered by industrial involvement in engineering development. Industrial participants are often far more effective in selling the technology than the government program manager.

A full understanding of commercialization requires an integration of these four elements. The relationships are illustrated by the balance beam on a fulcrum shown in Figure 9. A balance must be found between the attributes of the technology developed and the demands of the marketplace. This balance has utility only if there is a foundation of property rights (incentives to produce) and the capacity to produce. The elements of market demand and capacity to produce constitute the primary components of a market—a demand sector and a supply sector. The elements of a viable technology and the incentives to produce represent the institutional and structural factors which determine the efficacy and efficiency of the market.

Market demand is derived from the wants and incomes of potential buyers. In the case of fusion reactors, demand is derived from the demand for goods which require electricity or fissile material as an input. Commercial accept­ ance inevitably depends upon the ultimate user's willingness to pay for an R&D product, either directly or indirectly through the purchase of some other good. Market demand works through the institutional arrangement of property rights to create incentives to produce. For a firm to undertake an investment to develop and produce a new product, the firm must be reasonably assured of recovering its investment. If the firm cannot establish and enforce rights to

85 VIABLE \ TECHNOLOGYX

INCENnVES CAPACITY TO TO PRODUCE PRODUCE

FIGURE 9. Four Essential Elements for Commercialization its product, that investment may not be forthcoming- This is the principal argument for the establishment of patent rights-

The property rights of consumers also influence market demand. Some types of goods, typically known as "public goods," are not subject to the principle of excludability in use. Because individuals cannot be prevented from consuming public goods once they have been produced, consumers will be unwilling to pay private producers of such goods. Thus, R&D products having attributes characteristic of public goods may have limited commercial potent­ ial unless corrective action is taken by public agencies.

The establishment of incentives to produce through the institution of property rights leads to the third element of the process, the capacity to produce. Two issues are associated with this element. The first is the pro­ blem of technological transfer which has arisen in the context of developed and developing countries, bur is also relevant to the flow of information between the research and production segments of an economy. Technology trans­ fer is vital to the commercialization process. The second issue is related to the behavior of the producing sector and has been addressed in the literature on market structure and innovation. Market structure characteristics can influence a firm's decision to enter a new market or adopt a new production technology. Thus, structural characteristics must be considered in formula­ ting commercialization policies.

The final element of the process is the technology's characteristics as they relate both to market demands and to the producing sector. The attri­ butes of a technology must meet the basic needs of the consuming sector to be commercially viable. In managing R&D activities, information on the market demands should guide the development of a new product's characteristics. In addition, attributes of the technology influence the structure of the pro­ ducing sector, and thus its conduct and performance. Such features as product

86 differentiation, economies of scale and economies of scope are important in determining market structure.

References

1. Maniscalco, J. A., Hovingh, J., and Buntzen, R. R. "A Development Scenario for Laser Fusion." Lawrence Livermore Laboratory. UCRL-76980. March 30, 1976.

2. Division of Laser Fusion. "Program Approval Document: Laser Fusion." Energy Research and Development Administration. December 20, 1976.

3. Booth, L. A. and Frank, T. G. "Commercial Applications of Inertial Con­ finement Fusion." Los Alamos Scientific Laboratory. LA-6838-MS. May 1977,

4. Varnado, S. G., Mitchiner, J, L., and Yonas, G. "Civilian Applications of Particle-Beam-Initiated Inertial Confinement Fusion Technology." Sandia Laboratories. SAND77-0516. May 1977.

5. Meinke, W. W. and Gomberg, H. J., "A Forecast of Civilian Applications of Inertial-Confinement Fusion." KMS Fusion, Inc., June 1, 1977.

6. Stickley, C. M. "Inertial Confinement Fusion Program." Statement Before the House Science and Technology Committee for the FY 1979 Authorization Hearings. February 7, 1978.

7. Stickley, C. M., "Laser Fusion." Physics Today . (May 1978) 50-58.

8. Maniscalco, J,, et. al. "Civilian Applications of Laser Fusion." Lawrence Livermore Laboratory. UCRL-52349. August 14, 1978,

9. Abernathy, W. J. and Utterback, J. M., "Patterns of Industrial Innovation." Technology Review. (June-July 1978),

10. Baer, W. S. et. al., "Analysis of Federally-Funded Demonstation Projects: Final Report." Rand Corp. R-1926-DOC. April, 1976.

11. M.I.T, Energy Laboratory Policy Study Group. "Government Support for the Commercialization of New Energy Technologies." Report No. MIT-EL 76-009, November 1976.

87 88 FOCUSING EXPERIMENTS WITH LIGHT ION DIODES*

D, J. Johnson Sandia Laboratories, Albuquerque, NM

Abstract

This paper presents a review of recent experimental and theoretical work at Sandia Laboratories on magnetically insulated single stage ion diodes for inertial confinement fusion experiments. The production, focusing and numeri­ cal simulation of a 0.5 TW annular proton beam using the Proto I dual transmission line generator is described. The modular magnetically insulated ion diode for the Hydra generator is also described along with recent experi­ mental results. A brief description of how an array of modular diodes similar to the Hydra magnetically Insulated diode could be used on the EBFA I genera­ tor for breakeven fusion experiments is presented.

Recently considerable progress has been made in the development of single stage diodes which produce intense pulsed light ion beams for inertial con­ finement fusion. * The pinched electron beam diode utilizes the self magnetic field from a pinched electron beam to retard electron flow and the magnetically insulated diode uses an applied magnetic field to reduce elec­ tron flow. Recent results ' obtained with magnetically insulated diodes driven by the Proto I and Hydra generators will be described here. The Proto I diode generates an annular proton beam which is suitable for inter­ mediate power target studies whereas the Hydra diode generates a circular beam which is suitable for channel transport studies. The Hydra is also being studied as a possible candidate as a modular front end for the EBFA I generator.

The Proto I diode, which is shown in Fig. 1, generates a peak proton current of 350 kA at a voltage of 1.2 MV with an electron loss of approxi­ mately 120 kA. The 15 cm radius of curvature spherical segment anode is pulsed positive via the center electrode of the disc triplate transmission line of the Proto I generator. The applied magnetic field reaches a peak value of 13.5 kG in 70 sec (approximately 2 mm skin depth of aluminum) and therefore is contoured into a spherical shape in the 8 mm wide anode-cathode gap. The diode utilizes a virtual cathode produced by electrons which are emitted from the cathode discs and spiral axially along magnetic field lines to establish a uniform equipotential surface near the anode. Anode plasma from a 414 cm surface area nylon mesh mounted upon the aluminum mode (thought

*This work was supported by the U.S. Department of Energy, under Contract AT(29-l)-789.

89 to be formed by surface flashover or leakage electrons) is the source of protons or higher Z ions which are accelerated. Since all magnetic field lines are contained between the anode surface (neglecting field soak in) and diode center line, the ions are emitted from the anode with zero canonical angular momentum and therefore can in principle be focused to the center-line. When drifting through the magnetic field, the ions are space charge neutral­ ized by electrons ^^hich are emitted from the walls of the drift region and transported along magnetic field lines or produced by ionization of the 10 -3 Torr background gas.

FIELD COILS

Fig. 1 Cross sectional view of the Proto I magnetically insulated ion diode.

A numerical simulation of the operation of this diode has been performed" using a particle-in-cell diode code which closely approximates the observed virtual cathode effect. At present difficulty has been encountered in properly simulating the space charge, neutralization process in the drift region between the virtual cathode and diode center-line. A simulation with ideal neutralization indicates laminar ion flow and self magnetic field pinching whereas an attempt to properly simulate the neutralization process indicates a divergent beam with only approximately 10% of the beam arriving near the center-line. This must be compared to 25% in the experiment indi­ cating somewhat better neutralization than the code predicted.

The total proton current was measured using the carbon activation technique^ whereby the decay of N"'"^ from the C"^ (p, )N^^ and C (d,n)N^ reactions are observed from the delayed positron emission from N , During data reduction an allowance was made for the yield due to the natural

90 abundance of deuterium on the basis of the simultaneous diode current and voltage. At the 5 cm radius one or two 34% transmission stainless steel flux screens were used to attenuate the ion beam and a peak ion current density of approximately 3.5 kA/cm was measured. At a radius of 13,5 cm, just behind the virtual cathode surface, the peak ion current density was observed to be approximately 1 kA/cm . These currents were in agreement with ion collector signals observed at equal radii. The ion collector signals were also in excellent agreement with calculated ion current densities allowing for ion time-of-flight. These diagnostics indicate a peak ion current of approxi­ mately 360 kA and 230 kA at the 13.5 and 5 cm radii, respectively.

Data obtained with thin conical targets, which allowed symmetric target irradiation and current return, indicate an on target current density of 25 kA/cm . The cones were fabricated from 4 m thick aluminum with 15° half angle, 1.24 cm length, and 0.9 cm center plane diameter. The current density was estimated from the absolute density of exposed film from a pinhole camera which observed the 1.49 keV aluminum K-line radiation produced by atomic exci­ tation due to the beam. This result was obtained using numerically calculated x-ray production efficiencies for the voltage and relative current throughout the pulse, the foil geometry used, and the sensitivity of the Kodak No Screen x-ray film used. A comparison value of 20 kA/cm was obtained using 1 cm diameter carbon activation target with three to five 34% transmission flux screens. This value is considered a lower limit because of the problems of carbon blow-off and improper attenuation of the ion beam while passing through the numerous screens.

o A numerical simulation of the conical target response to the 25 kA/cm beam was performed using the LASNEX computer code and the result was in good agreement with the experimental inner surface temperature of the foil measured with aluminum cathode photodiodes (XRD's). Initially the temperature rises to approximately 12 eV as the foil self-collides at the axis at a velocity of greater than 3 cm/ysec,

A modular magnetically insulated ion diode is shown in Fig. 2 as it would be configured in an 18 module array for the 36 pulse line EBFA I generator being constructed at Sandia Laboratories, As shown the diodes are configured for channel transport to the target which allows ion beam bunching and power multiplication. When so configured the combined beam on target is again annular and simply a high power version of the Proto I diode beam-

A single diode of this type has been tested on the Hydra accelerator and has produced an effective forward directed beam current of 150 kA at 900 kV. This diode is driven by two coaxial self-magnetic insulated transmission lines which feed current into the opposing ends of an ion emitting electrode within an elongated solenoidal applied magnetic field coil. To power this diode the single Hydra output was split into two such transmission lines via a vacuum convolute. Because the requirement for a continuous electron E x B drift necessitates ion flow off the rear surface of the anode this diode has only demonstrated a useful ion production efficiency of 30%, It may be possible to increase this efficiency by shaping the diode structure to bunch electrons in the forward anode-cathode gap or by generating a high-Z ion beam on the rear of the anode. Initial experiments with this diode have demonstrated a peak focused proton current density of 30 kA/cm^ with a 120 cm*^ circular beam with

91 dtscharge channel

Fig. 2 Artists conception of modular magnetically insulated ion diodes coupled to EBFA I pulse lines.

15 cm focal length. Experiments planned for this diode include injection of gas plumes into the beam as it undergoes ballistic focusing and holographic observation of the anode plasma.

Future efforts will be directed toward increasing the efficiency of modular diodes, and studies of the feasibility of joining many self-insulated vacuum transmission lines together to feed a high power version of the symmetric Proto I diode design.

References

1. Shyke A. Goldstein, G. Cooperstein, Roswell Lee, D. Mosher, and S. J. Stephanakis, Phys. Rev. Lett. ^, 1504 (1978),

2. S. Humphries, Jr., R. N. Sudan, and L. Wiley, J. Appl. Phys. 47, 2382 (1976). —

3. D. J, Johnson, G. W. Kuswa, A. V. Farnsworth, J. P. Quintenz, R. J. Leeper, E. J. T. Burns, and S. Humphries, Jr. (to be published).

4. D, J. Johnson, G. W. Kuswa, R. J. Leeper, and J. P. Quintez (to be published).

5. F, C. Young, J. Golden, and C. A, Kapetanakis, Re. Sci. Instrum, 48, 432 (1977). —

6. S. Humphries, Jr., D. Elchenberger, and R. N. Sudan, J, Appl. Phys. 48, 2738 (1977). —

7. B. G. Zimmerman, W, L. Kruer, Comments Plas. Phys. 2, 51 (1975).

92 HIGH CURRENT LINEAR ION ACCELERATORS FOR INERTIAL FUSION

S, Humphries Jr. Sandia laboratories

The Pulselac Program at Sandia laboratories was Initiated to study the feasibility of very high current, pulsed linear ion accelerators for Inertial fusion applications. The essential feattire of the research is the electrical neutralization of ion beams within the volume of an accelerator by electrons, with the electron dynamics controlled by magnetic fields. The physics and technology of the systems involves an intimate combination of accelerator theory and plasma physics. This paper simmarizes the experimental and theoretical program to date and the logic of the program with respect to the ultimate fusion application.

Major Program Concerns

The high current linear accelerator shares with conventional accelera­ tor concepts the important advantage among potential inertial fusion drivers that there is a clear path to a realistic reactor if certain clearly defined physical problems can be iresolved. Its chief advantage over conventional accelerators is economy. The Pulselac Program is attempting to address the major physical questions related to beam neutralization to construct a solid basis for engineering extrapolation. The Immediate goals are: 1) The development of intense pulsed injectors of intermediate mass ions (i.e., 1 - 5 kA of 0**") with repetition rate potential, 2) The theoretical description and study of electron neutralization of ion beams in vacuum, either in free space or in the presence of transverse magnetic fields. 3) The development of large area, pulsed electron sources with low energy investment and long lifetimes, L) The post-acceleration of intense ion beams by magnetically instilated gaps with high efficiency, 5) The transverse confinement of ions by magnetically insulated electrostatic lenses utilizing the priinary acceleration fields, 6) Investigation of the longitudinal stability of non-relativistic beams in pulseline driven linear accelerators. 7) Demonstration of the velocity compression of intense beams, 8) Focusing of high current beams on axis by magnetic and electrostatic lenses and the transport of beams through plasmas.

The present experiment is a five stage device capable of driving currents in the range of 10 kA at 300 kV per stage. (To date, two stages

93 have been used simultaneously,) Current levels can approximate those of the reactor regime. It should be noted that the Pulselac experiment, although relatively small, represents the most difficult period of the ion beam acceleration history, the injection and low ^ region where space charge problems are most severe. Since the high current linear accelerator concept for inertial fusion involves a modular extension of the basic unit, useful physics and engineering data can be obtained from a steadily evolving series of experiments.

Origins of the Field

The basis for the beam neutralization procedures being investigated has come from the technology of intense ion beam Injectors, a field roughly five years old. In this area, involving currents approaching 0.5 MA^-, neutralization is essential for propagation more than a centimeter. It is necessary to consider the behavior of electrons in the presence of magnetic fields and fast rising ion charge densities on an equal plane of importance with the dynamics of the ions themselves. Most of the unique properties of intense ion beams proceed from the intimate presence of a second charge species. Phenomena from the intense ion diode field that are useful in the development of high current linear accelerators are magnetic insulation at high voltages^, enhancement of ion flow above the Child-Iangmulr limit In vacuum gaps3»^»5^ the formation of virtual electrodes"*'7, and neutralization of ion beams in vacuum by electrons produced on surroiinding physical bo\mdaries^>9. The technology of pulsed linear Ion accelerators must also borrow from other areas of plasma physics, such as surface spark plasma sources and high intensity plasma guns for the injector stage. For fusion applications, plasma behavior will be particularly important in determining the beam transport properties If a high vacuum cannot be maintained in the reactor chamber.

The multistage acceleration of intense ion beams is a more involved process than simply stacking a number of high current capacity diodes in series. With more than one stage, the assembly rapidly becomes an interacting system where the history of the beam in previous gaps determines the current characteristics at any point. Concepts and theory from conventional linear accelerator practice must be modified to understand transverse beam confinement and the preservation of emittance, the longitudinal stability of beams, and systems for temporal beam compression under high current conditions'*^. Departures of focusing elements from linearity are of major theoretical importance. The area of existing accelerator technology that is particularly relevant to high current ion beams is that of inductively driven linear accelerators^*-*-^. The current levels that can be transported with beam neutralization provide almost an ideal match with inductive accelerator capabilities. In our program, we have not concentrated on pulsed power considerations since the studies and publications of the LBL Group are directly applicable in this area.

Reactor Parameter Range

With freedcm from current transport limltations'3^ there is no intrinsic reason to choose high energy, heavy ions as the accelerated species. One of the major cost advantages of the neutralized regime is the theoretical

94 ability to meet reactor requirements with beam energies 10"' to 10"^ that of the conventional accelerator approach. A summary of the discussions of Ref. H is given here. If target standoff is the major requirement, then the beam must have a small enough final divergence angle, A6f, to be focused on the target from the distance of the final lens, L. If the target has a radius rt, then ^Qf ^ rt/L- If the transverse phase area of the beam is preserved, then the divergence Is decreased by post-acceleration according to ( tBf^l A&Q) - (Et)o/Ebf)2> where AQQ ^^d Ebo are the divergence angle and energy at Injection, and E^j^ is the final energy. The final energy is determined by the characteristics of target and injector and the standoff requirements. For rf^O.S cm, L*^ 5 m, Ebo'^ 0,5 MeV and £^©0*^ 1°, the final energy is in the range 2CX)-800 MeV. The choice of ion species is determined by the desired energy deposition range for the target in question. Oxygen would be a typical choice. The total beam current is P^bf» where P is the required power. For P = lO'^ W and E^f = 500 MeV, It = 200 kA, If this were supplied at the final lens at a conservative current density of 50 A/cm2, the beam entrance ports would occupy only a fraction 0,002 of the reactor wall. There are of course a number of possible choices for arriving at the final current. One attractive path would be to supply the bulk of the beam energy in two iron core inductive units with microsecond pulselengths. In the final stage, each beam would be split into five parts for a strong velocity compression to 20 nsec using ferrite cores. Each main unit would handle 2 kA of beam current, while the compression units would drive 20 kA at the output. At these parameters, the self magnetic fields of the beam produce a negligible perturbation within the accelerator.

In comparing reactor parameters to present experience, the intense linear ion accelerator has penetrated as far into the "modest extrapolation of existing technology" regime as conventional accelerators. From the point of view of pulsed power technology, the requirements are well within the sophistication of machines at I£L and planned at LLL. The current transport levels in the main accelerator are two orders of magnitude less than those typically available from proton diodes, so significant transport experiments can be carried out immediately. Even the proton currents in the Initial P\ilselac experiment are high (5 kA at the first gap). A recent breakthrough at Sandia Laboratories has removed one of the pending areas of extrapolation, that of ion mass from the injector. A linear beam of C+ at greater than 2 kA was extracted at 100 keV in a 0,5 >usec pulse. An equally important aspect of the experiment was the fact that the carbon ions were produced by plasma guns decoupled from the injector gap, a promising development from the point of view of injector lifetime.

Advantages of High C\irrent Linear Ion Accelerators as Fusion Drivers

The electron neutralization of ion beams during acceleration and transport is a relatively new field, and its development will not be without difficulties. In any area where an order of magnitude or more extrapolation is necessary, there is always the possibility of unanticipated fatal flaws. Nonetheless, it Is informative to consider the advantages of the approach if the devices continue to obey theory as well as experiments to the present have. In listing the advantages, it should be noted that

95 other fusion driver approaches may share th© listed benefits with respect to a third (i.e., the efficiency of light ion diodes).

A. In comparison to lasers 1. Ions have classical interactions with targets and a favorable energy deposition profile, 2. Direct acceleration devices can have high efficiencies (10-30 %), 3. Capacitively stored energy is relatively inexpensive and can be converted directly to beam kinetic energy. This should be compared to the sequences of (capacitors)/(flashlamps)/(population inversion)/ (beam energy) for glass lasers and (capacitors)/(discharge electrons)/ (molecular excltatlon)/(population inversion)/(beam energy) for gas lasers, 4-. Hiyslcal elements in the beam path are not needed for transport and isolation. 5. High repetition rate can be obtained without major engineering breakthroughs. (Consider, for example, the thermal recycling problem of glass lasers). 6. There is no physical final focusing lens or transport mirrors to be exposed in the reactor chamber, B. In comparison to single stage electron and light ion diodes

1. Post-acceleration reduces beam divergence to achieve standoff with simple geometric focusing. 2. The conversion of electrical energy to particle kinetic energy is expanded in space and time. This implies that only a small fraction of the total energy must be added per stage, reducing the power flow and energy flux requirements to that accessible to high repetition rate technology, 3. There are no physical electrodes or replacable components that need be located in the beam path. 4.. The final power level is approached by the linear addition of stages, so that a demonstration device can be built up in parts rather than as one large unit. 5. The beam entrance ports would occupy only a small portion of the reactor wall area. 6. The greater control of longitudinal velocity inherent in a multistage device would allow power multiplication by strong beam compression.

C. In comparison to conventional accelerators 1. The high current linear accelerator resides in the middle of Ion species parameter space rather than at an extremum, so that it would be possible in breakeven experiments to study various targets by changing ions (and hence the energy deposition range). 2. It should be possible to run well below the theoretical limiting currents for neutralized beam transport, rather than at the transport limits, 3. The single pass linear accelerator is relatively insensitive to vacuum quality. 4. The high current accelerator would be a simple, straight-through, one-component device that could be funded and built tectonically.

96 This would allow the evolution of a strong engineering data base before proceeding to major expenditures. 5. The neutralized linear accelerator shotild have a lower cost per length than a conventional machine through the use of inexpensive energy storage (capacitors compared to precision RF cavities) and electrosta­ tic focusing elements. Magnetic focusing of heavier ion species is relatively inefficient. 6, The total cost of accelerator development and construction should be lower because of the greatly reduced final beam energy requirements.

At the same time, there are two potential disadvantages with respect to heavy ion beams that should be listed.

1, Although the propagation of a neutralized ion beam in the form of a plasmold through vacuum appears to present no major difficultles'5, the higher current, lower mass, and lower energy of the beam compared to heavy ion beams means that It will be more sensitive to perturbations in the presence of a plasma, 2, The longitudinal stability of a non-relativistic beam driven by loaded PFN's needs study with respect to possible velocity bunching instabilities. J-°

Physics of the Standard Pulselac Configuration

The Pulselac acceleration gap (used in present experiments) is shown in Figure 1, A radial magnetic field is produced by foiir colls located around the annular propagation region. The magnetic fields provide insulation against electron flow in the longitudinal potential. This allows concentration of the field gradient (limited by external insulators) in a small fraction of the accelerator length. This is important since the beam is unneutralized in the acceleration gap and there is a limit to the accuracy with which space charge fields can be balanced by applied fields. The magnetic field performs two other functions. It provides a barrier against electron leakage from the drift tubes so there is no electron energy dissipation and the proper negative distributions can be set up in the tubes to provide effective neutralization. Also, the flow of electrons along boundary field lines can determine equipotential surfaces that act exactly as physical electrodes. By curving the magnetic field lines as shown, the electrostatic accelerating field can be used to provide strong focusing forces to maintain the annular beam. It can be shown (through the conservation of canonical angular momentum) that the magnetic field provides no net azimuthal ion deflection. Inside the drift tubes, sources on the boundaries provide free electrons that can rush in along field lines with the arrival of the ion beam. If the electron velocity distribution can be randomized (viiich occurs naturally in real systems), then the light electron mass allows almost complete cancellation of space charge forces on nanosecond time scales.

More detailed discussions on these subjects are given in References 9 and 10.

97 Figure 1, Magnetic field geometry in the Pulselac acceleration gap.

98 Recent Program Developments

A number of developnents have taken place at Sandia Laboratories related to the basic physical pict\ire sketched above. The followi.ng list summarizes theoretical and experimental progress,

A. A computer simulation code developed by J. Poukey'^ has been used to investigate the electron neutralization process in the presence of transverse magnetic fields. For the geometry considered, less than 1% residual space charge effects were present within 1 nsec of the beam arrival, even for ion beam density risetimes of 0,5 nsec, B. The neutralization of ion beams in free space has been considered'^ , The role of the electron distribution in limiting the ion focus has been investigated, and the requirements for a good focus are found to be modest. C. A computer code is being developed to study the longitudinal stability on ion beams driven by PFN's'O , A high power voltage clamping device has been described , and will soon be investigated experimentally, D- A theoretical paper describes a new accelerator geometry utilizing coils external to the beam only'' . This geometry should be capable of trans­ porting many kiloamperes wile maintaining a transverse beam temperature adequate for focusing in reactor applications. Also, initial steps have been taken to tmderstand transverse beam behavior in the presence of non-linear focusing forces. Methods are being developed to derive self- consistent beam distributions that will propagste without change of properties- E, Excellent magnetic insulation has been demonstrated for acceleration gaps with radial magnetic fields , The perveance reduction in the absence of ion flow is the best obtained to date on any system. F, Large area pulsed electron sources have been developed in cooperation with J. Ramirez. These sources, in the form of sheets that can be adapted to any conducting surface, operate by the production of hundreds of ballasted surface sparks. They produce microsecond bursts of localized plasmas capable of supplying ^^ 1 kk/crtr- of electrons with the investment of a few joules per m^. Even in the initial configurations, lifetimes are good. G, A proton gun has been operated with a geometry identical to Figure 1 except for the inclusion of a flashboard proton source'^ • The gun produces an average of 15 kA of protons over a microsecond pulse at voltages around 100 kV and current densities exceeding 100 A/cm^. Beam divergence is 3°. An instantaneous current of over 5 kA can be supplied to the first acceleration gap with somewhat over 1° divergence. The gun was fired over 100 shots with no maintenance and high reproducibility. The lifetime should increase significantly with better postpulse protection and choice of electrode materials, H. An acceleration gap has been operated using the proton beam from the injector described above. The 5 kA beam was postaccelerated electrostati­ cally an additional 200 keV. As expected, the proton current in the gap was unaffected by the application of the voltage. Electron leakage

99 currents could be measured directly and were shown to be small, I. The post-acceleration gap has been used as an electrostatic lens to produce an annular line focus of the proton beam. The effective focal length of the gap could be changed by moving the gap boundary trimmers to regions of differing magnetic field line curvature. The focal properties were in qualitative agreement with predictions based on the existence of virtual electrodes,

J. A pulsed carbon plasma gun array (developed by C. Mendel) was used to inject carbon ions directly into an acceleration gap. Up to 2 kA of C+ was extracted at voltages up to 300 kV with current densities exceeding 20 A/cm2, Uniformity, reproducibility and efficiency were very good.

In the future, the major goal of experiments will be to bring additional accelerator stages on lines. The next two peripheral experiments planned are; A, Tests of vacuum, magnetically insulated gaps as voltage clamping devices, and B, Detailed Investigations of the propagation of ion beams in vacuimi with active electron supplies.

References

1. See, for instance, D,J. Johnson, these proceedings, 2. T.J, Orzechowski and G, Bekefi, Phys. Fluids 12, U3 (1976). 3. S.A. Goldstein and R, Lee, Fhys. Rev. Lett, 3^, 1079 (1975). U. J.W, Poukey. Appl. Phys. Lett. 26, U5 (1975)7 5, R.E. Kribel, S,C, Luckhardt and H,H. Fleischmann, Bull. Am, Phys, Soc, 22, 1130 (1977), 6, S. Humphries, R.N, Sudan and L, Wiley, J. Appl, Phys. ^7, 2382 (1976). 7, S. Humphries, Proc. of Lth. Conference on Applications of Small Accelerators. Denton. Texas. 1976 (IEEE, New York, 1976), 203. 3, S. Humphries, C. Elchenberger, and R,N, Sudan, J, Appl. Fhys, ^, 2738 (1977). 9, S. Humphries, J. Appl. Fhys, ^(2), 501 (1978). 10, S. Humphries, Proc, of 2nd International Topical Conference on High Power Electron and Ion Beams. Ithaca. 1977 (Laboratory of Plasma Studies, Cornell University, Ithaca, New York, 1977), 83. 11, See D, Keefe and A, Faltens, these proceedings, 12, A, Faltens, E. Hartwlg, D. Keefe, and W. Salsig, IEEE Trans. Nucl. Sci, KS-20. 1010 (1973). 13, A,W. Maschke, cited in Final Report of the ERDA Summer Study of Heavy Ions for Inertial Fusion (Lawrence Berkeley laboratory, LBL-554-3,1976). H. S. Htamphries Jr., J.W. Poukey and G. Yonas, Proc. of 3rd International Topical Conference on Collective Methods of Acceleration. laguna Beach, 197?^ 15. S. Humphries Jr., Appl. Phys, Lett. i2('^)* 792 (1978), 16. J.W, Poukey and S. Humphries Jr,, Appl. Phys. Lett. ^(2), 122 (1978). 17. S, Humphries Jr,, submitted to Particle Accelerators. 18. S. Humphries and G. Kuswa, submitted to Appl, Phys, Lett,

100 DIAGNOSTICS FOR PELLET EXPERIMENTS

R.R. Johnson KMS Fusion, Inc.

Introduction

The target diagnostics which are being used and planned in current laser driven ICF Experiments will be described. ' Most of these diagnostics can be easily applied to future ion-beam fusion experiments. The status of laser fusion diagnostics has been much improved in the last 5 years and further im­ provements can be expected and should be available when the first ICF experi­ ments using ion beams are performed. As an example, x-ray temporal and spa­ tial resolution are now approximately 5 psec and 3 ym; which is approximately a factor of 4 better than the resolution reported in the first implosion ex­ periments.-^ As one plans ahead for ion-beam fusion experiments it should be emphasized that "high yield" experiments are easier to diagnose provided ade­ quate shielding is employed. However, in the event that the first "high yield" experiments fail it will be necessary to have diagnostics available to determine where the problems lie. In laser fusion it is interesting to note that higher laser powers are required now for breakeven experiments than first anticipated, mainly because some aspects of the laser-interaction phys­ ics were not recognized until the experiments were carefully diagnosed. Thus as has been pointed out, it may be necessary to increase the energy of the ion-beam driver to enable us to do breakeven experiments with high confidence.

Transport of Thermal Energy

The transport of the absorbed energy to the fuel in laser fusion has aroused considerable interest in recent years as a result of experiments in which it was apparent that the thermal energy was not being transported as predicted by classical thermal conduction. As reported by most of the labo­ ratories, thermal energy flux is less by a factor of approximately 40 than the classically predicted flux. An "inhibited" heat flux has a deleterious ef­ fect on implosion efficiency. Tt forces the absorbed energy to be shared by fewer particles and thus causes an increase in the temperature of the corona. As a result, fast electrons and ions are generated which leave the target without doing work on the fuel. There are indications that fast electrons also travel inward and preheat the fuel. This effect causes the compression to follow a higher adiabat and thereby degrade the implosion. Another aspect of energy-transport inhibition which must be considered is its effect on ab­ sorption. Should this inhibition occur also in ion-beam fusion then it would be necessary to evaluate its effect on ion-energy deposition.

Although thermal-flux inhibition has been measured, the mechanism by

101 which it occurs has not been established. It has been suggested that induced magnetic fields may be responsible. Recent measurements at NRL on laser- irradiated spherical targets have shown that magnetic fields of the order of 1 megagauss are generated near the surface of the target. Another suggested mechanism is ion turbulence.

C £L ~7 Q Experiments at LLE, NRL, SANDIA, and LASL have shown that for planar targets coated with a thin layer of different material, the time for laser energy to bum through the coating is much longer than expected from classi­ cal conductivity. These measurements were made by observing the x-ray spec­ tra of the coating as well as the spectra of the base material. The thickness of the coating was varied in some of these experiments and it was observed that the x-ray spectrum was generated primarily from a much thinner portion of the coating than expected from classical considerations. Similar experi­ ments can also be performed with ion-beams, where one must take into consider­ ation the ion range.

In experiments at KMS Fusion with coated spherical targets the fast-ion component of the corona has been measured. The KMSF experiments have taken advantage of the unique properties of cellulose-nitrate-film detectors and the Thomson-parabola ion analyzer to study fast ions. Commerically avail­ able cellulose-nitrate film (Kodak LR 115 Type II) records the passage of the individual heavy ions of energy 10 keV/nucleon or greater. The insensitivity of this film to ions below this threshold and to electrons, x-rays, and visi­ ble light, makes it an especially convenient tool for discriminating fast ions in a plasma environment. The single-ion sensitivity of the film allows the use of a small entrance aperture in the analyzer, which in turn permits very good resolution.

The depth of the region in which fast ions are generated has been esti­ mated in experiments using spherical targets of solid boric anhydride (B2O0) coated with very thin layers of silica (Si02). The ^2^3 beads were about 70 pm in diameter with very smooth, glassy surfaces. Silica overcoats of 30, 50, and 100 nm were sputter-deposited onto the beads. Scanning-electron- microscope examination of the thicker coatings showed smooth, uniform layers. The 30-nm coating was thinner than the resolution of the SEM, however, and one cannot be certain that the surface was uniform. Four targets, one un- coated and one for each of the three coating thicknesses, were irradiated with laser pulses that delivered 30 to 36 joules in approximately 80 psec. Among these four targets the total number of fast ions observed varied by no more than 20%.

Because fully stripped boron ions have a unique charge-to-mass ratio (5/11) they can be readily identified in the Thomson-parabola analyzer. For the various coating thicknesses, the ratios of fully stripped boron to non- boron fast ions provide an estimate of the depth profile of the fast ions. A portion of each velocity spectrum is shown in Figure 1. The data from ions with a charge-to-mass ratio of 1:2 (0°"^ and C ) were obtained with the 100- nm-coated target and are typical of all four targets. The measured ratios of nonboron to boron ions are 2.9, 7.5, 21, and 25 for layer thicknesses of 0, 30, 50, and 100 nm. These are average ratios over the portion of the spec­ trum for which boron ions are observed. The 30-nm coating is sufficient to reduce the number of detected borons by a factor of two, A comparable reduc­ tion is observed with the 50-nm coating, but very little change occurs in

102 going from 50 to 100 nm.

M

10-

*«rt,

102 I I

Velocity (10° cm/sec)

Figure 1. Fast-ion spectra from Si02-coated B2O3 targets. Solid circles are the 0°'*"-plus-C spectrum from a target with a lOO-nm coating. The other spectra are for boron 5 ions observed with various coating thicknesses. Open squares — uncoated; open triangles — 30-nm coating; solid triangles — 50-nm coating; open circles — 100-nm coating.

The rapid decrease in boron yield in going from 0 to 50-nm layer thick­ ness and the leveling off of the boron yield in going from 50 to 100 nm strongly support the conclusion that the fast ions are generated within an outer layer no more than 50 nm thick. With better characterized thin coat­ ings, it should be possible to define the fast-ion emission region more pre­ cisely,

Hydrodynamic Coupling of Absorbed Energy to the Fuel

After a portion of the absorbed energy is transported into the pusher, there is an acceleration phase in which the pusher velocity increases asymp­ totically. After the limit is approached the fuel is compressed and raised to a high temperature and nuclear reactions take place. LLL has developed a sim­ ple model calculation which illustrates well the important features of the implosion physics. These calculations are applicable to a certain class of ion-beam fusion experiments, since they were used for strongly preheated tar­ gets in which the pusher was isothermal, with half of the pusher mass moving outward and the rest pushing against the fuel. The asymptotic kinetic energy

103 of the pusher is given by,

n /P,dt (1) 2 p p /' where Mp = 27rroWp is 1/2 the pusher mass, PQ is the absorbed driver power, n the fraction of^the absorbed energy performing the useful work on the fuel and t(, is the time required for the useful energy to be absorbed.

The time t is determined from the following relationship c

-1/3 V (t)dt = 0.44r^(l - C ) - 2w (2) /' p 0 where C is the measured compression, and w is the wall thickness. The value of tc (for a square driver pulse) is then determined to be

1/2 87Tr^wp .3/2 _ 0.66r (1-C ^^^) - 3w (3) 0 The useful absorbed energy provides heating of the fuel ions at stagna­ tion and the expression for ion temperature is given by 1.11 P t 0 c T = (4) r^wp (1+10-3 ^^) Op w ' where PQ 's the initial fuel density. The neutron yield is calculated from the peak ion temperature and the bum time, using the nuclear reaction rates for deuterium-tritium. The bum time At is proportional to the ion sound speed in the compressed fuel and is given by

,-1/2 At = 1.12 r T (5) 0 where At is in psec, r in ym, and T in keV, The neutron yield is given by

N = 2.9 X 10-28 „2 r^ c^l^ x^/2 (6) 1 0 where the nuclear-reaction-rate curve is fitted by a power law in T, for the range from 1 to 10 keV, and n^ is the initial fuel density. With this equa­ tion, is possible to make useful predictions of the neutron yield as a func­ tion of known target parameters and the incident laser power. For the spe­ cial caser where w is small, one finds that

104 14/6 N^w^/^f^ ^-11/6 -7/2 0 0 (7)

Experimental data on neutron yield and fuel-ion temperature have been obtained at KMSF, LLL, and LASL. The results of these experiments are shown in Figure 2 together with the model-derived neutron yield. As can be seen, the experimental data follow the curve closely. It should be mentioned that (as can be seen from Equation 6) the neutron yield is not sensitive to the value of the compression, and therefore large variations in compression values could still give good agreement. 4/3 10/3 2/3

10 10

10" :^^- 10 •i^ N(exp)

10 • 0 0 6 10 •^^^O HYPERION 1 -^^^—Q HYPERION 1. 10 '"^'^i Large diometer long pulse / A HYPERION II ,0* / T HYPERION 1, LASL A^ • HYPERION 1, KMS

10 • _—1 1—i 1 J., i . • 1 0.4 06 0.810 2 34 6 8 10 MODEL DERIVED FUEL AVERAGED ION TEMPERATURE. keV

Figure 2. Neutron yield as a function of the model derived fuel averaged DT ion temperation. The neutron yield is normalized with 4/3 10/3 2/3 as suggested by the model equations, assuming the com- o u w pression C is proportional to v/p r ,

High Density Implosion Experiments

The most important experimental observations in laser fusion studies are those relating to the target implosion and fusion reaction processes. The fol­ lowing experiments were performed with an ellipsoidal mirror illumination system which produces nearly uniform illumination at near-normal incidencel2 of DT- filled glass microshell targets. Measurements of neutron yield, alpha par­ ticle energy spectra, and x-ray pinhole camera images together with numerical simulations are used to form a picture of the laser-driven implosion pro­ cess.-'-^

The energy spectrum of alpha particles from the DT fusion reaction pro­ vides an upper limit to the fuel ion temperature at peak compression,-*-^ The alpha particle energy loss can provide a measure of Jpdr as it traverses the compressed fuel and shell material. The magnetic spectrograph used to mea­ sure the alpha particle spectra is described in Reference (8).

105 The time integrated x-ray emission from the target is imaged using two pinhole cameras.-'"^'-'-^ Each camera has an array of four 5-ym pinholes, each of which is filtered with beryllium foils of various thicknesses. The inner region of intense x-ray emission occurs when the imploding tamper material is stopped by the back pressure of the compressed DT gas. If the compressed core is larger than the resolution of the pinhole camera, the inner feature will appear as a ring from which the volume compression can be estimated. In some instances, the inner feature of the image appears as a peak in the mi- crodensitometer trace rather than a ring. Computer simulations described in Reference (16) show that this could result if the compressed core radius is less than the camera resolution.

The peak compressions and densities (on the order of 500-fold reduction in volume and 1 g/cm^) reported by the various laboratories for gas-filled targets at room temperature were achieved using po = 2 mg/cm^ of fuel (10 atm). Much higher densities have been achieved with cryogenic targets. At KMSF, targets have been imploded in which the fuel gas, initially at 20 mg/ cm^, was condensed in a liquid layer on the inner surface of the shell at the time of irradiation. Peak densities as high as 7 g/cm^ were observed.

In the KMSF experiments the target pellets were supported from below on a conducting fiber that transferred heat from the pellet to a cryostat. The targets giving the highest neutron yields had a nominal diameter of 60 ym and a wall thickness of 0.7 ym. If the liquid layer were spread uniformly on the inside of a target of this size, the thickness of the layer would be 0.94 ym, taking the liquid density at the triple point (equal proportions of deuterium and tritium) to be 220 mg/cm^. Unfortunately, in these liquid-layer-target experiments, the fuel was not spread uniformly on the inside of the shell. There was, characteristically, a substantially greater thickness (y 2:1) in the region of the shell opposite the cold-tip support (at the top of the tar­ get in these experiments).

The x-ray pinhole camera photographs for all of the liquid-layer targets show the compression region to be displaced well away from the target center toward the top of the target where the liquid layer was thickest. This dis­ placement occurred only for liquid-layer targets. Identical targets cooled to 40 K (which is above the condensation temperature) did not have off-center compression regions.

The highest density estimated from measurement of the pinhole camera images was 7 g/cm^. The target in this case was 55 ym in diameter with a 0.7-ym wall. The laser pulse delivered 64,9 J in 177 psec and the neutron yield was 2,3 x 10''. Lacking an alpha-particle spectrum for this shot, the peak fuel-ion temperature was estimated from the yield to be 1.5 keV.

There was one liquid-layer target shot for which both a definable com­ pression (as seen in the pinhole camera image) and an alpha-particle energy spectrum were obtained. The target was 55 ym in diameter with a 0,7-ym wall and 81-atm DT fill pressure (at room temperature), The laser pulse delivered 58 J on target in 200 psec. The neutron yield was 4.3 x 10*^. The compres­ sion ratio was approximately 100 and the compressed-fuel density was 1.6 + 0.8 g/cm^. Using these values in the model calculation, the inferred fuel^ion temperature was 1,6 + 0,1 keV, The width of the alpha-particle spectrum for this experiment gives a fuel-ion temperature of 2.2 +0.5 keV, The discrepancy

106 between the two determinations of the fuel-ion temperature could result if the fuel density and temperature profiles were different from those of the model calculation, or if the actual fuel density were substantially less than the pinhole-image measurement. More comparisons will be required to resolve the differences.

The high densities estimated from pinhole photographs of imploding cryo­ genic targets are consistent with measurements of the energy loss of the alpha particles. If the alpha particles lost no energy, their energy spectra would be centered at 3.52 MeV. This evidence of increased fuel densities in cryogenic targets comes from alpha particle energy spectra which are down­ shifted from 3.52 MeV by as much as 300 keV for liquid layers but not more than 100 keV for gas-filled targets. This effect is shown in Figure 3,

100

6 40

Figure 3A. Alpha particle energy spectrum for cryogenic liquid-layered tar­ get shot 3046, The fitted gaussian (solid line) has mean energy of 3.33 + 0.07 MeV and FWHM of 265 + 20 keV, corresponding to a fuel ion temperature of 2.2 + 0.4 keV.

Figure 3B. Alpha particle energy spectra for gaseous target shot 2833, The fitted gaussian (solid curve) has an FWHM of 250 + 20 keV, corresponding to a fuel ion temperature of 2.0 + 0,3 keV, The mean energy is 3.49 + 0,07 MeV,

The gaseous target was 52 ym in diameter, with a 0.7-ym wall and lO-atm- fill pressure. The laser energy was 31 J in 90 psec, and 1.9 x 10^ neutrons were produced. The cryogenic target was 68 ym in diameter, with a 0.7-ym wall and 81-atm fill pressure. The laser energy was 86 J in 138 psec, and 3.1 x 10"^ neutrons were produced. The alpha-particle energy spectrum shows a measured downshift of 5% + 2%, Computer code simulations of the implosion of liquid-layer targets indicate that the alpha particles should lose energy not only in the compressed fuel but also in the surrounding glass, so that

107 the /pdr for the fuel cannot be obtained directly from the energy-loss mea­ surement. The same calculations show that a 5% energy loss is consistent with compressed-fuel densities of a few g/cra .

The energy loss rate can be calculated for both glass and DT-fuel as a funciton of the fpdr of the material. The loss rate also depends on the electron temperature and density of the medium as shown in Figure 4, Assum­ ing an electron temperature of 1 keV which is consistent with the measurement of the compressed core electron temperature using the pinhole photographs taken through various thicknesses of beryllium foil, the Jpdr for the glass would be 6 X lO"'* g/m^. The value of Jpdr would be 9 x 10"^ g/cm^ in the fuel assuming an average alpha-particle path length of -r^.

» yem^i

Figure 4. Alpha particle energy loss for D-T fuel and glass (Si02) as a function of fpdr. E is the initial alpha particle energy (3.52 MeV),

Additional experiments were performed using solid-DT-layer targets. The neutron yields were comparable to those of the liquid-layered targets at e- quivalent laser power on target. The implosion symmetry was improved; peak fuel densities of 7 g/cm^ were determined by x-ray pinhole photographs. The highest density was achieved on target shot 3723. The cryogenic target was 88 ym in diameter, with a 0,8 ym wall and 92-atm-fill pressure. The laser energy was 60 J In 132 psec and 1.5 x 10^ neutrons were produced. The alpha particle spectrum showed a measured downshift of 9%. For this experi­ ment, the value of Jpdr.at 1 keV electron temperature corresponds to 1.0 x 10 ^ g/cm^ in the glass and 1.9 x 10 ^ g/cm^ in the fuel. The measured vol­ ume reduction of 380 obtained from the pinhole photograph results in a ipdr in the fuel of 4,3 x 10"^ g/cm^. An electron temperature of 2 keV would

108 bring these two values into agreement.

Conclusion

The diagnostics that have been emphasized in this discussion are con­ cerned with the high density core. In particular, these diagnostics have pro­ vided measurements of the density and ion temperature in the core and of the electron temperature in the tamper an independent determination of the pR in the tamper and fuel should soon be possible. The observations are critically needed to determine how the laser energy couples with the fuel. In principle, the diagnostics developed to investigate laser-generated plasmas are quite adaptable to experiments in ion-beam fusion.

Reference

1. R.L, Berger, P.M. Campbell, G, Charatis, J.G. Downward, T.M. Henderson, R.R. Johnson, T.A. Leonard, F.J. Mayer, D. Mitrovich, N.K. Moncur, G.R. Montry, D.L. Musinski, R.L. Nolen, L.V. Powers, S.B. Segall, L.D. Sie- bert, R.J. Simms, D.C. Slater, D.E, Solomon, and CE, Thomas, Plasma Physics and Controlled Nuclear Fusion Research (Proc. Int. Conf., Inns­ bruck, 1978), IAEA, Vienna,

2. L.W, Coleman, UCRL - 81088 (1978).

3. D.T. Atwood, UCRL - 81156 (1978), (Submitted to IEEE J. Quantum Electron)

4. H.G, Ahlstrom, D,L. Banner, M.J. Boyle, E.M, Campbell, L.W. Coleman, L.N, Koppel, H.N. Komblum, Jr., F. Rienecker, Jr,, J.R. Severyn, and V,W. Slivinsky, UCRL - 80230 (1978).

5. B. Yaakobi and T. Bristow, Phys. Rev. Lett. 38 350 (1977).

6. F. Young, R. Whitlock R, Decoste, B. Ripin, D, Nagel, J. Stamper, J. McMahon, and S. Bodner, Appl. Phys. Lett. 30 45 (1977).

7. J. Pearlman and J, Anthes, Appl. Phys. Lett. 27 581 (1975).

8. A.W. Ehler, D.V. Giovanielli, R.P. Godwin, G.H. McCall, R.L, Morse, and S.D. Rockwood, Los Alamos Scientific Laboratory Report La-5611-MS (1974).

9. D.C. Slater and F.J. Mayer, Laser Interaction and Related Plasma Phen­ omena , Vol. 4B, H.J. Schwarz and H. Hora, eds. (Plenum, NY, 1977) p. 603.

10. E.K. Storm, J.T. Larsen, J.H. Nuckolls, H.G. Ahlstrom, and K.R. Manes UCRL - 79788 (1977).

11. CE. Thomas, Appl. Opt. j3 1267 (1975).

12. K.A. Brueckner, J.E. Howard, Appl. Opt. 14 1274 (1975).

13. P.M. Campbell, P. Hammerling, R.R. Johnson, J.J. Kubis, F.J. Mayer, and D.C. Slater, Plasma Physics and Controlled Nuclear Fusion Research, (Proc, Int. Conf., Berchtesgaden, 1976) IAEA, Vienna (1977) Vol. 1, p. 227,

109 14. V.W, Slivinsky, H,G. Ahlstrom, K.G. Tirsell, J, Larsen, S, Glares, C Zimmerman, and H. Shay, Phys. Rev, Lett. 3^ 1083 (1975); R.R. Goforth, F.J. Mayer, H. Brysk, and R.A, Cover, J. Appl. Phys. ^2850 (1976).

15. G. Charatis, J, Downward, R. Goforth, B, Guscott, T. Henderson, S. Hil- dum, R, Johnson, K. Moncur, T. Leonard, F. Mayer, S, Segall, L. Siebert, D. Solomon, and C Thomas, Plasma Physics and Controlled Nuclear Fusion Research, (Proc. Int. Conf,, Tokyo, 1974) IAEA, Vienna (1975) Vol. II, p. 314.

16. P.M. Campbell, G. Charatis, and G.R. Montry, Phys. Rev. Lett. 34_ 74 (1975).

110 SCALING LAWS FOR INERTIAL CONFINEMENT FUSION

Keith A, Brueckner University of California, San Diego

Thermonuclear burning under optimized conditions results from the central ignition of highly compressed fuel leading to the for­ mation of a spherically expanding burning front which ignites the

surrounding cold and stationary fuel. The burning front is ini­

tially driven by alpha particle deposition but can accelerate for high yields as neutron heating becomes important. Under these con­

ditions the fusion yield can be estimated from a simple analytic model,^ ^ with the result

, \1 4 Y- . = 1.20 E (kilojoules) ' megajoules , (1 fusion \ o^ •' -^ I

= Y^ . = 1200 (E (kilojoules))^*"* , (2 fusion fusion \ o -^ ' ' E o with E the input energy delivered to the compressed fuel.

The pellet gain is lower than the fusion gain defined in Eq.

(2) because of losses from the incident beam by reflection, by inefficient transfer of energy from the deposition region to the ablation front, and by the loss of energy into ablation products.

We define a factor A , to include the effects of inefficiency plasma of transfer from the ablation front into the implosion of the fuel.

The factor A^ , can also include the effect of departures from hydro

111 the ideal implosion history for which Eqs. (1) and (2) are valid.

Including these factors, E^^^.^^^^ = E^^ \i\y- ^^^ efficiency for electrical conversion of the fusion output we denote by A and the efficiency of conversion of electrical energy to conv "^ beam energy by A, . The overall system gain we define to be

output electrical power (3 system electrical power input to beam

= Acon v A,bea m Aplasm , a ^ihy, dJ Gfusio^ . n

For a laser system we assume that reflection and/or fast ion gen­ eration reduce the plasma coupling to 50% and that the hydrodynamic efficiency is 10%, typical of energy deposition at 1/2 micron wave length. The efficiency of energy transfer into the laser beam for CO2 or an excimer-pumped storage medium we assume to be 4%. The fusion-to-electrical conversion efficiency we assume to be 40%. For a system gain of ten, Eq. (3) gives

G-fusio . n = 12500

The corresponding pellet gain, beam energy, and fusion yield, from Eqs. (1) and (2), are

pellet = ^25

112 E = 7 megajoules "beam A ,A,, pi H

^fusion ~ ^'^'^^ megajoules = 1.09 tons HE equivalent

The laser beam energy and the fusion yield present major problems

in driver and reactor technology.

For an ion or electron beam driver, we again assume a plasma

coupling efficiency of 50%, The hydrodynamic efficiency we assume

to be 30%, the higher efficiency resulting from the deeper deposi­

tion of the energy and the lower energy loss into ablation products.

The electrical-to-beam efficiency we assume to be 50%. For those parameters the fusion gain required for a system gain of 10 is

G- . = 222 for which the beam energy is much less than one kilojoule. For such low energy, however, the elementary analysis

leading to Eq. (1) fails. For the more realistic choice of

E, = 50 kilojoules, beam •' *

G- . = 2687 fusion

G _. ^ = 403 pellet

Y- . =20 megajoules fusion *=• •'

G ^ =81 system

113 The beam power necessary for the pellet implosion depends on the pellet configuration. For an initial tamper/fuel mass ratio 3 of 10, a tamper with initial density of 11.3 gm/cm , an aspect ratio (initial tamper radius T tamper thickness) of 50, and

assuming 40% fuel bum up, the initial radius is 0.89 millimeters 2 and the tamper thickness 0.020 gm/cm . The implosion time is

approximately 9 nanoseconds giving an average beam power of S.6 (2) terawatts. For uranium atoms, the energy for a range^ -^ equal to the tamper thickness is about one Gev. The total ion current therefore is 5.6 kiloamperes. The space charge limit on beam transport at 1 Gev is about -'''--' 1/4 terawatt/beam requiring about 20 beams to deliver the total power necessary.

These results suggest an interesting possibility for heavy-ion fusion with driver parameters far below those usually considered, which are more appropriate for the requirements of a laser-driven system.

114 REFERENCES

1. BRUECKNER, K. A., JORNA, S. , Rev. Mod. Physics 46_, 325 (1974).

2. Proceedings of the Heavy Ion Fusion Workshop, edited by Lyle W.

Smith, held at Brookhaven National Laboratory, Upton, New York,

October 17-21, 1977.

3. ERDA Summer Study of Heavy Ions for Inertial Fusion, edited by

Roger 0. Bangerter, William B. Herrmannsfeldt, David L. Judd,

and Lloyd Smith, held at Claremont Hotel, Oakland/Berkeley,

California, July 19-30, 1976.

115 116 IV. REPORTS OF THE WORKSHOPS

ATOMIC AND MOLECULAR PHYSICS

Joseph Macek* Department of Physics and Astronomy University of Nebraska-Lincoln Lincoln, NE 68588

1. Summary

Introduction

The key problems of atomic and molecular physics for heavy ion fusion have become more sharply defined in the intervening year since the Brookhaven workshop. While some new questions requiring new theoretical developments have emerged from discussions with the plasma group, these are not of critical importance at this time. Accordingly the atomic and molecular physics group concentrated on reviewing existing calculations, particularly those related to ion-ion collisions in the heavy ion beam, and on the task of providing cross sections for well tinderstood processes on a more or less "demand" basis. Both activities are summarized in this report.

Atomic/Molecular Physics in Accelerators and Storage Rings

Two broad classes of atomic scattering processes affect beam lifetimes in accelerators and storage rings, namely collisions of ions with background gases in the transport vessel and charge changing collisions between ions in the pulse. No experimental program is underway to measure relevant cross sections, however theoretical calculations of some representative cross sections are in progress.

Collisions of fast ions with the background gas results in some stripping of electrons from the ions. Because the ion velocity is high (3 - v/c>0.01) the Bom approximation can be used to reliably calculate stripping cross sections. These calculations were discussed at the Brookhaven conference, and the cross sections given in Gillespie's report and in table V-A-2/2 of the report by Cheng, et al.^ may be referred to. Similar cross sections for other ion-gas combinations can be calculated on demand by Y.K. Kim or George Gillespie.^ Additional stripping cross sections for Xeq"*" and U^"*" by N2 for all possible q were calculated by Y.K, Kim during this workshop.

Charge changing collisions of ions in the beam pulse typically occur at low relative energy, of the order of 10 to 100 keV. In this region theoretical calculations are considerably more difficult, partly because heavy ions can change charge by a variety of processes including charge transfer

117 direct ionization

A1+ + A<1+ - A^"^'^^ + A"* + e- (b) and inner shell processes followed by auto-ionization.

Inner shell processes are sufficiently well understood to estimate their contribution to ion-ion collision cross sections. Such estimates are given inCheng et al's, report^ at the Brookhaven conference. They correspond to Omin given in that report. The values of Omax given in that report are now considered unreliable and should not be used for design work. Cross sections for inner shell processes are seldom larger than 7 x 10"^^ cm^ and are frequently smaller.2 Cross sections for the outer shell processes are almost always larger than those for inner shell processes so no further estimates of the latter were made during the workshop. Instead, attention focused on process (a) and (b) involving outer shell electrons.

The ion-ion charge changing cross sections play a role in all schemes for beam acceleration and storage. In those devices which envision an acceleration/storage time of the order of 1 sec, accurate cross sections are essential with cross sections of the order of 10"-^^ cm^ being unacceptable. For those devices which require a storage time of 10 ms, cross sections of the order of lO"'^^ cm^ are unacceptable. Such cross sections can occur, particularly with singly ionized species, thus they will be a design consideration. For lifetime of the order of 1 ys, atomic cross sections will probably not play a key role.

Ionic species fall into two broad categories with respect to outer shell processes. Ions with one or more loosely bound electrons exchange electrons relatively easily and for these ions charge transfer is expected to dominate. Ions with no loosely bound electrons such as Cs and Xe ®, do not exchange electrons easily thus for these ions reaction (b) is expected to predominate, or more correctly reactions (a) and (b) are expected to proceed via similar mechanisms. For both reactions, the process is viewed theoretically in terms of transitions between states of transient diatomic molecular ions, Calcula- tions of the relevant molecular curves have been completed for Ba^ ^nd Cs2 •

Collisions of Ba"*" + Ba have been studied by Sramek, Gallup and Macek^ as a prototype for collisions involving ions with loosely bound electrons. They find that the incident and charge transfer channels strongly couple at a distance of 13aQ(ao = 5,3 x 10"® cm). The corresponding cross section is then of the order of 7T/4(13ao)^ = 10"^^ cm^ where the factor of h enters as the statistical weight. Another factor of h is introduced because alterna­ tive final states, not all of which correspond to charge transfer, are populated, thus the calculations place the cross section between lO"^'* and 10~1^ cm2. Since the cross sections vary strongly with energy, calculations are in progress to determine the energy dependence. Because the calculations neglect spin-orbit coupling they are not definitive, however, they show that when ions have loosely bound electrons, charge exchange cross sections of the order of 10"^^ cm2 are expected.The group noted that since U^ has several loosely bound electrons, it would not be an optimum choice for minimizing

118 beam losses due to ion-ion collisions.

Das and Raffenetti^ have calculated the relevant potential curves for Cs'f*' as a prototype for ions with no loosely bound electrons. They find no strong channel coupling for interatomic distances greater than 4ao, accord­ ingly, one expects no inelastic transitions unless the ions approach more closely than 4ao, At such distances the simple adiabatic approximation no longer applies and new simplifying assumptions must be introduced.

The Fano-Lichten model,^ which works well for inner shells, has been applied by Olson to outer shells of C2 ^t internuclear distances between 2a and 4ao. He finds a curve crossing near 3aQ and by using reasonable statis­ tical assumptions concludes that the charge changing cross section including both reactions (a) and (b) is of the order of 2 x 10"^^ cm^. This is the most well founded estimate that can be made theoretically, however there are experimental indications from ion-atom collisions that it may be too large in the 50-300 keV range. For example, this model with a similar mechanism applies equally well to Ar - Ar, Ar + Ar and K^ + Ar collisions, and predicts cross sections of the same order of magnitude, whereas experiment^ gives cross sections equal to 6 x 10"^^ cm^, 10"^^ cm^ and 10"^' cm^ respectively in this energy range; a variation of nearly two orders of magnitude. The model must be partially correct however, since at higher energies these cross sections tend to the same limit which is of the order of 10"^^ cm^. A determination of the energy dependence is urgently needed and it appears that this must be done experimentally. At least any calculations must be checked by some direct measurements of ion-ion stripping cross sections. At present we can only state that the best estimate for the Cs + Cs"*" charge changing cross section is 2 x 10'^^ cm^, but that it might be as small as 10"^^ cm^ in the 50-300 keV energy range.

Macek,® in a paper presented to this workshop, has applied the Fano- Lichten model to Xe ° + Xe"^® collisions and estimates a charge changing cross section of 10"^^ cm^. This estimate, which applies the model in a charge state region where it has never been tested, could be in error by an order of magnitude. Since calculations are now using models in parameter regions where they haven't been tested, future determinations should place a high priority on experimental measurements to check the theory, where possible.

Atomic and Molecular Physics in Gas Filled Reactors

The propagation of the ion beam to the target pellet through a gas filled reactor depends upon plasma properties such as density, conductivity and temperature. The low energy electron spectra in the medium is the key input information in the plasma modelling. Such spectra depend upon^ - secondary electron spectra from ionization of back­ ground gas by fast heavy ions - secondary electron spectra from the ionization of background gas by slow electrons - excitation cross sections for background gas by slow electrons - photoionization processes.

Primary ionization can be calculated in the Born approximation for single

119 electron ejection. Multiple ionization of gas ions by highly ionized species represents a problem requiring further theoretical development. Much informa­ tion on the other processes is available in the literature. Such data are essential to a realistic modelling of plasma properties in the reactor chamber. References

1. George H. Gillespie, Proceedings of the Heavy Ion Fusion Workshop, October 17-21, 1977, BNL 50769, p. 45.

2. K. T. Cheng, G. Das, Y. K. Kim and R. C Raffenetti, Proceedings of the Heavy Ion Fusion Workshop; October 17-21, 1977, BNL 50769, p. 43.

3. C H, Gillespie, Y. K. Kim and K. T, Cheng, Phys, Rev. A17, 1284 (1978).

4. S. Sramek, G. Gallup and J. Macek, this workshop.

5. G, Das and R. C Raffenetti, this workshop.

6. U. Fano and Wm. Lichten, Phys. Rev. Lett., 1^, 627 (1965).

7. R. C Dehmel, H. K. Chau and H. H. Fleischman, Atomic Data _5, 231 (1973).

8. J. Macek, this workshop.

9. R. T. Poe, Proceedings of the Heavy Ion Fusion Workshop, October 17-21, 1977, BNL 50769, p. 41. See also Simon Yu's report on page 50 of this report.

* Members of the Atomic and Molecular Cross Sections Group: R. Bock (GSI), K, Cheng (ANL), G. Das (ANL), G. Gallup (U. Nebraska), G. Gillespie (Physical Dynamics), Y. Kim (ANL), J. Macek, Chairman (U. Nebraska), R. Olson (SRI), R. Raffenetti (ANL), S. Sramek (U. Nebraska), S. Yu (LLL)

120 REFERENCE DESIGN COST ANALYSIS

Cost Analysis Group*

INTRODUCTION

The systems and cost analysis group was chartered by the Reference Design Committee (Chaired by L. Teng of FNAL) to:

(1) Attempt to resolve present glaring inconsistencies in cost estimates, in particular RF Linac costs and unit costs,

(2) Obtain, evaluate, and compare cost estimate break­ downs for each reference design for:

a) Consistency of direct cost elements where applicable.

b) Consistency of inclusions and exclusions of A&E, R&D, site costs, various burdens, overheads, and escalations.

c) Develop new total costs for all reference designs on a consistent basis.

The cost analysis group spent most of its time trying to resolve and analyze a direct approach to be used in costing the reference designs which were presented to them. No attempt was made to dictate a consistency between the reference designs for such items as A&E, R&D, and overhead charges since those additions to the capital costs were felt to be a common multiplier for each of the reference designs. The group analyzed three systems: a) ANL Hearthfire #2, b) LBL Induction Linac, and c) BNL R.F. Linac with multiplier rings and accumulators. These scenarios are outlined in great detail elsewhere in this report. The ANL Hearthfire #3 scenario was not analyzed due to a time limitation and some technical uncertainties of the design. The group made no attempt to cost the reactor chamber or any subsystems which were physically located after the final beam transport system. Some of the group's effort concentrated on the normalization of the unit costs which are common to most accelerator systems. Much time was

*The members of the Cost Analysis Group were: E. K. Freytag (LLL) - Chairman, I. 0. Bohachevsky (LASL), R. Burke (ANL), C. Driimm (U. of Mich.), S. J. Grammel (ANL), J. Hovingh (LLL), E. H. Hoyer (LBL), T. Kammash (U. of Mich.), A. Pascolini (U. of Padova), and E. W. Sucov (Westinghouse).

121 spent trying to understand in enough engineering detail the accelerator designs, so that reasonable estimates could be made as to how to apply the normalized costing schemes to the individual subsystems of the accelerators.

COSTING GROUND RULES

The guidelines which the group established and followed for the cost analysis are listed below:

(1) Each scenario was broken down into workable subsystems which are shown in Figures 1, 2, and 3. The subsystems were costed based on the technical components of the various subsystems (accelerator, beam transport, ion source, multi­ plier and accumulator rings, etc.) and the conventional facilities of the subsystems.

(2) Included in the cost of technical components were the accelerating modules and structure, power supplies (for either magnets or the accelerating modules), vacuum system, support and alignment, accelerator control room, computer systems, and beam transport magnets (if part of the accelerator).

(3) Included in the cost of conventional facilities were site work, accelerator housing (buildings, tunnels, etc.), mechanical facilities, electrical facilities, and personnel and machine interlock systems.

(4) The basis for the normalized costs of the subsystem components (except in a few isolated cases where recent data was available) was those unit costs derived for the Proceedings of the Heavy Ion Fusion Workshop (BNL 50769) held at BNL in October 1977. Some escalation of the 1977 costs was included so that the costs presented here can be considered to be in 1978 dollars.

(5) Not included in the subsystem costs were (a) facility Architectural and Engineering (A&E) fees, (b) the Engineering, Design, Inspection, and Administration (EDIA) for the technical components, (c) any R&D effort to develop the technical components, (d) site purchase costs, and (e) contingency monies.

(6) No attempt was made to weigh the technical credibility of the performance parameters of the proposed system concepts, but the group did try to apply good engineering designs to those subsystems which we understood and could analyze.

122 REFERENCE DESIGN COST ESTIMATES

The final subsystem costs for the three reference designs are outlined below. A general concern which the group had with each scenario was the lack of sufficient detail of hardware design and engineering completeness which was presented to the group. It is a difficult task to take a "one line" diagram of a facility which may cover over five square kilometers or be eight kilometers long and convert that into a list of components to be costed. The subsystem costs listed below represent just the summation of the rather extensive lists of components and subsystems which were costed in detail. These system designs are of course very fluid and almost certainly don't represent a cost effective or performance optimized design.

ANL HEARTHFIRE #2 SCENARIO

CONCEPT PARAMETERS Particle: Mercury Final Charge State: +8 Final Kinetic Energy: 20 GeV Target Beam Energy: 1 MJ Target Beam Power: 160 TW Repetition Rate: - 10 Hz

SUBSYSTEM COST ESTIMATE

1 INJECTORS RF DEBUNCHER DELAY DELAY STORAGE COKTRESSOR AND FINAL LINAC LINES RINGS RINGS TRA;:3P0RT LIKES FOCUS 1 , , 1 * 1 ^ 7^$ 217 M$ 22 M$ 120 M$ 72 M$ 18 K$ 17 M$ ho M$

Total System Capital Cost: 513 M$

FIGURE 1

COMMENTS AND CONCERNS

The designs for those components and subsystems after the RF Linac were at best preliminary and did not contain enough engineering detail to allow for a better than medium confidence level by the group on those cost estimates. R.F. power for this scenario was costed at $.15 per watt peak power. Cost reductions due to large scale production were considered not to apply to a system of this size. It was particularly difficult to examine the compressor and transport lines in sufficient detail to be comfortable with the design of those necessary components to make that subsystem sound.

123 LBL INDUCTION LINAC SCENARIO

CONCEPT PARAMETERS

Particle: Uranium Final Charge State: +4 Final Kinetic Energy: 19 GeV Target Beam Energy: 1 MJ Target Beam Power: 160 TW Repetition Rate: 1 Hz Accelerated Charge: 210 uC

SUBSYSTEM COST ESTIMATE

ION PULSED LOW ENERGY ACCELERATOR- TPJ\:;sPORT FINAL SOURCE DRIFT TUBES INDUCTION LINAC BUNCHER FOCUS T LINES 2 M$ 12 M$ 32 M$ 300 M^ 16 M$ 32 M$

Total System Capital Cost: 39^ M$

FIGURE 2

COMMENTS AND CONCERNS

It should be noted that the large cost item (300 M$ for the accelerator-buncher) is the result of a brief cost optimization study by LBL and may represent the cost of an accelerator system which does not have optimum beam performance. It is our opinion the cost estimate for the accelerator-buncher may be low by 20^ (60 M$) if the estimate was made for an optimum accelerator. Our estimate is that 2556 of the 300 M$ represents the fabricated core material (metalic glass) costs and is an optimistic figure assuming that the magnetic material will go into mass production by 1984 and therefore make it very cost competitive. If some combination of iron/ferrite cores had to be used, the total cost of the accelerator-buncher subsystem would be 380 M$. Approximately 50;6 of this cost represents the accelerator module (including the mechanical structure and magnetic core) and is an estimate based on a preliminary design by LBL and is not totally substantiated by existing accelerator designs. Note also that this estimate includes only earth filled shielding for the entire length of the accelerator which may not satisfy the necessary shielding requirements. These LBL computer codes may be of some benefit if used by other accelerator laboratories for such studies.

124 BNL R.F. LINAC AND ACCUMULATOR RING SCENARIO

CONCEPT PARAMETERS

Particle: Uranium Final Charge State: +2 Final Kinetic Energy: 20 GeV Target Beam Energy: 10 MJ Target Beam Power: 200 TW Repetition Rate: 15 Hz

SUBSYSTEM COST ESTIMATE

LARGE 8 FINAL INJECTORS LOW P RF MULTIPLIER MULTIPLIER ACCWTULATORS TRANSPORT LINAC LINAC RING RINGS LINES FOCUS I T" 1 11 M$ 157 M$ 696 M$ 73 M$ M$ 116 M$ 231* M$ 125 M$

Total System Capital Cost: 1420 M$

FIGURE 3

COMMENTS AND CONCERNS

One of the major uncertainties of the above unit costs was the cost of the R.F. power for the Linac which was scoped at 240 M$ (out of the total Linac cost of 696 M$) and reflects the estimate of $.1 per watt peak power. Most engineering realists would cost out R.F. systems at $.15 per watt peak power which would drive the total cost of that system to 816 M$. Mass production techniques may be able to drive the costs down to $.1 per watt peak power, but the group did not have a high confidence in that prospect. The same uncertainty applied to the high power R.F. systems used in the accumulator rings. These systems represent 77 M$ out of the 234 M$, but so little design information was available that our costs could be low by perhaps a factor of two. Note that cost reductions could result for this scenario by way of 1) creative engineering, 2) package design, 3) mass production price decreases, and 4) significant advances in R.F. systems technology.

125 GENERAL COMMENTS

It was the opinion of this group that perhaps at least another year of preliminary design and engineering would be necessary before "high confidence" cost estimates could be assembled. As these designs are developed into rough engineering drawings, additional insights into the cost definitions and trade-offs should be forthcoming. Realistic performance parameters will also emerge for the various subsystems and accelerator components which would help generate confidence in the costing efforts, as well as the projected overall performance of these scenarios. This group made no attempt to normalize the costs of the 10 MJ scenario with the other two 1 MJ schemes. The same costing ground rules (except for the R.F. costs) were used for the 10 MJ concept as were used for the others. The cost benefits, which may be forthcoming for a large facility (10 MJ) because of mass production savings, were not considered in enough detail to help the group with unit cost differentials. The group made no effort to analyze extensions of the 1 MJ scenarios to 10 MJ facilities. Consequently there is no immediate comparison or normalization between a 10 MJ Induction Linac scheme (or 10 MJ Hearthfire #2) and the 10 MJ R.F. Linac scenario of BNL. It is clear however, that the scaling of cost with beam MJ is much less than linear.

SUMMARY

The cost analysis group believes that a 1 MJ heavy ion driver could be built for a capital cost of between 400 M$ and 550 M$. The group has a moderate confidence that a 10 MJ driver could be built for a capital cost of 1500 M$. It is recommended that no cost analysis be carried out in future workshops until the proposed overall accelerator designs (well thought out and with engineering detail) have been accepted by the accelerator community as reasonable approaches to HIF,

Several group members investigated the impact of high and low pressure reactor designs on the overall performance requirements of the accelerator system and the final beam transport. Reactor design constraints may set stringent requirements on such accelerator parameters as repetition rate, beam emittance, efficiency, and final beam transport designs. The permissible operating envelopes of the reactor cavity parameters should be determined so that total costs may be derived for a complete HIF engineering prototype, as well as to help assess the impact of the reactor cavity on the cost and performance of the accelerator driver system.

CHAIRMAN*S NOTE

Membership on the Cost Analysis Group does not necessarily imply full agreement with this analysis. Differences of opinion may exist as to the real cost of components and subsystems. Questions regarding these costs should be directed to the chairman.

126 ION SOURCE GROUP SUMMARY* D. J. Clark Lawrence Berkeley Laboratory R. L. Seliger Hughes Research Laboratories

Laboratory Programs

The ion source group heard presentations of the develop­ ment programs of the various laboratories. The present status of these programs is briefly summarized in Table 1, and describ­ ed in more detail in individual contributions to the Conference, In Table 1 the characteristics of each type of source are given. The normalized emittance in one plane: e^ = Area x BY/'"'- Brightness is informally defined as l/z"^. Beam current measure­ ments have been made by all labs. Emittance measurements have been made by most groups, but in some cases at low current. The most promising sources for producing 30-100 mA of Xel"^ - Hgl"*" with emittance acceptable to a column and rf linac appear to be the Hughes single aperture Penning source, and an LBL/LLL type multi-aperture source. The LBL/LLL source can probably be improved by using higher beam energy and slit extraction in­ stead of round holes. Also a duoplasmatron with large plasma expansion cup and single or multi-aperture extractor should be competitive. A single aperture source requires high extraction voltage of 100-200 kV for these currents, but is simple in construction and can have higher brightness than the multi­ aperture source, if the plasma surface is stable. The LBL contact ionization Cs^"*" source designed for 1 ampere is making good progress, with currents consistent with the predicted values at the extraction voltages used. This type of source would be required for injection into an induction linac,

During the coming year it is important to continue the present development programs. The work to be done includes demonstrating beams at the 30-100 mA level, accelerating them through a column, and measuring the emittance at the ground end. The beam should show good stability during the pulse and also pulse-to-pulse.

127 Reference Designs

In Table 2 the sources for the various lab reference designs are summarized, giving estimated confidence levels for each one. The confidence levels are below "high" where the design calls for performance which is a significant extrapola­ tion from standard demonstrated performance. It is quite likely that these lower confidence cases will rise after the coming year's R&D.

Measurement Description Guidelines

In our discussions of ion sources from various labs, we have found that it is sometimes difficult to make direct comparisons. So we make the following suggestions for future discussions and publications of ion source development work. Accurate measurements of beam current and emittance of these high current beams is not easy. Various methods are used at different labs. For beam current measurement, collector cups or plates are used, sometimes with a bias on the collector, sometimes with a bias ring upstream which is shielded from the beam and sometimes with magnetic suppression. Size on a phosphor and thermocouple readouts are also used. Electrical readouts can be misleading because of secondary electrons and plasma produced by the beam. For understanding and evaluation of the measurements the authors should describe the measuring system and also show data of beam vs. strength of electric or magnetic suppression, whenever they are used. Emittance measurements also have difficulties. They are made by slit and scanning systems which interrupt most of the beam, by beam size on a phosphor, or by beam through collimators into a cup. Here again the method should be described. Pulse width of the beam is important for estimating space charge compensation. The background pressure and the fraction of the beam converted to neutral atoms are also useful in understanding the transport. Authors of ion source papers should describe as many of the above parameters as possible.

References 1. ERDA Summer Study of Heavy Ions for Inertial Fusion. LBL-5543. (July 1976) . 2. Proceedings of the Heavy Ion Fusion Workshop. BNL-50769. (Oct, 1977).

128 Table I. Source Test Results. Transport T^ ^ Ions B= I/en ^ No. D-C.or or Group Source Ion Aper. I Pulsed Energy Atoms Dist. (cm-mr) L(cm-mr)J Accel. Ref. (peak mA) D.C.& (keV80 ) This ANL/ Penning Xe-'-"'" 1 2.5 Ions .7m .001 2500 Pulsed Conf. Hughes Xe"*-"*" Mult. 100 Pulsed 2.5 IOC Xe^^ 1 3^ -^.01 >1000 ^00 ^^0 1+ Xe Source 1.5 MV 1+ ' 1 ICO 200 Ions on <.01 Hg Column Column BNL Duoplas, Xe^"*" 1 2 Pulsed 500 Ions .01 20 500 kV This column conf. 1+ * New Hg 40 Im .02 100 400 kV " Column

LBL LBL CTR Xe-L"^ 13 35 Pulsed 20 Ions 1.4m .035 29 This +LLL Extr. Conf. n Xel+ 13 60 500 1.2m 500 kV To Column Column Contact Cs^^ 1 400^ 20C .

* " Cs^^ 1 7500 5000

Ref. 1, LBL- LBL CTR 1+ 105^ 6500^ Ions-> .28X.01 Mobley (Slit Extr.) Xe Pulsed 35 3.3m p. 505 180 Atoms 800 This Conf. Ions + LLL- MATS III ^1+ 25 75 D.C. 20 1.1m '\^.02 190 Ref. 2 Osher Atoms p. 92 *Planned A/B = Measured/Expected Table 2. Sources for Reference Designs,

Source Pre. Accel^ Confidence Confidence Lab Ion (peak mA) Type Level Type Level

1+ Hughes High 1500 kV Medium ANL-2 Hg 50 Penning Column

1+ Hughes 1500 kV ANL-3 Xe 20 Penning High Column Medium

1+ Low BNL U"'"'^, 40 U 500 kV High (Hg-^"^) Hg-'-'^'High Column

1 + Surface Low, Drift Low LBL U 4000 Ioniz. Needs Tubes Needs R&D R&D

Members of the Ion Source Group: N, Angert (GSI); D. Clark, Chairman (LBL); W. Herrmannsfeldt (SLAC); M, Mazarakis (ANL); R. Mobley (BNL); M, Nahemon (Westinghouse); R, Seliger, Chairman (HRL); J. Shiloh (LBL); R. Vahrenkamp (HRL); G. Wakalopulos (HRL); and J, Watson (ANL),

130 LOW BETA LINACS*

1, Summary

J. Keane, R. Adams, F, Cole, A. Faltens, R, Gluckstern, W, Herrmannsfeldt, H. Kim, J. Klabunde, A, Moretti, R. Sanders, J. Staples, R. Stokes, and D. Young

Introduction

Since the three reference designs were an initial attempt at designing an overall system, many of the details of the low Beta sections were at best inferred. In order to evaluate these low Beta sections it was first necessary to expand on the information submitted. Keeping in mind that there are numerous options available to the designers the committee tended to highlight weak points rather than strengths.

The Brookhaven RF Low Beta Design

The BNL design shown in Figure 1 utilizes a funnelling scheme. This system could deliver 960 microcoulombs of charge when pulsed at 6 millisecond. It is characterized by a low voltage preinjector as well as a low frequency accelerating section. This lower frequency was selected to minimize space charge effects with the added benefit of increased cell length to accommodate focussing elements. In addition the peak current at the output of the Low Beta section are increased due to the multiplicity effect of 8 sources. This approach tends to increase the number of duplicate stations required as well as increasing the frequency jumps and beam manipulations (summing and matching) required.

In the 2 and 4 MHz sections of the linac, the rf resonator can be placed outside of the vacuum vessel thus incurring savings in manuacturing costs. Slab lines were chosen over foreshortened lines, to relax construction tolerances. This tends to increase lengths considerably (80 feet for 2 MHz section). This approach does not seem feasible however for the 8 Megahertz sections since the accelerating section is an appreciable part of a wavelength. Structures similar to the GSI Wideroe would be applicable,

*Research carried out under the auspices of the United States Department of Energy under Contract No. EY-76-C-02-0016,

131 TABLE I

BNL PARAMETERS

Total Energy In/ Length(m) No. No. Peak kV rf power -^-(cm) Bean Section Out sec Sections Gaps sap (kW) Load]

2 MHz .5/2 6 1 25 100 22.5 60 50

4 MHz 2/6.4 5 4 73 100 26.2 255 70

4 MHz 6.4/12.8 5 4 54 100 33.7 340 76

8 MHz 12.8/30 6 5 143 100 25.3 1500 92

8 MHz 12,8/30 5 3 72 200 25.3 1620 85

Table I sunmiarizes the parameters of each of the funneling sections. The cell lengths, RF power requirements and overall length for all sections appear reasonable. It should be noted that all sections, particularly the 8 megahertz section, are heavily beam loaded. The consequence of this should be studied thoroughly.

Electrostatic quadrupoles are proposed for focussing during acceleration. Vulnerability to voltage breakdown during beam time should be investigated. Reliability and damage incurred due to beam mis-steering should be important considerations.

Matching hardware between sections will be required. It was pointed out that these matching sections will have to change phase space shape even more than in an Alvaraz type accelerator. Table II results indicates that between the 8 and 48 megahertz section considerable manipulation will be required, since the longitudinal phase length exiting the lower frequency section is much larger than the phase acceptance of the 48 megahertz section, (insufficient dampening.)

132 TABLE II

PHASE DAMPING IN BNL SECTIONS (NO MATCHING)

Section Phase In Phase Out

2 MHz 60° 42°

4 MHz 84° 52°

8 MHz 104° 98°

48 MHz 600°

Calculations showed that beam switching circuitry to combine two beams into the subsequent tank is reasonable. Using equations from Betz, Rev. Mod Physics, 44, 465 (1972) theoretical stripping efficiencies stated in both rf linacs are achievable.

More detailed beam calculations are required in both rf linac designs. Questions of emittance blow-up, etc., are raised (see J. Staples paper in this workshop proceedings). These questions should be answered.

Alternate structures for the early stages of acceleration may be of value. The radio frequency quadrupole (RFQ) structure invented by Kapchinskii and Teplyakov have the advantage of offering focussing as well as acceleration along the beam path. With this structure it may not be necessary to go down as low as 2 megahertz to avoid phase space dilution. An alternate scheme is shown in Figure 2.

The Argonne RF Low Beta Design

The ANL design is shown in Figure 3. The peak current specified is 5 times that of the BNL design but it only requires one frequency jump. Since there is less funnelling, less duplication of hardware is required. Due to stripping to a higher charge state the resultant linac is much smaller than the BNL design. Because of the small value of 3A, TT -nTr cells have to be used. This requires longer vacuum vessels supporting the accelerating structures.

A summary of the parameters of this system are given in Table III. As in the BNL design there is heavy beam loading in the 25 megahertz system.

133 TABLE III

ANL PARAMETERS

Energy No. // gap, Peak kV Total rf -2-(cm) Beam Type Struct. In/Out Section Quad Gap Power kW Loading

7r/2 1.5/2 1 100 5 75 50

Tr-5Tr 2/5 2 8/4 250 7 220 50

77-377 5/10 3 8/4 250 11 330 50

7r-57r 10/20 2 20/10 325 15,8 1160 50

Tr-37T(25 MHz) 30/100 2 20/10 250/390 33 10300 95

The Lawrence Berkeley Low Beta Linac

Pulse technology is utilized in this design (see Figure 4), A 4 amp, 50 ysec beam electrode is pulsed to a million volts at the same time as the 1st drift tube is pulsed negatively, resulting in a 2 megavolt accelerating potential across the gap. At the conclusion of the beam drift time this first drift tube is switched to plus a megavolt. The drift tube length of 50 meters is dictated by the 50 ysecond beam pulse width. Drift tube 2 is alternately pulsed plus and minus 2 megavolt resulting in an energy level of 5 meV, The increased length of this tube is related to the increased particle velocity. At the exit of the second drift tube the beam is stripped and analyzed. Upon beam entry, the last drift tube is pulsed negatively by a megavolt. At the completion of the beam transit time the tube is then ramped up to a megavolt. This ramp provides the initial bunching to the beam.

Trim magnets similar to induction linac sections are placed in the gaps to provide small corrections to the leading and trailing edge of the beam. Large superconducting solenoid magnets are placed around the vacuum vessel to provide focussing.

The solenoid required for focussing would be difficult to fabricate. Alternate focussing schemes are already being studied at LBL,

High voltage feedthrough assemblies required for the vacuum-air interface to the pulsed power supply system should be studied in detail.

134 Conclusions

Fortunately the ANL and BNL designs represent appropriate extremes in the design of RF linacs. The ANL pre-injector voltage is 3 times higher than the BNL design while the BNL 's initial drive frequency is a factor of six below that chosen by ANL. Magnetic quadrupoles are specified in the ANL design while BNL chose electrostatic quads. As a consequence of these differences the modeling work now in progress at both laboratories should provide much more insight into the choice of an optimum design.

The confidence level in both rf linac designs is high except for emittance blow up and difficulty in manipulations.

The LBL design in some respects is simple, but there has not been a device of this size built and it is difficult to assign a confidence level. It is probably high. Again more will be known when the LBL test linac is in operation.

There is a need for extensive computational investigation of orbit dynamics. It is extremely important to preserve emittance under severe space-charge conditions and when shifting frequency.

The models now being built at all three laboratories will be of great help in searching for an optimum design.

135 20 mA 500kV

30 MeV

2 MHz 4 MHz 8 MHz 48 MHz

Figure 1. BNL Reference Design

2 MeV 7 MeV 500kV 12 MHz 24 MHz 48 MHz

Figure 2. RFQ Structure Design

40 mA Hg"*"^ 64 mA

1.5 MV 120 mA Hg 24 MHz

12 MHz

Figure 3. ANL Reference Design

136 llkl. ^ '^^•^^ ^«>

/ -1 Ct^ STUtP v/» T icom^t^t^ S0^<^. lNk\/d^.r<^ HM^\/ ^"^^^ ANi^i^i^^ "^fA^Sj 2/

~\ ^IMV --IM^ 1/1V

Figure 4, LBL Reference Design

137 138 BEAM MANIPULATIONS AND BUNCHING*

Tat K. Khoe "^ Argonne National Laboratory

One of the main problems in beam manipulations has been that of satisfying the following requirements:

1. Very small beam losses in order to prevent damage of surrounding materials.

2. Minimize the dilutions of the transverse and longitudinal phase space density.

The goal of the workshop has been to determine the technical feasibi­ lity and the amount of phase space density dilutions of the operation. The following topics are considered:

1. Combining two or more linac beams in transverse and/or longitudi­ nal phase space.

2. Beam splitting in two or more beams. The splitting in two beams has been used in the slow extraction of beams from proton synchrotrons. No quantitative values of the phase space dilutions are available. The beam losses range from a fraction of a per­ cent to more than 50%,

3. Multiturn injection of a linac beam into a circular machine has been in use at many accelerator laboratories. In general, small phase space density dilutions imply large beam losses and vice versa. There are no experiments using nonlinear bumper fields in multiturn injection,

4. Beam stacking in transverse phase space.

5. Bunching, debunching and longitudinal phase space matching.

Conclusion

Rigorous theoretical calculations, which take into account space charge effects, etc., are necessary to obtain reliable values of dilution factor and confidence level. Although many beam manipulation concepts do not

*Work supported by the U,S, Department of Energy

139 have this quantitative analysis at this time, the methods are well known to do this analysis and computer simulation. Rigorous engineering design cal­ culations and prototype low energy experiments can be carried out to establish dilution factors and technical feasibility.

•^Members of the Beam Manipulations and Bunching Group: D. Bohne (GSI); Y, Cho (ANL); R, Cooper (LASL); M. Foss (ANL); A. Golestaneh (ANL); R. Juhala (MDRL); D. Keefe (LBL); T. Khoe, Chairman (ANL); J. Klabunde (GSI); J. Leiss (NBS); V. Neil (LLL); D. Neuffer (LBL); and H, Takeda (ANL).

140 SUMMARY OF THE WORKING GROUP ON HIGH CURRENT TRANSPORT AND FINAL FOCUS LENSES*

A. A. Garren Lawrence Berkeley Laboratory

Introduction

The group reviewed recent work, and then addressed itself to relating the current understanding of relevant beam transport effects to the four reference concepts. In addition there was discussion on plans for future experimental and theoretical work.

Discussions covered the following topics:

Transverse instabilities on intense beams through periodic focusing systems,

Evaluation and correction of chromatic aberrations in the final beam transport lines,

Evaluation and correction of geometric aberrations due to quadrupole fringe fields.

Ion focusing by electrons.

To evaluate the current reference concepts, the group concentrated on three salient characteristics of the transport and focusing systems:

The zero-current transverse oscillation phase-advance per period and its space-charge induced depression,

The momentum spread in the beam,

The beam emittance in the final transport.

The group established approximate criteria for safe values of these three parameters assuming "no correction" or "correction" as currently en­ visaged. These criteria were compared with values quoted for the reference designs. While this exercise was rather imprecise, we believe it served to delineate roughly some of the most important requirements, and point to changes needed in the present designs.

*This work was supported by the Offices of Laser Fusion and High Energy and Nuclear Physics of the Department of Energy.

141 Transverse Instabilities

Instabilities of intense beams in periodic transport lines have been investigated through parallel analytic and computer-simulation approaches'»0 with impressive agreement. The results can be described in terms of the bet­ atron oscillation phase advance per period -- a^ in the zero intensity case, and a in the presence of space charge. During the bunch compression process a decreases monotonically with increasing current, and the practical impor­ tance of these studies is the charting of relatively safe values of this parameter. The instabilities are characterized by the electrostatic potentials arising from density perturbations. Potentials of second order in the trans­ verse coordinates are envelope perturbations. A result of the analytic work is that these instabilities may be avoided if the zero-intensity phase o^ is 90° or less. For a Kapchinskij-Vladimirskij (K-V) distribution, work by Haber and Laslett has uncovered very troublesome third-order instabilities for a- trajectories starting at OQ= 90 degrees, that center at a tune depression a - 46°, and begin at 57.5°. Thus a Og= 90° transport system can probably only operate in the range 90° > a > 60^, which strongly limits the maximum transportable current. It appears likely at present that substantially more current can be transported by choosing a transport system that operates in the range from ao=60° down to a final phase a not less than 24°. In such a system the third-order instabilities do not occur at all, and higher-order ones appear only below 24°.

The promising OQ = 6Q° system has not received as much attention as has the 90° system. Such work is very much needed and is now in progress.

Another important area for future work is the simulation of beams with non K-V distributions. The K-V distribution has been used because it leads to linear space charge forces which make the analysis far more tractable. Because of the good agreement between theory and simulation with the K-V distribution, one may have confidence in simulation studies done with other more realistic distributions.

The group concluded from the work done on this subject, that based on present knowledge, long transport lines for Heavy Ion Fusion should be designed to operate either in the range 90° > a > 60° or 60° > a > 24°, with the latter promising higher current, but being less certain until further studies are completed.

Final Focusing

By this phrase we designated that part of the transport system that carries the beam from a storage ring or periodic transport line onto the target,

1. Linear beam matching - The system must accomplish first-order beam- matching between the periodic line and the target, so that all particles within the transverse emittance ellipses of the periodic system are

142 focussed to the target spot size,taking account of the expected momentum spread.

2. Chromatic effects - The system must be adequate to handle the expected momentum spread considering second-order chromatic effects. The group classified systems to have moderate or high confidence levels depending on whether sextupole corrections are required or not.

The allowed momentum spread is determined by the estimated size of second-order chromatic transfer matrix elements between the entrance to the final lenses and the target. One finds

P £L

where rj is the target radius, L is the distance from the target to the center of the lenses, and e is the unnormalized emittance/iv. Beam line examples worked out at ANL^) and LBL are consistent with the above ex­ pression.

3. Geometric aberrations - in the final lenses limit transverse emittances. From work by Neuffer^) one finds a limit that depends on various system parameters. One way of writing this is

e ~< 0.1n i5c rj 5/'4 p -1/4

where p is the radius of curvature in a field equal to that of the quad­ rupole pole tip.

4. Corrections - A beginning has been made on methods to reduce chromatic and geometric aberrations in beam line examples. So far this work has ignored space charge effects, and the complications that these will introduce account for the group's caution in predicting dramatic improvements.

a) Chromatic Corrections - In one example at ANL of chromatic cor­ rection,7) two sextupole pairs are used. Runs were made using the program DECAY TURTLE,«) which gave 40% transmission of a ± 1% momentum spread beam onto a 1 mm target, representing a factor of two improvement due to the sextupoles. Similar work is in progress at LBL, using four sextupole pairs.

Another approach was reported by J. Steinhoff,^0) who developed a search computer program to adjust the parameters of a large number of quadrupoles so as to maximize the transmission of a large sample of particles onto a target spot.

In the light of such work in progress, and aware of space-charge complications, the group felt that at this time one might predict a factor of three improvement with corrections.

143 b) Correction of geometric aberrations - Analysis of geometric aber­ rations from quadrupoles and their correction with octupoles have been made by S. FensterS). He shows that for point-to-point focus­ ing there are four third-order aberrations to be corrected, of which three are independent. An example has been worked out in which six octupoles are placed among the final lenses. He succeed­ ed in cancelling the relevant coefficients, but the system has not yet been tested with ray tracing. Ray tracing is essential here for two reasons: first, in systems with large aperture quadrupoles, higher order aberrations can produce effects as large as third- order (octupole) effects; and second, the non-linear part of space charge effects may be important. Nevertheless, it is the general belief of the group that suitable compensation of geometrical aberrations can be designed into the system, and therefore, as with chromatic corrections, the group predicted that corrections may allow a factor of three increase in emittance, or z < 0.5 ro5/4 p -V4.

Implications for the Reference Designs

An attempt was made to compare the values of tune depression, momentum spread, and emittance suggested above with those of the reference designs, so far as these were known. The time available for this exercise was very limited, so the results should not be taken literally, but rather as indica­ ting areas requiring future attention. The results are summarized in Table I. The numbers on the first line are those currently predicted by the designers, those bracketed below recommended values (without/with) corrections.

We see that Hearthfire II has a very good (small) momentum spread but somewhat large emittance, as does Hearthfire II; the latter also has too much space-charge tune depression. The numbers given for both linac systems satisfy the criteria, though chromatic correction is needed for the rf linac.

144 Table I - Parameters of Reference Designs Relevant to Transport and Final Focusing* Hearthfire Hearthfire RF Induction II III Linac Linac

Phase advance per period at zero current OQ (deg) - 60 60 60 (60) (60) (60) at maximum current a (deg) - 11 24 24 (24) (24) (24) Momentum spread at final lenses Ap/p (%) 0.035 0.25 0.5 0.1 (.12/.36(t) (.11/.33) (.14/.42) (.37.9) Emittance/fT per beam (unnormalized) e(cm-mrad) 4.4 4.75 6.0 0.75 (1.1/3.3) (1.1/3.3) (10/30) (1.1/3.3) Emittance/iT (normalized) e^. (cm-mrad) 2.1 2.85 3.0 1.5

*The numbers in brackets are values suggested by criteria in the text, (without/with corrections).

Other Topics

1. Electron Focusing - Possible use of electrons to focus the ion beams was discussed. An account of the theory of the Gabor Lens, in which the electrons are confined by a solenoid, was given by A, A, Irani,H) and R. Mobley discussed experience with these lenses at BNL. Gabor lenses give quite linear focusing. The scaling is such that they will be most useful at low ion energies.

Another electron focusing scheme was presented in a formal talk by S. Humphries,12) who gave further details to the group. 2. Transport Experiments - M. Reiser gave a talk on plans at the University of Maryland to set up an experimental 40 period electron transport line to observe emittance growth at high current. Similar experiments with heavy ions are being prepared at ANL and LBL. These experiments will then be compared with numerical simulation predictions.

145 Acknowledgments

This summary is a very imperfect attempt to summarize the hard work of the participants of the High Current Transport and Final Focus Lenses group listed below:

K. Brueckner (UCSD) N, M. King (Rutherford) E. Colton (ANL) P, Lapostolle (GANIL) G. Dan by (BNL) L. J. Laslett (LBL) S. Fenster (ANL) D. Neuffer (LBL) A. Garren (LBL) S. Penner (NBS) I. Haber (NRL) M. Reimer (Univ. of Maryland) S. Humphries (SLA) L, Smith (LBL) A. A, Irani (BNL) J. Steinhoff (Grumman Aerospace)

References

1. I. Haber, L. J. Laslett, and L. Smith, "Comparison of Instability Theory with Simulation Results, (in these proceedings).

2. S. Penner, "Emittance Growth in High Current Beam Transport", National Bureau of Standards Internal Report, Nov. 30, 1977. S. Penner and A. Falejs, abstract submitted to March 1979 Accelerator Conference, San Francisco.

3. P. F. Meads, Jr.. Ph.D. Thesis. UCRL-10807, May 15, 1963.

4. D, Nefffer, HI-FAN-36, May 18, 1978,

5. D. Neuffer, (in these proceedings).

6. A.A. Garren, Appendix 8-7. ERDA Summer Study of Heavy Ions for Inertial Fusion, LBL-5543, July 1976,

7. E. Colton, "Correction of Chromatic and Geometric Aberrations", (in these proceedings).

8. K. L. Brown and C. Iselin, DECAY TURTLE, CERN 74-2, 5 February 1974.

9. S. Fenster, ANL/IBF notes 82. 84, and 86, (in these proceedings).

10. J. Steinhoff, (in these proceedings).

11. A. A, Irani, Gabor Lens Theory, BNL-25023.

12. S. Humphries, (in these proceedings).

146 WORKSHOP ON PLASMA EFFECTS

William B. Thompson University of California, San Diego

1. Introduction

The major problem studied here has been the propagation of the high current, high energy, but unguided ion beam across the 5-10 m radius tar­ get chamber onto the 1 mm target. Very briefly, our conclusions have been as follows: If the target chamber pressure is less than 10"^ torr, number density n< 10^^ cna"^, the beam propagates as though in vacuum, and in a low enough charge state even an unneutralized beam should reach the target ballistically. At pressures > 10"^ torr, the high value of the cross section 1 A 1 7 for ionization of the beam particles a~ lO"-^"-lO"-^' means that the beam charge state grows while the background gas is ionized. As a result the beam is charge neutralized and to a large extent, current neutralized; how­ ever, a two stream instability is excited and the electric fields produced seenn great enough to deflect the beam by ~ 1 aim, enough to nniss the target. As the pressure is increased to ~ 1 torr, collisions in the background gas inhibit the growth of this mode; however, a second mode, which leads to current filamentation then grows, and can produce substantial nnagnetic fields ^ 1-10 kG and deflections of order 1 cm. There are some unresolved implications in the treatment of this process, but there is a general agree­ ment that for n ^ 2-5 • 10^^ collisions wdll inhibit its growth; and for pressures of orSer 2-5 torr the beam can propagate in spite of this insta­ bility.

At the highest densities the neutralizing current decays because of plasma resistivity and significant self magnetic fields appear. These are strong enough to magnetically focus the beam and counteract a modest amount of scattering, but at the same time to not appear strong enough to induce the firehouse instability, and it may be possible to propagate the beam at even higher pressures. In summary, the three most likely propa­ gation regions are:

at low pressures p< 10"^ torr high confidence

147 at intermediate 2-5 torr nrioderate confidence pressures

at high pressures 10 torr low confidence/ magnetically constricted beam

2. Beam Conditions

To discuss these questions in a little more detail, we look first at the nature of the beams that have been suggested. There is general agreement that the beam should enter the target chamber with a cross section radius of TQ ^ 10 ^ TQ ^ 30 cm, and propagate for a distance L, 5 m < L ^ 10 m; although the lithium shower chamber design may permit a somewhat smaller radius L =- 2 m. At the end of its flight the beam should target on an area of radius r^ 1 mm ^ r^ ^ 2 mm, although some very high energy designs permit this to go up to ~ 0. 5 cm.

Again there is general agreement that the particle energy should be ^ 20 GeV and the power needed is p—- 200 Tw, hence the total current must be Igq =« 10^ amps. This is divided annong a number of beams which in some models is as low as 2, and in others as large as 24; hence, 400 < I^Q < 5000, The beam compositions considered have been U"*"^ or U "^^ , M = 238; Hg+2^ Hg+8 ^ M = 207 and Xe+8 ^ u = l3l: hence the beam is composed of initially lightly ionized heavy atonas. At these energies, 3 = 0. 4 for the heavier ions, and = 0. 5 for the light ions; hence the time of flight ^ 10/0. 4 X 3.10^ ^ 8. lO'^ sec. Since the energy must be delivered in ~ 10"° sec, the beam segment has a length of 1, 2 m.

The beam density, (particles/unit length); N = 2.1 x 10^ ^ea^^ cm"^; N^ 2,1 X 10^1 at I = 400; N = 2.6 X 10^^ at 1 = 5000. The beam plrticle N 6,6x10*7 J__ 1.65 XIO^ density (particles/cc) = 1 at 3 = 0. 4. At the nr entrance point, for 5000 amps, n = 2. 06 X 10^, and for 400 amps, n = 1.65 X 10^. At the target for 5000 amps, n = 8.2 X 10^^, and for 400 amps, n = 6.6 X 10^^. Associated with this density is an important angular) frequency, the beam plasma frequency uj^^ = [4n (Z'^e'^n/M)] 92 Z Jn^ 1.18 • 10° Z l/r. This varies from U), = 1.18 X 10^ for I = 400 amps at the entrance, for singly charged ions to uu. = 7,5 X 10.1 0 for I = 5000 at the target, with a charge of 90,

3. Background Conditions

There is more variety in ways in which the target chamber should be filled. Suggested pressures have varied from p ^ 2 • 10"^ torr to '^ p ==* 10 torr. The upper limit is determined by the effects of small angle scattering. The cross section is

148 z^z^ -30 B G 1 -- 2X 10 -^ (£ in GeV) e (AS)

Since A9 = lO'^; Zg^^ 90, for ZQ = 1 and & = 20, a =- 4 • lO"^^ and the density is limited by I /3 na L =* 1, the factor of 1 /3 arising from the varia­ tion in A6 along the path; hence for L = 10 m, n < 7, 5 X 10^^; p ^ 9 torr.

The lowest pressure allows the beam to propagate without serious plasma effects, but puts on the wall the entire burden of absorbing the energy released by the fusion explosion, an energy which may be as much as 200 MJ and probably be significantly greater than -^ 2 MJ. This also fornns a considerable challenge to the pumping system; gettering would take times considerably greater than 0, 02 sec =* (L/vp); and this may Umit repetition rates to 1/sec,

If the energy is extracted by a lithium shower, the minimum pressure would be given by the Li vapor pressure ^ 0. 02 torr at 500". There is a strong case for raising the gas pressure so that a good fraction of the X-ray flux can be absorbed in the gas. This becomes significant when p =« 2 torr, 1 "y n =^ 10^ ; hence, there are arguments for working at the highest pressure, although even for the magnetically confined case snnall angle scattering linnits the pressure to about 10 torr. The connposition of the background gas may be air, or hydrogen, and the residue of burnup. Other schemes use a heavy inert gas, neon or xenon, although since the scattering cross section ^ Z^ , the advantages of this seem debatable. 4. Effects of the Beam on the Background

As the beam passes through the neutral background gas, it produces ionization by several processes. Two of these seem universal, ionization by direct collision, and, until the beam is neutralized, annplification by field breakdown. Other processes, e. g. , breakdown by X-rays from the last aperture, may enhance the ionization rate but these two determine the nnini­ mum. Both processes depend on the composition of the beam and the back­ ground gas, and the value of ionization and excitation cross sections, hence a detailed analysis becomes a considerable numerical exercise. This exer­ cise has been undertaken by two groups: in Livermore and in Maryland, who have calculated the rate of beam neutralization.

A rough order of magnitude can be obtained by the following argu­ ments: From -[(dn /dt)]/n_ = n, CTv, it follows that the degree of ionization of the background gas due to the first process is

149 n r -n (r)az'l ^(r.z)= [l-e -^ J n g where r is the local beam radius, a fixed function of the distance into the chamber, and z measures the distance from the head of the beam (0

-n^(r )aiy n 1 - e S.= n OIL n, ai n. b

z

10-1^ „ 1 -e g L

For small values of x(z/i ), nVn, ^ 5 10-14 „ (z /i ) and for n > 2* 10^^ the plasma density reafiies the beam density in -^ 1 cm. Of course, this is not the only ionization process; the electrons produced in the ionization process usually have an average energy of -^ tv^ice the ionization potential and have a high probability of producing one secondary ionization. Moreover, if the beam is unneutralized or neutralized by a fraction f , it produces a potential of order

<^ ^ (1 -f) 60 Z„ I volts B eq and an initial field

E(r) =- (1 -f)60 Z„ I —volts/cm > 1 keV/cm B eq r

Since the ionization cross section decreases more rapidly then '^ l/v for energies t> 2£^ ; and maximum cross section ^ 10"16 cm, the ioniza#- tion rate is of order 1 ^"- ^ -T—• < n (av)' ; n_ dt g max since the time taken for the beam to pass a given point is ~ 10 nanosec breakdown occurs rapidly only if n ^ lOl' cm"^, Fronn these rough orders of magnitude arguments are seen that for n < iQl^, the beam will not pro­ duce enough ionization to be neutralized; while for n> 2- 10 ; p = 0. 06 torr collisional processes alone will produce enough ionization to neutralize the

150 beam a few centimeters from the beam head. At high densities > 10^^, this will be rapidly enhanced by field breakdown.

5. Effect of the Background on the Beam

The ionization cross section for further ionization of the beam par­ ticles is a slowly varying function of the degree of ionization, and is of order 10-1^-10"^^ for Z = 2-50 in U^. The mean free path for higher ionization is then — 1 /lO"^ ' n. For n < lOl*^ , Z changes only very sUghtly, but for n-^ 10^^ the charge rises to ~ 50 or more in a few tens of centimeters. This has the serious effect of multiplying the beam plasma frequency by a factor of 10, and making instabilities serious.

In addition to altering the degree of ionization in the beam, the back­ ground alters the beam propagation characteristics by neutralizing its charge and current. Once an electron density of ^ 10 n^ is produced, neu­ tralization occurs at a rate determined by the plasnna frequency:

= A/lrTTn" = 5, 6 • 10 ^/n~sec =^5,6*10 sec" for n = 10 P and at roughly the same rate, the electric current is neutralized; but, be­ cause of the plasma electron collisions, occurring with a frequency -6 - 3 /2 V = 5 • 10 n T , there is a resistivity and the plasma current channel " -3/2 expands out of the beam at a rate AR(z) == 0, 1 T^ '/z~, which depends on the electron temperature; hence, on the energy balance of the plasma. There is Sonne disagreement among groups as to the value of this tempera­ ture. It clearly depends on the beam radius, r, being greatest near the tar­ get. There seems, however, a general agreement that the increase in plas­ nna current does not exceed ^ 1%; hence that the uncompensated current is always ^ 1% of the unneutralized beam current; and is greatest near the back of the beam at the end of its flight. It also increases as the gas pressure is increased (above n^ lO-^")^ since the electron density is then large and the tennperature low. The net exposed current nnay, however, be as great as ^4000 amps since the charge may go up to 90. The corresponding nnagnetic field can reach values of ^ 4000 gauss near the target, A transverse mag­ netic field induces a radius of curvature in the beam particles of -^ r = (1,5- 106)/B (M/Z) and the deflection experienced by the beam particles is, where Lj-j is the distance over which the field acts

where B is in kg and L is the total flight path (= 10 m).

If charge separation occurs, electric fields may appear and these can

151 induce a deflection of the beam of order

Z /T ' ^''-°-lM<^keV/cm'- - \ o •7 where T is the fraction of the total flight time T = 10 sec, that the field acts. Thus fields of order B ^ 500 g and E > 1 keV/cm acting over the entire flight path are enough to deflect fully stripped ions; but if the ratio Z/M ^ 0, 01, the required fields are ~ 20 kg, 100 keV/cm, A magnetic self field of ^ 1000 gauss can effect a substantial deflection of the particles, but the geometry is such that the beam is self focused. This raises the pos­ sibility that the beam may be propagated at pressures above the small angle scattering linnit in a magnetically self focused mode. Some experiments vdth electron beams lend partial support to this possibility. Groups at Livermore, Maryland and N, R. L, have explored this possibility. The N. R. L, group points out that although magnetic confinennent occurs, it also defocuses the beam (unless B^ r), yielding a nninimum radius of ~ 1 cm, hence may not be adequate for targeting,

6, Beam Stability

In the low density case, in which the beam Z/M remains of order 1/50, the electric fields required to produce deflection are of order 50 kV/ cnn, acting throughout the whole path length, and the total charge on the beam does not produce a large enough field to deflect the beam.

In the high density case, on the other hand, the beam Z/M reaches a ~ 1/4-- 1/2, and the destabilizing effect of the charge goes at (Z/M)^, and unless the plasma screening is quite effective, the beam may be seriously deflected or defocused,

a) Macroscopic Modes

The most serious mode which can induce a large scale deflection of the beam is the "firehose" or "wriggle" mode whose origins can be most easily visualized by considering the self force on a cylinder of charge which is sinusoidally curved. It is then easily shown that the net force enhances the growth of the curvature which grows exponentially at a rate

^ =y%^(f)

where uJn = 4TTn„Z_.4l-; ^r, = l. 2 at M = 200 and F ^ 1. D B B M B r Since uUg depends on r which decreases linearly with time, it is readily shown that the amplification factor is

152 <-- -,Y„T o o 0. oo25yrz a = (200) fj

For Z =^ 1, or 2, this is modest even at the largest currents; however, for large Z (^ 50), the instability grows to saturation even in the low current case.

The presence of a plasma background means that the self interaction of the beam takes place in an environment with a dielectric coefficient

uu e = 1 - (U (uj - i v)

and in the plasma frame, O) = kV, If tw < uu , which is the case for k < 2TT /r,^, at least except very near the target, the self field is screened and this mode is stabilized by the plasma. Charge neutralization also inhibits its growth.

If the beam moves in a self-pinched mode, and the plasma is also magnetized these considerations become a good deal more connplex, but the present consensus is that the plasma background inhibits the growth of these firehose modes. The predictive record of plasma stability theory for such systems is, however, not very good, so only a modest confidence can be assigned to this conclusion,

b) Two Stream Modes

The electrostatic two stream mode in which small charge accumula­ tion produces a field which partly dams the flow, hence enhancing the charge accumulation, is a most familiar plasma instability and is driven by the beam. The growth rate in the simplest case is

,1/3 'OJ Y=yyy^B\uj Bl 2 2 4 f— where cUp is the plasma frequency, (u)p = 4TT ne /m)a.'p^ 5- 6- 10 Vn . This instability is quenched if the velocity spread in the beam is great enough. The requirement is 1/3 AY. 'UU 1/3 B' -3 ,1/3 4. 2 X 10 '2 uu where p is the gas pressure in torr multiplied by the degree of ionization

153 -3 {n_/n ). Since in the beam AV|| /V|| ^10 to avoid unacceptable chromatic aberration in the last lens, this is usually not satisfied. Collisions, on the other hand, drastically reduce the growth rate. If V> Y , the usual two stream mode is suppressed, however, it is replaced by a resistive mode growing at the rate 1/2 B / p Y = /I V

o % I y ,— Since uu N ^ 4, 5 • 10 TI l\fri (where the Coulonnb logarithm in the cross section has been taken as 4, corresponding to n = IQI', T^ = 2), 17 For n = 10 , Tg = 2, this ratio is — 4, y ^ 1. 4 uug , and the resistive two stream mode has a growth rate about 3 times that of the vacuum macro­ scopic mode. This is stabilized, again, by a spread in the parallel compo­ nent of velocity provided 1/2 1/2 ^B > A - 1.5. . ,0-^^ /i (!P) ID \ V / ^ ^/ P \ V / ^11 P

^ 5. lO' — for n= 10 , I = 5000 and r = 0. 1 cm . r

At these extreme conditions it is satisfied except near the end of the beam path (in the last 20 cm) where the instability has scarcely time to develop. The ratio scales as n"-^''*, however, and at densities of n < 10l6 (cm"3), pressures of 0. 1 torr, begins to become serious.

Even if the two stream mode does grow, it is not at all clear that it can have any great effect on the beam. The nonlinear theory of the small cold beam has been fairly well established both theoretically and experi­ mentally; and it indicates that at saturation the beam particles are subject X 2 to an acceleration of order —— v where X is the beam wavelength X V ^"^ "- ——= —, produced by a fluctuating field both growing and oscillating with a frequency of order y ^o that the maximum displacement is of order X , which for n= lO^" is of order 10"-^ cm. The radial defocusing, however, has not been evaluated, and only low confidence can be placed in this result. c) Filamentation

The instability that seems nnost important is a transverse mode, which leads to a current filannentation and to the appearance of substantial magnet­ ic fields. In the simplest case, neglecting beam spread in velocity and

154 plasma collisions, the growth rate is of order

V Y^ ^B- and for low Z is unimportant. At high Z, however, a more careful study is required. The most rapid growth rate in the simplest theory occurs if k|| = 0, in which case the instability is non-convective, and does not propa­ gate with the beam and the maximum growth time is ~ 10"^ sec, the time for the beam to pass a fixed point.

This has been studied by several groups, including one at Livermore and one at Maryland. The latter group has stressed the importance of the spread in transverse beam velocity, and of the plasma collision frequency. These effects are easily included for the simplest case of transverse modes growing in a "water bag" nnodel of the beann [i, e. , f(v) = const, for 1^1 I < vj^ I f = 0 elsewhere] , where the dispersion relation for the growth rate may be reduced to a simple cubic which has a positive real root pro- ^b '^ll % vided -. > 1, Since as the Marylandgroup observes — , is constant along "^1 ^i .4 "^1 . the beam, and =« 10 at the entrance, and oj. ^ 4. 10" here this re- quires k < 0. 75 cm ^, The corresponding value of the growth rate is in the simplest approxinnation

5. 10"^ vZ^ ^ 8. 10^ Z^

Since this is non-convective, it grows only as the beam passes a fixed point and yt ^ 8 X lO'-^ Z , and the instability is unimportant unless the beam is fully stripped when the growth becomes e^'^ "^ 670. If the plasma density is reduced, the temperature rises, v decreases and the growth drops slightly.

The Maryland group has done a careful analysis of this, using a Maxwellian model for the beam when the dispersion relation becomes trans­ cendental. They have used numerical computations of the plasma tempera­ ture and the ionization state of the beam, and conclude that this mode is un­ likely to be serious for background pressures above 1 torr.

The Livermore group observe that the instability depends on the dis­ tance along the beam, k|| > TT/I^, and that {n/i^)^^^ ~ 3 • 10^ sec exceeds the growth rate, hence concludes that longitudinal variation of the instability cannot be neglected, but that a simple Fourier analysis of this variation is inadequate, since unperturbed beam parameters vary on the same scale as

155 the perturbation. Their preliminary results are in essential agreement with those of the Maryland group.

7. Conclusions

These calculations suggest that there are two or possibly three pres­ sure regimes in which a beam could be propagated through the target cham­ ber and strike the target. Lf the pressure is less than 10"^ torr, the beam propagates without producing much ionization, so that the beam is unneutral­ ized and propagates as though in vacuum. Even if the background gas is preionized, the beam charge state remains low and plasma effects are un­ important. At pressures of between 1 and 5 torr, the beam is ionized to a high charge state, but neutralized by a background plasma. The most seri­ ous instabilities, however, are quenched by collisional effects again. The beam now neutralizes, propagates to the target. At pressures between lO'^ and 1 torr, the background gas can increase the degree of ionization of the beam, so that instability growth rate is enhanced, but the collision frequency is not great enough to stabilize the dangerous modes.

At pressures in excess of 10 torr, the background plasma remains fairly cool, and resistivity is high enough to cause a partial decay of the neutralizing current, and the beam may propagate in a self-pinched nnode. At the same time, the current is fairly low, and macroscopic modes are inhibited by the plasma. However, the stability analysis for the magnetized non-uniform beam plasma system is fairly complex and has not so far had a very good predictive record (although this is steadily improving). More­ over, in both the high pressure modes, the analysis relies on self consistent calculations of the beam and plasma properties. These calculations are sensitive to a large number of cross sections, and depend on the details of beam and background composition. They involve calculation of reaction rates, breakdown rates, of electric and magnetic fields, and of the two dimensional dynamics of both the beam and the plasma particles. Elaborate codes have been developed for the propagation of electron beams, but no published data gives one high confidence in the predictive capacity of these codes. The problem for ion beams is significantly simpler, however, but codes have yet to be tested against observation.

Most of the stability analysis has been directed toward locating stable regions of beam propagation; but little has been done in studying nonlinear saturation, and the effects of the plasma on the beam propagation. One may suspect that the inertia in the beann is so great that not much deflection occurs even in unstable regions. In this not completely satisfactory situa­ tion, experimental studies of closely related problems would be of great help. It is interesting to note that most of the beam transmission problems depend on current rather than energy, and that high current experiments at quite modest energies could be enlightening. In this connection the high cur­ rent experiments at Sandia are of particular interest. High currents have

156 been obtained, but the initial energy spread, and transverse velocity spread in the beam have not yet been described. At low energies, the range of the beam against small angle scattering limits the background densities at which propagation in the unpinched mode is possible. At higher energies (several lO's of MeV) and lower currents (tens of amps) the beam plasma frequency becomes small, and path lengths of several tens of meters are needed to get beam instability growth; however, the emissivity can be kept small and known, and useful experiments are possible. Plasmas in the appropriate density range can probably be produced independently of the beam, and while exact scaling is probably impossible, dependable computation codes and theories may be developed.

*Members of the Plasma Effects Workshop: R. Bangerter (LLL), D. Colombant (NRL), A. Drobot (NRL), G. Gammel (BNL), Z. Guiragossian (TRW), R. Hubbard (U, Md. ), S, Humphries (SLA), D. Johnson (SLA), R. Johnson (KMS), T, Kammash (U. Mich.), C. Kim (LBL), E. Lindman (LASL), G. Magelssen (ANL), T. Mochizuki (Osaka), D. Nicholas (RHEL), W. Thompson (U. Calif.), D. Tidman (U. Md.), and S, Yu (LLL)

157 158 V. REPORT OF THE REFERENCE DESIGN COMMITTEE

REPORT OF THE REFERENCE DESIGN COMMITTEE

Lee C, Teng (Chairman), David L. Judd, Frederick E. Mills, David F, Sutter

INTRODUCTION

Many months ago it was anticipated that the work at the Argonne Nation­ al Laboratory, the Brookhaven National Laboratory and the Lawrence Berkeley Laboratory would lead to development of several preliminary but reasonably complete conceptual designs (including cost estimates) for heavy-ion ignition systems to be presented, evaluated, compared, and perhaps improved at this Workshop. The Workshop organizers made plans for creating this Committee to lead in conducting evaluations and comparisons of these so-called "ref­ erence designs". In this report we begin with a brief description of the four designs considered, followed and augmented by functional sketches of these systems in which most of the important parameters are indicated. More details on the reference designs and our technical evaluations are presented in the next section, first by component systems and then in a tabular form to facilitate comparison. Finally, in the concluding section we present our evaluations and comments. Also included in the Conclusions are our recom­ mendation for the future program and some general observations unrelated to the specific designs. We worked under several constraints the most severe being the small amount of time available at the Workshop. The reference designs presented are not sufficiently complete in details, nor are they optimized with regard to cost or technology. Furthermore, they do not all address a common regime of performance. In spite of these handicaps it was possible to collect a substantial amount of information, to make some evaluations and comparisons, and finally to draw some conclusions,

BRIEF DESCRIPTIONS OF THE REFERENCE DESIGNS

Four designs were studied, and are identified as BNL, HF2, HF3, and LBL in this report. BNL. This design is described in Brookhaven National Laboratory Report BNL 50817 UC-21, dated March 13, 1978 entitled "Conceptual Design of a Heavy Ion Fusion Energy Center", by A. W, Maschke. The main accelerator is a sequence of 3 Alvarez rf linacs operating at 48 MHz, 96 MHz, and 192 MHz, and producing 160 mA of U"*"^ at 20 GeV. ^^ The injector begins with eight conventional ion sources producing U ions which are accelerated to 6 MeV by 2-MHz Widerbe linacs. The eight beams are stripped to U and further accelerated by two WiderSe linac stages while merging in three binary steps (funnel loading) to a single beam of 160 mA at 30 MeV for injection into the main linac. Following the linac, current multiplication by a factor of 100 is provided by successive 10-turn injections into a large multiplier ring and a small one. The small

159 ring successively charges eight accumulator rings. Additional compression by a factor of 150 occurs in the accumulator rings and during transport. The eight beams are transported to the target in two bundles, delivering 10 MJ at a peak power of 200 TW. HF2. This design was prepared shortly before the Workshop at the Argonne National Laboratory and is described in an informal paper dated September 18, 1978 and titled "HEARTHFIRE Reference Concept No.2. Outline: An RF Linear Accelerator System", by R. Arnold, R, Burke, M, Foss, T. Khoe and R. L. Martin. Its main accelerator is a sequence of 2 Alvarez linacs at 100 MHz and 200 MHz, producing 120 mA of Hg"*"^ at 20 GeV. The injector starts with two Hg''"-'- ion sources and 12.5 MHz Widertte linacs accelerating the ions to an energy between 10 and 20 MeV appropriate for stripping to Hg"*"", The beams are combined and further accelerated by a 20 MHz Wideroe linac to 160 MeV for injection into the main Alvarez linac system. Current multiplication by a factor of 256 (with assumed 25% loss) following the linac is achieved in a system of delay-stacking hairpins and rings which feeds eighteen "compression rings" with harmonic number h=22. Following debunching/rebunching at h= 1 and extraction, the 18 separate beams pass through external linear-induction compressors and are reinjected back into the compression rings. A 74-fold compression of the beams occurs in the rings and en route to the target where they deliver 1 MJ at 160 TW. HF3. This design is described in Argonne National Laboratory's Accelerator Report ACC-6, dated June 16, 1978 and titled "HEARTHFIRE Reference Concept No. 3; A Rapid Cycling Synchrotron System", by the same authors listed above for HF2. The main accelerator consists of eight rapid-cycling synchrotrons, fed from a linac injector system similar to that of HF2. A single step merging from two sources and 12.5 MHz Wideroe linacs is used; stripping is from Xe+l to Xe"*"^ at 11 MeV. Following this, two more linac stages provide 30 mA at 4.4 GeV for 3x3 turn injection sequentially into the eight synchrotrons. These synchrotrons operate at h= 80 and accel­ erate the beams to 20 GeV. The accelerated beams are brought successively to a debunch/rebunch ring (h = 80 to h = 2) and thence to sixteen compressor rings in which an additional debunch-rebunch (h= 32 to h = 1 or 2) and a 65-fold compression take place. The beams are extracted as 24 segments with two different lengths which when striking the target provide a rough simu­ lation of pulse shaping and deliver 1 MJ at 100 TW peak, LBL. This design is discussed in Report HIFAN-58, dated September 6, 1978, by the staff of the heavy ion fusion group at the Lawrence Berkeley Labora­ tory, entitled "Linear Induction Accelerator Conceptual Design". The design has evolved from an earlier preliminary example with somewhat dif­ ferent parameters (described in HIFAN-54, dated December 12, 1977) for which a preliminary cost estimate was included in the group's Half Year Report (LBL-7591). This is a single pass, straight through system without accumulator or bunching rings. The main accelerator is an induction linac which is made up of sections of induction modules of different types. The beam is accel­ erated and compressed simultaneously by the induction modules. The injector has a novel design. A A Amp U**" beam is provided by a large-aperture surface ionization source and accelerated by a section of three long-pulsed drift tubes. The ions are stripped to U"*"^ coming out of the second drift tube at 5 MeV and further accelerated to 13 MeV by the

160 third drift tube. The drift tubes are followed by a low-velocity stage of low voltage induction modules. At 200 MeV and 60 A the ion bunch enters the main linac. There it is accelerated first by induction modules with iron cores to 8 GeV and 800 A, and then by modules with ferritic glass cores to the final energy of 19 GeV and current of 1600 A. A rapid-bunching section provides final compression, and the beam is split transversely (4x4) into sixteen beamlets of 2.1 kA each on target, delivering 1 MJ at 160 TW.

DESCRIPTION AND TECHNICAL EVALUATION BY COMPONENT SYSTEMS

In evaluating the component systems of the reference designs the only systematic rating we used is the "confidence level". This reflects primar­ ily the degree of extrapolation from present experience needed to arrive at the desired level of performance. This measure of confidence, based on familiarity, can change radically with time as new experiences are gained. In some cases questions of inadequate design or expected technical diffi­ culties have also contributed to such ratings; in other cases these questions are tabulated as comments. Some important overall features such as estimated costs, are discussed in the next section on Conclusion.

CONCLUSIONS

Perhaps the most significant conclusion we reached confirms a consensus clearly emerging from this Workshop that the synchrotron main driver option (represented here by the HF3 design) has become less promising. The reasons are not difficult to discern. First, the originally-perceived potential cost advantage has diminished. It is important to recall that two years ago ion energies up to 100 GeV were considered, but since then a more realistic evaluation of target requirements has focused attention on energies of order 20 GeV and correspondingly higher beam currents. The synchrotron space charge limit occurs at injection. Higher beam current requires higher injector linac energies. Thus the energy range for synchrotron acceleration has diminished from both ends, leaving too small a range to provide a cost advantage. Second, early hopes of finding a special ion of significantly lower charge exchange cross section are fading, largely as a result of the work of a few atomic physicists who have been able to place rather general bounds on the cross sections. Third, the difficult vacuum require­ ment remains at the border of technical feasibility. Finally, the well- known repetition rate limitations of synchrotrons appear to prevent the design of an economically or technically viable driver for power plant applications. We consider this narrowing of the driver options an important contri­ bution to the heavy ion fusion program. A great deal of manpower has been devoted first to classifying and parametrizing, and then to evaluating and comparing the large range of possible and distinctly different accelerator systems. This effort was spent with precisely the expectation that one might be able to find some unequivocal preference for some systems over some others. This has now materialized. One important general property of a complete driver system, derived from the separate features of all its components, is the factor by which it can accommodate unwanted but inevitable phase space dilutions of the beam and still satisfy all target requirements. Estimates of the available six-dimensional phase space dilution factors are:

161 Available Dilution Factor

BNL HF2 HF3 LBL 9F 4F IF ?

Here F is a factor (estimated not to exceed 5) by which the chromatic aberration of the final beam transport-lines could be reduced by the use of sextupole magnets. Further studies of ion dynamics in the induction linac are needed to provide an estimate for the LBL design. The amount of dilution one should expect is more difficult to estimate, even for the relatively familiar operations such as multi-turn injection, and becomes rather uncer­ tain for as yet untried procedures such as synchronous capture and adiabatic debunching of an rf linac beam in a ring. However, in general more dilution is expected for a greater number and complexity of beam manipulations. None of the designs appears excessively generous in this respect, but in particu­ lar the HF3 design is submarginal. For this reason and because of its complexity we assign to this design a low level of confidence. Another overall system parameter is cost. The report of the Workshop's cost estimate group appears elsewhere in the Proceedings; we have rounded their estimates to indicate our feeling of the uncertainties.

Cost (10^$)

BNL HF2 HF3 LBL 1 1/4 1/2 ? 1/2

Waning interest in the synchrotron option led the estimators to focus their attention on the linac designs. From these rough figures two conclusions may be drawn: 1) The capital cost per pulse energy (or cost per average beam power, since linac repetion rates are comparable) decreases with increasing pulse energy, the 10 MJ BNL design being much less than ten times as costly as the 1 MJ designs. 2) The rf and the induction linacs appear to be comparable in cost. The main driver options we consider viable are the rf and induction linacs. The BNL and HF2 rf linac designs cannot be compared directly because of differing performance goals. Several other differences, such as choice of ion and charge state and of the schemes proposed for combining beams, arise primarily from the absence of sufficient studies to determine optimum parameters and configurations and the sensitivities to departures from them. Differences of this character can be resolved, we believe, by more detailed analyses and optimizations. The induction linac has many attractive promises, simplicity being the most striking. It may in time emerge as a strong contender, but its capability as a heavy ion accelerator needs to be demonstrated. Until some experimental demonstration is made we believe it should be assigned a low confidence level. These conclusions may be summarized as follows:

162 COMPONENT DESCRIPTIONS, EVALUATIONS,AND COMMENTS

(Encircled numbers are numbers of parallel units)

DLSIGN BNL HF2 HF5 LBL

ION SUURCE U* ; plasma Hg , plasma Xe^ , plasma U1* 1 , surface ionizat ion 40 mA (20 mA captured) 50 mA (40 mA captured) 20 mA (10 mA captured) 4 A - 2 mA/cra^x2000 cm^ E -O.OZ cm mrad £ -0.01 cm mrad £ -0.02 cm mrad RL SOO keV 1.5 MeV 1.5 MeV 40 usee

Evaluation High confidence Fairly high confidence High confidence Low confidence, should be demonstrated. Comments 40 mA captured may be too high; if 20 mA Surface contamination? use four sources Emittance?

LOW VELOCITY Wideroe linac Wideroe linac Wideroe linac Pulsed drift tube ACCELLRATOR (8)2 MHz to 6 MeV (2)12.5 MHz to 10-20 MeV (7)12.5 MHz to 11 MeV crt (2 MeVl 5 0 m ,. ,, ,,; strip to U*'^(50i) strip to Hg*^C20*) strip to Xe**(20*) 70 m *'' "^^^ '" •" (S MeVl (4)4 MHz to 13 MeV (1)25 MHz to 160 MeV ©^5 MHz to 160 MeV strip to U** (37.St) (2)8 flMz to 30 MeV '"" ""(13 MeVJ Electrostatic focusing Magnetic focusing Magnetic focusing Low voltage modules 160 mA (^dilution - 2x2) 128 raA 30 mA (200 MeV)

LvaIllation Fairly high confidence High confidence High confidence Low conf idence ,. should be demonstrated, Conments Bunch combination and Bunch combination and Bunch combination and matcning aitficuli matcning uifficult. iiiatcliiiig uifficult. Cuulti neutral iZdLiuii Emittance growth during Emittance growth? Emittance growth? be used to help? stripping? 30 MeV too low to start Alvarez section. TraTiiition from 8 MHz to 4a Mil; difficult. LBL UNL MF5

Alvarez 1inac Induct ion 1inac HIGH VELOCITY Alvarez linac Alvarez linac ACChl.LHATOk 48 MHz to 120 MeV 100 MHz to 4.4 GeV 100 MHz to 4.4 GeV/0.5S GV Fe cores to 9b MHz to 480 MeV 200 MHz to 20 GeV/2.5 GV 8 GeV, 300 nsec 196 MHz to 20 GeV/10 GV Fe glass cores to 160 mA 128 mA 30 mA 19 GeV, 150 nsec e -0.6 cm mrad e -O . 16 cm mrad e -0.1 cm mrad ni- nj- 1600 A (j. dilut ion = 6) (j^synchrotrons (60 Hz) e .~3 cm mrad 3x3 turn injection (^dilution = 3x3) to 20 GeV h = 80, 6x10 ion/pulse

Mid-confidence, should Evaluation High confidence High confidence Fairly high confidence except for charge be demonstrated. exchange lifetime. 4> Compression during Coiiiinonts Matching difficult, Matching difficult 3x3 turn injection difficult acceleration needs especially 8 to 43 MHz. demonstrat ion. Velocity too low in la MHz soiJt iun , should be Wideroe.

1 debunch-rebunch ring Not needed MULTII'LILK- (?)Multiplier Rings 7 + 4/2 delay stacking h = 80 to h = 2 SlACki:R- (R = ! km, 10 turn bypasses and rinys 2 turn injection yU\Clli:k liori zoiital injection, (4x4 horiz.)x(lx4 vert .) turns, h = 22 ^ \i = lOli m. 10 turn vort ical injection) (i di lut ion = 1.5 // di lut ion = 2)

Mid -confidence Evaluation ligh confidence Low confidence Beam manipulation Beam manipulation Not needed Comments difficult difficult' BNL HF2 HF3 LBL

COMPRESSOR ©Compressor rings (18) storage rings (j^ compressor rings Ferrite-core pulse- Compression 30x in return injection 16 pulse injection gap compressor, ring, Sx in transport Debunch-rebunch, h = 22 from debunch-rebunch ±1 MV/m gradient 10 MV/turn, 20-40 turns to h = 1 ring, then debunch- 150 nsec in, External induction pulse- rebunch , h = 32 to 30 nsec out. line compressors 74x h = 1 or 2 7 nsec on target Compress 55x with sawtooth rf (total ^dilution = 3x3, // dilution = 1)

Evaluation Mid-confidence Low confidence Low confidence Higli confidence

Comments Large (150x) com­ Nine beams simultaneously Beam maniuplation at pression with space thru one compressor injection, with charge must be difficult 25 nsec kicker rise studied Large C74x) compression time, difficult with space charge must Sawtooth rf difficult be studied Many debunch-rebunch operations cause large // dilution Tune shift Av too large at maximum compression

TRANSPORT (8J2.5 kA each (fs) 3.5 kA each (2^ 2.6 kA each 16) 2.1 kA each Ap/p -SxlO"^ Ap/p -3.5x10"* Ap/p -2.5x10'^ £ ,-2.8 cm mrad E -0.7 cm mrad E -3 cm mrad e .-2.1 cm mrad nj_ ni. nJ- nX Panofsky quadrupole Panofsky quad matrix Panofsky quad matrix Panofsky current- matrix sheet quadrupole matrix, armored ablator guard on splitters

Fairly high confidence Evaluation High confidence High confidence High confidence Overall Evaluation

BNL HF2 HF3 LBL Accelerator High High Moderate Low for ions (High for Electrons) Beam manipula.tion s Moderat: e Fairly Low Low Fairly high

Total system Fairly high Moderate Low Moderate, needs demon­ stration

Recommendation:

We recommend that effort be concentrated on a two-prong program. On the one hand we should fill in as much detail as possible on the design of optimized rf linac driver systems to provide a realistic evaluation of per­ formance and a trustworthy estimate of cost. On the other hand we should pursue vigorously a program of research and development leading to qualifi­ cation of the induction linac driver as an alternative with potentially better performance.

General Observations:

The overall progress of the heavy ion fusion program since its formal start at the 1976 Summer Study is quite satisfactory when one takes into account the small total program budget during the eighteen months it has been funded. Many of the tasks stated or implied at the outset show sig­ nificant levels of accomplishment. Significant among these is the reduction, through design studies and physics research, of the main driver options from three to two. The importance of this achievement has been mentioned above. Encouraging progress is evident in many areas where investments have been made in prototype research and development or in theoretical and com­ putational studies. As examples we list the following: 1. Conventional ion sources of relevant ion species are now producing currents in the 30-60 mA range with good measured emittances. 2. A surface ionization source has yielded O.A A of Cs"*"-*- ions. 3. Prototype low-velocity accelerating structures, of both Widerbe and pulsed long drift tube types, are being studied and developed. 4. Good agreement is emerging between the results of analytic and computer simulation studies of high current beam transport limits. 5. Analytical and computational studies of ion-ion charge exchange and other charge-changing cross sections have yielded important results. 6. There have been significant advances in understanding limitations of final focusing systems and techniques for optimal lens design. 7. Phenomena affecting beam propagation within the reactor environment and possible regimes for proper beam transport have received detailed study.

166 iir i -rtiNij . 1 MJ, 160 TW, RF linac base

+ 1 Conventional Sources (2)—• 5 0 mA, Hg (2512.5 MHz WiderKe 40 mA, 10-20 MeV Linacs It strip to Ha'^S, 20% eff, 2 5 MHz 128 mA, 160 MeV

100 MHz

Alvarez 128 mA, 4.4 GeV Linacs

2 00 MHz

128 mA, 2 0 GeV Debuncher, -^ x ^oT Delay-Stackinj: -r stacking multiplication Hairpins 5 Rings (4x4)x(4x4) = 256, 75% eff, h = 22 H V

24 A

Compressed 2x74x, 3.5 kA debunch/rebunch h = 22 -»- 1' CoTTipression Rings 5 Cavities

Beams on Target (18) total current on target 63 kA total power ^^^x20 GeV = 160 TW

167 FUNCTIONAL SKETCHES OF REFERENCE SYSTEMS (Numbers in parentheses are numbers of parallel units) BNL; 10 MJ, 200 TW, RF linac base

Conventional Sources(31 40 mA, U""-^ (8) 2 MHz 20 nA, 6 MeV Wideroe strin to W^ ^ 505 eff, Linacs (4) 4 MHz 4 0 mA, 13 MeV (2) 8 MHz 8 0 mA, 3 0 MeV

160 mA, 120 MeV

Alvarez Linacs 160 mA, 480 MeV 192 MHz

160 mA, 2 0 GeV

10 turn H inj., 1.6 A Multiplier Rings

interchange H 4 V

R = 100 mO 10 turn H inj., 16 A

Accumulator Rings (8) R = 100 m q- compressed 30x, 500 A Beams on Target (8) compressed 5x, 2500 A

€v^ total current on tar.qet20k\ total power iP^Mx2nneV

= 2 00 TW

168 HF3-ANL: 1 MJ, 100 TW, synchrotron base

Conventional Sources (2) 2 0 mA, Xe+ 1 _ (2) 12.5 MHz Wideroe 10 mA, 11 MeV Linacs 2 5 MHz strip to Xe+8, 20% eff. 30 mA, 160 MeV

Alvarez Linac, 100 MHz

30 mA, 4.4 GeV

Synchrotron, (8) 3x3 turn inj., h = 80 60 Hz 0.6x10-^^ ion/pulse

20 GeV

Rebuncher 1 2 Ring 2 turn inj., 1.2x10 ion/pulse debunch/rebunch h = 80 -• 2

Compressor 16 pulses inj., 2x10 ion/ring Rings (16) debunch/rebunch h = 32 ^ 1 or 2 compressed 65x

Beams on total energy on target Target (24) 16x2xl0-^-^x20 GeV = 6. 4xl0-'-^GeV = 1 MJ

169 LBL: 1 MJ, 160 TW, induction linac base

Surface Ionizatioat ionn —*HLrf- U""-^ , 2 MeV, 4 A, 40 ys Source 4 McV Pulsed Drift Tubes 5 McV, strip to U"^"^ , 6 A, 3/8 eff

13 McV Low Voltage Induction Cavities 200 MeV, 60 A, 4 ys

0.8 reV Fe-Core Induction Cavities 2 GeV

GeV, 800 A, 300 ns

Ferritic Glass Core Induction Cavities

19 GeV, 1600 A, 150 ns Buncher, ±1 MV/m 19 GeV, 8 kA, 30 ns Beam Splitter split 4x4 = 16

Beams on Target (16) ®-^--^ total current on target 34 kA, 7 ns total power 11^^x19 GeV = 160 TW

170 VI. CONTRIBUTED PAPERS A. ATOMIC AND MOLECULAR CROSS SECTIONS

CHARGE CHANGING CROSS SECTIONS FOR Cs"*" + Cs"*" COLLISIONS

R. E, Olson Molecular Physics Laboratory SRI International, Menlo Park, CA 94025

In the heavy ion inertial fusion program, interest has centered on the use of accelerated Cs ions to compress the deuterium pellet and induce fusion. Various accelerator scenarios have been proposed which are based on the use of linac or synchrotron accelerators or combinations thereof. However, because of the long confinement time of the ion beam in a synchrotron ('^ 0.5 sec), there is concern that internal collisions within the beam which change the ion charge state will give rise to an unacceptable loss of beam intensity. The energy of these internal collisions is on the order of 100 keV and charge -16 2 changing cross sections larger than 10 cm will be deleterious to the synchrotron approach. We have therefore begun an investigation of Cs + Cs collision processes in order to estimate the needed cross sections. Our first step was to cal-

1,1 culate the relevant potential curves for the Cs systems. We have employed the SCF method with a single zeta basis set of Slater orbitals for the Cs core electrons and a double zeta basis for the 6s/6p states. Collision spectros- 2 3 copy studies on the heavy symmetric rare gas systems ' (same outer electron configurations as Cs ) indicate that the inelastic collision processes in Cs can be understood after two potential curves are calculated. These potentials correspond to the X £ ground state with the configuration (core) 2 2 4 4 2^2 1 5sc 5sa 5pn 5pll 5pa 5pa and a £„ state arising from the doubly g UfiUEU S 2 2 442 2 excited state configuration (core) 5sa 5sa 5pn 5pn 5pa 6sa , A gu'^g^ugg

171 pseudo-curve crossing between the two molecular states lies low on the repulsive wall of Cs and is due to the promotion of the 5pa orbital to the highly excited 7f united atom limit while the 6sa orbital correlates to the low lying 6s united atom state.

Our preliminary calculations yield a pseudo-curve crossing between the above molecular states at R - 3.5 a with an energy threshold of only 45 eV.

Related studies on the rare gases indicate there is almost unit probability for inelastic transitions in collisions with impact parameters less than R .

Therefore, the cross section for inelastic loss will be given by 2 . ,^-15 2 a = TTR w 1 X 10 cm . X The difficulty now arises as to determining the branching ratio between charge changing inelastic products and those products where one or both of the ions is left in a harmless excited electronic state. At the first avoided crossing, these products correspond to +* 2 + -H- + - Cs (6s ) + Cs -+ Cs + Cs + e (la) Cs +Cs -» {Cs^ (5pa 6sa )} 2 g g Cs"'"*(6s) + CS'^*(6s) (lb)

Secondary reactions will also yield Cs + Cs charge transfer products via a second interaction with the doubly excited molecular states on the outward portion of the collision trajectory. Experimental measurements of the ionization cross sections in the similar U -16 Ne + Ne and Ar + Ar rare gas systems yield cross sections in the 2-4x10 2 + cm range at an equivalent Cs energy of 100 keV, implying the branching to charge changing products will be approximately 407o of the inelastic products. This branching ratio is consistent with differential cross section ionization 3 measurements on the Ar + Ar system. This large ratio indicates the impor­ tance of higher lying double excited molecular states that would yield auto- ionizing Cs (5s 5p 6s nX) and Cs (5s 5p ni) products. Therefore, by combining the information gained from our potential curve calculations with an interpretation of ionization in rare gas-rare gas collisions, we conclude a good factor of two estimate for the Cs + Cs charge 172 changing cross section at 100 keV is

,«-16 2 a = 4 X 10 cm , (2) cc ^ •'

This cross section will primarily be the sum of the cross sections for the reactions

Cs + Cs + e (3a) Cs + Cs »-» Cs"^ + Cs"^ + e . (3b)

The charge transfer cross section for the reaction

+ + I I Cs + Cs - Cs + Cs (4)

is a two-step process and will be smaller than that of the simple ionization process discussed above. Also, our calculations of the orbital energies of the promoted Tfff orbital indicate a diabatic crossing into the continuum for double electron ejection at R «* 1.9 a , Thus, other secondary reactions will o be Cs + Cs + 2e (5a) C^s + + C^s + Cs"*" + Cs"^^ + 2e . (5b)

In conclusion, our studies indicate that the charge changing cross section for Cs + Cs collisions will be primarily due to simple one electron ionization. Reaction (3), not charge transfer as assumed previously. The molecular process responsible for the ionization is the promotion of the 7fa orbital arising from the 5pa state of the reactants which leads to transitions to doubly excited product states. The charge changing cross section is esti- — 16 9 mated to be 4 x 10 cm at 100 keV (this estimate is expected to be accurate to a factor of two), and will increase with increasing collision energy.

* Work supported by Department of Energy Contract No. EY-76-C-03-0115, P/A No. 137,

173 References 1. R. E, Olson and B, Liu (to be published). 2. J, C. Brenot, D. Dhuicq, J, P. Gauyacq, J. Pommier, V. Sidis, M. Barat, and E, Pollack, Phys. Rev. A JJ,, 1245 (1975). 3. F, J. Eriksen, S, M. Fernandez, A, B. Bray, and E. Pollack, Phys. Rev. A il, 1239 (1975). 4. V. V. Afrosimov, R. N. Il*in, V. A, Oparin, E,S. Solov'ev, and N. V, Fedorenko, Sov. Phys.-JETP 14, 747 (1962).

174 ATOMIC CROSS SECTIONS FOR FAST Xe*^"*" AND U*^"*" IONS COLLIDING WITH ATOMS AND MOLECULES*

George H. Gillespie Physical Dynamics, Inc.

Kwok-tsang Cheng and Yong-Kl Kim Argonne National Laboratory

Introduction

During the workshop a number of high-velocity atomic cross sections were calculated for collision processes involving Xenon and Uranium ions incident on atoms and molecules. The goal was to provide additional atomic data relevant to the establishment of vacuum requirements and for the study of beam-plasma interactions in the reactor chamber. The results obtained significantly expand the available data base from that previously reported ». Ions considered included 13 charge states of Xe (q = 1-6, 8, 18, 36, 44, 50, 52, 53) and 9 charge states of U*^ (q = 1, 2, 4, 6, 8, 10, 20, 52, 82); 8 targets were included in the calculations (H2, Li, C, N, 0, Ne, Ar, Kr). This paper summarizes only a portion of these results which appear to be the most relevant; detailed results for any of the ion-atom combinations may be obtained from the authors.

The method employed for the cross section calculations utilizes sum- rules within the context of the Born approximation^. Relativistic Hartree- Fock wave functions are used for the heavy ion (or target atom) and the results are expected to be reliable for sufficiently high velocities (3 = v/c > 0.2). The cross sections obtained in this approach are those for total inelastic scattering and thus provide rigorous upper bounds to the cross sections for electron stripping from the ion, or for ionization of the gas atoms in'a reactor chamber. As will be discussed in more de­ tail later, most of these upper-bound cross sections are expected to pro­ vide a reasonable estimate of the actual cross sections desired for the applications considered here.

Cross Sections For Vacuum Requirements

Of primary concern for establishing the minimum vacuum requirements for synchrotrons or storage/accumulator rings are the cross sections for the loss of one or more electrons from fast ions passing through the back­ ground gases present in these devices. These cross sections have received the most attention in the previous workshops^ and those results have gen­ erally been sufficient for estimating the vacuum requirements for the reference designs examined at this meeting. In Fig. 1 we summarize the

175 upper-bound cross sections for this process for Xe and U incident on H2 and N2 gases. We have plotted the product 3^o (versus q) since this combination is independent of 3 at high velocity. As expected from the previous work these upper-bound electron-stripping cross sections for low q decrease slowly as one increases q. These low-q ions are of primary interest in the accelerator and, within a factor of 2 or 3, the cross sections are all essentially the same for a particular gas (for ion masses greater than 100 AMU and q < 10). The present theoretical understanding indicates that these low-q upper-bound cross sections are unlikely to be more than a factor of 2 above electron-stripping cross sections, and even for very high q are no more than a factor of 4 too high . There is, of course, no direct experimental data for heavy, low-q ions in this velocity range, although the Born approximation and experiment are in accord for lighter ions carrying only a few electrons .

While electron-stripping cross sections essentially establish the minimum vacuum necessary for a desired beam lifetime, the ionization of the residual gas by the beam can also have adverse effects which may re­ quire a higher vacuum. This phenomenon was the origin of some vacuum prob­ lems in the proton ISR, but only a preliminary analysis of this potential problem has been attempted for the HIF application . Upper-bound cross sections for the ionization of a gas atom or molecule may also be obtained using the sum-rule approach, and results for Xe and U ions incident on H2 and N2 are shown in Fig. 2. For this type of cross section we have independent checks on our calculations, since for large q the cross sections must approach q times the corresponding Bethe cross sections for inelastic scattering of fast electrons by these gases. In Fig. 2 we have also shown these Bethe cross sections as calculated by Liu^ (for H2) and Inokuti ^ aJ^ (for N2 assuming a(N2) ~ 2a(N)). Our results are in good agreement with that work for q > 20. It should also be mentioned that the Bethe cross sections are no more than a factor of 2 above the experimentally observed cross sections for the ionization of these gases by electron impact in a relevant velocit> regime (3^ = 0.30 to 0.97)®. This agree­ ment with experimentally established limits provides some confidence in the methods used to calculate these cross sections. However it must be emphasized again that there is no direct experimental confirmation of these results for heavy, low-charge state ions in an appropriate velocity range. As a final comment in this section we note that the quantity ^^0 given in Fig. 2 is not strictly energy independent (as it is for the cross sections given in Fig. 1), but has a weak logarithmic dependence on 3^, and the results given were calculated for 3^ = 0.2. However, for 3^ between 0.1 and 0.4 corrections for the logarithmic term are at the few percent level.

Cross Sections for Reactor Chamber Studies

A number of problems associated with the propagation of an intense ion beam through a gas/plasma require atomic data input for their analysis. Most of the data required, in order to determine the charge states of the ions as well as the temperature and conductivity of the plasma, are consid­ erably more detailed than the sum-rule cross sections calculated here can provide. Nevertheless, such cross sections provide a strong (upper-bound) constraint on more detailed calculations^, and also provide information with regard to systematic variations such as the charge-state dependence

176 of cros| sections. In Figs. 3 and 4 we show the results of our calculations for Xe^ and U^ ions incident on Li and Ne, two atoms of potential interest in the reactor chamber.

The upper-bound cross sections for the stripping of electrons from the ions (Fig. 3) are quite similar to the results shown in Fig. 1 for Hz and N2 targets: a slow variation with respect to q for low charge states, but a rapid decrease for high q reflecting the tight binding energies of the last few electrons. The cross sections shown in Fig. 4, which provide upper bounds to the cross sections for the ionization of Li and Ne, are also simi­ lar to the corresponding H2 and N2 results of Fig. 2. However, an interest­ ing cross over in the relative magnitudes of the Li and Ne cross sections occurs in the region of q between 4 and 6. At low q the total inelastic cross section for Ne is considerably higher (factor of 5 at q = 1) than the corresponding Li cross section. At large q the cross sections again approach the Bethe theory results of Inokuti et al^ for these atoms. It is well-known in this case that Li has the largest cross section of any atom between H and Ne due to its loosely-bound outer electron, and at 3 = 0.2 the Li cross section is about 4 times that of Ne. Experimentally, the cross section for ionization of Ne by electrons^ at high 3 is within 20% of the theoretical upper bound. This is about what one expects theoretically^»^^ for Ne. For Li, however, the actual ionization cross section is an order of magnitude lower than the upper bounds given in Fig. 4. There is a large contribution ('^ 90%) to the total inelastic scattering cross section from discrete ex­ citations of the Li, which do not lead to ionization. This discussion indi­ cates the need for a more detailed analysis of the collision processes, particularly for alkali atoms such as Li.

Summary

The atomic cross sections presented here as upper bounds on the electa ron-stripping cross sections for fast ions of Xe and U [Figs. 1 and 3] should be sufficient for estimating vacuum requirements in circular devices (3 > 0.2) and provide some guidance in determining the charge-state of an ion beam in a reactor chamber containing some gas (or plasma).. We believe these upper bounds may be a factor of 2 above the electron-stripping cross sections for the lower charge states, and a factor of 4 larger for the very high charge states. The cross sections given as upper bounds to those for the ionization of atoms or molecules [Figs. 2 and 4] are also expected to be approximately a factor of 2 high, except for the case of Li targets, where the cross sections in Fig. 4 could be as much as a factor of 10 too high. Finally we note that the sum-rule formalism utilized for these cross sections also forms the basis for a fundamental calculation of the energy loss of partially stripped ions^^. This is an additional piece of information re­ quired for reactor chamber studies where it is difficult to extrapolate from known data since the ions do not have time to reach their equilibrium charge state in the gas or plasma.

References

1. Proceedings of the Heavy Ion Fusion Workshop held at Brookhaven Nat­ ional Laboratory, Upton, New York, 17-21 October, 1977; Report No. BNL- 50769; see especially section V-A.

177 2. G. H. Gillespie. Y.-K. Kim, and K. T. Cheng, Phys. Rev. A37, 1284 (1978),

3. G. H. Gillespie, to be published, Phys. Rev. A.

4. See, for example, Ref. 2 above and work cited therein; also J. Alonso, R. Force, M. Tekawa and H. Grunder, IEEE Trans. Nucl. Sci. NS-24, 1015 (1977). [Both the theoretical (see Refs. 1 or 3) and experimental numbers (J. Alonso, personal communication) have undergone some cor­ rections (< factor of 2) from the preliminary results given in this reference, but the agreement between theory and experiment is still quite satisfactory.]

5. D. Blechschmidt and H. J. Halama, p. 136 of Ref. 1.

6. J. W. Liu, Phys. Rev. AT^, 103 (1973).

7. M. Inokuti, R. P. Saxon and J. L. Dehmer, Int. J. Radiat. Phys. Chem. 1_, 109 (1975).

8. F. F. Rieke and W. Prepejchal, Phys. Rev. A^, 1507 (1972).

9. S. S. Yu, page 50 of Ref. 1.

10. R. P. Saxon, Phys. Rev. A8^, 839 (1973).

11. Y.-K. Kim, in preparation.

This work was partly supported by the U.S. Department of Energy.

178 I I I 11 III

c a + X

tio n X 0o) c C/) o c o 0) "D u^ "o c ^10 cn a C Q. o '*->w ^— CO + c C3T o •a ^ c _a) CD UJ + c c0r) o X Ul ^ •D o C 1^- 3 o CQ 10" & a 3

Fig. 1. Sum-rule cross sections (times 3^) which provide upper bounds to electron-stripping cross sections for Xe*^ and U^ ions incident on H2 and N2. Circles are the results of explicit calculations for selected charge states, connecting lines are simply smooth curves drawn through those points.

179 Fig. 2. Sum-rule cross sections (times 3 ) which provide upper bounds to the cross sections for the ionization of H2 and N2 by the impact of fast Xe^ or U*^ ions, evaluated at 3^ = 0.2. Circles are the results of explicit calculations for selected charge states, connecting lines are simply smooth curves drawn through those points. Also shown are the Bethe cross sections for bare inci­ dent ions on H2 (Ref. 6) and N2 (2xN results of Ref. 7), which are proportional to q .

180 Fig. 3. Sum-rule cross sections (times 3 ) which provide upper bounds to the electron-stripping cross sections for Xe and U ions inci­ dent on Li and Ne. Circles are the results of explicit calculations for selected charge states, connecting lines are simply smooth curves drawn through those points.

181 Fig. 4. Sum-rule cross sections (times 3 ) which provide upper bounds to the cross sections for the ionization of Li and Ne by the impact of fast Xe^ or U^ ions, evaluated at S^ = 0.2. Circles are the results of explicit calculations for selected charge states, con­ necting lines are simply smooth curves drawn through those points. Also shown are the Bethe cross sections for bare incident ions (Ref. 7), which are proportional to q^.

182 PRELIMINARY ESTIMATE OF HEAVY ION ELECTRON-TRANSFER CROSS SECTIONS

Stanley Sramek, Gordon Gallup, and Joseph Macek University of Nebraska, Lincoln, Nebraska

Introduction

We report preliminary estimates of cross sections for the electron- transfer process

Ba"^ + Ba"^ -> Ba + Ba"^"^ ,

for energies in the range 100-300 kev. At these energies the deBroglie wavelength associated with the heavy ions' relative motion is on the order of -4 10 au, and the angular deflection due to the ions' Coulomb repulsion is on -4 the order of 10 radians for impact parameters of 1 or 2 au. Therefore, the nuclear motion can be treated as a classical motion along straight line trajectories. Our calculation therefore consists of two steps: First, we obtain the molecular states of Ba^ as functions of inter­ nuclear separation, treating the nuclei as stationary point charges. Second, we solve the time-dependent Schroedinger equation for the system treating the nuclei as moving point charges, using these molecular states as a basis.

Molecular States and Energies

The molecular states are obtained by the Valence Bond Configuration Interaction (VBCI) method. We model the Bap^* molecule as a system of 110 electrons interacting with each other and with two stationary point charges,

183 each of charge +56, and separated by distance R. We choose a set of atom- centered one-electron basis functions {u^(£)}, and construct from this set a set of multi-electron basis functions U !• We use gaussian lobe functions for the {u.}, and use a {7s,6p,2d) set at each charge center. We thus use a total of 70 one-electron functions. The multi-electron functions {A } are constructed from the {u.} according to the usual VBCI procedure: each A is a linear combination of products of Slater-like determinants formed from appropriate subsets of {u.}. The coefficients in the linear combination are 1 + chosen by requiring that each A have the Z molecular symmetry. We compute Hamiltonian and overlap matrix elements in the {A } repre­ sentation, and solve a matrix eigenvalue problem to obtain the molecular states: %^W- (AJ^IAJ.S^^(R) = (AJA^),

H{R) a.{R) = E^{R) S(R) aj(R),

X.(R) = Z a. (R) A .

The x.{R) and E.(R) are the desired molecular states and energies for separation R. In our calculations this entire procedure required approxi­ mately 7 hours of computer time on an IBM 370-148 system, for each separation R between the nuclei.

Figure 1 shows our three lowest energy curves. The lowest curve {j=l) represents a state in which both Ba ions are in their ground state at R=«'. The 3=2 curve represents a state in which one Ba ion is excited to its first 2 P state at R=~. The j=3 curve represents the lowest of the electron-transfer states. These are the states leading to dissociation into a Ba atom and a Ba ion at R=^.

Solution of Time-Dependent Schroedinger Equation

We now treat the nuclei as point charges moving with constant velocity. That is, the internuclear separation now becomes a vector quantity:

R = vt + b ,

184 ^Ig States of Ba^"^"^ Ab Initio VBCI Energy .. 0.4 Curves E-(R) J'

Energy Ej{R) (au) •• 0.3

0.2

• 0.1

10 15 20 —*— _H— Internuclear Distance R (au)

Figure 1. Energy curves for Ba^+ + system

185 where y_ is the relative velocity and b_ is the impact parameter. We write the wave function as a time-varying superposition of the previously obtained molecular states:

'l'(R_.t) = l. Cj(t) T(R.,t) expr-aj(t)J E{R) XJ(R) .

c.(t) is a time-varying coefficient to be determined by solving the Schroedinger equation. T(R^,t) is the well known translation factor, neces- 2 ^ sary to assure proper behavior of ¥ in the R -> «> limits. i?(R) is a time- dependent rotation operator that aligns the molecular state XAW along the time-varying direction R.

aj(t) = Nv^/8 + !l Ej(R') dt' ,

where N is the number of electrons.

We substitute the above expression into the Schroedinger equation, make a change of variables z = vt, and, after standard manipulations, obtain a set of coupled differential equations for the coefficients:

dc,^ /dz = Z. Cj(z) exp[i3y(z)/v] M|^^(z,v,b),

3,,j-(z) - Jl [E^{R') - E.{R')J dz' .

The coupling matrix element is a sum of terms independent of v and linear in v:

M^j(z,v.b) = Mjj(z,b) + ivM^j.{z,b) .

Once numerical values are obtained for the coupling matrix elements and for the energy difference integral s3(^-, the coupled differential equations can be integrated numerically. |C|^(z -^ <») | is then the probability of excitation to state k.

Simplified Estimate of Cross Sections

We estimate the electron-transfer cross section using two means of simplification.

First, we neglect most terms in M, .(z,v,b). The exact expression for M. .

186 is complicated but we expect that terms involving the translation factor should be approximately cancelled by terms involving differentiation of the basis functions {u.} with respect to R. The remaining terms involve differen­ tiation of the coefficients a. with respect to R:

Thus, the coupling is strongest for separations where the coefficients vary most rapidly.

Second, we use perturbation theory to integrate the coupled differential equations. The equations can be written in the integral form

c,^(") = c^(-oo) + I, /-Icj(z') exp[i3,^j(z')/v] M^j(z'.v,b) dz' .

for k ?* 1, first order perturbation theory simplifies this expression to

Ck(") " /.!Iexp[i3,^l(z')/v] M^^(z',v,b) dz' .

Examination of figure 1 shows that coupling should be significant be­ tween levels 1 and 2 in the region near R = 13 or 14, because the local maximum in 1 and local minimum in 2 in that region represent a strongly interacting avoided crossing between the two curves. Coupling between levels 2 and 3 should be significant at the close avoided crossing near R = 17. We therefore expect excitation to level 3 to occur by the following mechanism: For impact parameters less than 14, the system is excited to level 2 by passing through the region of strong interaction between levels 1 and 2. The transition probability is estimated by computing the perturbation theory integral for impact parameters greater than 10, and is assumed to average 0.5 for impact parameters less than 10. The system then is excited from level 2 to level 3 by passing once through the avoided crossing near R = 17. Because of the curves' nearness at this point the transition probability should be large, but we conservatively assume it to be 0,5 , The electron- transfer cross section for singlet collisions is thus estimated as

a^^iv) - (7T/4)b^2 + nJl b|c2(~)|^db . b^ = 10 au.

187 Ba"*" + Ba"*" -^- Ba + Ba "*" Electron Transfer "13 Cross Section (a/)

..150

100

.. 50

100 200 —H

Collision Energy E (kev)

Figure 2. Estimated electron-transfer cross sections. A cross section value of 1 a^ is equal to 2.7 x 10"^'^ cm^.

188 Figure 2 shows the results of our cross section estimate. The lower curve excludes the contribution {•n/^)b^ from a-^^\ the upper curve includes this contribution. Our estimate indicates that the electron-transfer cross section for singlet collisions is of the order of a few hundred square angstroms, although the size of this result shows that the perturbation theory estimate is not valid. Because the singlet state has a statistical weight of 1/4, its contribution to the total electron-transfer cross section equals one fourth of the values shown in figure 2.

An accurate determination of the cross section requires that the coupled differential equations be numerically integrated. We are presently performing such a calculation.

Acknowledgment

This research was supported by the Department of Energy. We wish to thank Mister Robert Vance for assistance in using the molecular quantum mechanics computer codes.

References

1. R. McWeeny and B. T. Sutcliffe, Methods of Molecular Quantum Mechanics, Academic Press, London and New York, 1969, Chapter 6.

2. J. S. Briggs. Re£. Prog. Phys. 3£, 217-289 (1976).

189 190 CHARGE EXCHANGE CROSS SECTIONS FOR THE REACTION Xe"*"^ + Xe"*"^ -*- Xe"*"^ + Xe"*"^

Joseph Macek University of Nebraska Lincoln, Nebraska 68588

The containment time of a high energy heavy ion beam in a storage ring is partially determined by the various charge changing reactions of the ion beam with the background gas, any electrons which are in the ring and by self collisions of the heavy ions in the beam. Ions change charge by a variety of reactions with like ions including direct ionization and charge exchange. It is desirable to select ions which have low charge changing cross sections, and calculations are underway to estimate the charge exchange cross sections for Cs"*", Ba"*" and Xe . It appears that closed shell configurations such as Cs"*" will have the smallest charge exchange cross sections. The direct ion­ ization cross sections are probably determined essentially by the size of the ion, and, although no calculations are available to provide a guide, it appears that closed shell configurations are favored. One such closed shell system of interest is Xe^, which has a 4d^*' closed outer shell. In this note we will estimate the charge changing cross sections for self collision of Xe"*"® ions with 0-150 keV relative translational kinetic energy on the basis of the Fano-Lichten^ electron promotion model.

This model has been quite successful for discussing inner shell excita­ tion in ion-atom collisions, and since we are dealing with ions whose outer electrons have been stripped off, the model can be expected to provide at least a qualitatively reliable estimate of reactions involving partially stripped ionic species. Construction of the relevant H2 like diabatic molec­ ular orbital single particle energy curves constitutes the first step in applying the Fano-Lichten model. Since the 4d separated atom orbital corre­ lates dlabatically with the 6ga united atom orbital, and the Ss separated atom orbital correlates with the 5s united atom orbital, we first construct a single particle orbital energy level diagram for these two orbitals, using the calculated H2''" energies of Bates and Reid.^ By extrapolating along the 4d^0 and 4d^° 5s isoelectronic sequence, we estimate that the 4d-5s energy separation is of the order of 5.2 Ry. Since an effective charge of 15 gives this separation in hydrogen-like ions we use Bates and Reid's results with Zeff = 15 to construct the curves in Fig, (1). Note that the 5so and 6ga curves cross at an internuclear separation of R = RQ " "4 a.u. Electron transfer from the 6ga to 5sa orbital becomes quite likely at the crossing, but, at the low velocities we are concerned with, is unlikely at other values of R. Since the maximum transfer probability is 1/2, we then obtain a cross section of l/2TrR^ for electron promotion from the 4d to the 5s orbital, pro­ vided the ions have sufficient relative kinetic energy to approach within .4 a.u. This energy we estimate to be of the order of 4 keV, thus the

191 SR) -20 -

-30-

R(a.uJ

Fig. (1). Single particle H2+ -lik e orbital energies for Z ^^ = 15. promotion cross section vanishes below 4 keV and rises rapidly to l/27rRc^ above 4 keV. To obtain the charge exchange cross section one conventionally introduces another factor of 1/2 because in 1/2 of the collisions the 5s electron will remain with the original ion and in 1/2 of the collisions it will transfer to the collision partner. One must also introduce a factor of 2 because there are two independent 4da electrons, thus the charge exchange cross section is 1/2TTR^ for E > 4 keV.

This estimate is undoubtedly far too large, primarily because the 4d^5s excitation configuration and the 4d^^5s charge exchange configuration are not likely to be equally populated. We may arrive at a better estimate by con­ sidering the energy level diagram in Fig. (2) where we have now included both the 5s excitation channel and the 5s charge exchange channel. [Relativistic Hartree-Fock calculations^ show that these channels are separated by " 15 eV.] Again we draw schematically the electronic energy levels with the internu­ clear repulsion (q + 1)(q - l)/n = (q^ -1)/R with q = 8 subtracted off. Note that the internuclear repulsion for the charge exchange channel is (q + 1)(q - 1)/R = (q^ -1)/R, but equals q^ for the ground state and the excitation channel, thus these curves incorporate a 1/R rise, so that the 5s excitation curve crosses the 5s charge exchange curve at R = 2 a.u. The two curves do not actually cross, in fact, the corresponding atomic states must mix strongly to form the 5sa united atomic orbital. We conservatively esti­ mate the corresponding curve repulsion to be at least 10 eV, but it could well be larger. We immediately see that the 4d ^ 5s promotion, which takes place at the square marked A, must be followed by a second vacancy sharing transition at B to effect a charge transfer reaction. By Massey*s adiabatic

192 R(au) Fig. (2). Schematic energy curves for the first three states of Xe« showing two crossing regions A and B.

criteria one must have AEJl/v ^ 1 for this sharing to occur with high proba­ bility. For AE == 10 eV, Jt = 1 a.u. we find that v corresponds to an ion translational kinetic energy of 3 keV/amu. We therefore conclude that for a Xe ° relative energy of 150 keV or less charge exchange to the 5sa state does not occur with high probability, although excitation to the 5s level does, and has a cross section of the order of 10"^^ cm^. Charge exchange, if it does occur requires closer collisions, thus a reasonable upper limit on Ogx is a^x 5 10"^° cm^. The Fano-Lichten model does not allow a more precise estimate.

One feature of our estimate is noteworthy, namely the importance of the 15 eV energy gap between the excitation and exchange channels. This large gap is likely to be a feature of all of the low-lying orbitals, thus whatever inelastic transition occurs via a near curve crossing, it will most likely lead to excitation rather than charge transfer. On this basis, one would conclude that for Xe"*"® + Xe"*"® charge changing collisions occur only infre­ quently with cross sections much smaller than 10"^® cm^.

It must, of course, be stressed that these estimates are based on the most approximate of the various reliable models for ion-ion collisions, and that the conclusions are subject to all sort of qualifications, mainly having to do with our estimates of the distances corresponding to points A and B in Fig. (2), Reliable, quantum chemistry calculations of the lowest XeJ^^ energy curves are needed to fix these distances more accurately, as well as to locate other critical points.

193 References

1. U. Fano and Wm. Lichten, Phys, Rev. Lett., j^, 627 (1965).

2. D. Bates and Reid, Progress in Atomic and Molecular Physics, Vol. 4^, 13 (1968).

3. Y. K. Kim, Private Communication.

194 LOW-LYING STATES OF (Cs^)'^'^

G. Das, R. C. Raffenetti, and Y.-K. Kim Argonne National Laboratory, Argonne, Illinois 60439

Abstract 1 + LTslng an MCSGF/CI method, wavefunctions for the ground stace 2 •11 1 • g and the excited states of the symmetries S , n / and A of the (Cs«) •^ g g g 2 ion are generated which asymptotically correspond to the single atomic excita­ tion and/or single electron transfer between the two Gs ions in their ground state. These molecular wavefunctions are needed In the calculation of charge transfer cross sections between the Cs ions. There are no curve crossings betweei; ^he ground and excited states for internuclear separation of -^4 bohrs or more. We infer, therefore, that the charge transfer cross section is unlikely to exceed geometrical cross sections at low collision energies.

I, Introduction Several heavy ions are possible candidates for use in the fast ion-beam induced fusion process. The Gs ion, because of the closed-shell structure, is likely to have low charge-changing cross ccctionc, and therefore, long beam lifetime in storage rings. The charge-changing cross section of the order of -17 2 10 cm is desirable to insure a beam lifetime of ~ 1 sec. The charge state of an ion may be changed either by charge transfer (Gs + Gs — Gs + Gs ) or ionization (Gs + Gs — Gs + Gs + e). Depending on the electronic configuration of ions, the charge transfer process may have a large cross section (> 10 cm) owing to a possible interaction of molecular states at large internuclear separation. To make a reliable estimate of the charge-transfer cross section at relative kinetic energies of interest

195 (< 150 keV), it is necessary to consider a molecular description of the com­ pound system. It is impractical to consider all of the energetically accessible states. Therefore, we restrict ourselves to only those states that asymptotically lead to either the ground state atoms and ions or to those singly excited to the low- lying levels, 6s, 6p, and 5d,

II. Basis Set, Configurations, and Other Details of the Calculations

Although the relativistic pseudo-potential method as developed by Das and Wahl is suitable for the system under consideration, we take the conventional all-electron approach and treat the resulting data as bench marks for later calculations. The basis set employed a minimal set for the core electrons (n=l to n=4) and double-zeta plus polarization functions for the valance electrons (n=5,6) is within the capacity of our programs . We start with a set of Slater-type orbitals (STO's) generated by least-squares fit applied to the numerical atomic orbitals of Cs . The exponents of the atomic STO's are then optimized by atomic Hartree-Fock-Roothaan calculations. The basis set is then augmented by suitable polarization functions. Table I shows the final basis set used for the all-electron calculations. The basis set for the molecular core orbitals (n ^ 4) is a minimal one and hence is not flexible enough for optimization as the internuclear separation is varied. At all internuclear separations considered, therefore, the core or­ bitals are kept frozen in their asymptotic forms (apart from slight changes brought about by the requirements of orthogonality between orbitals at different centers). Valence orbitals are kept orthogonal to these frozen cores. Corresponding to the atomic orbitals 5s, 5p, 6s, 6p, and 5d, we have to deal with five MO's each of the species (J and a , three of u and -n , and g u u g one 6 and 6 in the molecular ion apart from 32 core orbitals. The predomi- ^ " 2 2 2 2 nant electron configuration for the ground state is (Sso ) {5sa ) (Spa ) (Spa ) 4 4 g u u g (SpTT ) (SpTT ) (omitting the core, occupancies for brevity). The ground state •-i y described by this configuration is first optimized, yielding the description of

196 Table I. All-electron Gs Slater-type-orbital basis set

Orbital type Orbital exponents

Is 53.90674 2s 20.23381 2p 25.41793 3s 12.10265 3p 12.15194 3d 13.66558 4s 6.83221 4p 6.53744 4d 5.74113 5s 3.42830, 2,20688 5p 3.15936, 1.91135 5d 1.87475, 0.69698 6s 1.29761, 0.77646 6p 1.16253, 0.67259 the above occupied orbitals. The higher orbitals are now generated in the following way. To the ground state configuration we add two configurations 5pa -^ dj and 5pa -^ dj and optimize ib and JJ for the first excited state of ^ g ^^g ^ u ^u ^ ^g ^u the Z symmetry, while keeping other orbitals already optimized for the ground g state frozen. The next higher solutions of the Pock equations for i|j and ^ are selected to represent the remaining four orbitals of the a-symmetry. The excited n and 6 orbitals are obtained in the same way using appropriate molecular states. After all the necessary orbitals are obtained, we consider all those configurations that asymptotically represent atoms or ions either in their ground states or those that are singly excited to the levels 6s, 6p, and 5d, The orbital occupancies for the configurations are listed in Table II,

II. Results 1 + 1 In Figures 1 and 2 we plot the potential curves for the S and n states. In both figures we include the ground-state curve for comparison. Some of the potential curves for the n excited states cross each other. This is due to the fact that some states have been treated dlabatically. Note that there are no crossings or avoided crossings between the ground state curve

197 Table II. Orbital occupancies for the various configurations used in the wave- functions for the S , n and A states of the (Cs ) system. These are 99 g 2 2 22 4 4 either as given by ijj^ = (core)(Ssa ) (5sa ) (Spa ) ppa ) (5pTT ) (5pTT ) or u g g g u u g various single excitations therefrom 1^+ 1 1 2 n A g g g Spa —^ 6pTT Spa ~* 5d6 ^0 g g g g Spa — 6sa Spa -* 6pTT Spa -* Sd6 u u u g g u Spa —^ 6sa 5pa -— 5dTT SpTT — 6pTT u u g g u u Spa ~* 6pa Spa —* SdTT SpTT -*• 6pTT u g g u g g Spa — 6pa SpTT -^ 6sa SpTT -^ SdTT u u u u g u Spa -* 5da SpTT -^ 6sa SpTT -* SdTT g g g g g g SpTT -^ 6pa Spa ~* Sda u g g u Spug -^ 6pTr 5pTT -^ 6pa u g g 5pug -*6pTT 5pTT -*- Sda g U u SpTT — SdTT SpTT — Sda u u g g SpTT -*SdTT SpTT -^ Sd6 g g u u SpTT — 5d6 g g

and those for the excited states for internuclear separation greater than 3.8 bohrs. Consequently, we can safely rule out the possibility of large -15 2 charge transfer cross sections (> 10 cm ) caused by formation of a tran- 2 sient molecular state at large internuclear separation. The charge transfer cross section is likely to be of the order of the geometrical cross section —1 fi ? (~ 4 X 10 cm ) or less at low relative kinetic energy of the colliding ions. While the above states are adequate to represent the charge-transfer process, there exist other states which can lead to a direct ionization 3 process. As reported by Olson, the potential curve for the doubly excited 2 2 state Spa — 6sa will intersect the ground state curve, since at very small u g internuclear separation 5pa reduces to a highly excited 7f state of the

198 3-0 S-0 7 0 9-0 R IBDHRI

1 + ++ FIG. 1.—Molecular potential curves for the S states of (Cs ) as a function of internuclear separation R.

a-

3-0 SO 9-0 ll-O R I BOHR)

1 "l"+ FIG. 2.—Molecular potential curves for the Hg states of (Cs^) . The ground state (^Sg) curve is included for comparison.

199 united atom, while 6sa correlates to the 6s state of the united atom. g Olson's preliminary calculation shows that the two curves meet near R =3.S X bohrs, from which he deduces the ionization cross section to be 9 —1 fi 7 0.4 X TTR W 4 X 10 cm . (The factor 0.4 comes from an estimate of the X probability that the ion be ionized by this particular process.) We have carried out a limited configuration interaction study for the lowest doubly excited state using the orbitals obtained already in the charge- transfer calculations. The configuration set employed consists of all double excitations from the 5p shell. For the lowest root of the corresponding secular equation we find that at internuclear separation R w 4.1 bohrs, 2 2 (5da) configuration mixes strongly with the (6sa) configuration, and at 2 R < 4 bohrs (Sda) dominates. Also the vertical excitation energies fall ap­ proximately on a straight line. Extrapolating from this, we estimate that the value of R , for which the excited-state curve intersects the ground-state X curve, is ~ 2.5 ± 0.5 bohrs. The lower value of R will lead to a smaller X ionization cross section than that estimated by Olson. Calculation of the charge transfer cross sections based on molecular- state coupled equations is in progress. Preliminary results indicate that matrix elements for the cross section change smoothly with internuclear sep­ aration even though the wavefunction parameters vary rapidly. Although we must carry out further calculations on the charge transfer cross section, it is very likely that the cross section for closed-shell ions such as Cs will be smaller than the ionization cross section. This work was performed under the auspices of the U,S, Department of Energy, References 1. G. Das and A. C. Wahl, I. Chem. Phys. 64, 4672 (1976), 2. As an example of large charge transfer cross section due to interacting molecular states, see S. Sramek, G. Gallup, and J. Macek, Prelim­ inary estimate of heavy ion electron-transfer cross section, this proceeding. 3. R. E. Olson, Charge changing cross sections for Gs"'" + Cs''' collisions, this proceeding.

200 CHARGE EXCHANGE BETWEEN SINGLY IONIZED HELIUM IONS

B. H. Choi and R. T. Poe Department of Physics University of California, Riverside, CA 92521

K. T. Tang Physics Department Pacific Lutheran University Tacoma. WA 98447

Plane Wave Born Approximation (PWBA) was employed to evaluate the charge transfer cross sections for the following reaction

He"'' + He"*" -»• He"*^ + He (1)

The form factor or the transition matrix element in this approximation is given by

Ffi(^,E.) = ^^r^^z^y^ipi^^^;n^z^ra^,nlilml^^f'^±^

= /d5d?^d?2Vf^

= <*!'j|v^|t > (2)

in post form. Here, ^ ikf-Rf Lf

*f"f "" ^ "ff iti-Si i n.A_,m. al n.x.m. b^ ill lii 2 2 2 2 V =Z^-Z£:-Z^ (3)

Ze and E. are the nuclear charge and the incident energy, respectively, and

201 ^ = ^^ - k.

S = ^A " ^B W

The r- and S^ B ^^^ the electronic and nuclear coordinates, and B.^ f are the relative vectors between the collision partners before and after collisions. Thus,

11 f f

= (-q^ + TnyrM+2 m k^,f ) -R + M+(rrrm - ki. + M+2.,.m- k-f ) -ra l^

with M, m the masses of atomic nucleus and electron. The spin-orbit inter­ actions were neglected in the present calculation. Therefore, the total spin is conserved (S = S^ = S^).

For the purpose of performing integration in Eq. (2), we have developed an efficient computer program which reduces the overlap integration between two atomic orbitals, which have different nuclear centers, to that of one- dimensional and thus it speeds up the calculation. The wave function ob­ tained by Roothaan and Bagus-*- was used for (neutral) helium atom.

The properly symmetrized transition matrix element which takes into ac­ count of the Identities for both electrons and nuclei is given by

^fi ^ ^^f|VfUl+PAB^^^'^^"^^%2^'^i^ ^^^ when (nf^f)?^(nfAf). Here P's are the interchange operators. If infif)= (ujJi^) , it is seen that Lf+S = even and symmetrized matrix element is given by ~s ^ -> ^

/2(-l)^T. „ .2, „ . ,„, ,(k.,-k.) (7) + (n^Ji^) L^M^rin^Jt.m^ ,n.Jt .m. f* i' If tt' ill' 111

The spin-averaged charge transfer cross section is then expressed as

10^31 ,„, i-j-f 4 i^f 4 i->-f

202 with S ^ S Vf n^il^,n^Jl|-^(n^£^,n^ApL^

(kf+ki)2 ^f dQ If? '2 Sir* E. (2£ +l)(2Jl*+l) m m!M^ fi' (kf-ki)^

(Q = q^) (9)

Sample result of the charge transfer cross section is shown in Figure 1 as a function of the incident energy, for the reaction

He'*"(ls) + He"*"(ls) -> He(ls^ -"-S) + He"^ (10) which is the dominant part of Eq, (1). No comparable experimental data exist. However, the charge transfer cross section for the following reverse reaction

He''^ + Heds^ •''S) -»- I He''"(nJl) + I He''"(n'Jl») (11) ni n'jl.' 2 have been measured. In order to check the present calculation, we have com­ puted corresponding cross sections. It should be noted that

= E,(2Lf+l) c'(„^,^.„-,')L^^.,^,„;,' . (X2)

The results are shown in Figure 2 compared with experimental data. The pres­ ent PWBA results seem to be better than those obtained from Continuum Dis­ torted Wave Approximation^ at around 300 keV which is the lowest energy in which the measurements were made. Some contributions of individual reactions are tabulated in Table I.

In spite of the simplicity compared with other approaches, PWBA calcu­ lations yield reasonable results. We plan to extend present calculations to some isoelectronic sequences as He + He"*" and to much heavier singly charged ion-ion systems, for which it is very difficult to carry out calcu­ lations with more refined methods such as the semi-classical impact parameter method or Continuum Distorted Wave Approximation, to study charge transfer reaction.

203 References

1. C. C. J. Roothaan and P. S. Bagus, in Methods in Computational Physics, 2^, 47 (Academic Press, 1963).

2. L. I. Pivovar, M. T. Novikov, and V. M. Tubaev, Sov. Phys. JETP, j^, 1035 (1962).

3. Dz. S. Belkic and R. K. Janev, J. Phys. ^, 6_, 1020 (1973).

204 TABLE I. Charge transfer cross section for the reaction. He +He(ls S) -> He (ni!.)+He (n'A'). in units of cm^. (The identities of electrons and nuclei were taken into account, and a-n

should read as axlO ).

300 1000 E(keV) 10 20 40 100 nil,n'Jl'

6.776-16 7.324-17 1.693-18 Is, Is 8.965-15 5.396-15 2.548-15

5.794-17 7.380-18 1.960-19 Is,2s 2.906-15 1.317-15 4.086-16

2.777-16 1.954-17 1.470-19 ls,2p 2.382-15 1.519-15 8.880-16 20 5

1.573-17 1.597-18 5.091-20 Is,3s 2.742-16 • 2.257-16 1.080-16

1.980-18 8.603-19 2.195-20 2s,2s 5.593-19 4.614-20 5.497-19 lO-'^n-TT -1 1 1—rn 1 1 r

He*"(ls) + He'^(ls) —* He(ls2 ^lc\_i 'S)_ +u«+ He+'

^15 10

CJ E o

10^-l 6 _

rl7 10 J L 10^ E (KeV)

FIGURE 1. Charge transfer cross section for the reaction, He"^(ls)+He+(ls)-^He(ls2 ls)+He'*'"'", as function of the incident energy E.

206 ^

.-14 10

10rl 5

CJ S u

10>-l 6

10.-1 7 —

FIGURE 2. Comparison between experiment and theories for the charge transfer cross sections for the reaction, He"^%He(ls^ "''S)->^ He"'"(nJl)+ I He"'"(n'£'). ni n*Jl' : present PWBA results, : Continuum Distorted Wave results taken from Ref. 3, A: experimental measure­ ments from Ref. 2.

207 208 B. COST ANALYSIS AND SYSTEMS DESIGN

PRELIMINARY SYSTEMS EVALUATION OF HEAVY ION BEAM FUSION DRIVERS*

T. Kaimnash and C. R. Drumm University of Michigan Ann Arbor, Mich. 48109

Abstract A systems analysis for a fusion reactor utilizing a heavy ion beam-pellet fusion is carried out to evaluate the perfor­ mance of certain designs of potential drivers. As a reference case we have used the Argonne National Laboratory's Hearthfire Concept #3 which utilizes a rapid cycling synchrotron system. It is shown that such an accelerator can be an adequate driver if certain minimal requirements are met.

Introduction The use of heavy ions in the implosion of Deuterium-Tritium pellets as a potential approach to fusion power has in recent years received added attention due to several important physical considerations. When contrasted with other inertial confinement schemes, especially those utilizing relativistic electron beams, heavy ions provide distinct advantages, the most cited of which are : i) higher stopping power, ii) negligible bremsstrahlung thereby drastically reducing or perhaps eleminating preheat problems. III) very little scattering of the beam ions in the target, hence virtually no "reflection" losses of ion beam energy, and iv) higher energy deposition near the end of the range for normal incidence on target surfaces. Large2ion energies, perhaps in the tens of GeV will however be required to ignite the ther­ monuclear microexplosions and for that reason special attention has been paid to the design of reliable, efficient high energy accelerators that could serve as drivers for ion beam fusion reactors.

Several such drivers have been proposed to accelerate mul­ tiply charged (uranium or xenon) ions to energies of the order 20-30 GeV. The Argonne National Laboratory has proposed several designs of which The Hearthfire Reference Concepts 1 and 3 uti­ lize a rapid cycling synchrotron system while the reference con­ cept 2 totally eliminates the use of synchrotrons. The Brook­ haven National Laboratory, on the other hand, has proposed the ''worK supported iDy uOE

209 use of an RF linear accelerator to produce a beam of 20 GeV ions at a current of 160 ->n-^ , while the Lawrence Berkeley Lab­ oratory has put forth an Induction Linac System which acceler­ ates U"*^ ions to about 26GeV. These various proposals are de­ scribed in these proceedings. In this paper an attempt will be made to evaluate heavy ion fusion drivers from the point of view of an overall systems anal­ ysis of a fusion reactor utilizing these drivers. Special atten­ tion will be paid to the Hearthfire, 3, concept although many of the conclusions could be readily applied to other drivers.

Analysis We consider the standard power flow diagram for the whole power plant shown in Fig. 1. Since only average power values will be considered for all the components in this analysis the diagram in question will also represent an energy flow diagram for the system: An energy vl^ is supplied to the accelerator whose efficiency is denoted by *7^<- ^^o™ which a beam of ions is delivered to the pellet which we characterize by a gain, Q, and an absorption or a coupling efficiency *]^ . For a D-T pellet whose fusion products include alpha particles the fraction of fusion energy released as charged particles which may be di­ rectly converted is denoted by

Using the power flow diagram shown in Fig. 1 we write energy conservation relations across each plant component and obtain an expression for the plant efficiency of which can be put in the form ,

I Q le (1) where Q is the pellet gain and Qc is the "critical" pellet again which corresponds to the value of Q when the plant's net electri­ cal energy output, iVV / iequal to zero. It is given by

210 1» with Oe being the efficiency by which fusion energy is con­ verted into electricity, or

The circulating energy ratio, C, can be written conveniently in terms of familiar variables: c - y^ = ^/-^^) (4)

and at times it is useful to employ a related parameter, & , defined as the circulating power fraction given by e . ^ - ^ (5)

We now introduce two additional system figures of merit which are independent of Q. They are Q* and h (Q*) which represent respectively the pellet gain and system efficiency when C = 1. The way these parameters change with the efficiency and gain of the various system components can yield information regarding the role of key components in certain ranges of system parameter space. These variables are given by

(6)

and a ncQ"). (•^-f-'^)7 (7) ^Ci^Ci)-nrH^'^n^^inr..-')i)

It might be noted that for ^fHt- ' % the plant efficiency ^7 (Q*) is independent of the accelerator efficiency, ^Jj^^t Inspite of this independence ^^^ must be positive or the values of Q* will be unphysical. Moreover it might be seen that ^ {Q"^) for n * > 7nyj_ has a higher value than that for ^^ ^^ffii- In order to compute the above system parameters we must first obtain *1/UJL / and for that we specialize in the case of the Hearthfire reference concept #3 whose accelerator power flow diagram is exhibited in Fig. 2. The major components of this driver are a 550 MV linac, eight 60 k\'^ synchrotrons, four matching rings, 16 storage rings, and 24 final beam lines and lenses. Using the accelerator power balance diagram shown in Fig. 2 the efficiency of this driver is computed from the gains and efficiencies of the individual components. The gain of a component is defined to be the beam energy output divided by the

211 beam energy input, while the efficiency is set equal to the beam output divided by the total energy input. Using energy conser­ vation relations it is clear that we can write for a system with Kl components connected in series:

•^s^,, - vv;^?^&,6;^ ...... G, (8) where Vt^ is the source energy, W, is the energy input to the first component whose efficiency is t^ , and G-y^ is the gain of the v\ th component. Noting that u.; + ^^V ^ ''^'3^ -- v^,. = \A4 or vV. --, ^^ ^ ^^^ ^ I (9) then the first term in Eq. (9) can be readily replaced by its equivalent from Eq. (8). Moreover, the efficiency of the second component can be expressed as 7 ^ w, ^^ g.^ which can be further written as

' ^ ^ (10) Similar equations can be obtained for the remaining components which when combined with Eq. (9) constitute a set of linear algebraic equations in the variables ^^/ni^ • ^f^l^ty These equations are then solved for ^t/v>l^ which when inserted in Eq. (8) will yield the desired quantity, namely *']4c^ . As pointed out earlier Hearthfire #3 employs more than one unit of each of several components e.g., 8 synchrotrons, 4 rebuncher rings, 16 storage rings etc., but these added components do not affect the efficiency of the driver since the efficiency of a system of parallel components is the same as the efficiency of the individ­ ual component. Results In order to examine the role of each component in the per­ formance of the overall system we have selected a reference sys­ tem on which we have carried out a parametric study. Hearthfire #3 whose basic parameters are displayed in Table 1 is chosen as the reference driver and its efficiency is seen to be 0-267- In obtaining this figure we have calculated the gains of the various

212 components using the procedure described earlier while the fig­ ures for the efficiencies of these components were obtained or estimated from data available from this or other Hearthfire reports. For the remaining components in the system we have used the following values: *J^ =0.80; *JrHi = 0.40; 7rNi =0; CL = 0,05; *7^^ =0.70; and o(* =0-20. TABLE 1

Reference Case Parameters Component Efficiency Gain Ion Source Low Beta Linac 0.40 Strippers 0.15 0.2 Linac 0.40 400 Debuncher 0.90 1.0 Synchrotron 0.40 4.05 Rebuncher Rings 0.90 1,0 Rotator 0.90 1.0 Storage Rings 0.80 0.89 Transport and Focus 0.90 1.0 Accelerator 0.267 The effectiveness of the reference accelerator as a driver is illustrated in Fig. (3) where we note that a pellet gain of about 50 is sufficient to yield a plant efficiency of about 35%. Such an efficiency is considered competitive with other types of power plants. Fig. (4) shows the variation of G?c (the value of Q that corresponds to zero net power) with the accelerator effi­ ciency for various values of deposition efficiency ^^ . We note that for the reference case, 7/t =0.8 and ^A^ =- 0.26, a Qc value of about 12 will be needed while a value of about 9 will be needed if the beam to pellet coupling can be made per­ fect. The role of the driver in the overall plant performance is depicted in Fig, (5). We observe first that increasing the accelerator efficiency much past 32% does not result in a sig­ nificant increase in the plant efficiency. At such an efficien­ cy, it is also clear from the figure that increasing the pellet gain much past 50 does not yield a large enhancement in the plant efficiency, although a substantial increase is obtained when Q is changed from 30 to 50- This information should provide a guide as to the direction one should follow in ion beam fusion research: improving the driver efficiency or increasing the pel­ let gain. Clearly the answer depends on which is the easier of the two technologies.

As pointed out earlier, one of the major advantages of using heavy ions for imploding pellets is the high deposition or cou­ pling efficiency, 'J/i . Fig. (6) reveals that large values of n are needed at low accelerator efficiencies but the enhance-

213 ment in the plant efficiency due to larger values of 7^ at higher accelerator efficiencies is indeed minimal. In Fig. (7) we focus attention on the role of the synchrotron in the perfor­ mance of the accelerator. For the reference case we note that Linac efficiencies of 0.40 and a synchrotron efficiency of 0.4 are needed to produce a driver efficiency of about 0.26. This figure also reveals the lesser dependence on the synchrotron at large Linac efficiencies but the importance of the synchrotron at low accelerator efficiencies. The role of the other major components in the accelerator is shown in Figs. (8) and (9). Fig. (8) shows that large synchrotron efficiencies are needed to compensate for low storage ring efficiencies while Fig. (9) il­ lustrates the dramatic increase in accelerator efficiency as a result of increasing the efficiency of the beam transport and focus system. Finally, Fig. (10) seems to inforce further the importance of the value of the pellet gain in the performance of heavy ion beam - driven fusion reactors. It is seen that a Q of 50 is needed to reduce the ratio of circulating power fraction to acceptable levels.

In summary this preliminary study seems to indicate that a driver of the reference type may be adaquate for a fusion reac­ tor if the gains and efficiencies indicated prove realizable. It also shows that the modest value of about 50 for the pellet gain is adaquate to operate such reactor at a competitive plant efficiency. References

1. M. J. Clauser, Phys. Rev. Letters, 35.' 848 (1975) 2. J. H. Nuckolls, ERDA Summer Study of Heavy Ions for Inertial Fusion, Berkeley, LBL-5543 p 1, July 1976 3. R. C. Arnold, R. J. Burke, M. H. Foss, T. K- Khoe, and R. L, Martin, Hearthfire Reference Concept #3, ANL Report, June 16, 1978. See also Hearthfire Reference Concepts #1 (July 1976) and #2. 4. M- Nozawa and D. Steiner, An Assessment of the Power Balance in Fusion Reactors, USAEC Report ORNL-TM-4221 (1974) 5. T, Kammash, Fusion Reactor Physics, Principles and Technology, Ann Arbor Science Pub, (1975) Ch, 16

214 PLANT POWER SALANCE

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215 UJ*,

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216 PLRNT EFFICIENCY VERSUS flCCELERRTOR EFFICIENCY FOR DEPOSITION EFFICIENCY-.8 AND FOR Q VALUES OF 30, SO. AND 70 3

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217 ACCELERATOR EFFICIENCY VERSUS STORAGE RING EFFICIENCY FOR SYNCHROTRON EFFICIENCIES OF .2 . .4 , AND .6

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218 ELEMENTS TO BE CONSIDERED IN PLANNING HEAVY ION FUSION PROGRAM A SUMMARY* Ihor 0. Bohachevsky Los Alamos Scientific Laboratory Los Alamos, New Mexico 87545

Introduction Characteristics of ICF Program

The Inertial Confinement Fusion (ICF) program is different from previous large national technological programs, e.g., the Apollo Lunar Landing Pro­ gram or the Nuclear Submarine Polaris Missile Program, because the scienti­ fic feasibility of its goal, i.e., attainment of controlled thermonuclear fusion utilizing inertial fuel confinement, has not yet been established. In this sense, therefore, it is a research program. However, unlike other research programs, the ICF Program has a narrowly specified goal which, to ensure the Program's success, must be attained within a fairly well-defined time span. This span extends from the time when fossil and rich-ore fissile fuels are exhausted to such an extent that their further utilization becomes impractical, to the time when alternate energy technologies, e.g., fast breeder reactors, have become operational in sufficient quantities to make their displacement economically infeasible. Based on our current knowledge and estimates, the time window for the economically successful introduction of fusion-based power technology is somewhere between the years 2000 and 2050.

The fusion program is also a technology development program because the utilization of its product, energy, i.e., commercialization of ICF fusion, requires the development of new technologies. This fact, together with the fast approaching success window and its short duration, require that the traditionally distinct research and technology-development phases of the program overlap in an intensive, well-coordinated effort.

ICF Program Planning Requirements The dual nature of the ICF Program and the dichotomy between the fact that the research breakthroughs are unpredictable and the requirement that milestones must be established and reliably attained because of the small size of the success window, impose stringent demands on program planning and

*Work performed under the auspices of the US Department of Energy, Contract Number W-7405-ENG-36.

219 management. The uncertainties inherent in any research program combined with the urgent need for definitive results require that several approaches to achieve fusion conditions be pursued in parallel. These different ap­ proaches are represented by gas, glass, and advanced lasers, and by elec­ tron, light-ion, and heavy-ion beams. Because of the unpredictable nature of scientific discoveries, schedules must be flexible and milestones set to promote increases in depth and breadth of our understanding of the relevant physical mechanisms over achieving specific results in definite experi­ ments. This implies that approaches based on nonscalable experiments and premature commitments to large and expensive facilities should be avoided, if possible.

The urgent need for definitive results requires that exploratory inves­ tigations be organized to promote the cross-flow of information and the synergistic effects between different approaches, allowing a rapid shift of emphasis from one approach to another with minimal disturbance to the over­ all program as soon as research results conclusively indicate a definite advantage of one approach. Synergistic effects are now apparent in fuel- pellet design and exploratory experiments: for low-yield pellets, the physics of beam-pellet interaction was defined by the particular driver; however, as the beam-power requirements increased beyond 1 MJ/pulse, pellets designed for different drivers became more and more similar.

A timely achievement of the ICF program goal demands a tight integration of its research and technology-development phases. Not only should the research results guide and define the needed technological developments, but, in close interaction, the technology developments and assessments should also indicate the needs for specific research results. Such coopera­ tion is required to ensure the economic success, i.e., timely commercializa­ tion, of ICF.

A sunmary of Battelle's Engineering Development Program Plan for ICF follows. It should be viewed in light of the above general remarks about the nature of the ICF Program.

Battelle Engineering Development Program Plan Development Objectives

The development objectives identified in the Program Plan are: 1. Commercial pellet designs, 2. Driver development and selection, 3. Pulsed power technology, 4. Reactor vessel and blanket designs, and 5. Reactor subsystems, e.g., a. pellet injection and tracking, b. beam steering, and c. lithium circulation system. Facilities

Facilities required to achieve these objectives are identified as fol­ lows:

220 1. Early a. Single Pulse Target Facility, b. Systems Integration Facility, 2. Mid-term a. Engineering Test Facility, b. Materials Test Facility, 3. Late a. Fusion Pilot Plant, b. Prototype Fusion Power Plant, c. Pellet Fabrication Facility. The principal functions, characteristics, and costs of each facility are described in "Engineering Development Program Plan for ICF, Vol. II, Program Strategy," Battelle report PNL2582, March 1978. Strategies

Different program strategies may be obtained with different juxtaposi­ tions of the above facilities. The particular selection will be determined by: 1. Scientific advances in our understanding of radiation-matter interac­ tions at high energy and matter densities, 2. Advances in technology developments, and 3. Availability of funds. Examples of different strategies, with discussions of their merits, are also presented in the above cited Battelle report. Heavy-Ion Driver Development

Heavy-ion beams became competitive drivers for ICF when the energy-on- target reguirements, which have been increasing monotonically in the past, reached the 1-MJ level. There are two philosophies on how to proceed with their development.

1. Build a Particular Driver-Accelerator on the Basis of Current Knowledge, and Commit the Necessary Resources to Solve the Problems as They Arise This approach was suggested by R. Carruthers (Culham Lab.) at the Third Topical Meeting on the Technology of Controlled Nuclear Fusion in Santa Fe, NM (May 1978) and was strongly advocated at this meeting by A. Mashke (BNL). There are compelling reasons to proceed in this way, some of which are: 0 It is reasonably well-known where and how to begin; 0 The challenge of the project and the prospect of near-term experiments tend to attract and hold the most-gualified and talented people; and 0 Something will certainly be learned from the project.

Obviously this approach contains many pitfalls; the alternative is the second philosophy. 2. Distribute the Resources as Required to Investigate Different Concepts, Analyze Anticipated Problems, and Select the Design on the Basis of Such "Optimization" Studies

221 Clearly this approach has many merits. It also has one characteristic property which may be either an advantage or a disadvantage, depending on its use. Namely, it is generally not possible to determine definitively when to terminate these studies, select the concept, and commit the re­ sources to design and construction. This is so because, at each stage of the studies, one can say: "If I only knew the answers to these additional questions, I could plan and design much better." It is, perhaps, for this reason that the "study first" approach is currently strongly favored by the executive and legislative branches of our Government, and therein lies its chief advantage. It does not appear possible to proceed in any other way.

Both approaches have been advocated and discussed at this workshop. To show that the first, "start building now and solve the problems as they sur­ face," approach is feasible, four specific conceptual designs of heavy-ion beam drivers have been proposed and submitted for technical evaluation.

1. Brookhaven Heavy Ion Fusion Energy Center is based on a 10 MJ Linac dri­ ver. Some of the specific arguments for building such a large facility in one step are: 0 Currently estimated driver and fuel pellet sizes to achieve fusion on power-production scales are large, and are steadily increasing in time; 0 Large pellets generate many neutrons and large amounts of tritium; and 0 Neutrons and tritium are undesirable from nonproliferation and environ­ mental points of view. It follows, therefore, that it will be necessary to build one large iso­ lated facility that remains government-controlled. Note that this single facility, with five to six different test chambers and reactor vessels, will be capable of performing all the program-development tasks for which Bat­ telle's Engineering Development Plan envisions six separate and distinct facilities.

2. Lawrence Berkeley Laboratory Induction Linac based on the once-through principle to avoid beam manipulations in accumulators.

Argonne National Laboratory proposed two designs: 3. Hearthfire #3 based on a rapid cycling synchrotron 4. Hearthfire #2 based on a RF linear accelerator These concepts are discussed in detail and evaluated elsewhere in these Pro­ ceedings.

To show that the second, "study now and decide later," approach is not being neglected, a list has been compiled of scientific and technical topi­ cal questions which, in the opinion of experts and therefore not unanimous, deserve and require satisfactory resolution before funds are committed on a large scale.

List of Scientific and Technical Topics and Questions to be Addressed Prior to Construction of High-Current Heavy-Ion Accelerators 1. Determination of the overlap of favorable parameter ranges for accelera­ tor operations and fuel pellet performance requirements. 2. Qualification of reguired ion sources and ion strippers. 3. Evaluation of effects during low-velocity acceleration and beam manipu­ lation (limits on low-freguency operation) such as:

222 a. preservation of six-dimensional brightness, b. acceleration, c. phase-space density (emittance, dilution), d. propagation, e. manipulation (bunching-debunching, splitting-combining). 4. Investigation of pulse compression, shaping, extraction at the high- energy end. 5. Identification of limitations on: a. transient violation of space-charge limit, b. beam neutralization. 6. Determination of performance characteristics of induction linac modules in parameter ranges different from those currently used. 7. Injection methods for induction linacs (currently available technigues reguire improvements). 8. Study of multiturn injection and beam dilution. 9. Identification of limitations of circular machines. 10. Determinations of relations between vacuum reguirements and ion life­ times for large circular systems. n. Development of designs for final focusing magnets compatible with test and reactor cavities. Reliability in long-term, uninterrupted operation and efficiency, which are problems for other drivers, appear to be well in hand for heavy-ion beams.

223 224 ELECTRIC POWER FROM INERTIAL CONFINEMENT FUSION: THE HYLIFE CONCEPT*

M, Monsler, J. Blink, J. Hovingh, W. Meier and P. Walker Lawrence Livermore Laboratory

Abstract

A high yield lithium injection fusion energy chamber is described which can conceptually be operated with pulsed yields of several thousand megajoules a few times a second, using less than one percent of the gross thermal power to circulate the lithium. The concept is suitable for either lasers or heavy ion beams propagating in background gases. Because a one meter thick blanket of lithium protects the structure, no first wall replacement is envisioned for the life of the power plant. The induced radioactivity is reduced by an order of magnitude over solid blanket concepts. The design calls for the use of common ferritic steels and a power density approaching that of a LWR, prom­ ising shortened development times over other fusion concepts and reactor vessel costs comparable to a LMFBR.

Introduction

The production of base load electricity in an economically competitive and environmentally acceptable manner is a major goal of fusion research and development. Should the progress of the Inertially Confined Fusion (ICF) physics program continue at the current rate, we will have demonstrated the scientific feasibility of ICF in the early to mid 1980's. The major effort will then shift to a technology development program in which the components and subsystems required in a commercial power plant will be designed, built, tested and integrated into working prototypes. The three major systems of an ICF power plant to be developed are:

1. A high average power driver, such as a laser or ion beam, with the required efficiency (>_ 1%), pulse repetition rate (>^ 1 Hz), and reliability ii T0$).

2. A manufacturing facility capable of producing DT pellets at the re­ quired rate, with the requisite tolerances on layer thickness and surface finish.

* Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore Laboratory under contract No. W-T^05-ENG-i+8.

225 3. An energy conversion chamber required to absorb a repetitively pulsed flux of neutrons, x-rays and debris and convert the pulsed energy to steady thermal power.

This paper is limited to a discussion of the energy conversion system, which itself requires the development of several elements:

a. A first-surface able to withstand the effects of x-rays, debris and neutrons,

b. structural materials able to withstand the cumulative damage effects of neutrons and cyclical thermal and dynamic stresses,

c. a repetitively pulsed target injection and beam focusing system, with elements lasting sufficiently long to not compromise the availability of the power plant, and

d. a tritium breeding and recovery system.

Over the past few years scoping studies and preliminary conceptual design efforts have been carried out at Lawrence Livermore Laboratory to identify the reactor concept of greatest promise in addressing these Issues.^"^ Our guiding philosophy is very important, for it differs from that of other reactor design groups in magnetic and laser fusion. First, we emphasize the charac­ teristics of advanced fusion pellets^ in determining reactor design, e.g. through the size of yield, energy spectra of the output, required irradiation requirements, etc. Second, instead of looking toward the development of exotic materials to withstand the expected radiation environment, we seek to modify the radiation flux and spectra in order to use ordinary reactor materials and techniques currently within the fission state-of-the-art. With this strategy we expect to fully capitalize on the unique simplicity of inertially confined fusion and dramatically shorten the period of technology and materials devel­ opment required to bridge the gap between scientific feasibility and commer­ cialization.

In October, 19TT, we began a laser fusion power plant conceptual design study based on an attractive fluid wall reactor concept. Approximately l6 man-years of effort are being invested in this study° which is now heading toward completion, with outside contractors such as Rockwell International, the Energy Technology Engineering Center, Bechtel National, the University of California at Davis, and the Colorado School of Mines contributing expertise.

We call our fluid wall reactor concept the HYLIFE converter; the acronym stands for H.igh Y^ield Mthium Injection Fusion Energy converter. This reactor concept constructively addresses the problems of pulsed energy release while maintaining all the positive features of the previous lithium waterfall reac­ tor concept.

In this paper, we describe the HYLIFE converter as it has evolved, and evaluate it in the context of a power plant with parameters which are repre­ sentative of our current understanding of the technology.

The target performance assumed is based on laser-driven target designs*^ which have features that can significantly affect power plant design. Energy

226 gains approaching 1000 are predicted when they are irradiated with 1 to i| MJ of short wavelength laser light (<_ 2 ym). Targets for heavy ion beams have been designed which result in similar yield with the deposition of similar energy per unit fuel mass. We are currently evaluating the mating of a heavy ion beam driver to the HYLIFE converter with particular emphasis directed to­ ward the expected propagation characteristics in 'v 0.1 torr lithium vapor, the possible need for an added background gas, and the positioning and sur­ vivability of the final focusing magnets with respect to the chamber.

The high target gains and high laser input energies result in high energy yields per pulse (_200 MJ <^ Y <_ i+OOO MJ), Some high gain targets also exhibit relaxed requirements for uniform target illumination and target surface finish tolerances. By relaxing the uniform laser illumination requirements, we can consider two sided target irradiation with longer focal length optics (f/lO to f/lOO). At focal lengths of 10 m, the final optics would survive the micro- explosion but might have to be replaced at relatively short intervals. At focal lengths of 100 m, the damaging effects are reduced by two orders of magnitude, thus assuring the survival of the final focusing elements for sufficiently long intervals to not adversely affect the plant capacity factor. This relaxation in target surface finish requirements also is expected to translate into a reduction in target fabrication costs.

Interaction of the Fusion Microexploslon with Lithium in the Cavity

The D-T fusion reactions in the compressed target (pR ^ 3 gm/cm^) release about Q0% of their energy as lU.l MeV neutrons with the remainder being 3-5 MeV alphas. However, the alpha particles are absorbed and some of the iH.l MeV neutrons are attenuated in the compressed target. Of the total fusion energy produced approximately 68% escapes as slightly degraded neutrons and the remaining 32^ as x-rays plus energetic target debris. The x-rays include a hard component generated from the hot burning pellet and a cool component radiated from cooling debris as it expands.

Radiation transport and hydrodynamic calculations have been made to deter­ mine the deposition of microexploslon energy in the fall and the response of the fall to this energy. In these calculations a one meter thick curtain of lithium is initially placed 2.5 m from the microexploslon with the first structural wall located at h m. The calculations have been performed in both spherical and cylindrical geometry. The results from the calculations are described qualitatively below and more details are presented in Refs. 7 and 8.

The debris and soft component of the x-ray energy is deposited in a very thin region of the fall. The hard component of the x-ray energy is deposited deep in the fall. More than 95^ of the fusion neutron energy is deposited in the one meter lithium region where it is multiplied by about 23% via the exoergic process of neutron capture in °Li. Although the energy deposited in the fall by each microexploslon is only enough to raise the mixed mean tem­ perature by ^ 15 degrees Celsius, the concentration of energy deposition in space (soft x-rays, debris) and time (neutrons and hard x-rays) results in violent disassembly of the fall. The liquid strikes the structural wall causing an inertial loading. The transient stress caused by this liquid-wall impact determines the design basis for the first wall. Three distinct effects contribute to the fall disassembly. The deposition of the soft x-rays and

227 debris in a thin inner layer (in about 8 ns) causes a shock wave to propagate through the layer. When this shock reflects, it spalls off an outer layer of liquid at relatively high velocity. About 50 ys later, as the blowoff vapor accumulates in the central high pressure region it exerts a significant out­ ward force on the curtain, accelerating it outward as an intact annular slug. The neutron energy is deposited throughout the fall in a few ys. The resul­ ting sudden temperature and pressure rise in the fall produces expansion waves that move inward from both surfaces of the fall. The hot vapor in the reactor center pushing outwards on the curtain will reverse the inward moving lithium, accelerate it outwards where it impacts the wall. Hydrodynamic calculations for the response of a single annular curtain of lithium represent the worst case, for the expected stress is the largest. The fluid configuration we anticipate using should cause significantly reduced stresses in the reactor structure than the single annular curtain, but it is far more difficult to calculate accurately.

Description of the HYLIFE Converter Reactor

In line with our philosophy of using only existing materials, we are only considering stainless or low alloy ferritic steels for the primary structural materials. Comparative analyses that consider lithium corrosion and resistance to radiation damage-'-^ currently favor ferritic steels.

A cross-section of the HYLIFE chamber is shown in Fig. 1, corresponding to a horizontal slice through the target plane. It features several concen­ tric annular regions: l) A thick outer pressure vessel which is primarily in steady compression due to the average inside pressure of less than 0.1 torr, 2) a graphite reflector to deal with the 3% of the energy and 35^ of the neu­ trons which initially escape the lithium blanket, 3) an erosion shield which covers the graphite and takes the liquid lithium impact. This shield does not support the weight of other components, k) An empty volume of 30-50 cm thickness which provides surge protection when there is transient fluid (liquid or gas) pressure on the first wall. 5) A perforated inner first wall, the primary purpose of which is to withstand the fluid impact loads on the erosion shield. It is supported only at the top and bottom and is primarily designed to take the transient tensile hoop stress. 6) The inner liquid lithium blanket region.

The fluid configuration currently favored is a close packed array of ^00 cylindrical jets, 10-30 cm in diameter, arranged in a hexagonal close packed pattern. This configuration removes the defect of the annular curtain geometry, i.e., the impact stress resulting from the Impact of the fluid accelerated by the inner high pressure blowoff gas. In the HYLIFE geometry this hot gas merely blows through the array jets, like wind through trees. The force of the expansion from neutron induced motion is primarily taken up in liquid-liquid impact of colliding jets.

The injection velocities of h m/sec will allow the jets to reestablish before the next microexploslon at the selected repetition rate of 1.1 Hz. Jet stability analyses presented by Kang^^ indicate that 30 cm jets with inlet velocities of h m/sec exhibit intact lengths which are longer than 20 m. This intact length is larger than the T meters that is required to insure the jets will not break up in the chamber. The area fraction occupied by liquid lithium is about 30^ at the midplane, perhaps 80^ at the top. We want to minimize the

228 empty space and lithium flow rate while providing the 'v^ 100 cm of lithium re­ quired to absorb the fusion energy and minimize neutron damage to the structure. The lithium jet diameter must be small enough so that a reasonably uniform average lithium thickness is provided; the jets must be large and "stiff" enough so that the gas from the x-ray absorption blowoff does not immediately push all the jets together to form a continuous sheet of fluid.

The array of jets can easily be arranged so that there are only two lines of sight "through the dense forest"; the target and laser beams are injected horizontally between the lithium jets in these places.

A conceptual view of the HYLIFE chamber is shown in Fig. 2. The pressure vessel consists of a cylindrical body, a hemispherical top with six or eight lithium inlet pipes and a surge tank 'cap' , and a bottom piece with a large cylindrical downcomer. The first wall assembly, which is a perforated basket supported at the top and bottom, sits inside the pressure vessel. Figure 2 also shows the injector plate or nozzle manifold which establishes the array of jets. The injector plate separates the high pressure plenum from the low pressure side of the chamber and is sandwiched between the top and main sec­ tions of the pressure vessel before bolting.

The lithiimi flow pattern is illustrated in Fig. 3. The lithium flows into the upper plenum from a half dozen or so inlet pipes and then is forced through the injector plate. Because the fusion pulse can cause significant transient overpressures (and possibly backflow), a surge tank is provided on the very top. The jets are formed in the chamber, and the basket is designed to accumulate some fluid although it continually pours out toward the down­ comer region. This prevents shock waves from propagating directly through a pool of liquid to the structure. This is an essential feature which solves a problem endemic to all our previous fluid wall concepts.

Note that the side view presented in Fig. 3 is in a direction along the laser beam axis. The beams project through a narrow ("^ 30 cm) separation between rows of crossing jets. Figure h shows the beam entrance more closely from another view. The pellet and the laser beams are injected from the sides. Underneath the laser beams, the slot is fully protected by streams of lithium injected in an arcing fashion to protect all the metal surfaces behind it. Finally, Fig, 5 shows a three dimensional view of this simple geometry.

Performance Parameters of the HYLIFE Converter

Feasible laser and target parameters have been selected in order to evaluate the HYLIFE converter concept in the context of a laser fusion power plant. The selected parameters and the resulting performance are presented in Table 1 for both a single and double chamber version. Several factors will affect the choice between one and two chambers: l) The cost of the laser per unit of power decreases with higher repetition rate. This factor favors one laser system serving two chambers. 2) The reactor building and plant piping will be less expensive for one chamber. 3) Higher plant capacity fac­ tors may be possible with two independent chambers. U) The higher yield per pulse in the single chamber design relaxes target fabrication constraints but exposes the reactor to a more severe environment. These factors and the inter­ play between them are being quantified in the remainder of the design study.

229 Neutronic calculations have been performed to determine several chamber parameters as a function of fall thickness. The parameters include system energy multiplications, power density, tritium breeding ratio, helium pro­ duction and atomic displacement rates (dpa) in the structure. Helium pro­ duction and dpa rates are used to estimate the damaging effects of 1^+ MeV neu­ trons in structural materials. Some of the neutronic results are summarized in Table 2 and more details are presented in Ref. 1.

Table 2 also gives the flow parameters for the HYLIFE converter based on single chamber design. In this design, fusion targets producing 2700 MJ of thermonuclear energy are irradiated by a 3 MJ laser at a rate of 1.1 pulses per second. The fusion energy is multiplied by a factor of l.l6 in the lithiimi filled chamber. This results in a power plant with a thermal power of 3^50 MW. The thermal power is converted to electrical power at 3^% efficiency. Of the total 12i+0 MWg produced, 236 MWg is circulated for power plant operation (.lasers, lithium flow, and auxiliary power). It is interesting to note that less than 1% of the gross power (15 MW^) is required to circulate the lithium through the chamber at the required flow of 120 m^/sec.

Approximately ii00-thirty cm diameter jets have been packed into a 3 m thick annular region with an inner radius of 0.5 m. The packing fraction of these jets at the reactor midplane is 0.35; thereby providing an equivalent 1 m of lithium between the target and first wall. Our neutronic analysis has shown that 1 m of lithium will attenuate the ih MeV neutrons to a point where common stainless and ferritic steels are predicted to survive for more than 30 years. The lithium inlet velocity of h m/sec has been set by the require­ ment to have the lithium jets reestablish their flow between pulses which occur every 1.1 sec. The power density within the enclosed volume of the HYLIFE vessel is 5-6 W/cm3. This can be put into perspective by comparing it to the power density enclosed within a boiling water reactor vessel which is 7.6 W/cm^. Because we are using comparable materials at about the same power density as a present LWR, we do not expect the costs of our laser fusion reactor vessel to greatly exceed present fission reactor vessel costs.

Environmental and Safety Analysis

Motivation for using advanced energy technologies stems primarily from the fact that they have inexhaustible fuel resources. All fusion reactor designs, both magnetic and inertial confinement, offer advantages in tapping the inexhaustible supply of deuterium present in seawater. Also, both systems produce less high level radioactive wastes than fission reactors and much less long-lived alpha emitting radioisotopes. Finally, fusion plants will be much smaller and utilize less land than solar central station plants.

The HYLIFE reactor concept incorporates the advantages in the social cost areas common to other fusion schemes while eliminating or reducing some of the problems inherent in the other systems. For example, the structural materials used are common steels which experience low activation rates because the lithium protection reduces fast neutron levels by a full order of magnitudt If low-alloy ferritic steels are .used, the variety of parents for short-lived radioisotopes will be significantly reduced. In addition, remote handling facilities will be simpler and less numerous than for magnetic confinement reactors, which must replace liners or entire segments regularly. Finally,

230 the HYLIFE reactor operates at power densities nearly as high as conventional boiling water fission power reactors, resulting in substantial resource savings in construction and equipment. The volume of low-level radioactive waste is also reduced by over an order of magnitude compared to other fusion designs because of the combination of high power density and 30-year structural life. Retention of these and other advantages is the continuing goal of our design effort. Consideration of environment and safety issues at all stages of the design will facilitate this goal.

Conclusions

We have described the Iligh Y_ield Mthium _Injection Fusion Energy (HYLIFE) converter. This concept has been shown to effectively cope'with the problems associated with pulsed energy release and ik MeV neutrons in inertial confinement fusion systems. Specifically, we have found that:

a) The HYLIFE converter can be operated with pulsed thermonuclear yields of several thousand megajoules and power densities approaching those of a LWR.

b) No replacement of the first-wall or blanket structure is required.

c) The power to circulate the lithium is less than 1% of the gross power.

d) The radioactive waste and biological hazard potential are reduced by more than 10 fold over concepts without fluid walls.

e) Common stainless or ferritic steels can be used for the reactor structure.

f) Operation with either laser drivers or heavy ion beams propagating in a background gas should ba feasible.

References

1. J.A. Maniscalco and W.R. Meier, "Liquid Lithium Waterfall Inertial Con­ finement Fusion Reactor Concept," Transactions, ANS Summer Meeting, 1977.

2. W.R. Meier and J.A. Maniscalco, "Reactor Concepts for Laser Fusion," LLL Report, UCRL-7965^, July 1977.

3. J.A. Maniscalco, W.R. Meier, M.J. Monsler, "Conceptual Design of a Laser Fusion Power Plant," LLL Report, UCRL-79652, July 1977-

^. J.A. Maniscalco, et al., "A Laser Fusion Reactor Design Study," Transac­ tions, OSA and IEEE Topical Meeting on ICF, Feb. 1978.

5. J, Nuckolls, "Laser Fusion Overview," LLL Report, UCRL-77725, May 1976.

6. J.A. Maniscalco, et al., "A Laser Fusion Power Plant Based on a Fluid Wall Reactor Concept," Transactions of the ANS Meeting on the Technology of Controlled Nuclear Fusion, May 9-11, 1978, Santa Fe, WM.

231 7. W.R. Meier, W.B. Thomson, "Conceptual Design and Neutronics of Lithium Fall Laser Fusion Target Chambers," presented at the Technology of Con­ trolled Nuclear Fusion Meeting, May 9-11, 1978, Santa Fe, NM.

8. J, Hovingh and J.A. Blink, "The Response of a Lithium Fall to an Inertial- Confinement Fusion Microexploslon," presented at the Technology of Con­ trolled Nuclear Fusion Meeting, May 9-11, 1978, Santa Fe, NM.

9. J.E. Selle and D.L. Olson, "Lithium Compatibility Research Status and Re­ quirements for Ferrous Materials," Paper #107, National Assoc, of Corrosion Eng., Corrosion/78 Conference, March 1978.

10. F.A. Smidt, Jr., et al., "Swelling Behavior of Commercial Alloys, EM-12 and HT-9, as Assessed by Heavy Ion Bombardment," Irradiation Effects on the Microstructure and Properties of Metals, ASTM STP ^11, 1976, p.227.

11. S-W Kang, "Jet Stability in the Lithium Fall Reactor" presented at the Technology of Controlled Nuclear Fusion Meeting, May 9-11, 1978, Santa Fe, NM.

Figures

Pressure vessel Graphite reflector Lithium jets Beam transports Jl i

Laser beam Erosion liner Perforated first wall, supported at top and bottom and allowed to take transient stress in pure tension

FIGURE 1. Top view of HYLIFE chamber: Cross section through target plane.

232 Graphite top plug — replaceable and / removeable for inspection Injector nozzles

Pressure vessel — Perforated first wall

Graphite reflector- Open volume for transient pressure relief

Erosion liner

FIGURE 2. Side view of the HYLIFE chamber showing separate first wall and pressure vessel construction.

View is in direction along laser beam axis

Lithium inlet pipe

Row of crossed jets over laser beams is seen behind central graphite plug

This jet is injected along and underneath laser beams from orthogonal direction

FIGURE 3. Flow pattern in HYLIFE chamber.

2 33 Pellet Injector

Laser beam f/20-f/50 \ Replaceable blast baffles Lithium jets protect bottom of slot

FIGURE h. Side view of HYLIFE chamber in plane of laser beams.

234 Table 1 - Laser and target parameters for the conceptual design

Double Single Feasible Chamber Chamber Range Design Design

Target gain, Q 100-1000 600 900 Laser efficiency (%) 1-5 3 3 Laser energy (MJ) 1-4 2 3 PRF per chamber (Hz) 1-3 1.5 1.1 Yield per chamber (MJ) 100-4000 1200 2700 POWER PLANT PERFORMAMCE Double Single Chamber Chamber Fusion power (MW^) 1800/3600 2970 Thermal power (MW^) 2090/4180 3450 Gross electrical (17^) 750/1500 1240 Laser input power (MW^ ) 200 110 Chamber fluid circulation (MW^) 20 16 Auxiliary power (MW^) 120 110 Net electrical (MW^) 1160 1005 System efficiency (%) 28 29

Table 2 - HYLIFE Converter Performance

Flow parameters Outer radius of jet array 3.5 m Inner radius of jet array 0.5 m Jet diameter at inlet 0.3 m Jet velocity at inlet 4.0 m/s Jet packing fraction at inlet 0.8 Jet packing fraction at midplane 0.35 Equivalent lithium thickness at midplane 1.0 m Lithium flow rate for jets 120 m^/s Pumping power for jets 11 MW Blanket parameters System energy multiplication 1.16 Tritium breeding ratio 1.6 Neutron wall loading 15.4 MW/m2 Power density within vessel 5.6 W/cm^ Structure Ferritic steel

235 236 PHASE-SPACE CONSTRAINTS ON SOME HEAVY-ION INERTIAL-FUSION IGNITERS

AND EXAMPLE DESIGNS OF 1 MJ RF LINAC SYSTEIE^

David L. Judd Lawrence Berkeley Laboratory

Introduction

In recent months workers at several Laboratories have developed concep­ tual designs for heavy-ion igniter systems. Although attention has been paid to phase space requirements in these studies it appears that they have been under-used as a primary guide to system design. The main purpose of this paper is to outline a method by which this can be done. In what follows attention is confined to systems using an rf linac either as the main accelerator or as an injector into one or more synchro­ trons. For an induction linac driver more information from computer codes designed to study transverse and longitudinal particle motions is needed before a corresponding analysis can be carried out. A second purpose of the paper is to develop a class of conceptual system designs. In the examples presented only a full energy linac with accumulator rings is considered so as to illustrate one method of system parametrisation in considerable detail.

Six-Dimensional Phase Space Volume at the Target

We define this quantity as

with n, the number of beams, subscript f = final, e.^ the normalized transverse emittance (area/Tr) per beam, and e^j^ the longitudinal emittance (area/Tf) in eV-sec. These quantities are given by

e,, = (BY)f r^(Rp/R,)

This wori^ was supported by the U. S. Department of Energy.

237 with r . R , and R the radii of target spot, beam port, and reactor s p v vessel, respectively; and

^ilf ^ (^^y)f% c^(Ap/p)^ (T/2) with final momentum spread ± Ap/p and T the pulse duration at the target . 1 associated with the peak power portion of the pulse shape required. This shape is imagined to be made up by an appropriately timed sequence of pulses, each of duration T„. The irradiated mass is Trn r W with {^ - the ion range in mass/area s s ^ *- and n the number of beam spots, so that the total energy E delivered is s 2, E = TT n r ^y. 's ss '^ -

with ^ the specific energy deposition (energy/mass ).

Phase Space Volume from the Linac

This quantity is defined (subscript L = linac) as

with £._ the normalized transverse emittance at the rf linac exit and Ij-, £.. its longitudinal emittance. The latter Is the product of occupied normalized longitudinal emittance e , per rf "bucket" and the number of buckets, the number being the product f^, At^ with f^, the frequency with which filled buckets emerge from the linac and At, its on-time. The on- time is At^ = qeE/(l^ T^) with ion charge qe, mean linac electric current I^ , and final ion kinetic energy T„. Dilution of phase space density during conversion of the linac bunches to a dc beam by debunching, and dilutions arising from other manipu­ lations downstream from this point, will be introduced later.

Ideal Available Dilution Factor We define this factor ^i^t^ as

"4 = \f/\L'

238 it is the factor by which phase space density may be diluted by all operaticns downstream from the linac exit without falling to meet target requirements. Rather than inserting the expressions above for the various factors to evaluate /ft at this point, we next consider certain properties of the final lens systems vdiich focus the beams on the target spots.

Properties of Final Lens Systems

First-order Monochromatic

A detailed first-order analysis of a class of final lens systems consis­ ting of quadrupole doublets without a gap between the elements has been presented by A. Garren, In subsequent work by D, Neuffer^it has been found that only small improvements on Garren's systems can be made by reasonable extensions of this class ( optimized Individual bores, use of triplets in appropriate cases, etc.). Therefore we adopt Garren's results, leaving open the possibility of shading a niamerlcal coefficient slightly to allow for such potential gains. An important proi)erty of Garren's systems (which can be deduced from his paper) is

with X the maximum radial beam displacement in the lens system, BQ the quadrupole pole tip field at radius X , and Cp a dimensionless coef­ ficient found from Garren's Table A8-7.1. With z^^ in radian-meters, B^ in Tesla, r and X in meters, one finds C^ by first evaluating Q 2 "^^^ k = qBQ R /(3.I3 3v A X ), then finding b and x corresponding to k from the table, and finally forming the product

• C^ = 3.13 bx.

The practical range of cases is stated by Garren as 7 ^b ^ 25, corres­ ponding to values of k varying by a factor 'v 8; however, the corresponding range of C^ is 100 ^ C^ ^ 150, showing insensitivity to k.

Chromatic Aberration From the numerical work of Neuffer it has been found that the approximate 5 ... relation (Ap/p)„ ^ r /R should be replaced by the less optimistic I s p

239 for lenses lacking sextupole elements (such as those in the periodic system proposed by K. Brown") arranged to correct chromatic aberration. We represent the effect of such corrections by a sextupole improvement factor F ^ l; "~"^^" ^^""^ "^^^—^^^^~ s the present hope of those trying to design such systems is F 'x. 5 but this s may be over-optimistic. Third and Higher Order Geometric Aberrations

This subject is not yet fully explored, but numerical work by Neuffer indicates that for beams of present interest these effects restrict X max to an upper limit of order 30 cm. As will be shown below, a numerical value for X , although required for lens design, is not needed for the phase max space analysis presented here.

Evaluation of ^,^J. - ; Discussion

Using the equations above and MKS units.

Note that charge state q and final lens bore X have cancelled. We max express spot size as above and employ

6^2 = [ (1 + Y )^/^/Y] [ T/( AnipC^)] 3/2 ^^ ^^at

3/2 T/(A^^)]^/2[AE/;?| ^ s We will see that it is desirable to use the minimum number of beam spotsj n^ = 2. Then the first square bracket is very close to unity for all Yf of interest. The factors are grouped as shown to display the ratio T /A^.'^J; explicitly; in simplest approximation the energy loss rate dT/dx «= z « A , so the ratio would be constant. In fact it varies by less than a factor of two over the range of interest, as shown in the following table (top of next page): Thus we have: ,

s'

240 Values'^ of T(GeV)/A^i!?(g/cm^) x 10^

T(GeV) 5 10 15 20 25_

131 (Xe) - 10 7.8 6,8 5.3 200 (Hg) 9.6 8.9 8.0 7.1 6.4 238 (U) S.S 8.0 7,4 6.5 6.1

Aside from the constants, the first bracket refers to target requirements, the second is nearly constant, the third constitutes a figure of merit for the rf linac, and the remaining factors are all constrained. Note that in any "funnel-loading" linac scheme the ratio ^T/^-TK ^^ ideally a constant; also, it has been commonly assumed that electric current I, may be con­ served during stripping to increase charge state at an early stage in the rf linac system. Therefore this figure of merit may be evaluated (with allowance for dilutions in the linac "tree") at its first stage, where I/(e| ) is a direct measure of source brightness. The system design problem starts with the necessity to choose parameters such that '''•^ is as large as the product of all expected transverse and longitudinal dilution factors. (Should it be too large one would reduce T^ to lower the system size and cost.) We discuss the factors in turn. The parameters E = 1 MJ, 'T = 6 nsec, w- = 20 MJ/g have remained constant during the past two years. For larger E the value of T^ may not increase faster than E , and there seems to be no change in the requirement (^ = 30 MJ/g for E = 10 MJ. Therefore the target factor in /^. increases only by about a factor 3.7 in going from 1 to 10 ^^ where x < 13 nsec. The linac figures of merit deduced from the assuii5)tions of several recent studies appear to lie within a range of a factor of four. We quote values from Hearthfire 3, denoted below by HF3; the 10 MJ design by n 8 A. Maschke, denoted by MJIO; and that reported by D. Young, Case 23, denoted by DY23:

241 Parameter HF3 MJIO DY23

+2 Ion A^ 131^« 238 200 ^

I(Amp) 0.03 0.16 0.40 e|^(cm-mrad) 0.2 'v 0.09 0.2 e,,^^(eV-sec) x 10^ 0.86 8 '\^ 1.6 fL^(MHz) 25 16 80

Figure of merit 35 154 78

It is advantageous to use the largest A(A = 238), smallest n^(ng = 2), and largest B^ (we use 5 T below). We set the Garren coefficient C^, = 100, expecting optimized design to lower it from the mid-range value 125, The parameters remaining with which to increase i/P. are F^, n^^, and T^. An upper limit on F (perhaps F < 5) will soon emerge from studies in s s progress. Aside from cost of beam lines and magnets, there is a practical upper limit on n, arising from geometrical effects; perhaps n, ^ 24. For each choice of A, E, and ^ an upper limit is imposed on T^ by the minimum spot size requirement r > 1 mm; the limit is higher for larger s values of A and E. The following table, employing the range-energy rela­ tions of Ref. 7, shows a few values: Values of Maximum Final Ion Kinetic Energy T„(GeV) E = 1 MJ E = 10 MJ, ^ = 20 MJ/g, 4 = 30 MJ/g Ion ^ •$ 0,8 g/cm ^^ 5,3 g/cm Xe 13 42 Hg 22 76 U 27 95 .

If the product of all expected dilution factors cannot be accommodated within the limits indicated the only path open is to start over with larger E. It is useful to give an expression for ^^(5; in the following units: K(MJ), -^(MJ/g), T^(nsec), T^(GeV),)f (g/cm^), l(A), BQ(T), e^(cm-mrad), e„j., (eV-sec), fj.,(MHz). Then

242 TO illustrate the use of this expression we give numerical values for the factors for HF3 and MJIO, using n^ (effective) = 32 for the former, T^ = 13 and n^ = 8 for the latter, and n^ = 2, BQ = 5, and C^ = 100 for both: HF3: ^ = (4.6 X 10"^)(0.067)(0.54)(35)(5)(32)Fg = 0.93 F^, MJIO: ^. = (4.6 X 10"^)(0.25)(1.21)(154)(5)(8)F^ = 8.6 F . *• s s Decreasing T^ in HF3 to 13 GeV to bring the spot radius upto l mm does not appreciably affect (fv. but requires 50^ more ions and therefore more or larger synchrontrons and rings. Even so, this design seems to require F = 10 to allow the total stated expected dilution factor of 3x3=9 (transverse only) which does not seem conservative. The value of ^u. 1 is larger for MJIO by a factor 8.4 arising from larger E and A, and the larger linac figure of merit compensates for smaller n, . The MJIO design also requires about 50^ more or larger fings to supply 10 MJ, and other changes to provide the smaller T which appears to be required. The total stated expected dilution factor for this design is 3x3 (post-linac transverse) x 3 (longitudinal) = 27, requiring F =3.1. s It must be emphasized that the estimates of oU * presented here should not be expected to agree with those of the workers whose designs are used for illustration because they have made different assumptions regarding final lens systems, A-Class of Linac-Accumulator Designs In the light of the information above, it was decided to examine the possibility of designing a system similar to MJIO but with E = IMJ by compen­ sating the smaller E by a larger n. , The exercise also provides an example of a design procedure based explicitly on phase space considerations. We have raised the ion (A = 238) final energy T„ to 25 GeV, near the limit set by r ^ 1 mm, and have assumed a linac figure of merit slightly more conservative than that m MJIO, with e«T-h ^ 10 eV-sec and other param­ eters the same as in DY23, giving the figure of merit 125 in the units used above. The value of (n/^ is then

243 ^. = (4.6 X io-^)(0.067)(1.4)(125)(5)nj^F^ = 0.27 n^F^ = Dj^D,,

with D, , Dji the total transverse and longitudinal dilution factors, respectively. As minimal lower limits we take Dj^Dj. = 16, a value lying be­ tween those of the designs cited above. Then n^ > 60/F^ = 12 for F^ = 5. The linac beam is to till n rings, each of radius R and mean bending field B, with n^. turns each. To match the transverse phase space \ 2 n 2

with e.p the ring emittance; we have assumed that all transverse dilution occurs during injection. If every beam bunch emerging from a ring is split 2 transversely into a beams, each with its own final lens.

With B in Tesla, the ring radius in meters is R = 363/(qB) and the total 2 number of turns in all rings is 5.74 q B. Combining these relations

q B Dj_ =^1.5 r 1? The space charge limit in a ring has been calculated in the usual way except that the allowable number of ions has been taken as one-third of that given by A v = 7- so as to allow adiabatic rebunching with quasi- parabolic charge distribution in azimuth to within a phase spread ± 7T/2 at harmonic h (with h bunches emerging from each ring) just before final imploslve compression in the rings. This gives ^sc ^ ^-^ ^ ^^^^ ^l<^^^, obtained from e, . = 0,58 q^ cm-mrad using X =30 t-n, R = 5m, C^ ^ 100, -LI max V G and the relations above. Because this design requires a total number N 14 -^ ^ of ions equal to 2.5 x iQ '^^ with total charge 4 x 10 q Coul, we find n, >. q3/2/„ . Combining this with the transverse matching requirement.

244 B > 1.5aq^/D, and = 8.4 o"^ q/D, n_"t. "*'* " ^'^1 ' To match the longitudinal phase space,

^riR " ^iiLb \b/c ^" with e p the longitudinal emittance in one ring circumference and n^, / = 27rR fj^^/Bc = 1400/(qB) the number of linac bunches per circumference. Extraction at harmonic h leads to

^lif " SR/^ = 1.4 D^/(h q B) = 0.25 F^ , so that h q B = 5,6 D„/F .

The final momentum spread is (Ap/p) = 1.75 x lo ^ F and the total number i- s of beams is n^ = a h n^.

One may then proceed to assume values of D, and a, and to calculate for each charge state q values of B . , n , n = integer 5 n , B, ^ min' r . r ^ r . ' \' ^max' ^min' "^ ' \ . ' ^«—I max' ^^ ^-^(imin^ '^^ maximum and '^'^ max mm minimum values arise from assuming a maximum value for n, and a minimum value for D„; there is also the requirement that h be an integer. Example designs based on Dj^ = 4, cr = 1, F =5, n^ < 24, D„ ^ 4 are givai in the following table:

RFL q n B(T) h h . D„ D„ . Case r ^t max mm ^h'^ma x I^KDun . n Hmax Hmm 2/25 2 3 0.55 2.1 8 4 24 12 8 4 3/25 3 6 0.73 6.3 4 2 24 12 8 4 4/25 4 8 0.73 8.4 3 2 24 16 8 ^.2

6/25 6 16 0.98 12.6 1 16 5.2 S/25 8 24 1.09 16,8 1 24 8

245 The larger values of D„ are safer because of anticipated dilutions in the funnel-loading linac, in debunching its beam, and perhaps in final compres­ sion. Note also that D,j is proportional to F^ so that if F is reduced from 5 to the smallest value (2.5) compatible with n^ ^ 24 the values of D,, are also reduced by a factor 2. The small value Dj^ = 2 x 2 = 4 for injection is less plausible for the larger values of n . In a detailed development of designs based on such parameters the number of turns per ring should be adjusted to be an integer, and advantage could be taken of the ingenious use in HF3 of longer pulses through some final lenses to increase their effective number. If one repeats this procedure for a = 2 with all other values held the same only q < 5 is allowed and larger n (17-42 turn/ring) is needed. Therefore D. = 4 is too small; taking it larger reduces D /F . However, if this problem is ignored the total circumference of all rings is reduced by a factor four from its value (6.2 km) for a = 1. One pays another price; the peak rf volts per turn required for final sudden compression in the 13 rings is of order 5/B MV/turn for 0=1 and is four times as large for 0=2. However, the corresponding azimuthally-averaged peak rf electric field for this class of systems depends only on the number of turns injected per ring and is equal to 1.1 n kV/m for our initial selection of general parameters. Expressions for total circumference of all rings and peak rf 2 ? voltage are 2TrRn^ = 1.55 Dj_/a and V (MV/turn) = 14 q/n = 20 a /(B DJ_). Conclusions

The linac on-time per target in the examples above is q/10 msec; it is evident that the system could serve several reactor vessels. When confronted with the tightness of the phase space constraint, which has been evident to all those who have tried to construct example designs, it is of central importance to emphasize the crucial role played by the linac figure of merit defined above, and the absolute necessity to minimize all phase space dilutions.

246 Parameter List for Case RFL 3/25 (h = 3)

General

E = 1 MJ,

Linac I = 0.4 A, ej_^ = 0.2 cm-mrad, f = 80 MHz (DY23) ^Lb " -^'^'^ eV-sec, At^ = 3 x 10-4 sec, e = 24 eV-sec.

Accumulator Rings

n =6, n = 6.3 per ring, D. = 4( assumed) implies D„^ 5.6. B = 0,73 T, R = 165 m. e,^ = 1 cm-mrad, f = 0.12 MHz, IR rev n,, , = 640, I . =2.4 A. Lb/c ' circ

Rapid Extraction

h = 3 (0.36 MHz), V 'x. 7 MV/turn (peak), ^ ^ 7 kV/m (peak). o t-o fast compression factor 'v 210 ('\'30 inside rings, '>^ 7 in lines). I at extraction 'v 150 max A. Number of turns during compression '\J 20.

Final Lenses

B„ = 5 T, X = 30 cm, R = 5 m, n, = 18. Q max V ' D C^ =; 100 (Garren's k = 3.44, b = 10.6, x = 3.2), e. „ = 1 cm-mrad, (Ap/p)^ = 1.75 x 10"-^ F = S.S >< lO'"^ for F = 5 (assumed). i- 1 s s e..« = 0.25 F eV-sec, bunch length at target = 0.8 m, current per beam = 1.1 kA,

All emittances In this paper are area/7T and are normalized.

247 References

1. Final Report, ERDA Summer Study of Heavy Ions for Inertial Fusion, July 19-30, 1976, Lawrence Berkeley Laboratory Report LBL-5543, p. 2, Fig. 1-2, 2. Ref. 1, pp. 102-109. 3. Internal reports, Lawrence Berkeley Laboratory. 4. Ref. 2, p. 105. 5. E. g., Ref, 1, p. 13. 6. Proceedings of the Heavy Ion Fusion Workshop, Oct. 17-21, 1977, Brookhaven National Laboratory Report BNL 50769, p. 107. 7. Ref. 6, p. 79. 8. E, g., Ref. 6, pp. 17-22, 9. Private communication, J. Nuckolls and R. Bangerter, Lawrence Livermore Laboratory, Sept. 1, 1978, 10. Argonne National Laboratory Report ACC-6, June 16, 1978. 11. Brookhaven National Laboratory Report BNL 50817, March 13, 1978. 12. E. g., Ref. 1, p, 16. 13. D. Judd, Ref. 6, pp. 34-40.

248 HEAVY ION FUSION DEVELOPMENT PLAN*

A.W. Maschke Brookhaven National Laboratory Upton. New York 11973

I. General Considerations

Before outlining a plan for the development of Heavy Ion Fusion, it is important to consider, in a broader context, the role which Fusion generally may be expected to play in the future. In fact, the Ad Hoc Experts Panel on Fusion** gave first priority to an assessment of the highest potential that Fusion might achieve. The discussion here will deal with the role of Fusion in the time span of the next 25-50 years. This time frame represents the "nearly foreseeable" future. That is to say, the Inertia of our present institutions and industries would tend to preclude "revolutionary" development on this time scale. Despite the enormous scientific and technical progress made in the past 50 years, the basic industries are not so much different. On a scale of 50-100 years, however, technological change has been so great as to be almost unrecognizable, as viewed from the past. The role of natural gas, petroleum and nuclear power could not have been foreseen, nor could nuclear weapons and the profound effect which they have had in the political sphere.

The conclusion which can be drawn from this is that in attempting to assess the role of fusion in the 25-50 year time span, we should not assume collateral changes of a revolutionary character which would change the social, economic or political considerations involved. On the other hand, looking at the 50-100 year time span, one may reasonably suppose that changes so profound will have occurred as to make attempts at prediction little more than exercises in science fiction. Therefore the assessment of fusion made here will be devoted to the 25-50 year time span. We will restrict ourselves to D-D and D-T burning fusion systems for the simple reason that more advanced fuels are so difficult to bum and require so much In the way of scientific extrapolation that it is not credible to suppose they will play a role in the 25-50 year time span. Scientific breakthroughs are always possible, of course, but you can not plan a development strategy on that basis.

The restriction to D-D and D-T burning systems brings with it a major technological and political consequence. Both the D-D and D-T reactions provide a copious source of neutrons. The radioactivation and materials damage caused by fast neutrons create a serious technological problem for the designer of a fusion machine. The political consequences stem from the presence of an intense neutron and tritium source. Any system which is capable of producing large quantities of "surplus" neutrons has the potential to produce nuclear weapons materials. Plutonium and Tritium are both nuclear weapons materials and are both readily produced in any D-D or D-T fusion device. In fact it is virtually assured that the first application of a

*Work performed under the auspices of the U.S. Energy Research and Development Administration. **Final Report of the Ad Hoc Experts Group on Fusion June 1978, DOE/ER-0008.

249 successful fusion device will be to produce nuclear weapons material. The political consequences of this are, of course, related to the proliferation issue We will discuss the proliferation problem in some detail a little later. For the moment it is sufficient to say that we can be virtually assured that fusion technology will remain classified for the next 25-50 years. One immediate consequence of this is the elimination of base-station electric power as an application of fusion. The notion that weapons materials production technology will be spread about, as are small power stations, is not credible.

One might wonder, at this point, whether there is any role that fusion can play in the energy field? The answer is, there is one. It is the production of fissile fuel for nuclear reactors. At present the technology associated with nuclear fuel production is isotope enrichment. This technology is kept secret in order to restrain nuclear proliferation. The secrecy is maintained by having only a few very large enrichment facilities.

Because the proliferation issue is so intertwined with the fusion program, it is worth delineating the problem in more detail. There are two general areas of the proliferation problem. One relates to the production of single nuclear explosives (proliferation of the first kind), whereas the other relates to the production of nuclear weapons systems. (Proliferation of the second kind).

Proliferation of the first kind is countered principally by safeguard programs which are aimed at preventing diversion of nuclear materials and weapons. This is designed to keep terrorist groups from producing a crude nuclear device, or stealing an existing weapon.

Proliferation of the second kind, which shall concern us here, relates to the development of significant nuclear weapons systems. At the present time, the U.S., U.S.S.R,, U.K., France and China have developed nuclear arsenals, India, although it has exploded a nuclear device, has not, to my knowledge, developed a nuclear weapons system. India illustrates the virtual impossibility of a safeguard program preventing a nation from building a nuclear device. However, this does not detract from the value of efforts to prevent proliferation of the second kind. Secrecy is the main deterrent to the proliferation of large scale weapons development. Whereas it can be argued that secrecy is never an absolute deterrent, it has the effect of significantly increasing the time and cost required for any nation to develop a nuclear arsenal.

The classification blanket is designed to cover all the approaches to nuclear weapons development. Because Tritium is used in nuclear weapons, both the production and handling techniques are kept secret. This fact is of considerable consequence for any D-D or D-T fusion reactor, since either will involve very large amounts of Tritium,

Similarly, plutonium production and reprocessing technology are kept classified.

The physics, as well as the technology, of nuclear weapons is kept secret. This is the reason that details of inertial confinement fusion are kept secret. If the classified tritium handling facilities were not enough to

250 guarantee that there will not be a wide-scale deployment of fusion devices, the pellet security will assure the limited use of inertial confinement fusion.

It has been suggested that maintaining classification in weapons physics and tritium technology is not necessary, and that the classification barriers should be lowered. However, the present standards are pretty much endorsed by all parties now having nuclear weapons, and by most countries who have renounced nuclear weaponry. Because the probability is not neglible that a number of countries will adopt nuclear arsenals in the years ahead, it is not at all plausible that the present classification guidelines will be subtantlally lowered. There is even the feeling in some quarters that too much has been declassified already.

Remembering that the principal line of defense to prevent proliferation of the second kind is to keep the technology secret, and thereby raise the cost of a nuclear weapons system, It is worth observing what effect success at fusion would imply.

At the present time Tritium costs about 20,000 dollars/gram.* If burned to produce heat which in turn produces electricity, the "fuel adjustment charge" would come to 40

So far, we have only discussed the aspects of fusion which are associated with the proliferation problem. In considering the pros and cons of classification, the question continually arises as to the risk benefit ratio. If a very large gain is to be made by declassifying certain information or technology, the proliferation risk may be deemed justifiable. This is particularly true if the benefits received lead to a more stable world order and/or less reliance on nuclear weapons. Many of the proponents of fusion have proclaimed it in such glowing terms (clean fusion, limitless energy from seawater, etc.) that one might indeed feel that the "gift of fusion" was worth the proliferation risk. The economics of fusion can be compared In a rather general was with that of nuclear power. The cost of nuclear energy is dominated by capital cost. These costs are dominated by the containment and safety considerations. These same considerations will dominate the fusion reactor. However, in addition there are very large scale tritium reprocessing and handling facilities, and a very large "ignition" system.** It is not rational to suppose a fusion power station could involve less capital cost than a nuclear station. Therefore the only way a fusion station could sell electricity cheaper would be for nuclear fuel to become very expensive. This could never occur, however, because a fusion plant would produce fissile material in such vast quantities that nuclear fuel would never be in short supply.

*Handbook of Chemistry and Physics, 57th Edition. **Neutral beam injectors, perhaps, for magnetic systems, Heavy Ion Accelerators for inertial confinement systems.

251 Given the necessity to maintain the secrecy associated with tritium production, and allowing for the fact that we cannot produce "pure fusion" electricity cheaper than nuclear, the options for fusion are rather limited. The clear first choice would be to make nuclear weapons material. Interestingly enough there is a compulsive logic that determines the site for such a facility. The Savannah River Plant is the only place in the U.S. that has the tritium reprocessing facilities and technology that would be required for a first generation fusion facility.* Furthermore the very large site is an important consideration when considering the environmental hazards associated with large tritium Inventories. The technology is not in hand to operate a fusion power plant with generally acceptable tritium losses. The costs of such a system are at present unknown, and the early plants are not apt to be the best in this regard.

The Tritium problem is not completely eliminated by burning deuterium in the D-D reaction. Half of all the D-D fusion reactions will result in producing an atom of Tritium. In general, since the D-T cross-section is much higher, most of the Tritium will be burned up by the D-T reaction. However, a significant amount of tritium will still be left in the "ash". For inertial fusion, tritium would be needed for the ignition portion of the pellet, in any event. In fact, when we refer to D-D burn we are really talking about a combination of D-D and D-T burn. A key question for the success of Heavy Ion Fusion will be the ratio of D-D to D-T burn which can be achieved. This plays a major role in determining the neutron economy of the fusion system.

II. Heavy Ion Fusion as a Neutron Producer

In this section we will outline the various factors which must be determined before a final assessment of heavy ion fusion can be made. The three key factors are ignitor economics, pellet economics, and "boiler" economics. The only one of the three which is well known is that for the ignitor. The key factor in heavy ion ignition systems is the cost/watt of beam power. A wide class of designs have been studied at Brookhaven National Laboratory to compare costs of various ignition parameters. To good approximation, the cost/watt for a 100 MJ, 1000 TW beam pulse versus a 10 MJ, 200 TW system, for example, are comparable. There are so many uncertainties in pellet performance at the present time that it would not be useful to speculate on what the parameters of a second generation facility should be. The heavy ion fusion ignition costs are about $5/watt. Starting from this point we can see what we can expect from such a plant as a function of pellet performance and boiler cost.

Ultimately, it may be possible to operate a Heavy Ion Fusion Plant on a pure D-D burn, using the tritium in the ash as the ignitor for the next pellet. However this is unlikely for a first generation facility. It will probably be necessary to breed some Tritium. An important feature of Heavy Ion Fusion is that the beam can easily be transported to any one of several boilers. Only one of these boilers need be a tritium breeder. This allows the design of the fissile fuel breeding boiler to go on without the added

*The U.K, obtains its Tritium from the U.S., in exchange for Pu.

252 complication of tritium breeding. Tritium recovery from the blast chamber will be necessary in any case, however.

Without detailed experimental results on pellet performance, it is not possible to make a realistic appraisal of the economics of Heavy Ion Fusion. However, we can parametrize the situation with an effort to see what might be achieved.

The most desirable pellet characteristic would be a low cost, high gain pellet with low input energy requirements. All three of these properties tend to be contradictory. High gain pellets are apt to cost more than low gain, and also apt to require larger input energies. A high gain pellet requiring a large input energy results in a rather large explosion, and therefore increases the cost of the blast chamber.

In order to get some idea of what might be expected from a first generation Heavy Ion Fusion plant, consider a heavy ion accelerator such as the one described in BNL 50817. This report describes a facility to produce 10 MJ bursts of energy at a rate of 15 times/sec, with an electrical efficiency (beam power out/electrical power in) of 40%. If we assume a pellet gain of 10, then the explosion has a yield of ^^ 100 MJ, or the equivalent energy release of 50 lbs of TNT. Since about 60% of the energy will be carried off by neutrons, and deposited over a large mass, the actual blast would more nearly approximate that of 20 lbs of TNT. A blast chamber designed to withstand such energy releases at a rate of several times/second has not yet been designed. An important element of the design will relate to the tritium handling and containment aspects, and as a result will no doubt be kept secret.

With the assumption that each thermonuclear neutron is used to produce one atom of fissile material (Plutonium or U233), the output of the plant would be about 6,5 tons of fissile material. If the material was sold for $30/gm, the gross income of all the plant would be around 200 M$ per annum. If the plant did not produce electricity, but purchased it at 2't/kwhr, the cost would be about 70 M$ per annum. The accelerator capitol cost, at 5$/watt would be 750 M$. If the rest of the complex was of similar cost, or fuel was worth more than $30/gram, the economics look interesting.

Estimates of required pellet performance are obtained from cost versus gain considerations. The facility described above would use 450 million pellets/year. If we paid 45 M$/year for the pellets, this would come to 10"^ apiece. Current prices for pellets are around $10,000 each. Whether or not mass production techniques can be designed to bring pellet costs into this range is not clear at present. It is in fact the most vital question outstanding. Before any such heavy ion accelerator based fusion plant would be built, one would have to be reasonably assured of a supply of pellets at a reasonable cost. Note that there is a relatively simple way to affect pellet costs. If we put 100 MJ on the pellet, and fired at a rate of 1.5 times/sec, instead of 15 times/sec, we could afford to pay more like $1 for a pellet. By the same token, if the gain was 100, the value would also increase. For either case, however, the gain is offset somewhat by the requirement of containing a larger explosion. By way of comparison, with G = 100 the fissile fuel production rate would be comparable to the entire isotope separation

253 facilities now in operation for the civilian nuclear power program. At 40$/lb for Uranium, this fuel would replace 13,000 tons of U3O8, for a 1 Billion dollar/year savings.

The Heavy Ion Fusion plant can be compared with the electro-nuclear breeder. The economics are about the same for the case with pellet gain'^l or 2. At a pellet gain of 10, the fusion breeder has at least a factor of 5 cost advantage.

We have now reached a point where we can clearly define the goals of the Heavy Ion Fusion program, and make some reasonable assessment of the impact on the world energy picture if these goals are realized. The goal is to produce low cost fissile fuel in sufficient quantities. The points of Impact are as follows:

1. The plutonium breeder would no doubt not be economically viable if HIF is successful.

2. A virtually inexhaustable supply of fissile fuel will eliminate the possibility of a uranium cartel.

3. Large fuel producing facilities lend themselves to International safeguards better than a multitude of plutonium reactors.

4. The growth of nuclear power would not be constrained by the limited availability of Uranium.

Whether or not heavy ion fusion can reach its goals is a question that can be definitively answered within 10 years, and for a cost of 1-2 billion dollars. Two questions need to be answered before one would proceed down this road.

1. If the HIF plant works, more or less as expected, is this worth the investment? Is it a goal the United States wants to pursue?

2. Is there a reasonable chance that the economics will be favorable? One must have the accelerator physics, the pellet physics, the pellet fabrication and the blast chamber design well enough in hand to answer this question.

254 REMARKS ON HIF DEVELOPMENT AND WEAPONS PROLIFERATION ISSUES

R. C. Arnold Argonne National Laboratory

1. Tritium, an essential ingredient in fusion reactors, is nevertheless useless as a weapons material without a fission weapon, which requires plutonium. Control of the latter is thus an effective proliferation deterrent. Therefore, fusion reactors as such do not have to be classified to maintain proliferation control.

2. The technology of high energy accelerators, all in the unclassified arena, is already sufficient to design a reactor driver, as this and earlier workshops have shown.

3. Some pellet technology is currently classified. However, some designs for HIF pellets have been published by leading experts in the open literature with predictions of fusion gains greater than 100, adequate for power reactors.

4. Therefore, to the extent that it is possible to foresee success in this field, it seems unlikely that weapons issues will require tight classification in the future development of power generation stations based on HIF. The choices in emphasis between secret and open programs will be driven to a large extent by considerations of coimnercial energy economics.

255 256 C. ION SOURCES

NEUTRALIZATION OF POSITIVE PARTICLE BEAMS BY ELECTRON TRAPPING*

R. M. Mobley, A. A. Irani, J. L, LeMaire,** and A. W. Maschke Brookhaven National Laboratory Upton, New York 11973

FROM: Proc, Symposium on Production and Neutralization of Negative Hydrogen Ions and Beams (BNL 50727, September 1977),

I. Introduction

The Heavy Ion Fusion (HIF) group at Brookhaven plans a series of experimental tests of positive beam neutralization. Present concepts of pellet fusion using heavy ion beams envision beam parameters something like those in Table I.

TABLE I

8 beams of 30 GeV U^+ 6000 amperes/beam for 4 nsec Beam power 240 x 10^^ watts Energy .96 megajoules Spot size at pellet 0.1 cm^

Problem areas in which space-charge neutralization will be extremely useful or indispensable include:

1. Final focus region—a 5 to 10 meter drift region where the beams are focused from a diameter of several centimeters to a fraction of a centimeter.

2. Final bunching—a 100 to 1000 meter region in which the final stages of bunching from several tens of amperes intensity to kiloampere levels occur.

3. Low 3 acceleration—conventional accelerator problem area in which the space-charge limits beam brightness.

We are using a 750 keV Cockcroft-Walton pre-accelerator with a duoplasmatron source to test various neutralization techniques. The source can deliver '\^ 200 mA of H+ and "^ 20mA of Xe"*" for 500 ysec or longer at 5 pulses/sec.

*Work performed under the auspices of the U.S. Energy Research and Development Administration. **0n leave from Saclay.

257 This report gives experimental results of transverse space charge studies of a 720 keV, 60 mA H+ beam in a drift region of 4.6 meters. The beam diameter was a. 2 to 'x- 5 cm, depending on intensity and degree of neutralization,

II, Experimental Set Up

The apparatus is shown in Fig. 1, The beam optics were adjusted, and the collimator sizes chosen (in a sequence of steps to be described), with the object being to provide a best-focus condition at Box 2, The best-focus condition was obtained with a low-intensity sample of the beam using a 10% mesh in Box 1, This beam, <10 mA, has negligible space-charge blow-up.

The sequence of steps was:

1. Calculate currents and set quad Triplet II to focus a parallel beam at Box 2,

2. Choose upstream beam defining collimator of 1-5/8 inches to match beam diameter filling Triplet II aperture.

3. Adjust source and Triplet I to get brightest spot on fluorescent screen in Box 2. Make visual observation of full beam (10% mesh removed) spot size to get estimate of space-charge size change.

4. Choose 1 inch aperture downstream collimator to pass low intensity beam, and to intercept a good fraction of the high intensity beam,

5. Adjust steering magnets for maximum current to Faraday cup.

6. Retune quad Triplet II slightly.

In practise, the above steps were done several times in different orders, but we soon arrived at source, quadrupole, and steering settings used throughout the experiment.

The upstream and downstream collimators were biased to serve as clearing-trapping electrodes for electrons. Inner sleeves of Al, insulated from the 6 inch vacuum pipe, were originally intended to serve this purpose. They were externally connected to supplement the collimators, as shown in the details of Fig. 1,

The Faraday cup is a 1/8 inch thick aluminum plate of 3 x 4 in,^. The plate is surrounded by an open-sided aluminum box which is wrapped with a tungsten wire grid. The box and grid are biased to -400 V to suppress secondary electrons leaving the Faraday cup surface, and to exclude electrons and collect positive ions from the background. With H^ at 720 kV, we find that with no bias the cup gives 20 to 50% higher signal levels, depending on the background vacuum condition, apparently due to vacuum surface layer effects.

258 III, Experimental Results

Visual observations had shown a bright beam spot of 3/4 to 1 inch diameters, with a halo filling a temporary 2-1/2 inch aperture. The spot grew larger with higher intensity, and when +300 V bias was applied to the clearing electrodes. These observations were confirmed with Faraday cup measurements of beam transmitted through the 1 inch downstream aperture.

The results are shown in Figs. 2-5. The upper trace is the beam current monitored by transformer 1 (120 to 140 mA), The lower traces are faraday cup currents at 20 mA/div. Figures 2 and 3 show transmitted currents of 50 mA and 15 mA, respectively, corresponding to -300 V and +300 V biases on the clearing-trapping electrodes. Even with electrodes at ground potential. Fig, 4 shows that neutralization occurs. Above +240 V clearing potential, little further de-neutralization occurs, as shown in Fig. 4,

Figure 5 shows that for the 10% beam, there is no change in transmission when the clearing electrode polarity is switched.

The rise time of the beam current signal is due to the rise time of the source. We applied a +130 V square pulse to the clearing electrodes, falling to ground when the beam had stabilized, and observed that the transmission (therefore the neutralization) changes level within 1 ysec. This is shown in Fig. 6.

We conclude that the beam is rapidly self-neutralizing. Furthermore, since increasing the clearing bias above +240 V has no effect (we went as high as 1 kV) we think that the electron removal is nearly complete.

IV. Discussion of Results

The change in H"*" beam transmission that we obtain with this particular geometry is short of a fundamental result. From an accelerator applications point of view, we would like to know the limiting beam brightness (the quantity intensity/transverse emittance)^) we can obtain with neutralization. From a beam propagation theory viewpoint, we need to know the source of the neutralization electrons, properties of the potential well of the H"^ beam, properties of the background plasma, and the degree of neutralization achieved. However, at this stage we can make two important conclusions described in A and B below.

A. The change in transmission observed is consistent with complete neutralization in the drift pipe for grounded or negative electrodes, and with complete de-neutralization in the case of > 240 V electrodes. The space charge calculation of the beam blow up goes as follows: A zero-current optics calculation yields a 1 in, diameter spot size at 4,6 meters for a beam of E = emittance/ir = 7 x 10"^ meter-radians, with a 2 in. effective aperture at the focal plane of Triplet II. Assuming a uniform charge distribution in x-y space the focal spot versus current with space-charge forces is as shown in Table II.

259 TABLE II

Current (mA) Spot Radius (cm)

1 1.27 10 1-54 20 1.88 30 2.25 40 2,61 50 2.97 60 3.32

The ratio of the spot area at 60 mA from Table II to the 1 in, aperture is 6,8, We observe transmitted current ratios of 3 to 4, If we choose a smaller e (say, that corresponding to a 3/4 in, spot), we can obtain agreement with the experiment. It is misleading to make that kind of fit, however, since our assumption of a uniform xy distribution is probably not valid. Hence, we say that our results are consistent with 100% neutralization, but we have not demonstrated neutralization to that degree.

B. Background gas ionization cannot be the main source of the electrons. The neutralization time of 1 ysec from Fig. 6 cannot be produced with the largest estimates of the ionization cross section, and the most optimistic assumption about electron trapping in the potential well of the beam. Moreover, measurements of the current to the electrodes in the clearing mode; allowing for positive beam cancellation (including secondary electron emission), yield'^ 100 mA of electron current. That corresponds to more than one electron per primary proton in the steady state.

A rough estimate of the background ionization goes as follows: An H^ beam of 60 mA forms a potential well for electrons. For a 1 in. (radius) beam in a 3 in. (radius) pipe the potential is -150 V at r = 0, -100 V at r = 1 in., and 0 V at r = 3 in.

Differential cross sections for the reaction:

H+ (750 keV) +H->H+ + H++e, from Bates and Griffingl show that collisions yielding electrons above 50 eV have a negligible contribution to the cross section. Taking the H2 cross section to be a factor of 2 higher, we get Cj < 5 x 10"^^ cm^.

The background density at 10"^ Torr is n^^ = ,35 x lO^^/cm^. (Ion gauges in Box 1 and Box 2 give background pressure readings of 1.2 and 1.8 X 10-0 Torr, respectively. The ion gauge correction factor for H2 is 2.2, giving approcximately 4 x 10"^ Torr if the background is H2. If the background is assumed to be air, there is no gauge correction, but the cross sections should be A2/3 'b 4 times higher./)

Taking 10 ^ Torr as an upper limit the mean collisional length Jl, is:

^c ~ 57 meters. Ox n^

260 Assuming that all of the electrons are trapped in the potential well, each proton has a .08 probability of creating a trapped electron. Thus, it would take'^ 12 protons to produce 1 electron in the pipe, or 12 proton transit times to produce 100% neutralization. Since the proton velocity is 12 m/ysec, the transit time for 4.6 m is .38 ysec. This gives 4.6 ysec for neutralization. In this linear model, it would take 2.3 ysec to reach 50% neutralization.

A detailed calculation allowing for the collapse of the potential well as neutralization proceeds, and integrating the differential form of the cross section, yields longer times as shown in Fig, 7.

The question remains, how are the neutralizating electrons produced? Further measurements of the rise time are in progress to help resolve this question. Three inch collars have been placed in the beam pipe to prevent grazing of the drift pipe wall, which should reduce secondary electron production to ,2 - ,5/proton. The vacuum can be improved. In addition, we have not fully considered what the H2"'" component of the beam contributes to the process.

V. Acknowledgments

Special thanks are due to E, Meier and K, Rlker of the Heavy Ion Fusion Group for rapid assembly and smooth operation of the apparatus. We also appreciate the generous help of many others in the Accelerator Department.

References

1, D. R. Bates and G. W. Griffing, Proc. Phys. Soc. (London), A66, 961 (1953).

261 MAG. QUAD. COCKCROrr-WALTON TRIPLET JZ + 720 kV \/€RT STCCRlNQ MAG.

HORZ. STEEPING, MAC

^

J500 J/sec. < '•• TURBO PUMP

XrMRS

rAPERTURE N COLLIMATOR

CLEARING, (•*•) CLEARINQ (•*•) SCALE TRAPPING (-) TRAPPING (-) (MCTCRS) BIAS aiAS

Fig. 1 The drift tube diameter is 6 in. The smaller pipes are 3 in. diameter. Vacuum components are nearly all aluminum.

Fig. 2 Upper trace, beam monitor (trans­ Fig. 3 Upper trace, beam monitor former 1) at 100 mA/div. Lower (transformer 1) at 100 mA/ trace, Faraday cup current at div. Lower trace, Faraday Box 2 at 20 mA/div. The elec­ cup current at Box 2 at trodes are biased -300 V. Re­ 20 mA/div. The electrodes sult is same from +20 ->- -300 V are biased +300 V.

262 Fig. 4 Multiple exposure. Electrode Fig. 5 Double exposure, to show bias varied from 0 ->- +320 V in that the 10% beam has same 40 V steps. No further de­ transmission with + or crease in transmission above -300 V electrode bias. The +240 V. current is 5 mA/div.

C 'V •« iccs

Fig. 6 A square wave voltage of +130 V Fig. 7 f is the calculated degree is applied to the electrodes at of neutralization vs. time. t = 0, and removed at t '\' 60 As neutralization proceeds, ysec. The beam transmission the potential well is de­ increases in '^' 1 ysec. pleted in this model.

263 264 NOTE ON XENON TESTS WITH LBL MATS SOURCE*

R. Mobley Brookhaven National Laboratory Upton, New York 11973

In the Claremont Conference report (LBL-5543), December 1976 p. 50) I reported a short test of the LBL "Multi-Aperture Tungsten Slit" source with Xenon, Some statements in that report are wrong. More careful measurements were made in September 1976 and reported at the APS Plasma meeting in November 1976. (Otherwise unpublished).

In fact, the source is extremely bright. The claims of the ion source development people in Magnetic Confinement Fusion haven't been heard and this note is an attempt to rectify the situation. Moreover, the brightness quoted at this meeting by Dave Clark for a similar source run with Xenon, but with an array of circular apertures, falls far short of the brightness obtained with the slit array.

The LBL MATS source had an array of 105 slits, each 0.2 cm x 7 cm, with 60% transparency in a 3 grid structure. The total current measured by a calorimeter 3.3 meters away was 6.5 amperes with 35 kV on the extraction gap of 0.210 inches. The current scaled very well with the V^'^ law from 20 to 35 kV, The mass scaling as compared to deuterium was corrects (reduced by a factor \/l32l\ 2.4, where 2.4 includes the effect of an admixture of D2'*' ions). The distribution as measured by a 2-dimensional array of thermistors on the calorimeter plate was identical to the distribution typical of an optimixed D2 run. Arc voltage was 19V, so the only ion species is Xe+1.

The emittance results, per beamlet, at 35 kV were:

^N ^ A(x,x') 0.2 cm x 35 mrad ^ 0.000732 n IT TT

^N ^ A(y,y') gy = 7 cm x 8 mrad ^ 0000732 V TT T\

N -3 E. = 1.63 x 10 cm-mrad h

N -3 e = 13.1 x 10 cm-mrad v *Research carried out under the auspices of the United States Department of Energy under Contract No, EY-76-0-02-0016.

265 The current per beamlet was 62 mA. To compare to the reference design of 100 mA into 0.02 cm-mrad, consider three beamlets. Allowing for transparency e^^ 'V' 0.01 cm-mrad, ej^ '\' 0.01 cm-mrad and I = 186 mA. This corresponds to a brightness 1.8 x 4 '^7 times the reference report desired design (J, Osher, LBL-5543, p. 5), and 16 times the brightness specified in the BNL HIF conceptual design.

The above tests were done under conditions of very good space charge neutralization, so that the only space charge blowup occurred in the extraction gap. Slit apertures are superior to circular apertures.

266 A CHARGE SEPARATING SPECTROMETER FOR ANNULAR ION BEAMS*

W. B, Herrmannsfeldt Stanford Linear Accelerator Center Stanford University, Stanford, California 94305

The need for very high currents of low-velocity heavy ions requires some new approaches to the transport and acceleration problem. One such approach, described in reference 1, would use a configuration of alternating accelera­ ting and decelerating fields applied by rails or rings to the ion beam, which is configured in thin sheets in order to make this method of focusing effec­ tive. The annular ring configuration of the focusing structure is attractive because of the absence of end effects. In applying this system to a heavy ion injector for a linear induction accelerator (LIA), it is noted that it may be desired to accelerate multiple- charged ions in order to reduce the length and cost of the accelerator. The same conclusion can be drawn for the drift tube linac, which could be very long if only 1 or 2 MeV are gained per section. Thus, in the example parameters shown in reference 1, it is sug­ gested that a stripping and charge- state separation system be located at the 4 MeV point between tanks No. 2 and No. 3. This report will describe an annular spectrometer system for the charge separator.

The proposed system consists of a gas - filled cell through which the singly - charged ions pass to strip off some additional electrons. This beam, consisting of several charge states, is then passed through a spectrometer which selects only that charge state chosen for further acceleration. The spectrometer is designed to use an annular - gap magnet which matches the geometry of the beam. Preliminary calculations for the acceptance and reso­ lution of the spectrometer will be shown below.

The annular ring focusing system will continue up until the entrance aperture to the stripping cell. Within the cell, it is expected that the space charge effects will be neutralized by the plasma. A stream of elec­ trons will likely be pulled along with the ions into the bending magnet to neutralize the excessive space charge there caused by the large number of multiple - charged ions. However, since these electrons cannot pass through the magnet, the beam emerging from the magnet will have a great deal of space charge. It may be useful to include one or more grid screens to cancel out some of the space charge. These grids could be part of a system of differ­ ential pumping baffles.

Work supported by the U. S. Department of Energy under contract number EY-76-C-03-0515.

267 The type and pressure of the gas in the cell will be the subject of stu­ dy and experiment. However, a promising lead is offered by A. W. Wittkower and H D. Betz^ who report that the equilibrium charge distribution of heavy ions such"as uranium passing through helium has a peak at about q = 4, At ion kinetic energies between 2 MeV and 15 MeV, the percentage of q = 4 ions exceeds 25 percent, so that as much q = 4 current would result as the q = 1 current which is injected to the stripping system. In Fig, 1, we have repro­ duced a curve from reference 2 showing the equilibrium charge distributions

8 0 2 4 CHARGE STATE

Fig. 1. Equilibrium charge state distributions of uranium ions in helium and oxygen at 2 and 6 MeV. Reproduced from reference 2,

for uranium beams in helium and oxygen. Although helium is distinctly more effective in producing a high charge state at moderate kinetic energy, the differences between target gasses is not so great as to rule out something, such as N2 or O2, which may be pumped more easily. Both N2 and O2 have more than 20 percent q = 4 from 2 to 10 MeV. Very similar results are reported for other heavy ion species such as tantalum.

The charge-separating spectrometer uses a pair of annular gaps with equal- strength, oppositely- directed radial magnetic fields. The annular shaped beam is first directed radially inward at a small angle, e.g., 10 milliradians, so that it has a radial slope as it is bent in the first magnet gap. The bend, which should be several times the radial slope, is in the azimuthal direction. The spectrometer resolution results from the fact that any straight trajectory which enters the side of a cylinder must even­ tually re-emerge at the initial radius. The distance in the axial direction between the point where the trajectory enters and leaves the cylinder is de­ termined by the bending angle in the azimuthal magnet, and thus by the charge state, assuming that all the particles have the same nominal radial slope be­ fore bending. Within the limits of radial phase space, this requirement is

268 met by locating the stripping gas cell after the elements which deflect the beam radially Inward, i,e,, immediately ahead of the bending magnet.

In Fig. 2, three views of the spectrometer are shown to illustrate the

Fig. 2. Annular Charge Separating Spectrometer, Trajectories with a radially inward slope ap. are deflected in the radial magnetic field by an angle t|i. They then continue on a straight path towards the second gap, which must be located the correct distance SB sjiiQ.y from the first gap for the trajectory to pass through the gap and emerge with slope ap after an azimuthal shift of 2cj) . Trajectory path between magnet poles is straight, but appears parabolic in the projection to the r-z plane in cylindrical coordinates, above discussion. The projected angle tf) in the end view is given by

-l/ sing \ * = tan '(I si:;"n ;e jI (1) where a is the initial radial angle after the particle is bent by an angle 6. The path of the trajectory between the gaps is a straight line, but projected on the r-z plane in radial coordinates, it is parabolic with a minimum value

^^A^ - R COS ^ . (2) min gap If the half length between centers of the gaps is ii^/2, then

R r . = (3) gap - mm o.^lk .

269 For the small angles anticipated in the system aaiotQ, but for larger angles /_tan^tan a, \ -1 ~ tan I cocoss 66 / • (4) where ao is the incident radial angle. From (2) and (3)

i^ = 4(R - r . )/a = 4R (1 - cos (5) gap min gap 0/a.

T is "reasonable," i.e., not greater than the diameter, for 9 ^ 10a, where ao Si 10 milliradians, A series of ray tracing computer runs graphed in Fig. 3 shows the radial path taken by three charge states: q = 3, 4, and 5.

20 60 100 140 ISO 220 260 300 340 380 420 460 ,.„ Z - Distonce From the First Pole Face (cm) »•'»!

Fig. 3, Computed ray- trace plots of two trajectories at each of three indicated charge states. The bending field is 0.28 T for 4 MeV cesium ions entering with an initial slope ao = -0.01 .

With subsequent aperture baffles set for a symmetric configuration, the case shown in Fig. 3 would transmit q = 4 and eliminate all other charge states within a couple of meters drift. The next accelerating gap would then be installed just down beam of the aperture baffles. The baffles are proba­ bly just a continuation of the annular focusing structure. Not yet included in the calculation of Fig. 3 is the effect of space charge on the beam drift­ ing between the pole gaps. It is assumed that the space charge effects there will be severe and that focusing rings will have to be installed within the drift space between the magnet poles. Part of the space charge could be e- liminated if atoms with the wrong q value, particularly ± 2 or more from the desired level, could be eliminated earlier. This might be done by some slanted baffles in the first magnet gap. Such baffles would also aid the differential pumping system and help as supports for the inner iron cylinder.

270 Preliminary results of the ray tracing studies show that energy spread and radial divergence do not particularly affect the conclusions suggested above and shown in Fig, 3. In fact, the spectrometer appears to have some mixing effect on radial and transverse phase space which is probably bene­ ficial since radial aberrations will have increased the radial emittance by this point in the system,

REFERENCES

1, W. B. Herrmannsfeldt, "A Multi- Ampere Heavy Ion Injector for Linear Induction Accelerators Using Perodic Electrostatic Focusing," Proceedings of the Heavy Ion Fusion Workshop, Argonne National Laboratory, September 19-26, 1978. 2, A. W. Wittkower and H. D. Betz, Phys. Rev. A, 1_, 159 (1973),

271 272 D. LOW BETA LINACS

A MULTI-AMPERE HEAVY ION INJECTOR FOR LINEAR INDUCTION ACCELERATORS USING PERIODIC ELECTROSTATIC FOCUSING*

W. B. Herrmannsfeldt Stanford Linear Accelerator Center Stanford University, Stanford, California 94305

Introduction

One of the key problems for the accelerator system for a heavy ion fusion (HIF) power plant is to provide a source of ions at the parameters, principally energy and intensity, that are well matched for the primary accelerator component. A promising candidate for the primary accelerator component is the linear induction accelerator (LIA). The LIA is well matched to the pellet requirements because it can accelerate very high intensity pulses of short ( < 1 ys) duration. The intensity in the LIA is only limited by the capability of the beam transport system and the capacity of the in­ jection system. Recent cost studies at LBL show that there may be some economic advantage in using multiple-charge ions. The space charge limited transport of a quadrupole system permits charge states of approximately four when the other considerations that have been previously defined^ are in­ cluded. Thus, for example. It would be possible to inject a pulse of approxi­ mately 150 yC of 238^+4 in a 3 ys pulse at 100 MeV. Such a pulse, while well matched to the LIA, is far from state-of-the-art for any existing injection system and even well beyond the practical limits of systems of conventional ion sources, low-3 linacs, accumulator rings, etc, that have been suggested for various HIF scenarios.

In this note, we describe two configurations for ion source and drift- tube-linac combinations that could provide the energy and intensity of accelerated ions needed for the HIF applications. The focusing for the sys­ tems is provided by a periodic structure of rectangular electrostatic lenses. Scaling rules and extensions of the ideas will be briefly described. Example systems are described that could provide 150 yC of uranium or cesium ions at 12 MeV.

The principal difficulty to be overcome in a high-intensity heavy-ion injector is, of course, space charge. The magnitude of the space-charge question can be grasped if one considers only the expression for potential depression from the outside to the center of a cylindrical beam of current I

Work supported by the Department of Energy under contract no, EY-76-C-03- 0515,

273 and velocity 3: 6V(volts) = 29,98 I(amperes)/e . (1)

For example, for a 1 MeV ^33^3+1 beam (6 = .004) of 7.5 A, the potential drop within the beam is 56 kV. Because of the low velocity, solenoid focusing is weak and a very strong solenoid (several Tesla superconducting) would be needed to contain the beam. Other focusing schemes, including an electro­ static system under construction at LBL, are either unsuitable for a long pulse length (needed to get sufficient charge) or are even more forbidding than the large solenoid. The longitudinal force generated by the potential drop at the ends of a beam pulse can only be contained at accelerating gaps. Since the ends of the pulse see these longitudinal fields continuously, very strong accelerating transients must be added to the ends of the pulse to constrain the bunch length.

In attempting to design around the space charge issue, it has been suggested to consider some type of space charge neutralization or to divide the beam into several lower intensity beams. Neutralization presents some awkward problems in the presence of accelerating fields and, even though it may always be present to some degree, seems only to complicate the problem. Dividing the beam among parallel transport systems is workable but does re­ sult in the proliferation of components. In this paper, it is proposed to create a configuration of sheet beams within the main accelerating system; each sheet focused separately to permit a reduction of the space-charge depression. The advantage of the sheet-beam configuration can be seen from the comparison of Eq. (1) with the expression for the space charge depression to the midplane of an infinite sheet beam of current density j and half- thickness x:

6V(volts) = 188.37 J(amperes per unit x^) x^ ^2) P

2 In the example to be considered, we will have about 2 mA/cm and a half- thickness about 2 cm, so at 1 MeV (6 = 0.004), 6V = 377 V. This permits using a much weaker transverse focusing system and also reduces the longitu­ dinal forces are the ends of the bunch by about an order of magnitude com­ pared to the single beam of circular cross section.

Drift Tube Linac Configurations

There are several possible physical configurations for transport systems for a sheet beam, among which large-radius annuli and plane sheets with some edge focusing scheme are the most obvious. A stacked array of ribbon beams will be recognized as a scaled-up version of the "rail" electrode geometry employed in the LBL 60-ampere hydrogen sources for the neutral-beam injection into Tokamaks, Results in this paper show that extensive scaling of this geometry is entirely feasible for the heavy ions.

Figure 1 shows an artist's conception of an annular drift tube linac with cylindrical rings providing the transverse focusing. A section view of the annular structure is shown in Fig, 2. The inner set of focusing rings can be supported with a minimum number and size of radial rods, A simpler

274 Vorlft-VFocus=^'06-lo5 Volts w

VDrift+VFocus=^'0^ + '0^ Volts

Annular Beam Ctiannel 10-71 Drift Tube 3MVAI0

Fig. 1 Annular drift-tube linac structure. Artist's conception of annular drift tube linac with periodic focusing structure.

275 , Puff Valve Jets Vacuum Tank .-^

Fig, 2 Annular ion source and drift tube linac.

mechanical design is shown in Fig. 3 for the configuration of flat parallel ribbons. The flat ribbons in this example have a total current equal to that carried by a single annular beam in a pipe of about 25% greater diameter than that needed for the ribbons. This assumes that the ribbon edges have been properly accounted for by counting only the current in the shaded areas. With some added mechanical intricacy, it is possible to have two or more concentric annular rings, so that the relative efficiency in utilizing the volume could favor the annular configuration. Ultimately, the choice between possible configurations will probably depend on details of the transverse recombination of the beam, and on mechanical engineering aspects. The rest of this discussion will be independent of the configuration.

Cylindrical sheets do not involve any three-dimensional calculations for fields and thus can be completely defined in available computer codes. Actually, in using the SLAC Electron Optics Program,2 ft is convenient to make the focusing calculations in rectangular coordinates, ignoring the effect of cylindrical curvature since it is assumed that the cylindrical radius is much greater than the radial gap between the rings (20 to 1 in the example case).

276 The ion-source Ion Beam partially defines the transport system. Based on the design for a cesium ion source for the drift tube linac experi­ ment at LBL, an ion current density of 2 mA/ cm^ or more is expected to be demonstrated to be feasible. This current density results from operating the gun at 500 kV with a second 500 kV acceleration stage into the first drift tube. The transport system consists of alternating accelerating/decelerating fields induced by static voltages on a structure as shown in Fig. 4. The structure is essentially a periodic system of rectangular Einzel lenses. The ratios of gap to width and gap to periodic spacing are not presumed to be optimized, but appear to be reasonable first choices to study the system. The beam shown in Fig. 4 is an Fig. 3 Flat ribbon configuration of periodic ordered beam assumed to focused drift tube linac. be injected into the structure. Figure 5 shows half of the beam, assuming mirror syiranetry on the midplane of the sheet, with an expanded vertical scale to show the focusing action. It shows the result of transporting the beam through 20 sections equivalent to 17.5 meters. From the scatter plots of R' vs R shown in Fig. 6, the resulting growth in phase space appears to be substantially less than a factor of two.

The potential growth of phase space due to all causes (aberrations, instabilities, grids, scattering, etc.) in such a focusing system is limited by the height 6R of the gap and the angle 66 of particles which can be focused by the structure. Eventually, however, the beam must be made to converge and merge into a cylindrical beam for transport through a more conventional quadrupole or solenoid system. The merging process will result in a phase area which at best conserves the four-dimensional transverse phase area. The relevant equivalent transverse coordinate then would appear

277 Fig, 4 Focusing structure of periodic rectangular Einzel lenses. For the annular drift tubes, the system axis is depressed by about 20 gaps, i.e., to -440 for the example case in which one mesh unit is 0,35 mm. Thus the aperture is 7 cm wide and the periodic length is 14 cm.

100 150 200 250 50 100 150 200

Fig, 5 View of the same structure as shown in Fig, 4 with scales distorted to show the focusing effect. The trajectories shown are in the 20th section, equivalent to 17.5 m of drift length. Midplane symmetry is assumed.

278 to be given by

(3) XXXXXXXKX •V TT V "FT

The normalized emittance of the

-K X -n M K-—*( *< M ^f-" beam should be less than the value assumed for the final transport system, typically TTEJ^ as 2Tr X 10"^

—"XXXKXXXK meter radians. Using R = 1,5 m, 6R = 0.04 m, we find, X = Injected Particle • = Transported 17.5 Meters -2 50 = __ = 14 milliradians (4) pr BEAM HALF-HEIGHT (cm) for 1 MeV Cs ions (6 = 0.004). This Fig. 6 Phase diagram of trajectories is substantially greater than the shown in Fig. 5, The 'x* spots indi­ 60 < 2 milliradians observed in cate the injected beam, the solid dots Fig. 6, and is probably greater than are for the transported beam. the focusing system will transport. Thus the periodic structure appears intrinsically suited to provide a low phase-space beam to a heavy-ion accelerator, provided, of course, that the merging of the beam can be accomplished without introducing excessive dilution of the phase-space volume. Figure 7 shows the focusing properties with zero current.

Fig. 7 Zero current case; transverse focusing for the bunch ends with no space charge.

279 The focusing properties of a system of periodic rectangular Einzel lenses have been estimated analytically by Lloyd Smith^ and tested numerically in a series of calculations such as that shown in Figs. 4-6. The agreement between the two methods is remarkably good; all scaling rules have been numerically confirmed and absolute magnitudes are within a few percent. To first order in x, the focusing deflection at each gap is

.J . q^^^x = 0) Av_x /^\2 ^x - - 2T V g \ 2T / ^^^ where q = charge state, V = gap voltage, g = gap length and T = kinetic energy of the particle. Since these impulses occur at points separated by the periodic length of the structure i, on the average

d X _ X /qeV \ ^2 gil \ 2T / ^^^ ds ^ ' The effect of the space charge is to cause a field E^ such that

qeE o 2 2 „ , ^ = 27Tq e ^ 27Tqejx 2 T ^"^ TV ^-^ mv 9 2 where j is the current density. Balance is achieved for d x/ds = 0 if

which can be rewritten for ions of mass number A as

4Tre 3 (gU3j/q) (9) m c e which, when solved for the focusing voltage, becomes

V(kV) = 594.6 (gJlABj/q)^^^ . (10)

In the example of Fig. 4, the effective gap is about A/2, Jt = 14 cm, g = 0.004, A = 133, and j = 2 mA/cm^, which yields V = 191 kV. The actual value found from the numerical work was 170 kV for the above parameters. Note that if we had estimated the effective gap to be i/3, the prediction would be V = 156 kV, so that it might be concluded that the effective gap lies between i/2 and i/3 for this case. More significantly, the numerical results con­ firmed the dependence of the focusing voltage on T-'-/^, 1^^^, and A^/2 gg predicted in (9) and (10).

280 Example Case: 7.5 A of Cesium

As an existence proof example we will examine a design for an ion source/ injection system for a 7.5 A cesium source capable of injecting 150 yC in a 20 ysec pulse at a low integer value of q, e.g., q = 4.

The system begins with a contact ion source whose design is based on the gun being built at LBL for a beam transport experiment. This gun, which is described in more detail in Ref, 4, is designed to emit between 1.4 and 2.0 mA/cm2. The thin ribbon version of the same gun is shown in Fig. 8, The grid on the right side covers the entrance to the periodic focussing system described above. The emitting surface is pulsed to about +500 kV and the drift tube, which begins at the gridded ring, is pulsed to -500 kV. The middle electrode in the gun is the grounded cesium injector which provides a puff of cesium to the emitting surface just prior to pulsing the gun.

Fig. 8 Rectangular "ribbon beam" gun with emitting surface 3.5 cm wide. The grounded center electrode is used for the puff value cesium injector which sprays cesium on the hot emitter prior to each pulse. Midplane symmetry is assumed.

281 The first drift tube consists of a large tank containing the drift tube focusing structure as described earlier. The length of each drift tube is determined by the drift length 3CT of a pulse. The thickness of beam ribbon that can be transported, which is determined by the focusing strength, in turn determines the transverse length of the ribbon stack, or circumference of annular beams. Thus, using 2 mA/cm2 from the gun, it is possible to transmit a 1 MeV beam 3.5 cm thick with a focusing voltage of 170 kV. A circumference or total length of 1070 cm by 3.5 cm wide for the emitting surface provides 7.5 A. At 1 MeV, gcT for the cesium beam is 24 m for 20 ysec. Adding 2 m for pulse rise and fall times makes the total drift tube 26 m long. By double pulsing each structure, that is, first negative to pull the beam in and then positive to expel it, the total system is made shorter and more effective. From the 1 MeV assumed for the injected beam, the energy could be increased to 3 MeV in the second drift tube, which would need to be 46 m long, if the succeeding pulses are all 1 MV. Table I provides a summary of the parameters through the third drift section.

Example Case: 7.5 A of Uranium

Everything in the previous section can be extended to the case of uranium (or other high mass) ions provided that a large area ion source5 can be developed. In Table II, the parameters for a uranium drift tube structure are given by scaling from the values in Table I. A lower current density (1 mA/cm2) has been assumed to avoid uncomfortably high focusing voltages. This results in a larger area needed for the emitter but, by way of partial compensation, all the drift lengths are shorter due to lower values of v/c for the same kinetic energy. The emitting surface area requirement could be met by three concentric rings in the annular structure, or by a large ribbon structure. Of course, trade-offs of current and pulse length are always possible.

Accelerating, Bunching and Combining

After several drift tube sections the beam velocity will become large enough that further acceleration in electrostatic focused drift tubes will be uneconomic. The drift tube gap voltages could be programmed to begin to bunch the beam, at least to the point of preventing the bunch from becoming physically longer with each acceleration. Bunching may extend the use of drift tubes until the beam reaches velocity and bunch lengths that make the LIA more economic; 100 MeV and 3 ysec for example. However, it is likely that the focusing structure will give way to a "conventional" cylindrical beam fairly soon. Thus the requirements specified by Faltens and Keefe^ would be met by the system already described. The beam would have to be combined into a "solid" cylinder before entering a magnetic focusing system such as they describe. Combining the beam can be accomplished by deflecting the beam inward along a converging trajectory and then causing it to flare out straight as it enters the next accelerating and/or focusing structure. These deflections are made by putting slightly different average dc voltages on the inner and outer sets of focusing rails. Figure 9 shows the deflection of a beam with a voltage difference of about 5% of the focusing voltage. Once deflected, the beam continues along the converging path provided, of course, that focusing is provided with an increasing strength since as the area decreases, the current per unit area increases. Although there will be

282 TABLE I

CESIUM DRIFT-TUBE LINAC PARAMETERS

2 GUN : V = +0.5 MV I - 7.5 A j = 2 mA/cm (1 m) Emitter: Ion Cs Length = 1071 cm Width = 3.5 cm

Pulse: Q - 150 yC T = 20 ysec

TANK #1: V^ = -0,5 MV I = 7.5 A T = 1 MeV

(27 m) V^ = -170 kV 6 = 0.004 T = 20 ysec q = +1 V2 = +1.0 MV L = ecT + 2 T = 2 MeV Bex = 24 m = 26m

TANK #2: Vj^ = -1.0 MV I = 7.5 A T = 3 MeV q = +1

(71 m) V^ = -224 kV 3 = 0.07 T = 20 ysec 3CT = 44 m

V2 = +1.0 MV L = 46 ra T = 4 MeV

STRIPPER AND CHARGE SEPARATING SPECTROMETER:

(78 m) Separate to select q = 4 B = 0.008 T = 4 MeV

L = 3.6 (magnet) + 2 X 1.7 (stripper) = 7 m

TANK #3: Vj^ = -1.0 MV I = 7,5 A T = 8 MeV q = +4

(146 m) V^ = -141 kV 3 = 0.011 T = 20 ysec 3CT = 66 m

V2 = +1 MV L = 68 m T = 12 MeV

NOTES: V^ and V2 are respectively the first and second pulsed voltage levels for the drift tube. V^ is the static focusing voltage applied to one set of rings relative to the others which are at Vj^ or V2. Cummulative lengths are shown in parenthesis.

283 TABLE II

URANIUM DRIFT-TUBE LINAC PARAMETERS

2 GUN V = +0.5 MV 1 = 7.5A j = l niA/cm (1 m) Emitter: Ion Cs"*"^ Length = 2142 cm Width = 3.5 cm

Pulse: Q = 150 yC = 20 ysec

TANK //I: V^ = -0.5 MV I = 7.5 A T = 1 MeV q = +1

(21 m) V^ = -140 kV 3 = 0.003 T = 20 ysec 3CT = 18 m

V = +1.0 MV L = 3cT + 2 T = 2 MeV = 20m

TANK #2: V^ = -1.0 MV I = 7.5 A T = 3 MeV q = +1

(47 m) V^ = -184 kV 3 = 0,0052 T = 20 ysec 3CT = 24 m

V2=+1.0MV L=26m T=4 MeV

STRIPPER AND CHARGE SEPARATING SPECTROMETER:

(54 m) Separate for q = 4 g = 0.006 T = 4 MeV L = 3.6 (magnet) + 2 x 1.7 (stripper) = 7m

TANK #3: V^ = -1.0 MV I = 7.5 A T = 8 MeV q = +4

(107 m) V^ = -117 kV 3 = 0.0085 , = 20 ysec 3CT = 51 m

V2 = +1 MV L = 53 m T = 12 MeV

forf the driflllffrlV^'V^^^^T''^^''t tube. Vf is the stati^^'^c focusin^^^'' g^" ^voltag "^^°"e ^ applieP^l^^d^ ^°ltagto onee selevelt of s = ^^^^ °"-^ "^"'^ -^ - ^1 - ^2- 'cumulative lengtC^rf

284 Fig. 9 Deflection within the annular focusing structure is needed for the charge separator and for recombining the beam into a cylindrical beam for further acceleration in a conventional trans­ port system. By making the average potential different in the inner and outer focusing structures, the beam is caused to deflect toward or away from the axis.

inevitable phase space dilution in this process, it presently appears as if the emittance of the electrostatic structure will be substantially below the values needed for transporting beams of the required intensity in the in­ duction linac. Thus the phase space dilution is needed for matching the LIA transport system.

Summary and Conclusions

The problem of providing a high intensity pulse of heavy ions requires some special tricks to avoid extremely expensive solutions to the space charge problem. Spreading the beam out between rectangular Einzel lenses arrayed as a periodic structure appears to provide a workable solution to the problem. The configuration suggested here should be considered as an exist­ ence proof that this is a valid approach but it has not yet been at all optimized. Presumably one would like to transport the highest possible current with the lowest possible focusing voltage. However, it is also necessary to consider the clearance between the beam edge and the aperture as

285 well as the aberrations that t3T)ically result from getting too near the focusing elements. The example cases appear to be conservative in all design respects. If the periodic structure is extended to higher velocities than those considered here, the practical limits on voltage standoff will have to be considered. To offset the 3 ' voltage dependence, it is possible to reduce the gap and length dimensions which were shown in Eq, (10) to reduce the focusing voltage proportionately to (gJl)^'2,

References

1. A. Faltens and D. Keefe, Quasi-static Drift Tube Accelerating Structures for Low Speed Heavy Ions, Particle Accelerators (to be published), (1978).

2. W. B. Herrmannsfeldt, SLAC Electron Optics Program, SLAC Report 166, September 1973.

3. L. Smith, private coimnunication.

4. S. Abbott, W. Chupp, D. Clark, A. Faltens, W. Herrmannsfeldt, E, Hoyer, D. Keefe, C. Kim, R. Richter, S. Rosenblum, J. Shiloh, J. Staples, E. Zajek, "The Experimental Program of Heavy Ion Fusion at Lawrence Berkeley Laboratory," Proc. of the Argonne Heavy Ion Fusion Workshop, Sept. 1978.

5. M, Hashmi and A. J. Van Der Houven Van Oordt, Conference on Uranium Isotope Separation, London, March 1975.

286 FACTORS CAUSING LARGE TRANSVERSE EMITTANCE INCREASE IN LINACS USING A HIGH-BRIGHTNESS ION SOURCE

John Staples Lawrence Berkeley Laboratory

All HIF scenarios impose strict limits on the admissable transverse emittance blow-up of the beam obtainable from the ion source. In those scenarios where a low-beta linac has been specified, a relatively low factor has been assumed for the transverse dilution generally in the region of 3 to 5, In this note we will investigate the validity of this assumption with a single coupling argument and with a simulation calculation.

Previous numerical work by Chasman has shown that the normalized output emittance of a proton linac with 750 kV injection energy has a lower limit when the input emittance goes toward zero. There are two major mechanisms which are responsible for this, neglecting those which were not modelled, such as imperfections in the machine. Those mechanisms are space charge L-T coupling and L-T coupling through the accelerating fields. In her paper, Chasman showed that for currents above a few mllllamperes the r.f. coupling was negligible and space charge forces were entirely responsible for the transverse emittance blow-up. She did not attempt to give analytical treatment of the value of the minimum output emittance. 2 In more recent work by Jameson and Mills additional numerical results are presented over a wider range of variables, including operating frequency and injection energy. This work supports Chasman*s results and suggests also that increasing the operating frequency may be of value in reducing the output emittance.

The fact that a lower bound seems to exist for the normalized transverse exit emittance seems to suggest that space charge forces are transferring energy to the transverse planes, this energy coming from the longitudinal motion. Strictly linear space charge forces would not cause this coupling, so a non-linear charge density must be assumed within the bunch, and the details of the coupling mechanism is then dependent upon the nature of this distribution.

1. R. Chasman, 1968 BNL PLAC, p. 372, also, 1969 PAC, NA-16, p, 202 2, R. A. Jameson and R. S. Mills, LASL Office Memorandum, 4/8/77.

287 Using a thermodynamic description, we assume that the initially low transverse temperature rises due to this coupling to the level of the higher longitudinal temperature. The coupling strength between the transverse and longitudinal motion is difficult to estimate on the basis of simple arguments, but it will be assumed that sufficient time exists for this equilibration to take place. To establish whether the HIF machines in question are operating at the equivalent level of space charge related effects as those of the proton machine in Chasman*s calculations, one can calculate the ratio of the space charge forces to restoring forces in both the transverse and longitudinal planes and compare those with Chasman's. This is equivalent to calculating the depression of the betatron and synchrotron tunes.

Consider a general linear accelerator (Alvarez or Wideroe) that has Ug gaps per Ngx« The maximum energy spread in the r.f. bucket is

1/2 A W = [- I (qeVg)(AmpC^)3^T -^ (s±n

One can calculate a longitudinal temperature from the corresponding A3z:

kT^=|Ampc2 (A6^)2 (2)

If the transverse temperature, which is initially much less, becomes equal to the longitudinal temperature in the interaction time allotted, then

A3^ = A3^ (3)

The normalized transverse emittance is related to the transverse velocity spread by

^ e ^ " "^(^^x^ X (4) where x is the mean beam radius. Because available sources have a very high brightness, more than customary proton sources by a good margin, the transverse emittance can be increased by a considerable fraction, giving rise to large apparent dilutions of the emittance of these bright sources.

288 For low-frequency linacs, typical of those being considered for the front end of a HIF driver and with a normalized source emittance of ,027r cm-mrad, dilutions of the transverse emittance are on the order of 10 with this model. The tune depressions for these linacs are large, and some particle loss would also be expected.

To verify these results, one of these linacs (the 2 MHz proposal) was briefly checked with a particle tracking program (PARMILA), suitably modified for 3^/2 structures and including a point-space-charge algorithm. Preliminary results indicate an overall transverse emittance blow up at the 7th gap of a factor of 12 with large dilutions already occurring in the first two gaps. There is a loss of some particles, mostly by aperture limitations, and the dilution seems to stop after the first two gaps. Without space charge, the same linac seems to maintain the input emittance through the critical first few gaps. N It should be observed that the value ofEt in terms of the variables in equation 1 has no 3 dependence, as the concept of beam temperature is independent of the longitudinal momentum. However, the L-T coupling mechanism, space charge, does depend strongly on 3, and higher injection energy would reduce the coupling, thereby reducing the dilution factor. As the coupling mechanism Is complex and dependent on the details of the charge distribution in the bunch, numerical calculations with particle tracking codes are probably the best way to determine the dilution in the front ends of these HIF driver linacs.

289 290 GABOR LENS THEORY*

A. A. Irani Brookhaven National Laboratory Upton, New York 11973

I, Summary

The principle of using the space charge of an electron cloud to focus ion beams was first proposed by Gabor.^ Electrons are to be confined radially by means of an axial magnetic field B^ and axially by means of externally applied electric fields Z^.' An ion beam of charge density n-j^ << n^, the electron charge density can then be focused by the radial electric field set up by the electron cloud. The case considered here is that of a hollow cylindrical con­ ductor charged to a potential +V with grounded rings on either side to set up the axial Eg field. A solenoid wound around the central conductor supplies the B2 field. Theoretical calculations are carried out for n^ maximum as a function of B^ due to radial confinement and V due to axial confinement and the focal length of the Gabor Lens is calculated,

II. Theoretical Calculations a. Radial Confinement

Bl

The equations of motion for an electron in an axial B^ field can be written as:

m X = -e -2TTn ex + -^ B (1) e [L - e c z m y = -e -2TTn ey - — B (2) e -^ |_ e -^ c zJ m z = 0 (3) e In order to find a self-consistent equilibrium we consider the constants of the motion of Eqs. (l)-(3). In cylindrical coordinates they are:

O T 0 0 H = -z- (v + V.) - Trn e r = constant 2 r 6 e

*Research carried out under the auspices of the United States Department of Energy under Contract No. EY-76-C-02-0016.

291 eB r^ P^ = m rv^ - —:r = constant 0 e 9 2c p = constant, z Any function of these constants is an equilibrium distribution function. An appropriate function for present purposes is the rigid rotor equilibrium.

n / m 2 f = -z-^- 6H-a) P. -^V )5(p -m V ) e 27rm V e 9 2 j_e / z e ze

where Wp is the constant angular velocity of the electron beam and V , V are constant characteristics of the electron beam. Then, -Le ze

n (r) = f dp e ^ e ^

= n for r < a e

= o for r > a

where V a = F J.e (4) 7. 2 CD ^ 0) - to e e e 2 L _ with eB 47rn e e e m c and CD e m

From Eq, (4)

m o 2 le n = (5) 2 r^e^e -^e - ^ e 2'rTe and

^_ - "e (i^^i ~ ^ gives ^e ~ ~2~ ^® ^^^ maximum value of the angular e velocity of the electron cloud.

292 Substituting for o) in Eq, (5) we get:

n maximum = (6) Sirm c e e 2x: 1 +

i-e where X^ = is the Debye Length. D 0)

2 a Figure 1 is a plot of n maximum versus B for the case where X << -r-. e z u £. b. Axial Confinement •»-V d , d -L Tb ~

Consider a hollow cylinder of radius b and length 2L charged to a potential +V. At a distance d away on either side we place the two grounded electrodes. The potential at the boundary is then given by:

(t)(b,z) = V for - L < z < L

= ^ (L + d - z) for L < z < L + d (7) d = ^ (L + d + z) for - (L + d) < z < - L d

= 0 otherwise

Since we use the technique of Fourier Transformation we define

(8) <|)(r,z) = 2^ J (r,z) e dk and its Fourier Transform

(l>(r,z:r,z)) = I/ (|)(r,z)e ^ ^ dz (9) •^ — a

Using Eq. (7) the boundary condition to be used for calculating ^(r,z) is given by:

- 4V k kd (J)(b,z) = —2 si^ ~2 ^^^ "'" ^^ ^^^ ~Y (10) dk

293 We next calculate the Green's function i.e., the field due to an electron in­ side the cylinder at potential V. According to Poisson*s equation

2 V c|) = 47Te 6(x - x')

Now, as is usually done for simplicity, we pick the origin of coordinates at x* and after obtaining the final result generalize the solution. Using cylindrical coordinates we have:

r —

Using the Fourier Transformer technique indicated and the Boundary Condition given by Eq. (10) ) I (kr) > T ,, , , - 2eK(|k|r ) J(r,z) = -^ sin I (2L + d) sin y- + 2eK^(|k|b) I I (kb) o { dk for (11)

0 j< r £ b

Now, using Eq. (8) - ,, I (kr) ^ 1 ik(z+L) . ik(z-L) ik(z+L+d) ik(z-L-d) e + e - e -e / (kb) dk o (12) I (kr) - 00 k O ^o^l^l^^rikby-^o^l^l-)

The first terra in the potential indicated by <^-^ comes from the Boundary Con­ dition and the second term (J>2 is due to the electron. The integrals are to be solved using contour integration taking care to include the poles of KQ and the infinite poles of I^ on the imaginery k axis.

The axial electric field is then given by

E = =-f^=E.+E- ^ = „ z dz zl z2

294 Now, using the Green's function technique and remembering to generalize the solution, E2 can be calculated due to a constant density electron cylinder of radius a and length 2L as follows:

E = E ^ (complementary function to meet B.C)

+ n^27T J r* dr* J dz* E^^ (>^ "^ ^ ' r' , z ^ z - z*)

The result obtained for -L < z < L and on axis (r =0) is:

00 -k d 1 n -k (L-z) -k (L + z) ^ J_ y 1 - e n n bd ^,1 k- J,o,(l k b) e - e n=l n 1 n

27T e n a «> J,(k a) Y (k b) -k (L-z) -k (L+z) e y In on n n -, k J,(k b) e - e (15) n=l n 1^ n

where the k are given by J (k b) = 0,

The maximum electron density due to axial confinement can be calculated from Eq. (15) by setting E^ (z = + L) =0- This is the case when the ex­ ternally applied field to contain electrons axially equals the self-defocusing fields of the electrons. Then, for the case a = b

^ " Y (k b) -2k L -k d -2k L o 2 r-- on n n n 27T e n ) 1 - e V r- 1 1 - e 1 -e P L-, bd k J.(k b) n=l n=^,l n 1 n with (16)

J (k b) = 0 o n

Figure 1 is a plot of n^ maximum versus V for the case a = b = 2 cms., 2L = 20 cms, d = 1 cm. From Figure 1 for a given value of ng maximum one can pick out the corresponding values of B and V,

It should be pointed out that by clever manipulation of the Bg field which confines electrons radially one can also enhance axial confinement. For example, if the solenoidal coil is wound around the central conductor at potential V then the magnetic field in the gap region is perpendicular to the direction of electron flows at breakdown. Hence one can make use of magnetic insulation so that much larger values of V are possible before breakdown occurs. Another technique would be to use the magnetic mirror effect to aid axial confinement of electrons. By having more turns of the coil in the region of the gap a magnetic mirror can be set up and calculations can be done to see how this effect aids electron confinement.

295 c. Focal Length

For an ion propagating through the lens the equations of motion can be written as:

F =m. (r-re')= ^^ ^ + ^) ^7) r 1

FQ = m. (r 9 + 2 r 0) = - -^ r B^ (18) where E is the radial electric field due to the electron cloud, r The calculation for the focal length is simplified by going into a rotat­ ing frame with the Larmor frequency

ZeB a. = -r—- i.e., 9^-0- Q.t 1 2 m.c 1 1

Going into the rotating frame and using the initial conditions that at t = t , r=r,9=9,r=0=Owe get °

^ + k^r = 0 dz^ where 2 2 2 2 2 2Trn Ze ZeB •^ -—72- + -rfTT (i« m.V. 4m. V^ c 11 i i The focal length of the lens is then

f = y^ Q^^ t^i with L' = 2L, the length of the lens. and J m. V. '^^'^ ^2L^ ^ / :nr2\ <2o)

in the thin lens approximation.

If n maximum a. e ""^ (J 2 OTITDe C

296 then in Eq. (20) the term due to E of the electron cloud is larger than that due to B by m./Zm , z -^ 1 e III. General Discussion

a. Stripping Action

The electron cloud in the Gabor Lens has the capacity to strip the ion beam. In general this is also true when one talks about space charge neutraliz­ ing an ion beam. The time required for the stripping of any element to any desired degree has been calculated for an electron density of 2 x lOl^ cra~^ and kinetic energy 13.6 keV. Looking at these results it seems that for a single Gabor Lens the mean free path between ionizing collisions is larger than the length of the lens and hence the stripping action is not important. However, if one plans on using a series of these lenses stripping can become a significant effect and calculations would have to be carried out for the electron cloud and ion beam under consideration.

b. Electron Cloud Setup

A constant density electron cloud can be set up by injecting electrons into a rising magnetic so that the magnetic field can carry the electrons to the region near the axis of the lens. Experiments on HIPAC-*»4,5 j^ave studied such injection schemes in a toroidal device. In present experiments on the Gabor Lens it seems that electrons are obtained either by the head of the ion beam interacting with the grounded electrode or by electron field emission from the electrode^. It is plausible that an annular electron beam can thus be set up. However, the annular beam would be unstable. This instability called the Diocotron Instability^ can stabilize by filling up the centre of the annulus. This could be a possible explanation of how a constant density electron cloud can set up by itself in the Gabor Lens. However, experimental measurements on the emittance of the ion beam would indicate if this is indeed the case.

Using Fig. 1 and Eq. (20) a comparison of the focal length can be made between experiment and theory. The agreement would be good only if the electron bottle in the Gabor Lens is filled to its maximum. This may require an electron injection scheme as indicated. The background gas pressure would also have to be kept low so that background ions do not appreciably affect the radial electric field set up by the electron cloud. Also, as in one of the assumptions used to set up a constant density electron equilibrium, the length of the lens must be larger than its radius.

Finally, a computer program is being written to trace the envelope of an ion beam as it propogates through a series of Gabor Lenses.

I would like to acknowledge many interesting discussions with Bob Gluckstern.

297 References

1. D. Gabor, Nature 160, 89 (1947). 2. J. D. Daugherty, L. Grodzins, G. S. Janes, and R. H. Levy, Phys. Rev. Lett. ^, 369 (1968).

3. G. S. Janes, Phys. Rev. Lett. J^* ^^^ (1965). 4. J, D. Daugherty, J. E. Eninger, and G, S. Janes, Phys. Fluids J^, 2677 (1969). 5. W, Clark, P. Kom, A. Mondelli, and N. Rostoker, Phys. Rev. Lett. 31, 592 (1976).

6. R. Mobley, Private Coimnunication.

7. R, C, Davidson, Theory of Nonneutral Plasmas (W, A, Benjamin, Inc. Reading, Massachusetts, 1974).

RGURE 1

Figure 1. Plot of n^ maximum versus Bz for radial confinement and V for axial confinement of electrons.

298 GABOR LENSES—EXPERIMENTAL RESULTS AT BROOKHAVEN*

R. M. Mobley Brookhaven National Laboratory Upton, New York 11973

Introduction

For heavy ion pre-accelerators and low 3 linacs, magnetic quadrupole focussing becomes much more difficult than for proton accelerators. The main reason is that the magnetic rigidity of heavy ions of a given energy is proportional to "X/A/q, where A is the atomic mass and q is the charge state.

For intense ion beams (tens of mllllamperes), q = +1 is the only option, and one is pushed to increased bore diameters compared to proton designs, which would further increase pole tip fields,

For these reasons, we were very interested in the focussing lens proposed by D, Gaborl and experimental results of Russian workers.2»3 Gabor's concept of the lens operation is the most direct we have seen in the literature, and several of his predictions have been verified by our measurements.

In addition, we were very encouraged in January 1978 by the experimental demonstration of Rex Booth and Harlan Lefevre^ at Lawrence Livermore Laboratory, They have a series of Gabor lenses after an ion source transporting 20-40 keV dc beams, exhibiting very stable operation and excellent optical quality.

Principle of the Lens

Consider a cylindrical electrode at positive potential in a solenoidal magnetic field (Fig. 1). The interior of the electrode is an electron trap with the electrons confined radially by the magnetic field and axially by the electric fields at the ends to ground rings or to larger diameter vacuum pipe.

Electrons can enter the bottle via cold cathode emission, secondary emission from a beam, or as Gabor suggested, a hot cathode in a cusp magnetic field region at one end. One can hope, that with the help of trochoidal magnetron orbits, collisional diffusion, and ionization of the background gas within the bottle, a uniform distribution of negative space-charge is established.

*Research carried out under the auspices of the United States Department of Energy under Contract No, EY-76-C-02-0016.

299 That this is indeed the case is established experimentally by the linear focussing of positive ion beams. The radial electric field is proportional to r for a uniform space-charge distribution from Gauss s Law.

Assuming the trap fills to the point that the axis is at ground potential, the transverse momentum p,- imparted to a parallel positive ion of p^^ at the full radius R is:

^ ^ VL ^ R (1)

^i ~ ^^ ~ ' in which V is the potential on the electrode, L is the length of the electrode, T is the accelerating potential for the ion, and f is the focal length in thin lens approximation.

We find experimentally that the focal strength (1/f) is'^ 70% of that given by Eq. (1).

Further assumptions made by Gabor have been indirectly verified. One of these is that the electron population is epithermal in a band near the electrode potential, and that the magnetic field for stable operation as well as minimum current to the electrode should be sufficient to give a Larmor radius < R/2, for electrons of kinetic energy eV:

6 V^/2 B > 6.75 X 10 —r— (mks units) (2) — K

A. W. Maschke has developed several corollary formulas (3) through (8) as follows:

n = 2.2 X 10^ V/R2 electrons/m^ (3) e

f = 1.33 X 10^ V^^^/R = plasma frequency in Hz. (4)

f = 28 B GHz = electron cyclotron frequency (5)

f2 and fdrift ' "^^'" ^^^ " ^^^ f^ ^^^ c for the frequency of revolution as electrons drift around the axis of the lens, for electrons at an average radius greater than their Larmor radius.

If we assume a thermal velocity of the electrons acquired by being accelerated to a potential V, then one can define the Debye length for the system. In general, the electron temperature will be somewhat less. Therefore,

A^ <^ R/2 = radius of curvature in the critical field, (7)

300 Eq. (2) has been verified experimentally. We find the optimum B field to be about twice the lower limit value, varying as V^/2. g^g^ (3)^ (4)^ g^^j (7) assume a pure electron cloud. Actually, the lens may have a low-density non-neutral plasma, in which case Eq, (3) represents the net negative charge density, but f can be higher.

We tentatively assume that the focussed beam current i should be less than a hypothetical i^iax ^^^ which the beam charge density equals the electron density.

i < ijnax =&V/30 amperes (8)

in which 3 is v/c for the ion.

If additional electrons can enter the lens as the beam current increases i«,omaxv is not a limit,

Experimental Results

A, Focal Lengths

We have built and operated several lenses of the type shown in Figure 1. The lens in Figure 1 was constructed inside a drift tube used in a bunching cavity operated at 16,6 MHz as described later. Basically, it has a 4-1/2" long X 2-1/8" I.D. electrode operated at 5 to 20 kV. A split solenoid of 120 turns of length 6" is wound around a 4" diameter grounded tube. The extensions of the drift tube bore hole serve as dc ground rings and a shield below cutoff from rf in the external gaps.

We have experimentally observed focal lengths with a fixed Faraday cup with slits of 1/16" width, or holes of l/4"-l/8" diameter, using proton and xenon beams from 300 to 750 keV. The results for the lens in Figure 1 and another lens of 2-7/8" I.D. are given in Table 1.

301 TABLE 1

Lens 1 Lens 2 (in drift tube)

I.D. (in) 2-7/8 2-1/8

L (in) 11 4-1/2

Coil (turns/in) 6.6 20

V(kV) 10 13

T(kV) 700 550 f (in)* 25.2 13.9 e f^ (in)t 14.7 11,3

.58 .81 ^t/^e -4 B (tesla) 377 X 10" 585 X 10"^ e B (tesla)** 185 X 10"- 4 285 X 10"^

* fg is the experimental focal length, including the effect of object-image distances. t fj. is the Eq, (1) focal length, including the thick lens correction:

** B is the field strength from Eq. (2),

302 These lenses were operated at vacuum pressures of 1-3 x 10"^ torr, as measured by ion gauges some distance away, varying from 1 to 3 feet depending on the setup. At higher pressures, a high density plasma discharge with a sheath at the inner surface of the electrode develops, and we observe a ring rather than a spot on downstream fluorescent screens.

In learning to operate these lenses, we were first able to observe focussing with dc fields and pulsed beams of'^ 500 ysec. This mode of operation depended on considerable outgassing of the lens under glow discharge conditions. Moreover, in many cases the lens was not filled with electrons until after the beam started through,

A more satisfactory mode of operation is to pulse the magnetic field, simply by closing an SCR switch between the power supply and the coil. The magnetic field rises in '\'50 msec, and the beam can be triggered with variable delay of 100 to 300 msec. In this mode, if the voltage is high enough, it is possible to have the lens trap filled with electrons from cold cathode emission, and we have sufficient time to trigger the beam pulse before a glow discharge develops.

Figure 2 shows a short lens for use in our pre-accelerator column. The positive electrode is a conic section tapered to graze the field lines of the pancake coil. The idea of this geometry is to provide a strong E^ component to prevent buildup of background positive ions (and a glow discharge). This works for Booth and Lefevre who operate their lenses in the 10"^ torr pressure range,

B. Linearity Test with Emittance Measurement

The lens quality is of particular interest. If dozens of lenses were to be used in an rf linac, for example, a 10% non-linearity in each lens would severely dilute the transverse phase space of a beam. Focussing the beam through holes doesn't give a definitive answer. The high intensity scraping a hole causes sputtering noise which makes it hard to tell if the lens strength is fluctuating.

We have carried out one emittance measurement. With the method we used, one obtains the focal length as well without the sputtering problem.

Lens 2 (in the drift tube) was centered 112 + 2" from the ion source extractor electrode. At 48-1/2 +_ 1/2" downstream from the lens center was a moveable vertical slit of ,025" width. At a distance 10 +_ 1/8" was a moveable .025" pickup wire.

With this setup, we measured the horizontal plane emittance with the lens off, and with the lens on to produce a crossover near halfway between the lens and the slit. The results are shown in Figure 3,

303 The furthest point with the lens on projects back to 0,63 inches at the lens position. Thus we sample'\'2/3 of the lens aperture. The points at .85 and 1.2 inches represent the maximum deviation from linearity, yielding an upper limit of the non-linearity of 5%, We suspect the non-linearity is substantially less, but a more careful measurement is required.

The beam was 500 keV Xe"*" and the lens was operated at 10 kV, One would expect the focal length to be greater by a factor 13/10 x 500/550 =1.18 than the experimental result in Table I, yielding 16.4", The emittance measurement yields 16.3". We simply use the slope in Figure 3 to deduce the position of the beam waist,

C. Gabor Lens in a Drift Tube

We wanted to know if rf fields in the vicinity of a Gabor lens would cause trouble. The re-entrant snouts shown in Figure 1 represent a wave-guide below cut off for 16.6 MHz. The lens was operated as a 16,6 MHz buncher for 500 keV protons and the results are shown in Figures 4 and 5. The detector was a Faraday cup with a 1" hole, and the rf signal was filtered out.

Figure 5 shows successful lens operation with'uSO kV rf voltage on the drift tube. Earlier tries without the re-entrant snouts failed. Even so, it is apparent from Figure 5 that secondary emission from the beam was necessary to ignite the lens, and that more shielding (meaning less effective lens length in the drift tube) is probably required.

Acknowledgements

All of the members of the BNL HIF group have contributed to this study. I particularly want to thank E. Meier for ideas and help with the early tests, J, Brodowski for design of prototype lenses, J. Keane for the rf equipment, and G. Gammel and L. Golding (a summer student now at UC Berkeley) for valuable experimental assistance.

References

1. D. Gabor, Nature, ^60, 89 (1947).

2. S. V. Lebedev and A. I. Morozov, Soviet Physics-Technical Physics, 11, No, 5, 707 (1966),

3. V, V, Zhukov, A, I. Morozov, and G. Ya Schepkin, Zh ETF Pis. Red. 9, No. 1, 24-27, p. 14 (1969).

4. R. Booth and H. W, Lefevre, Nuc, Inst, and Methods, 151, 143-147 (1978).

304 Figure 1, Gabor lens in a drift tube. The +HV electrode is the inner cylinder and is 4-1/2" long x 2-1/8" I.D, The coil is a split solenoid 6" long with 60 turns in each of two 2-1/2" long solenoids. The overall length of the drift tube is 11",

Figure 2. This lens has a 1" long x 3" focussing electrode, which flares to a 4" diameter. The pancake coil will provide up to 500 gauss field strength and is freon cooled at the end plater. The coil spool and the end ring serve as ground electrodes.

305 50 ^ X LENS ON • LEMS OFF

.e .A .G .8

SLIT POStTlOM fiw)

Figure 3, The lines indicate the tilt of the emittance "ellipses", and the associated numbers are full width divergences in mrad.

Figure 4. Double exposure, showing H beam signals with the lens off (4 mA) and lens on (12 mA). The Faraday cup had a 7/8" diameter hole, positioned 20" from lens center. The tilt of the signals is due to ion source adjustment. 306 Figure 5, Same arrangement as in Figure 4, with rf buncher on at'^50 kV, The rf signal exhibits beam loading. The rf field, although attenuated by the re-entrant extension in the drift tube, inhibited lens ignition. Lens action has'^ 50 ysec delay before ignition by secondary electron emission.

307 308 E. BEAM MANIPULATIONS AND BUNCHING

INSERTION OF SKEW QUADRUPOLES TO EXCHANGE X - x' AND y - y' PHASE SPACES*

David Neuffer Lawrence Berkeley Laboratory

1 2 Some suggested HIF accelerators ' require exchange of horizontal (x-x') and vertical [y-y*] emittances in beam stacking and bunching. This can be accomplished by a 90° rotation in a solenoid. The purpose of this note is to demonstrate that this can also be accomplished in a skew quadrupole transport system, and to demonstrate necessary and sufficient conditions for such a system.

The skew quadrupole system considered is a normal quadrupole lattice rotated 45° in the transverse (x-y) plane. The equations of motion in the usual quadrupole coordinates

x" = - Kx n.

y" = Ky ^^

are rotated -45° to the lab coordinates to become: x" = - Ky (lab) (2) y" = - Kx For our purposes it is simplest to express the problem in matrix terms. The effect of an arbitrary quadrupole transport system (not skew) can be re­ presented by a 4 X 4 matrix Q for (x, x', y, y') as:

0 \ o\ A 0 0 Q= s^ D^x (3) 0 V \ ^y \o 0 s •^y The effect of a skew quadrupole array can be represented by a matrix Q' where

Q' = R-^ Q R and R is the matrix for a rotation of -45°. * This work was supported by the Offices of Laser Fusion and of High Energy and Nuclear Physics of the Dept. of Energy.

309 p 0 -1 0 X 1 0 -1 R = -^ r (4) Jl [ 0 1 0 \o 1 0 L

Then Q' becomes:

/A +A B +B„ B -B ^ / X y X y \-^ y X / C +C D +D, D-D X y ^y-'^x «•=! X y y X (5) B -B B +B A -A X y \ y X y X \c -c D -D D +D,, \ y X y X '.''y X y

Complete exchange of horizontal and vertical phase space can be accomplished if

\ ^x 'y 'y (6) Cx "^x S °y since then

'0 0 A^ B\

0 0 C D Q' = y y (7) 'y 'y ' ' .c, D^ 0 0

connects (x, X')^.^^T only with (y, y')ipTtiai ^"^ (y* ^'^final ^^^^ ^^' ^''initial *

If we represent (in betatron notion):

I QL 3 \ \ ^x\ = I COS Vi + J sin y , where J = (8A) s D XX X -y -ot and

\ 'A = Icosuy + J^sinuy (8B) s 'y\

310 and choose a FODO quadrupole lattice such that y = 2n TT and MX = (2n - 1) TT

then: A B \\ /--1I 0]0\ X x' (9) C D 0-1

and: h 0 \ 'y\ (10) \o 1/ \'y ^ and:

'0010

0 0 0 1 Q' = (11) 10 0 0

\0 1 0 0,

Which simply exchanges (x, x*) with (y, y').

As an example, we note that this can be obtained by choosing a skew FODO lattice with 90° phase shift per period in the skew-y plane and 45° per period in the skew x-plane and following 4 periods to \iy = 360°, y^ ^ ^^0°. Such a lattice can be constructed easily using SYNCH and allowing the F quads to be set at a lower field gradient value than the D quads»

Necessary and Sufficient Conditions:

For a quadrupole lattice skewed at 45°, equation 5 gives the proper trans­ fer matrix and the condition

A B \ y y (6) ^x ^x C D \ y y must be satisfied if x and y phase spaces are to be completely exchanged. In place of (6), a lattice skewed at an angle 6 other than 45° requires con­ tradictory conditions of form

A^cos^ 9 + A^, sin^ 6 = 0 X y (12) A sin^ e + A cos^ 6=0 X y for A, B, C, and D, which can be satisfied only if 0 = 45° (0° < 6 < 90°). Therefore, the 45° angle is necessary.

With condition (6) expressed in the form of equation 8, we are

311 immediately led to the requirement cos Mx = ~ cos Uy which requires either Px + Uy = n fT or My = px •*' " f^ where n is an odd integer. If Ux '*' ^y ~ " •"" (n oddi, then sin ux - sin py and the condition Jx sin Px ^ -Jy sin Uy cannot be satisfied (since 3x> 3y > 0).

Thus, a necessary condition is py = y^^ + n TT (n odd). Also, if sin liy^H then equation (6) requires J^ = Jys since sin yx " - sin Uy. Therefore, we have two choices of a second necessary condition: Either: 1) y^^ = m TT (m any integer) as in the above example, or 2) u can take any value but Jx = Jy is required. We can demonstrate this possibility by generating a FODO lattice as above (Bp f -BQ) and requiring that at the center of the F (or D) quad 3x = 3y Instead of a requirement on Ux- ^^ ^^""S center point symmetry requires a^ = A = 0; also y = 1/3, Then J^ = Jy. The skew Insertion would begin and end at such a center point. Such a lattice is not difficult to generate. In both cases 1) and 2) the condition Uy = y^ "*'"'"• ("^ odd) for the skew Insertion must also be satisfied.

We thank Lloyd Smith for suggesting the problem and useful comments.

FOOTNOTES

1. RoC. Arnold, et.al., "Hearth Fire Reference Concept #3: A Rapid Cycling Synchrotron System", ANL Report ACC - 6 (June 16, 1978).

2o A, W. Maschke, "Conceptual Design of a Heavy Ion Fusion Energy Center", (March 13, 1978), BNL 50817.

312 COMBINING BEAMS IN TRANSVERSE SPACE IN A LINEAR SYSTEM*

M. Foss Argonne National Laboratory

1 Two beams can be combined with a septum. C. Bovet, et. al show that beam can occupy a fraction 4/(3/J) (or 0.7698) of the phase space ellipse which contains both beams. I have calculated this fraction in the cases where 1, 2, 3, 4, & 15 beams are combined (see Table I). The resulting brightness is greater than 3/4 of the original brightness in every case.

To attain such a result it is necessary to combine the beams more or less at the same time, before the phase space has had time to scramble. Thus, to combine 16 beams to 8, 8 to 4, 4 to 2, and 2 to 1 would have a minimum dilution of 0,77 . Whereas, to combine 16 beams, 4 at a time, that is, to four quadruplets in one plane then to a single beam in the other would have a minimum dilution of 0.76 . With some allowance for septums, the brightness would be twice as large in the second case.

If the beams from 16 linacs were to be combined, 4 horizontally then 4 vertically, they could go through 4 sets of vertical septa and the result­ ing 4 beams through a set of horizontal septa. If there are less than 16 linacs then some method of chopping and delaying must be devised.

Figure 1 shows one way of increasing the current from one linac by a factor of 16 for injection into a storage ring. The beam is first chopped by a square wave switch with a period 2T. The linac has full buckets for a period t when the first switch is held in one direction and empty buckets for a time t while the first switch is in transit. Thus,

T = t + t, o 1 Since the total delay required in Figure 1 is 21 T it is desirable to keep tj^ as small as possible. Downstream switches can be much slower, for example, switching in the next fastest switch takes place in a time T + t,.

While a delay of 21 T is required the cost per unit length will be much less than an equal length of storage ring. Note that the beam is smaller and goes mostly in a straight line. If, for example, the cost were 20% of the cost of an equal length of storage ring and the decay time of the storage ring kicker were equal to the first switch transit time, then the cost of the delay lines would be (20% * 21) 4.2 times the cost of one storage ring. Switches and septa would add to the cost of the system.

Work supported by the U. S . Department of Energy.

313 I n I DELAY n PERIODS rT= PERIOD) U^ COMBINE BEAMS (HORIZ.)

(1^ SWITCH EVERV n"' PERIOD, T K> COMBINE BEAMS iVERT.i

(-.t-mi Ti IS THE NjMBtR OF THE BtAM GROUP,

Figure 1 CanEining 16 beams wilh delays totaling 21 periods

Figure 1

In Figure 1, 16 bursts of beam each t^ long enter from the left. The first switch directs the odd numbered bursts down through a delay T. Bursts 1 and 2 arrive at switches 2 at the same time. The lower switch 2 directs bursts 1, 5, 9, and 13 through a delay of 2T. Bursts 4, 3, 2, and 1 arrive at the horizontal septums at the same time; 8, 7, 6, and 5 arrive 4T later. The delays for the vertical septums are similar.

314 number resulting of brightness beams factor

1 1.0

2 0.76980

3 0.76092

4 0.76135

15 0,77468

Table I

Reference

1. "A Selection of Formulae and Data Useful for the Design of A. G. Sjrnchrotrons", C, Bovet, R. Gouiran, I, Gumowski, and K, H. Reich, CERN/Ml'S-SI/Int. DL/70/4, April 23, 1970.

315 316 F. HIGH CURRENT TRANSPORT AND FINAL FOCUS LENSES

HIGH CURRENT TRANSPORT OF NON K-V DISTRIBUTIONS

I. Haber Naval Research Laboratory

It has been established that space charge driven instabilities can cause emittance growth in the transport beams with Kapchinskij-Vladimirskij (K-V) distributions. Because the actual beams in a transport system will not be K-V in form, questions have been raised about the quantitative appli­ cability of these results. In the absence of an analytic method for constructing non K-V, high current, equilibria in alternate gradient trans­ port systems, numerical simulations have been undertaken to explore this question,

A series of computer experiments have therefore been performed in which an initial matched equilibrium is established in the absence of current. The current is then linearly increased as the beam is transported through 100 pairs of thin lens magnets with a 90 degree phase advance per cell. After 100 magnet pairs the current has reached a value which would have corresponded to a depressed tune of 30 degrees for a K-V distribution. It is then held constant for another 50 magnet pairs.

Figure 1 is a plot of the rms emittances in the x and y planes for an initial K-V distribution. After 60 magnet pairs, the current has reached 0.6 of its final value and the emittance has started to grow, indicating that the system has gone unstable. At the end of the run the emittance has reached a value approximately 2,6 times its initial value.

Figure 2 is a similar plot of the behavior of emittance for a different initial distribution. This distribution was constructed as an attempt to approximate the actual distributions seen in some previous numerical experi­ ments. The distribution is the sum of two populations. The first, con­ taining three fourths of the particles, is a sum of K-V distributions with the density in phase space falling quadratically to zero from the center. The second, containing the remaining quarter, has a linear falloff in density, but goes to zero twice as far out as the first. The effect of this superposition of populations is to give a distribution which falls off quadratically except for a linearly decreasing tail. It should be noted that the behavior of the emittance is quite different from the first case. The violently unstable behavior is not present and the final emittance has only grown by a factor of about 1,5.

Several different simulations have been run with different initial distributions. The two presented here represent the approximate limits of behavior. While the K-V distribution appears to be the worst behaved of

317 those tried, it is in terms of emittance growth, nevertheless, within a factor of two of the others. However, in terms of the growth rates of emittance, the deviations are somewhat greater.

This work is supported by the U.S. Department of Energy.

318 4 . 0

E M I T T h-' A N c E

. 0 . L 1 ' 1 U. -JL^ l_ U. _x» _J_ K_ 1 -I . 0 DOUBLETS 150.0

Figure 1 - Evolution of the x and y rms emittances of a beam with a K-V distribution as the current is increased linearly for 100 doublets and then held constant for 50 more. 4 . 0

O

DOUBLETS 150.0

Figure 2 - Evolution of the x and y rms emittances for a distribution with a quadratically decreasing main body and a linearly decreasing tail. COMPARISON OF INSTABILITY THEORY WITH SIMULATION RESULTS*

L. J. Laslett and L. Smith Lawrence Berkeley Laboratory

I. Haber Naval Research Laboratory

Introduction

For the past year and a half, a parallel effort of analytic work and simulation computations has been in progress for the purpose of understanding the nature of instabilities which arise in the transport of intense ion beams and finding safe regions of operation.' The two approaches have agreed qual­ itatively in that simulation runs using initial conditions predicted by the linearized theory to be highly instable indeed distinctly show instability, and subsequent saturation may occur only after an increase in emittance by a factor of two or three. Since the theory predicted pronounced instability for a large number of modes concurrently, no attempt was made at a quantita­ tive comparison. Only recently we found a combination of parameters for which the theory predicts only one unstable but rapidly growing mode, and the corres­ ponding simulation run shows an orderly growth in the early stages (presumably the linear regime) with the expected qualitative appearance. Since the linear theory provides definite predictions of the evolution of various moments of the distribution and the distortion of the boundaries of the various two- dimensional projections of the distribution, we undertook a quantitative com­ parison as a means of simultaneously establishing the validity of the theory and the reliability of the simulation procedure.

Method^

The KV distribution is the only one we have found to be amenable to theoretical analysis for a quadrupole-focussed beam^ and consequently has been used most often also in the simulation work. The case to be discussed is a FODO lattice with a phase advance of 90° per cell at zero intensity, but de­ pressed to a = 45° by the beam loading. According to the theory, a fluctua­ tion of charge density from the unperturbed uniform density giving rise to a deviation from the quadratic electrostatic potential of the form V = Ax^ + Bxy^, or Ay^ + Byx^, should alternate in sign and grow in magnitude each period of the transport structure. The specific comparison between theoretical and simulation results that we report here for this "third-order" mode considered odd moments (such as y^ y^Py» •••) ^^^ the y,Py projected

*This work was supported by the Offices of Laser Fusion and of High Energy and Nuclear Physics of the Dept. of Energy.

321 distribution obtained for a 2048-partlcle sample available from the 16000- particle simulation run mentioned above. According to the theory, the bound­ ary of the y,py projection should develop as described by the equation

Pw ^2 Pw \ w / P., ? (1)2 . (/^) . C [r^(^)3 . r, (^)2 (^ + r3 (^) (/^ , ^y,max^ L V^y,max/ V^y,max/

;i)

V^y,max _ ^^y,max^ J where C should grow, as the instability develops from the noise. In direct proportion to X^ — \ being the theoretical eigenvalue of the unstable mode {|X| > 1) and P the period numbero The coefficients r],r2, .., t2s however, are uniquely given by the theory, once the tunes OQ and a are specified, as values that are rather Insensitive to the fractional amount by which the lengths of the quadrupole lenses occupy the transport lattice. The growing y-moments, moreover, similarly are expected to bear a definite ratio to one another and to the factor C in Eq. (1), so that in principle only one ad­ justable parameter is available for fitting simulation results of the type mentioned.

Results^

For purposes of the comparison, theoretical coefficients were evaluated for a 90-degree lattice, one-sixth occupied by quadrupole lenses, in which (as estimated from trajectories of the simulation particles) the space-charge forces depressed the tune to a = 45.85 degrees (near the expected center of the predicted strong third-order instability). The theoretical value of A under these circumstances Is X = - 1.2676 (real, but negative)^, and the expected ratios (normalized so that = 1) are as shown by the first line of entries on Table I.

The growth of moments obtained from the simulation data was examined only beginning with period number 8 or 9 (where the results began to emerge some­ what consistently from the noise) through period 19 or 20 (at which point some indication of incipient saturation became apparent). Taking into account the possible presence of some constant background noise in these moments, we estimated their growth as characterized by X values in the range between -1,22 and -1.28 (average value for the six moments examined = - 1,26, in good agreement with the theoretical value) and obtained the moment ratios shown by the second line of entries in Table I.

The coefficient C in Eq. (1) for the y,Py projection was adjusted for a best fit of the simulation data only for periods 8, 13, and 18. The values so obtained suggested a growth rate characterized by A = - 1.2 -- i^eo, some­ what less than estimated from the growth of the momentSo To relate the magni­ tude and sign of C to values found for the moments at period 18, the observed moment reduced to "scaled variables"^ is approximately +4.07 x 10"^ and the corresponding expected value of the dimensionless parameter C is close to this value, while the best fit to the boundary of the y,py projection

322 TABLE I

Normalized Moments

^y

Theoretical 1. 1.35 -0.665 -0.94 111, -66,

Simulation 1. lc23 -0.63 -1,08 111. -67,

at period 18 gave the similar value 3,84 x 10"\ Although it is our expecta­ tion to examine the simulation data in further detail, the evidence cited above indicates that the theory for the third-order perturbation modes of a Kapchinskij-Vladimirskij distribution provides a good account of the initial instability exhibited by simulation computations for a similar initial dis­ tribution.

Conclusion

Numerical calculations based on the theory just mentioned suggest that, with a zero-intensity tune OQ = 90 deg., stability cannot be assured for beam intensities that depress the tune to below a = 57.5 degrees. It is found, however, that this limitation is relieved by designing the transfer lattice so that OQ <_ 60 deg., because third-order instabilities then are not to be expected. Accordingly, with OQ £60 deg., intensity limitations would be imposed only through the action of other, higher-order instabilities. Speci­ fically, with OQ = 60 deg., intensities that result in a tune depression to o in the neighborhood of 24 or 28,2 deg^ (where substantial instabilities of 6^" or higher order may appear) may be permissible and permit the transport of significantly greater currents than would be possible with a lattice de­ signed for OQ = 90 degreeSe The use of a transport lattice designed for OQ = 60 deg., and a comparison of its characteristics with those of a lattice with OQ = 90 deg., will be discussed in detail (with tables) in a LBL report now in preparation ["Concerning an A-G Transport System with o^ = 60 Degrees", LBL Report HI-FAN-56 (1978)]. Simulation runs will be made to determine whether or not the 60''-24° range is indeed free of unstable regions.

Acknowledgements

For assistance in the work summarized in the present note we express our thanks to our colleagues Jo Bisognano, V.O. Brady, and S. Chattopadhyay of the U.C. Lawrence Berkeley Laboratory.

References lo See Laslett, p. 112 and Haber and Maschke, p. 122 and references in those articles, BNL workshop.

2o This work is described in greater detail in HI-FAN-43o

3, See HI-FAN-13, 14, and 15.

323 4. The distinctive signature of this instability (associated with a negative real eigenvalue) is that the odd moments (of order 3, or greater) and the boundary in phase space (or of any projected distribution) oscillates with a "frequency" of one half period of the transport lattice and with growing amplitude, but the particles distribute themselves within the boundary so that their centroid remains stationary.

5o G. Lambertson, L.Jo Laslett, and L, Smith, "Transport of Intense Ion Beams", IEEE Trans. NS-24, 993 (1977).

324 THE ARGONNE NATIONAL LABORATORY HEAVY ION BEAM TRANSPORT EXPERIMENTS WITH A 2 mA 80 KeV Xe SOURCE*

M. Mazarakis, D. Price, and J. Watson Argonne National Laboratory

Experimental Set-up

This set-up is put together from existing vacuum components. It is to serve as an intermediate arrangement while a stainless steel high vacuum system is being manufactured. The present system consists mainly of alumi­ num parts and regular 0-rlng seals. The best static vacuum (with no source gas or beam loading) obtained with this system is about 3 x 10 Torr. The operating vacuum was in the range of 5 x I0~" to 5 x 10" Torr. Figure 1 outlines the experimental set-up, giving critical dimensions for the beam transmission experiments.

The photograph in Figure 2 shows an overview of the experimental set­ up. A 2 to 3 mA Xe ion beam was obtained and accelerated to 80 keV, This ion beam was then injected into the first vacuum box. (The first box is on the right side of Figure 2, The ion source is to the right of the first box, in the high voltage cage.) The intensity of the beam was measured de­ structively using the Faraday cup in the first box. This Faraday cup can be removed from the beam path so that the ion beam can continue through the beam pipe and downstream to the second box. (The second box is on the left side of Figure 2.) The Faraday cup in the second box is located about 4,2 m from the source aperture. This second Faraday cup is also removable from the beam path. The beam is transmitted through and focused by a magnetic quadrupole triplet, Ql, Q2 and Q3. The transmitted beam cross- section can be observed and measured on the Pyrex glass plate at the end of the second box. Figure 3 is an end-on shot of the beam taken from the glass endplate of the second box. This glass plate mates to the 8 in. diam. port on the end of the second box, directly behind the second Faraday cup.

Two sets of 36 in. long clearing electrodes are inserted inside the beam pipes in two locations. These clearing electrodes are in the middle of the beam pipe line, almost midway between the first and the second box. A clearing bias potential can be applied to the clearing electrodes through vacuum feedthroughs. The generated electric field can remove the neutral­ izing electrons out of the beam potential well, thus deneutralizing the beam. Experiments are under way with dc, rf and pulsed biasing potentials on the clearing electrodes.

Work supported by the U. S. Department of Energy.

325 Results of Experimentation

A, Transmission

A systematic study of the source parameters and their influence on source current beam emittance and transmission has been undertaken. Figure 4 gives a schematic view of the source elements and configuration. The electron suppression electrode proved to be very effective in reducing the beam divergence and greatly improving the transmission. With a bias of -350 V on the electron suppression electrode, the emittance was found to be better than 1.0 mrad-cm. The plot in Figure 5 gives the beam cross-section diameter at approximately 65 cm from the source as a function of the electron sup­ pression electrode voltage. The electrode voltage did not exceed -350 V because a protection spark gap operates at that point. In the plot of Figure 5, the beam size was measured on a grid positioned on the front of the Faraday cup in the first box.

The maximum transmitted beam to the second box Faraday cup was 2 mA, while the current in the first box was less than 2,25 mA. Hence the trans­ mission of the beam from the first box to the second box was in excess of 90% over a length of 3.6 m. All of the transmission results reported here have been obtained with the source operating in a dc mode.

B. Emittance Measurements

Almost all of the emittance measuring devices designed to date are main­ ly for low intensity beams. The obtained 2 mA 80 kV Xe beam is quite power­ ful and intense. It can melt, or otherwise permanently destroy, many of the previously available diagnostic devices. New designs, implementing freon or water cooling and heat resistant apertures, must be made to obtain direct and precise beam emittance measurements.

In the present experiments, an attempt was made to improvise and mea­ sure beam emittance with a minimum of cost, time, design and construction effort. A grid of 0.030 in. tungsten wire was fabricated and positioned in front of the Faraday cup in the first vacuum box. The distance between adjacent wires is 0.25 in., so that the grid is divided into 0.25 in. squares. When the beam impacts the grid, the tungsten wire becomes red hot. The red hot wires define the beam cross-section at the plane of impact. Figure 6 shows the grid deformed after repetitive beam exposure.

The beam cross-section may be measured by visual observation or photo­ graphs of the grid. The photographs of the beam in the first vacuum box must be taken through the 6 in. diam. lucite side port on the first vacuum box. Figure 7 shows a photograph of the grid with the beam on the grid.

Numerous observations of the beam size and shape were made and photo­ graphs were taken. The smallest beam size observed at the grid was a small circle less than or equal to 0,5 in. diam. At the same time, the waist of the beam was observed. Its diameter, 2 r visually estimated to be 2 mm. The distance between the waist and the grid was 63 cm. The emittance can then be estimated according to the scheme shown in Figure 8, In this figure.

326 the beam envelope is drawn from the waist to the grid plane. The angle of beam divergence turns out to be / 0.635 , a - ( —To" ) = 10 mrad which gives a source emittance of

—=r a=0.1cmxl0 mrad = 1 mrad-cm TT O

This result compares favorably with similar measurements made by HRL^ before the source was delivered to Argonne.

The authors would like to acknowledge the guidance of E. Colton and S. Fenster in designing these experiments.

References:

1, R. L. Seliger and V. P. Vahrenkamp, "Ion Source for Ion Beam Fusion," Proceedings of the Heavy Ion Fusion Workshop, October 17-21, 1977, BNL 50769.

327 BOX BOX 2 BEAM WAIST 02 03 D ^t Z] BEAM FARADAY FARADAY CUP CUP

62.6 22.0 27.0 27.0 282.5

DIFFERENTIAL LENGTHS, CM.

62.6 64.6 III.6 138.6 430.3

TOTAL LENGTH FROM BEAM WAIST, CM. DRAWING NOT TO SCALE

Fig. 1 Critical dimensions of the beam transmission experiments.

Fig. 2 Photograph of the experimental set-up.

328 .MillUil

Figure 3 Photograph of the Xenon beam impacting on the glass port at the end of the second box.

ELECTRON FARADAY CUP SUPPRESSOR 500 V lOOOV lOOmA lOOm A

±500^A HIGH VOLTAGE INTERMEDIATE l50kV ELECTRODE lOmA 30kV 10mA

Figure 4 Source schematic diagram.

329 Figure 5 The beam size as a function of the electron suppressor potential. _l a. o 3 - -

I- i } -

UJ CD

-100 -200 -300 -400 ELECTRON SUPRESSOR BIAS, volts

Figure 6 Photograph of the grid. The distance between adjacent wires is 0.64 cm. The wires have been deformed by repeat­ ed exposure to the Xe ion beam.

330 Figure 7 Photograph of the grid with the beam on it.

2mm 13 mm

GRID BEAM PLANE WAIST Fiqure 8 Beam envelope,

331 332 GEOMETRIC ABERRATIONS IN FINAL FOCUSSING FOR HEAVY ION FUSION*

David Neuffer Lawrence Berkeley Laboratory

The final focus of a heavy ion fusion (HIF) accelerator requires focus­ sing of an intense ion beam on an extremely small target spot. This require­ ment has led to some concern that third-order aberrations will significantly distort focussing determined by first-order theory.1*2 Earlier calculations have confirmed that this is true for a number of possible HIF beam/target combinations."^ This note develops these calculations to a more general for­ mulation which can be used to estimate third-order distortion without detailed calculations. Several candidate HIF beams are presented in some detail as examples. Some general ideas on the constraints which third-order aberrations place on HIF parameters are developed.

I. Theoretical Formulation

The non-relativistic equations of motion to third-order can be derived from the Lorentz equation: m^ = ^\?xS (1) c We change the independent variable from time t to the longitudinal position z using

(The notation u' = ^ is used throughout.) dz

Equation (1) becomes two equations:

(H-y'2)x"-x'y'y" = jjjf^ (1+x'^ + y'2)^/2(-By+y'B^) (2) - x'y' + (l + x'2)y" = J-^ (l + x'2 + y'2)^/2(B^-x'B^)

This work was supported by the Div. of Laser Fusion and the Div. of High Energy and Nuclear Physics of the Dept. of Energy

333 The magnetic field 5 is obtained from the gradient of a scalar potential $ with quadrupole symmetries: $ = -xy(t)(z) +yg- (x^ + y^) xy(I)"{z) (to third-order) (3)

We use the relation -~rT = - V$ to define the units of $. mv c 0

Substituting t into the equations of motion, separating x" from y", and keeping terms only up to third order, we find for x":

x" = - c|)X+(-| x'^x-iy'^x + x'y'y)(t) 2 ^ (4) 2 3

This equation of motion is applied to a quadrupole system, with * con­ stant throughout the interior of the quadrupoles and (p* and 4)" nonvanishing only at the edges. To first order particle motion is given by the unperturbed equations: x" = - (fix, y" = (t>y and a Green's function integration can be used to find the higher order corrections. The correction to x is

Ax = / "^ G^(zp>C) • I (- f x'^x-ly'^x+x'y'y)4) I (5) 2 3 ^ where G^(Zp,C) = \(^f)\(^) ' ^e^^F^^o^^^ *^' and Xo> Xg are the odd and even solutions of the unperturbed equations. If we choose the points 0 and Zp where (f = cf)' = 0" = 0, we can use partial integrations to remove the derivatives of ^ from the integration 5. 4 The result is, as previously derived by Meads,

Ax = / ^ 4>^ GX f-xy^-lx^)d-^ 3 C 0 z. + 7/"S G^ X' (x ^+y ^)dC B (7) '^ o ^

+ / ^|G (-x(x'^ + y'^) + x'yy')dC C 0 ^ In deriving 7 from 5, we have used relationships such as x" = - cjjx, y" = + 4iy> G^ = - (|)Gx. The expression for Ay is obtained from 7 by the trans­ formation X ^-^ y, (fl -> - (I), with the warning that Gy, also given by equation 6,

334 is different from G>^.

Equation 7 can be compared with equation 5 to separate the contributions of fringe fields (<{»', (f)" f 0) from geometric contributions.

Particle acceptance may be increased in final focussing by use of octu­ pole magnets. An octupole field adds a term

A$ = - 1 (x^y-y^x)i^{z)

to the magnetic potential and a term ^Vt = ^ f "^ '^x * (V - y^^)'^? D (7)

to equation 7. Ayoct ""^ obtained from equation 7D by the exchange x -«-^ y and ip -> + i|^. In the calculations of Sections II and III no octupole elements have been included, however.

The third-order corrections Ax, Ay to the particle positions can be calculated for individual rays using equation 7 and such calculations are used to determine the particle acceptances displayed in Section III. However, in the following section approximations valid for the HIF final focus are used to derive simplified formulas which can be used to estimate the effect of third-order aberrations in an arbitrary HIF system.

II. Approximate Formalism

We reduce equation 7 by expressing its terms using the transfer matrix from z = 0 to z = zp

X3(z) x^(z)j /M^T(Z) M^2(^)j ^^^

^x^'(z) X^'(Z)/ \M2^(Z) M22(2)/

We assume the beam is parallel at the entrance to the final focus (M2I(0) = 0) and the target is at a point focus (Mii(2p) = 0). Also because of the final focus constraints,M-12(ZF) ~ ^^^^ ^ 3X{0)3F where XQ is the max­ imum beam amplitude at z = 0, rj is the ^ target spot radius, -m is the transverse emittance, and 6x(0)» 3F ^^^ ^^^ initial and final beta function values.

Then G^(Zp,C) = M^^(0 B^(0)Bp ^^^

Gj^'(zp,C) = M2^(C) 3^(0)6p with similar expressions for G , G '.

We calculate (Ax, Ay) for a distribution of particle rays, each with some initial coordinates (x,x',y,y') with

335 (x,x'.y,y') = (X^u, ^u', Y^v, ^v') = (X^u, X'^u', Y^v, Y;^V') (10)

XQ and YQ are the maximum x and y amplitudes of the beam envelope at z = 0 and {UjU',v,v!) are numbers which lie between -1 and +1. (For a K-V distribu­ tion u2 + u'2 + v2 + v'2 = 1)

The first order value of x(z) is x(z) = X^u Mii(z) + XQ U' M-|2(z) (11) with similar expressions for x'(z), y(z), y'(z).

Equations (9) and (10) can be inserted in equation (7) obtaining an expression for Ax of the form

Ax = U,,,, X^^u^ + UT.^.,X Y^uv^ 1111 0 1133 0 0 ;i2i + ^iii2^o^K ^^"' ^ ••'CO terms total)

In (12) the U--|.i ai^e third-order transport coefficients. For HIF final focussing XQ and YJ"^ are large, and we can find approximate expressions for Ax and Ay by ignoring all terms proportional to powers of XQ' and YQ'. Then Ax ^ U^^^^ Xo^u^ + U^^33 X^Y^^ ^^2 (^3j

z (J)2M ^ ^1111 = - ^(°)% /'(-T^^l"n'^2i')^^ (^^'

'^^3z-'^^'^h /''t*'^>33'-|^2^^33' :i5i ^*"llV-*Mn^3"21^33]^^

with a similar expression for Ay.

To evaluate these coefficients we consider the family of final focussing solutions derived by Garren in the 1976 HIF Summer Study.^ These are doublet solutions with the x-coordinate the FDO coordinate and the apertures of the two quads given by Rp = RQ " ^o* ^^^ solutions are expressed in terms of a LBr^ single parameter b where b = -g^^ , and L is the final drift distance, B the FD pole tip field and Bp is the ion rigidity. Other Garren parameters are

^ = B^* ^ = rf ' ^^ L^' ^^^^ ^^~~^'

We define normalized third-order matrix elements U^j^j^] in terms of these parameters by

336 "nil - ^ "nil ^ ^^o '' '^ oJ "ll ^^-^-^T'''''- 2* ' ^^^' where d^ - l^'ldz which we write as Uiin' = -Leo'9x(b)

Also we write U^^^^^ = U^^33 Xj/ = . LB \ (b) U X

"3333' = U3333 C = - Leo\(b) (17)

"3311' = "3311 ^0=^0'= - ^'o\^'^ which defines parameters g^j gy* h^* hy which are functions of the Garren parameter b. It can be shown that, for parallel to point focussing, Ussil*^ " '^IISS'^ ^"d hx = hy E h. The parameters gx, gy and h are tabulated in table I, which supplements Table A8-7I in reference 5. Figure lA displays the same information graphically.

For FDO focussing Ax > Ay and Ax = Umi'^u^ + Un33Nuv2. The maximum value of uv2 is .39 for a K-V elliptical distribution and the evaluation of Ax is dominated by U-]]]-iN (see Figure 1) We define a quantity N Ax = U,,Ti max 1111 and in Figure IB we have graphed particle acceptance at the focus as a functiofunct n of Axrnax/n assuming two possibilities of initial particle distributions at z = 0: 1) a K-V distribution, or 2) a "W" distribution (particles uniforml populating the interior of the K-V hyper-ellipse). The criterion for acceptance is

r/= xp^ + y/ = (Xp° + Ax)^ + [y^^ + Ay)^ < r/ (18) where xp , yp are first-order values. Figure IB shows particle acceptance falls off steeply with AXmax/^ ^ ^* ^^ noted in Reference 3 particle accep­ tance is improved by moving the target from the focus to the position of least confusion, i.e., maximum particle acceptance, which is about ^% closer to the focussinq doublet. The effect of this is also displayed in Figure IB. Figures lA and IB can be used to determine the acceptability of a par­ ticular HIF final focussing system.

HI. Examples of Final Focussing Systems for HIF

As individual examples of final focussing for HIF we consider two possi­ ble cases in detail. The first example we consider was suggested by Keefe^:

337 19 GeV l/with r-r = 1.25 mm, B = 4T. The Garren parameter b can be found from K - o 7 L(m) ^ " ^'^ £^(cm-mRJ where EM = B Y c is the normalized emittance. We calculate final focussing with L = 10 m and L = 5 m, which demonstrates that smaller L is favored, but L < 5 m is probably impractical. The results are displayed in Table 2A.

If we require an acceptance of a "W" distribution of greater than 75"/ at the focus (~ 90°/ at the point of "least confusion"), we require £N < 0.98 (cm-mR) for L = 5 m and ^N < O-^ for L = 10 m. In both cases the maximum quadrupole aperture XQ must be less than 0.18 m.

Keefe^ has suggested that this value of e^ can be obtained from a larger value of emittance at the exit of the accelerator EQ by splitting the beam transversely into N separate beams. If this is achieved without dilution, a final emittance per beam ec = eo/\/N"can be obtained at the final focus. Thus if c;^ = 3 cm-mR, N > 9 (for L = 5 m) is required.

A second example is suggested in the Hearthfire III proposal of Arnold et.al."•:

20 GeV Xe"^^ r^ = 0.8 mm, L = 5 m, Bp = 30.3 T-m, and b = 6.3 ^ (cmlmR)

at B = 4T. The results for our calculations are contained in Table 2B. 75% acceptance demands ^^ ^ ^-^ ^"^ ^o ^ ^-^^ ^' '^^'^^ ""^ ^ smaller value of ^1^ than the 2.8 cm-mR value desired in Reference 1.

IV. General Comments on Geometric Aberrations A general requirement for a successful final focus (for FDO focussing)is: Ax Le ^ jax < 1 -^g(b) < 1 (19) ^T ~ ^ This can be re-expressed in terms of £> r-j-, b and p(p = Bp/B) as

^ b g{b) £ 1 or e < p "^/V^'^(b9(b))-^/^ (20) r^S T We define a parameter r(b) = (bg(b))"^/^ which is tabulated in Table I. r{b) is maximum at b = 6 witb a value of 0.17; it is roughly con­ stant for b 5 20, and varies as 1//D for large b. It is important to note that for b < 6 the Garren doublet solutions become somewhat unrealistic and triplet solutions are preferred, and Table I is not useable.

Equation (20) can be used to estimate maximum allowable emittance for a given HIF system. Larger target size is greatly favored. It has not yet been determined how equation (20) is modified by including octupole elements for correction and/or by higher order aberrations. These questions will be investigated by a number of researchers.^>^

338 We thank A. A. Garren, L. Smith, S. Fenster, E. Colton and D. Keefe for useful comments.

References

1. R. C. Arnold, et.al., "Hearthfire Reference Concept 3: A Rapid Cycling Synchrotron System", ANL-ACC-6, June 16, 1978. 2. L. Smith, private communication. 3. D. Neuffer, HI-FAN-36, May 18, 1978. 4. P. F. Meads, Jr., Ph.D. Thesis, UCRL-10807, May 15, 1963. 5. A. A. Garren, Appendix 8-9 in the ERDA Summer Study of Heavy Ions for Inertial Fusion, LBL-5543, July, 1976. 6. D. Keefe, private communications. 7. S. Fenster and E. Colton, private communications. 8. D. Neuffer, private communications.

339 Table I - Geometric Aberration Parameters Garren Parameter b gx(b) gy(b) h(b) r(b) -6 1.0 1744. 1. X 10' 0.3 0.155 1.5 1125. 1. X 10--4 0.9 0.156 2.0 790. 9. X 10--4 1.9 0.159 2.5 592. 4. X 10--3 3.7 0.161 3.0 460. 1.4 X 10--2 5.9 0.164 3.5 371. 4. X 10-•2 8.5 0.167 4.0 310. 8. X 10--2 11.4 0.169 4.5 266. 0.2 14.6 0.170 5. 233. 0.3 17.9 0.171 6. 192. 0.7 25. 0.172 7. 167. 1.3 32. 0.171 8. 153. 2.2 39. 0.169 9. 144. 3.3 46. 0.167 10. 139. 4.5 54. 0.164 11. 136, 6.0 62. 0.161 12. 135. 7.5 70. 0.158 14. 135. 11.1 87. 0.152 16. 139. 15.2 104. 0.146 18. 143. 19.7 122. 0.140 20. 150. 24.3 141. 0.135 22. 156. 30. 161. 0.131 24. 163. 35. 180. 0.126 26. 171. 40. 201. 0.122 28. 179 46. 222, 0,119 30. 187. 53. 245. 0.116 35, 209. 68. 300. 0.108 40. 232. 85. 360. 0.102 45. 256. 102. 420. 0.097 50. 280. 122, 480. 0,092 55. 306. 138. 540, 0.088 60. 331. 163. 610, • 0,0842 70. 386. 203, 750, 0.0780 80. 440. 248. 890. 0.0730 90. 496. 297. 1040. 0.0688 100. 555. 343, 1200. 0.0652

340 Table II: Sample Cases of FDO Focussing

A: 19 GeV U"^^, rj = 1.25 nm, Rp = XQ, RD = 0.85 XQ. B = 4T. L Ax ^N LF h 0 ^0 ^0 max Acceptance at Focus (cm-mR) M (m) (m) im} (m) ^T (K-V) (W) 2.0 3.36 3.76 10. 1.00 0.275 58.5 6% 21% 1.5 2,59 2.73 10. 0.64 0.203 26.2 10 32 1.0 1.84 1.84 10. 0.37 0.137 9.5 19 47 0.75 1.46 1.42 10. 0.25 0.104 4.8 31 61 0.50 1.07 1.00 10. 0.15 0.071 2.0 56 83 2.0 3.14 4.22 5. 0.78 0.15 37.3 11% 31% 1.5 2.39 2.93 5. 0.46 0.104 13.2 18 46 1.0 1.65 1.84 5. 0.24 0.068 3.7 40 74 0.75 1,29 1.36 5. 0.16 0.051 1.6 66 92

20 GeV V +8 0.8 mm. B = 4T B: Xe , ry = 2.80 2.03 2.39 5. 0.903 0.222 175. 6% IT 1.50 1.14 1.17 5. 0.334 0.113 31. 10 28 1.00 0.800 0.817 5. 0.194 0.076 11.2 16 41 0.75 0.655 0.620 5. 0.134 0.058 6.0 25 55 0.50 0.476 0.440 5. 0.082 0.040 2.5 49 76 0.40 0.402 0.367 5. 0.063 0.032 1.6 62 88 0.25 0.283 0.253 5. 0.036 0.021 0.6 100 100

341 4,000 -

QpQo Figure lA - GEOMETRIC ABERRATION PARAMETERS: ^ J'

Figure IB - PARTICLE ACCEPTANCE AS FUNCTION OF "^^^ *"T

342 r = 1.25mm

L^=5m l9GeV U*^ B = 4T

Acceptonce at Focus (%} 100

0.5 1.0 1,5 2.0 0.5 0.2 0.4 0.6 0.8 r,, (c m - m R) X^im)

Figure 2A - PARTICLE ACCEPTANCE AS A FUNCTION OF NORMALIZED EMITTANCE (£fP AND QUADRUPOLE APERTURE (X^) FOR 19 GeV U+^

+8 20 GeV Xe r-p = 0.8 mm, L^ = 5 m, B = 4T

Acceptonce 100

0.5 1.0 2.0 3.0 0 0.1 0.2 0.4 0.6 e^, (cm- mR) X^(m) N Figure 2B - PARTICLE ACCEPTANCE {%) FOR 20 GeV Xe+8

343 344 QUADRUPOLE SYSTEMS FOR FOCUSSING ION BEAMS WITH LARGE MOMENTUM SPREAD

J. Steinhoff Research Department Grumman Aerospace Corporation

Introduction

The final focussing of achromatic beams is an important issue in the design of heavy ion igniter systems: In some envisaged systems the momentum spread (Ap/p) may be as high as ±1.5%. As a step towards understanding how to focus such beams, we have studied the effectiveness of simple quadrupole systems. In particular, we have done a series of computer optimization studies for systems with 6,28 and 64 quadrupole magnets, focussing beams with different momentum spreads. Ideal magnets were assumed and only chromatic abberations were considered. Also, space charge was neglected. Since Ap/p was allowed to be large enough to substantially change the trajectories, the equations of motion were not expanded in Ap/p. Instead, the spot size at the target was computed and minimized over an interval of p.

In addition to looking at single beams with large Ap/p, we considered the possibility of simultaneously focussing, with the same quadrupole system, two beams, each with moderate Ap/p (±k%) but differing by 10-40% in charge/momentum (Q/p). Such a system would allow two pulses, each in the same charge state but with different velocities to propagate separately through the system and "telescope" into each other at the end. In this way, space charge effects could be reduced. Current ideas on telescoping apparently require separate charge states arranged so that Q/p would be the same for the two pulses. Alternately, our "double focussing" system could be used to focus one pulse consisting of two different ion types moving at the same velocity.

Equations of Motion

T'he equations of motion, linearized in transverse dimensions, x, y. are = K(s)x

d^ = -K(s)y ds^ where

345 K(s) = ^ G(s) and G is the qxiadrupole field gradient. For ideal magnets with no fringe field, the transfer matrix for one element of length Z^ and strength G, separated from the next by a drift space Z^, is

/ C(u) Z^S(u)^ M(u) = -:^S(uu ) C(u), V ^M where

C(u) = 1 - u/2! + u^/4! - u^/6! + ... S(u) = 1 - u/3! + u^/5! - u^/7! + ...

and

u = K Z. 'M • The final state of a particle with initial coordinates x^, x^, y^, y^, after traversinfei g the set of magnets {u.}, is A V

s;({-u.}) r* 3

where

S^({u.}) = M(u^)M(u^_^) M(u^) (1)

For our study, the values of Z and Z were fixed and the strengths, u., were adjusted to minimize the final spot size at the target. The interval p -Ap

^^(o) = y/o) = 5 cm.

346 xf (o) = y^'(o) = 0.

x^(o) = y^(o) = 0.

x^'(o) = y^'(o) = 10"^rad, and the normalized emittance (area/fr) was 5 cm. mrad. Also, 20 Gev. X ions were assumed for this study ^ , The beam radius, or envelope function is, in this notation,

and r^ and r^ at the target are denoted r^(T), r^(T). The final (reactor chamber) drift space was taken to be 5 meters. Specific values of Q, p and emmittance are given as an example: Other values can be chosen if the final mag­ net strengths and spot sizes are scaled accordingly.

Optimization Scheme

To optimize a realistic system, a model for the beam density as a function of momentum should be used, and the fraction of the beam within a final target should be maximized. For our initial study, however, we minimize the function

P^^^ = Z Ej(r^(T))2 + (ry(T))^] where E are weighting functions. In our study, we took E = 1, corresponding to a step function in raomen__tum . Then, P^^) ^g effectively the integral over the momentum range of the sum of the squares of the x and y spot sizes. For a beam that is denser at p = p we should make the values of E large for values of £ such that p is close to p . (2) To minimize P , a sequence of one dimensional searches were done in the N dimensional u. space. Each search was in a direction determined by the present and past gradient of P^^/ : (2) new , , 9P . „ , oldx^ u. = Uj +a x(--3^ + 6 X (Uj - u^ )) where N (2) ^ N ^p(2^)old ^

1 J 1 J ,(2(2) As a result of each search a value of a was determined that minimized P {u.} in one direction.

347 (2) The gradient SP*" /9u. required at each step, for each j, depends on the matrix 9S ({u. })/9u.. ~' Generally, in the optimization of functions with a large number of parameters, the gradient computation can be the most time consuming part, requiring about N function computations. For our product representation (1), however, we can compute the N derivatives of each element of SNF in only about 4 times the time required to compute S^, for any N. Writing the gradient explicitly,

3M. 3u. ^ Vl ^j+1 9u "j-i •••"i J " j or

= 3u. 3 ou. ^j • J 3

we can do the following sequence of computations (separately for x and y, for each Jl). N 1. Compute S_({u.}) by doing N-1 matrix multiplications ^ J (this is the final computation in the last one-dimensional search). 2. For each j = 1, 2. ... N, in turn, do 2,1 and 2,2

2. .1 compute

M., M."-^ > 9M../9u. . J 3 ) J

2. ,2 compute A A -1 s. S. X M." -1 3 J- J

A 3M. ^4 s. X ,1 X S. 9u. 3 9u J 3 j

^j+i = M. X s. . J 3 Then, with the initial conditions S = S , S = I,we can efficiently compute the N derivatives at each step.

It should be mentioned that this method can be generalized so that other systems that cannot be reduced to this simple matrix form, but that satisfy

X..T = f.(u., X.) 1+1 1 i' i'

348 where x. and u. may be vectors, can also be optimized with a similar scheme. 3 Examples include the general equations of motion in systems with imperfect magnets, dipoles, and higher order multipole elements.

Single Focussing Systems

Optimization Results

Computer optimization runs were made for systems with 6, 10, 28,64 magnets. The 6 magnet system consisted of two triplets with internal separation of .5 meters separated by a drift space of 10 meters. The magnet lengths were each 1.0 meter. Magnet strengths, G,, were computed such that P^^-' was minimized for a fixed momentum dispersion, 6 = Ap/p. Runs were made for values of 6 from .0025 to .015. For each 6, the maximum values of r and r^ X V were for i = ±i , corresponding top=p ±6xp. Although r„ and r„ were m' '^ ^^ ^ *^o *^o ^ i i not equal, we always round r ~ r and r^ ~ r;' , as expected for mm mm an optimized system. Values of • / ^ y \ m m and r = max (r^^^ , r^^^ ) m m

are plotted in Fig. 1 as a function of 6 , Similar results were obtained for systems with 7 magnets upstream of the (10 meter) drift space and 3 magnets downstream. Values of G are given in Table 1 for this system, for 6 = .0025 and .015.

Systems with no large drift space were also treated. In Fig. 2, results are presented for the 28 magnet system, each magnet 1 meter long with a .5 meter separation between each. The optimization runs were started with an FODO configuration with G. ., = - G., with \G\ equal to 20 Teslas/meter. The final optimized system in each case consisted of a final triplet separated from the rest of the system by a 5-20 meter "drift space" in which the G. were essentially driven to zero. An example of this is depicted in Fig. 3, where values of G. are shown for the final magnets, after optimi­ zation, for a 28 magnet system with Z = 1.0 meters and .5 meter separation. In almost all of the runs made for this study, a final triplet or a final doublet appeared, separated from the rest of the system by a drift space. For example, one run was started with each of the magnets in a (previously computed) final triplet divided into two of equal strength, so that there were six magnets with initial signs (+H H-). After optimization a final triplet appeared with the three upstream magnets driven to zero (OOOH—h).

In Fig. 4, the spot sizes

+ / X y^ r^ =max(r^, r^)

349 are presented as a function of A = p/p^-1 for the 28 magnet system optimized for fixed 6 (.015). It can be seen that the 28 magnet system essentially created an achromatic spot over the range -5 < A < + 6 with r~ and r"*" increas­ ing sharply outside 6 of these limits. The dips correspond to two of the dis­ crete values of p contributing to P^2),

Analysis

The variation of r" with 6 in Figs. 1 and 2 can be understood using a simple argument based on equations linearized in Ap/p. Taking one direction, (y), the chromatic abberation, n^ is given to first order by '

L+D

^f^f - "^f^f = H I ds[y'(s)]^-yfyf + y^y^

where L is the length of the magnet system and D that of the final drift space (reaction chamber). Considering abberations of about the same size as the final spot (y^) and trajectories where the spread in y in the system near the end magnet is small (ri(s) << y(s))^we have Hf << yf.

Assuming A << 1, splitting the integral and discarding small terms, we have -n^y^ = AD(y^/) -+ A^J I ds [y (s)] . (2)

Since the right hand side is positive definite, for fixed y^ the best that can be done under our assumptions is to make the integral over the magnets small. Then

n^ ~ -ADy^ == Ay(L) where y(L) is the value of y at the last magnet (assumed to be >> y^).

To first order the phase space ellipse at the target is sheared by the chromatic abberation. Looking at the trajectories corresponding to y^ = 0 and y£ = 0 on the ellipse for A = 0(y|(A) and y9(A), respectively), assuming that for A = 0 the ellipse is alligned with the y, y' axes,

y^(A) : -ADy^'

y^(A) = y^(o) = r^(o) , where r^(A) is the envelope function at the target (r^, r^):

350 2 r^(A) = [(ADy^') + [r^Co)]^]*^ or 2 r^(A) = [(ADy^') + 4'(y]')^f'' where S' ^N " ^f "" '^T^''^ is the phase space area/ir.

In terms of y(L), 2 2 ^ r^(A) = r*[(y(L)/y*)^ + (y*/y(L)) ]^ (3) where (dropping the subscript N),

rA(A) = /AeD and

y*(A) = /GD/A . Assuming that the magnetic fields can be adjusted so that a given value of y(L) and y' can be obtained without contributing to the integral in (2), (probably by increasing y over a length of the system and sharply focussing the trajectory near the end), then the optimum r for A = ±6 can be obtained by finding the y(L) that minimizes (3).

Then,

y(L) = y*(6) and rf-'^{&) = ^r*(6) . (4)

These results are for one direction only: similar results were obtained in computer runs designed to optimize r only. For simultaneous focussing in two directions, however, it appears that approximately 75% larger spot sizes (r ) are obtained. The relation (4) is plotted as a dashed line in Figs. 2 and 3.

It should be noted that the inverse-square-root dependence of y(L) on 6 predicted above is closely followed by the computed optimal systems.

Multiple Focussing Systems

The single focussing systems can be thought of as simultaneously focussing, in one direction, two beams with

351 m -6m

-m - 6m < m < -m + 6m o o - - o o where

and the variables appearing in the transition matrices are

u. = m G.. 3 3 Since we can focus two beams (with some degradation compared to one beam), we can think of simultaneously focussing, say, four beams, or two beams in both the X and y directions. We found systems of magnets that focussed two beams (m , m-^, in both x and y) . As expected, there was a further degradation. Values of r~ and r-*- found were '2.5 mm and "'3.5 mm respectively, for m /m^ = .9, .8 and .7, for a 64 magnet system. Runs with more than two beams Yin both x and y) showed still further degradation. Conclusion

We have presented the results of computer optimization studies of 6, 28 and 64 magnet quadrupole systems, for achromatic beams with different momentum spreads (6). The dependence of the final spot size on 6 is similar to the square-root dependence predicted by simple linear theory, although the values of the spot sizes are about 75% larger. Also, the dependence of the beam size at the last magnet is very close to the inverse-square-root dependence predicted.

The spot size for a system optimized for a specific, large 6 (.015) was presented as a function of momentum. The nonlinear aspects of the computed optimization results were evident in the rapid increase of the spot size when the momentum went outside of the range for which the system was optimized. Also, for this large 6, the trajectories corresponding to the different momentum components within the range p -6p '^ p ^ p +6p varied substantially in position near the end of the magnet system (when there was an FODO lattice upstream), implying that results of linearized studies may not be accurate in this case. This spreading occurred even when systems were optimized for successively larger 6 starting from a small value, and the previous optimal magnet strengths used as starting conditions in each case.

Any configuration other than an isolated triplet or doublet near the end of the system was found to be non-optimal, and magnetic fields in this region besides those of the final triplet or doublet were driven to zero in the process of optimization. It was also found that increasing the number of magnets from approximatel> 20 to 64 did not result in any significant reduction of the final spot size.

352 As the minimum spot sizes were about 4mm for the larger values of 6, it appears that sextupoles would be needed to get 1 mm spots. Magnet systems containing sextupoles usually have a large number of quadrupoles, and the optimization of these combined systems should be a good application of the techniques used here.

Finally, some studies were done on quadrupole systems capable of simultaneously focussing two beams, each with small momentum spread but differing by 10 - 40% in mean Q/p, It was found that, with about a 50% increase in spot size, both beams could be focussed. Such systems might be useful for reducing space-charge effects, or if two separate ion types are found to be better than one for pellet ignition. The positioning of higher order multipoles in these systems to further reduce the spot sizes in the presence of abberations might present a very difficult problem, however.

Footnotes and References

1. K.G. Steffen, High Energy Beam Optics, Interscience, New York, 1965, Ch. 1.

2. R.C. Arnold et. al. , "Hearthfire Reference Concept //3: A Rapid Cycling Synchrotron System," ANL Report ACC-6, 1978.

3. A.E. Bryson, Jr., Yu-Chi Ho, Applied Optimal Control, Blaisdell Publishing Co., Waltham, Mass., 1969.

4. K.G. Steffen, Op. Git., eqn, 1-3. X v 5. Values of r and r-' closer to each other (more symmetrical spots) were obtained when a different performance function P^^^ = I E [(r^(T))^ + (r](T))''], which weights the larger value more, was used. Only P was used in this preliminary study, however.

6. If values of E were used that were not constant in i, this i dependence would change.

7. K.G. Steffen. Op. Git,, eqn. l-33a.

TABLE 1 FIELD STRENGTHS - 10 MAGNET SYSTEM G(Teslas/meter) 5/j 1 2 3 4 5 6 7 8 9 10 .0025 +12.8 -17,8 +13.5 -18.6 +11.1 -18.9 +7.9 -11.0 +20.2 -13.1 .015 -4,4 -7.2 +25.3 -33.4 -22.7 -8.2 +1.0 -7.5 +19.3 -15.3

353 •r.r (mm)

y. w.n

OS 10 i.r

Fig. 1 Target Spot Size vs. Fig, 2 Target Spot Size vs. Momentum Spread: 6 Magnet Momentum Spread: 28 system - error bars denote Magnet System variation for different weighting functions.

1 . ( 1 <-\A<.O / /<-;j>o lO. 1 // ^ 1 / ^'^^'^ / 8. rnr fwM.) 1 / // / 7 /r^./*v 6- 1 / / ^""^^S^. /I y ^. ^^-—-^N^^ / 1 I'

"" ^^^^^^^^V .-^A 2. ' -\ . 1 -2.C.- o

Fig. 3 Field Strengths for Final Fig. 4 Target Spot Size vs. 8 Magnets: 28 Magnet Momentum Deviation: System Optimized for 28 Magnet System Optimized ±,25% Momentum Spread for ±1.5% Momentum Spread

354 Octupole Correction of Third Order Aberration S. Fenster Argonne National Laboratory

These aberrations have been shown to be significant. Let X, x', y, y' be the displacements and slopes of a particle trajectory at an arbitrary longitudinal location Z and let X , x', y , y' be the corresponding quantities at Z , Assuming that each'^of the former set has an expansion in terms of the latter we define a third order aberration to be a term having one of the following forms:

A. x'^, A^ x' y'^, A., x'^y', A,y'-^ -L o ' 2 o •'o ' 3 o -^o 4-^0 2 2 BTloX Xo' , B-2x o-'y*o ,' B-3-'y o x'y'o-'o, 2 2 B.y y' , B^y x' , B^x x'y' 4-'o-'o ' 5-^0 o 6 o o-'o 2 2 C-,x x' , C^y x' , C-x y y' loo' 2-^0 o 3 o-^o-'o

2 ' 2 * ' C-4-'o-'oy y ', C^5x o-'y o , C^5x o-'y ox o 3 2 3 2 DTX , D^x y , D-,y , D.y x 1 o' 2 00' 3-'o 4-'o o A term has been "corrected" between Z and Z if a particular coefficient, which depends on the focussing elements between Z and Z, is zero due to choice of element placement and strengths. A common procedure is to ignore aberrations in the first round of design and then calculate them for a system sat­ isfactory in first order. It is usually feasible to correct the larger aberrations by adding octupole elements to the first order system without causing significant first order damage. The feasibility of this method depends on the strength required for the octupoles. Since the parameter values required in ion beam fusion are new a first stage keeps only the point-to-point aberrations (coefficients A ) and finds an octupole system which will completely correct a typical final focussing triplet at the level in which fourth order aberrations are negligible. Only three A are independent so one must begin research with at least

355 three octupoles. In MKSA units the notation is p = particle momentum qe = particle charge a = aperture radius B = pole tip field B , B , B = magnetic field at the test particle X, y = transverse particle coordinate s or z = longitudinal coordinate X' = dx/dz = dx/ds The magnetic fields of quadrupoles are: „4 1 3 , , 1 2 , , B^ = y u - JJ y u» • - ;^ X y u' ' o4 1 2 , , 13,, B=xu- T^y ^12"^ ^ ^4 '\j B z = + X y u' and octupoles B« -,8 qe pt /, 2 2\

•^ a The equation of motion with quadrupoles and octupoles becomes

x"+ 2£ u X = f'* (s) + f^ (s) P X ' X y"- ^ u X = f"^ (s) + f^ (s) p y y u 2,3 whe re ' fj^(s)= ^ (- i X y'^u + x'y- y u + x y y'u* + T ^ y^u' ')

+ 3|(-1XX.2U.T|X^U")

fy (s)= ^ (| y x'^ u - y' x'x u - x y x'u* - i y x^ u' ')

^ qe /3 ,2 1 3 . ,\ -H ^ (2 y y ^ - T2 ^ ^ )

356 ^8 , , qe pt /-, 2 2, f^(s)= ^ -^ X (3 y - x ) a

RS ^8, , qe pt /-, 2 2, y p 3~ y (3 X - y ) a

It is convenient to use the sinelike S (s) and cosinelike C (s) solutions of the homogeneous system: x^(s) = C^(s) x^ + S^(s) x;

yj^(s) = Cy(s) y^ + Sy(s) y;

In first approximation, and assuming no secular term effects, x, is substituted for x in f. The resulting inhomogeneous equation has a particular solution x u^(s), y h^^^' ^^^^ having zero initial conditions, which reads

X ^(s) = S (s)f C (s') f (s') ds'-C (s)fs (s')f (s')ds' ab x Js X X X "'Js X ' x' o o s s y^j^(s) = Sy(s)| C^(s') fy(s') ds»-Cy(s)|s^(sMfy(s')ds» ^o ^o and is the aberration for a given x , x', y , y'. ^ o o o o To see how strong octupoles have to be it is sufficient to limit consideration to the point-to-point case ^o~yo~^v^^f' ^ Sy (s^f ) = 0 where s^f is the final location. We find

yab' = f'= 4b ( = f' = 4b < = f> where x\=-^ C (s^)(x'y2h+x'^r (- I S^S'^u - i sVu')ds| ab p X f I o^o o-'sV 2xx 3xx/ ^ o s^ y4 se c (s^)(y'x'2h+y3 f (3 s^s ' ^u + i s V u') dsl •'ab py^fj-'oo -'oJ^2 yy 3yy'' I s o

357 with f f h = -'^2x( ( -i S^ yS'^ u + S Sxxy' S Sy' u o

+ i S^ S S' u'- i S S'S^ u') ds 2xyy 2xxy /

The endpoints s and s^ lie in free space outside of fringe fields so u(s )°= u' (s ) = u (s^) = u' (s^) = 0. Also a short octupole of length £g placed at Sg adds B^ . I x„(sj = - 3£ . ^Pt 8 ^3 ^. .2s2(3 J ^2 8 f p 3 L o-'o X 8 y 8 a - K.. 3 c44 ' = 8)]- ^x t^f'

B , • 8., = - a£ . jpl yQ(s<=f) " P a3 3 -o'y;4< = 8' ^l ' = 8' - y;'4 '"s'ls '^f'

If three octupoles are located respectively at three values of So called s,., , ^oy ^Q-5 they will cancel the aberration A if tne following equations are satisfied:

^ V( = 8k) ^8 I. a ^ 3 B^^(s„, ) i^ , f f y ^tl8k_8 s4 r (3323.2^ ^ 3 X 8k J V 2 X X k=l ^ s o

- i S-^ S' u' ^ ds 3 X X /

358 3 R^ ^c ^ . 0 ^f ST , , ^pt^^Sk^ ''8 . c4 .^ V _ r /3 „2„,2 2 (-) -^ 3 ^y ^^8k^ - -J (2 Vy "^ k=l ^ s o

+ \ S-^S' u') d£ 3 y y >'

These are three equations in three unknowns. A solution for B ^.{Sni.) ^o ^s considered good if it is small. The major con­ tribution to the r.h.s. will come from the u' term. B may be obtained by clever methods of displacing quadrupoles to obtain octupole effects; the approximation of short Sip as given here is useful as a feasibility check.

In examining several cases we found that only the terms on the r.h.s. containing u' were large. This is due to a cor­ relation between u' and S' and S*. The oscillations in u together with its positive definite coefficient make its term negligible. Note that some of the u' terms arise from an inte­ gration by parts of u''. The important terms then involve three integrals

"' 3 h = - ± \ S"^ S* u' ds X = -13 J/ X X o ^f h = i r S S (S S' - S S') u' ds "o 2j xy'xy yx s o

h = k \ S^ S' u» ds y 3 J y y s o which give the aberrations of the quadrupole fringes (we have dropped the smaller terms in u for this paragraph). It appears that u' is correlated with S* but anticorrelated with S' in an example we are practicing on. Also, S > 0 and Sy > 0 so X

h , h , h < 0. X o y

359 Introducing notation

X X 2 3 S , b = 4 a" - h a = x o .4 V

^i = (Bg ^a'i 1 1 i IN where 1 labels a particular octupole at s s., we cancel the aberration if

n a. X. = b 1 1 1 1=1 One notices immediately that the components in b have different signs while those of a have the same sign so a solution with all X. > 0 is impossible. Some octupoles must cancel the effect of others in a given channel and one might be forced to large values of x.

We assume first that neither S nor S vanishes anywhere (except at s and s^). Then the coefficient matrix has no zeros and it is hard to see what to do. Let us choose N = 6 and de­ mand that

^2 ^1' ^4 ^3' Xg = - X3.

Such an arrangement will be said to consist of three conjugate octupole pairs. We choose the s. so that

S (sJ = S <^2'' ^ (=5' = <=6' X 1 X %

^ (^3' ^(^3' = ^ (=4' Sy (S4)

Then the 12 pair will contribute zero to b,; the 34 pair will contribute zero to b^; and the 56 pair will contribute zero to b^. The 3x6 matrix can be written as a 3 x 3 matrix by putting

360 c^ = a^ - '2' •^3 ~ ^3"^4' ^=5= =5-^6-

Then

V c. X. = b. Z 3 3 j=l,3,5

As a convention we take

S^(s_) > S^(s.), S„(sJ > S„(s„), S„(s^) > S,(s^) X X X X

Then necessarily S (s^) < S (s .). The matrix for Eq. (1) has zeros on its main diagonal," To get small x one must choose large c, which means, for example, that S ,-S ^ should be large, This should not be overdone, however, becXuse^ due to signs, another channel may be spoiled by an attempt to reduce x in a particular channel. The trial-and-error process converges, A figure-of-merit for the system is the ratio of total absolute magnitude (Bil)^ quadrupole to {Bi) ^ octupole, which should be as large as possible.

Example (MKS Units) + 3 A previously designed triplet for 20 GeV Xe "^ (B = 80) is used. ** The quadrupole lengths are 1.2 m, 2.4m, and 1.2 m with spacings 0.6 m between. The bore radius is 0.3 and the pole tip fields are 5.54 Tesla, 4.85 Tesla, and 5.54 Tesla. The TRANSPORT code started with x = 0.00346, y = 0.00482, x^ = 0.01024,, y' = 0.00726 at°a point 30 m upstream of the triplet and focussed to a spot 5 m downstream of the triplet. The unnormalized emittance is 3.5 • 10 Chromatic aberration is ignored. The aberrations come out

(Ax|x'^) = -0.0055, (Ax|x'^x ) =-0.02084, (Ay|y'^) = -0.01256 while

(s^) -0.3133, C (s^) = -0.2197. X One chooses points s,-s, by inspecting the printout of S (s) and S (s) taken every O.I m. The choice in Table 1 was deemed optimal.

361 Table I point s S^S _ S^,S _ S^. ' S„ —X— -y- 1 33.. 4 16-00 46.35 2 16.. 0 16.00 16.00 3 24., 4 24.43 24.43 600.0 4 34,, 5 16.568 36.000 600.0 5 31., 6 23.552 40.285 6 34., 1 16.017 40.285 7 35., 2 17.295 28.174

We found for S - 0.142 • 10^ g = j( 1.071 • 10^ - 1.30 • 10^

The equations for x are

0.280 x^ + 0.242 x = - 0.142 " ^

1.46 x^ + 1.452 X = 1.071 • ^

4.55 XT - 1.323 X, = - 1.300 " T

They are solved by

x^ = -0.206, x^ = -0.465, x^ = 0.390, with a total

(B£)g = i (0.825 + 1.860 + 1.560) = 2,125

362 Now for the quadrupoles.

(Bi)^ = (5.54)(1.2) • 2 + (4.85)(2.4) = 25.

The ratio (B^) -fB^y-= 0.085 (2) may be compared to a figure of 0.18 obtained by H. Enge.^

Possible Nodal Solution

One should try to improve this result. A different ap­ proach would be to get two a. to have only one component. To do this requires one to construct two single-plane nodes (foci) with respectively S = 0 and S = 0. Such a system would read

^12^2 ^ ^13^3 = ^

^22^2 " ^2

^31 ^1 ^ ^32^2 = ^3 where S^(s^) = 0 and S (s ) = 0. S (s,) and S (s ) should both be large. A rough estimate for the^above system assumes that S would remain unchanged after the addition of the new quadrupoles to make the ribbons at s, and s^. If we took point 7 in Table I we could use a solution (divide B^ by 4.0 below) x^= - 1.5, X2= 1.5, x^= - 0.75, Sy(s3)= 18., S^{s^) = 28.17 for a total (BJl) g = 3.75. This gives a ratio of 0.15. A complete system of nodal type is being designed to see whether nodes can be constructed.

In a realistic design one should eliminate all aberrations A-D (eight independent^ in x). Avoidance of crosstalk with nodes is an advantage in general. One must also check for higher order aberrations with a ray tracing program.

Acknowledgement

Helpful remarks on this subject were made to me by K. Brown (SLAC), E. Colton (ANL), H.A. Enge (MIT) and D. Neuffer (LBL).

363 References 1. David Neuffer, LBL unpublished, May 18, 1978. 2. P. F. Meads, Jr. UCRL-10807 (1963). 3. Klaus G. Steffen, High Energy Beam Optics Interscience (1965), p. 53. 4. E. Colton, unpublished. 5. H. Enge, private communication. Our bore radius is three times the one used by him, so his original figure of 0.02 had to be multiplied by 3^= 9.

364 CORRECTION OF CHROMATIC AND GEOMETRIC ABERRATIONS USING SEXTUPOLES AND OCTUPOLES

Eugene Colton Argonne National Laboratory

Introduction

In this note we explain the procedure for applying some chromatic corrections to a final transport line, neglecting space charge, utilizing the method suggested by Brown.^ We also research the possibility of includ­ ing octupoles into a point-to-point triplet system, as outlined by Fenster.- Positive results were obtained in both cases: (i) using 2 + I correcting sections with two pairs of non-interlaced sextupoles increased the fraction of beam with AP/P = ± 1% onto a 0.1 cm radius target by more than a factor of 1.75; (ii) six octupoles placed into a point-to-point triplet system in­ creased the fraction of a full emittance AP/P = 0% beam striking a 0.1 cm radius target by a factor of 2.5.

Basic Transport Line

The beam parameters chosen were: T = 20 GeV Xe+3 ions, a normalized emittance ep = 2.0 TT cm-mr, reaction chamber radius 5.0 m, and target radius of 0.1 cm. This corresponds to an ion momentum of 72.671 GeV/c and rigidity Bp = 80.745 Tesla-meters. The beam was assumed to exit achromatic- ally from a storage ring or long transport line with identical upright ellip­ sis in both transverse phase planes XQ = YQ = ± 3.36 cm, and XQ = YQ = ± 1.0 mr. The XQ and YQ represent initial horizontal and vertical sizes, respec­ tively; similarly the XQ and YQ represent the initial divergences (dx/ds and dy/ds, respectively). The final transport line consists of two quadrupole triplets and drift spaces: (a) the first section (7.31 m long) satisfies a parallel-to-point condition and transforms the initial beam profile (given above) to a tiqht focus (X = ± 0.35 cm, Y = ± 0.48 cm, X' = ± 10.2 mr, and Y' = ± 7.26 mr); (b) the second section (41.0 m long) basically is composed of a 30 m object distance, symmetric triplet of 30 cm bore radius, and 5 m image distance. This section satisfies point-to-point optics and demagnifies the "object" down to approximately a 0.1 cm radius spot. The quantitative final first-order conditions are Xf = Yf = ± 0.11 cm, and Xf = Yf = ± 33.0 mr. In Table I we present the listing of beam elements for the 48.3 m trans­ port line. The quadrupole strengths were obtained using the program TRANS­ PORT. 3 Figure 1 illustrates the optics, beam envelopes, and apertures of the system as a function of length(s).

365 Correction of Chromatic Aberrations

Realistic operation of the transport line requires consideration of a finite momentum bite (± AP/P). When we consider the spread AP/P = ± 1.0%, then the second-order chromatic aberrations of the transport line drive the final beam envelopes up to Xf = ± 0.53 cm, and Yf = ± 0.83 cm. The growths are mainly due to contributions of (XfIXQAP/PJXQAP/P to Xf and (XfIYQAP/P) YQAP/P to Yf, and to a lesser extent, by (Xf|X,;,AP/P)X(!)AP/P to Xf and (Yf|YQAP/P)YOAP/P to Yf. In order to get a quantitative estimate of the chromatic degradation, we ran the Monte-Carlo program DECAY TURTLE.^ The transmission in the presence of apertures, and fraction of rays arriving at the final focus with radius rf (= /X^ + yf) 5 0.1 cm was evaluated for |AP/P| 5 1.0%. Of 5000 rays started, 4591 reached the end (91,8%), and 1110 had rf < 0.1 cm. This corresponds to a useful efficiency of just 22.2% (E 1110/5000).

The next step was to attempt a partial chromatic correction by utiliz­ ing sextupole magnets. Following K. Brown,^ we added two similar 47.0 m transport sections upstream of the final transport line. These added trans­ port sections are nominally termed +1 (or identity) sections. They contain quadrupoles, dipoles, and sextupoles; the quadrupoles and dipoles effect a first-order identity transform, and the sextupoles are placed and powered so as to cancel all geometric and chromatic aberrations (thus a +1 transform good to all orders). In principle, the chromatic correction at the final focus is effected by altering the sextupole strengths; of course, this modifies the upstream +1 sections. The quadrupoles of a +1 section are arranged into a FODO lattice with 90O phase advance per period (or cell). Each +1 section is composed of four identical cells. We have adopted a cell design developed by D. Carey.^ Table II lists the beam elements of one 900 cell for a 20 GeV Xe"'"^ system; this arrangement has a beat factor of 2.25, and quadrupole packing factor of 0.34. The sextupoles are not included in Table II as they are placed in a special manner as explained below.

Using sextupoles, the second-order chromatic contributions to final spot sizes (at Sf) are given by (for a parallel to point system) '"f - hf^ilV'K ' Kf'W"", :i) (ff ("''(0). and V - Vo^(v,|v„f)^ ^ ^ifi^fKfl i^)

366 where the corrected aberration coefficients are subscripted with the letter c. They are defined here by

(X^|X^AP/P)^ = (X^|X^AP/P) -^ a XI Bpt / "^X ^X "^^ '^^' sext

(x,|x;,AP/p)^ = {X,|X;AP/P) + a T B^^ f c, s, D^ ds ^ tl A L / 3b^ )

s {3c)

6 The Bnt represents the sextupole pole-tip fields and the integrals are taken over the length of the sextupoles. The C, S, and D functions are the co­ sinelike, sinelike, and dispersion functions, respectively.^ The a = - 2 Sx{sf)/(a2Bp) and B = 2 Sy(sf)/(a2Bp) where a is the sextupole bore radius. We use MKSA units so a = 2.563 and 6 = - 2.648 for a = 0.1 m. The (X|(AP/P)2; term arises from the presence of dipoles in the overall system.

Correct placement of sextupoles depends upon the s dependence of the integrands in Eqs. (3)2and (4). In Fig. 2 we show the s dependence of the first-order products CxDx,CxSx,CyDx, and CySyDx for a 47.0 m + I section. The sextupoles should be placed in such a way as to reduce certain aberra- tion(s) while not increasing others. Two identical 1 m long sextupoles were placed 23.5 m (180*^) apart with centers at S] and s^ in the first +1 section; another two identical sextupoles were placed .it u^ and s^ in the second +1 section. The program TRANSPORT^ varied the sextupole strengths in order to cancel the main aberrations (Xf|XQAP/P)p and (Yf|YQAP/P)J,. Cancellation was achieved for SI strength 0.373 Tesla-meter, and -1.46 Tesla-meter for S2. Table III lists the corrected aberration coefficients with the sextupoles on, and off (same as uncorrected). With the exception of {Xf|(AP/P)^) all aber­ rations were reduced significantly. We also list the transport beam envelope sizes for AP/P = ± 1.0%; a dramatic reduction in beam size is indicated for the system with sextupoles energized."^

Rays were traced using DECAY TURTLE'* for the cases with sextupoles on, and off. The initial conditions were identical to those quoted above for the bare run without added +1 corrective sections. The results are listed in Table IV along with the r.m.s. half-widths indicated. The transmissions were down in both cases: to 86.9% with sextupoles off, and 66.9% with sextu­ poles on. The strong sextupoles in the second +1 section (S2) introduce

36 7 excessive centroid shifts resulting in aperture losses. The useful efficien­ cies in both cases were 17.4%, and 38,6%, respectively. These can be compar­ ed to the value of 22.2% obtained with just the basic transport line. On the other hand, if one judges a system by the ratio of efficiency to transmis­ sion, then the basic system has 24,0% while the corrected system has 57.7%, Further work is certainly necessary on the technique of chromatic corrections - e.g., basic quadrupole systems should first be optimized for minimum second-order beam sizes instead of relying upon first-order tech­ niques. Then perhaps more, and less strong, sextupoles can be placed which do not degrade the transmission significantly, while reducing aberrations. Of course, programs such as DECAY TURTLE or RAYTRACE must be run in order to verify the TRANSPORT predictions.

Use of Octupoles to Correct Third-Order Aberrations

Neuffer has shown that third-order aberrations can increase final spot sizes significantly in quadrupole focusing systems,® Therefore, we have investigated the higher-order effects using the point-to-point quadrupole triplet section of our final transport line (Section 2 in Fig. 1 and Table I). Chromatic and space-charge effects have not been included. There are actual­ ly 20 third-order aberrations, but we only consider the contributions of the three independent aberrations representing point-to-point optics. We assume Xo = YQ = 0, which is not unreasonable since the actual beam has XQ = + 0.35 cm, and YQ = ± 0.48 cm. Then, following Fenster^ we can express the third- order contribution to final spot size (at Sf) in terms of initial divergences at SQ (E 7.31 m) by

AXf = (Xf|x;3) x;3 , (x^ix; Y;2) X; Y;^ (sa)

,Y^ = (Y,|Y;3) Y;3 . (Y^IY; X;^) Y; X^^ {5b) where the aberration coefficients are given by

^^fl^o') = Cj({s,) /f (I S2 S'2 G 4 S3 Sji G') ds (6a)

(YflY; X;2) = - Cy(s,) h (6c)

(YflV) = - V^f) ^J. (|s^s-G.is3s;G')d, s :6d; with

368 h = =0 (6e; + ''(j'l'y'y - ?SxSiS^))ds

In Eq. (6) G represents the gradient function with G = 0 in a drift space and G = Bp^/(aBp) for a quadrupole with bore radius a and pole-tip field = Bp^. Note that the third-order aberration coefficients are expressed as integrals over products of first-order functions (S and S').

The program TRANSPORT was utilized to calculate the S and S' functions and the aberration coefficients were obtained by a numerical integration utilizing a 0.1 m step. This was done first assuming square-edge magnets (i.e., G' E 0 everywhere) with the indicated beam elements (#8 - 14) in Table I. The procedure was repeated assuming quadrupole linear fringe fields with the magnitude of the gradients increasing from zero at 30 cm outside the magnets to the full gradient at 30 cm inside the magnets. Thus, the net focusing strength / Gdl was preserved. The aberration coefficients calculat­ ed according to the above two procedures are given in Table V. Units are MKSA. We also list the AXf and AYf for the extreme ray X' = 10,2 x IQ-^, and YQ = 7.25 x 10-3. j^g results in Table V indeed verify Neuffer's find­ ings® that the quadrupole fringe fields are responsible for large aberrated images - |AXf|= 2.73 cm and |AYf|= 3.50 cml

Following Fenster^ we can write the contributions to AXf and AYf due to a short octupole of length i^ placed at S3 as

ic ''f - - i^4(M KW(^8)S^(S8) - X;3s;;(s8)](7a)

''f - - ?K^y^f)K^^oSt(^B)S^(S8) - Y;3S^(S8)] (7b) where a is the bore radius and Bg^ is the pole-tip field of the octupole. The best locations for placing three octupoles is where Sjj is large and Sjj is small, Sx is small and Sjt is large, and where SxSy is large, respectively. This reduces the octupole strengths (Bg^ i!.s) required. Investigation of the s dependence of the considered system indicates that nowhere is S^ > S^. In fact, as explained by Fenster^ placement of three conjugate octupole pairs (six octupoles) are used for this less than ideal case, in order to reduce the aberrations in Eq. (6) to minimum values. Figure 1 also shows the longi­ tudinal placement of six octupoles; they are labeled 0^. Their strengths are listed in Table VI.

When the effect of the six octupoles was computed for the extreme ray with XA = 10.2 X 10-3 and Y' = 7.26 x 10-3, ^e obtained AXf = + 0.0255 m and AYf = 0.03396 m using Eqs. (/a) and (7b), respectively. We add these numbers to the system values given in Table V and obtain the net third-order contri­ bution for a point-to-point system using quadrupoles with linear fringe-field

369 behavior: AXf = - 0.0273 + 0.0255 = 0.0018 m and AYf = - 0.0350 + 0.03396 = 0.0010 m! The six octupoles indeed correct the third-order aberrations for the considered system. The above analysis represented the work completed by the time of this conference. As of the present time (December 1978), we have extended the analysis to non-point sources (XQ, Yoy'O) and to fifth-order using the program RAYTRACE.^ This program calculates the actual trajectories of the rays through drift spaces and magnetic elements. The fringe field behavior of magnets is assumed to follow the behavior of (1 + eA)-i where A = aQ+aiS+a2s2 +a3s3+a4S^+a5S^. We have run this program in two modes; (a) the basic system of Fig. 1 (Section 2) in order to check that it agrees with the find­ ings above which utilized a linear fringe-field behavior of quadrupoles, (b) the same, but including the six octupoles (listed in Table VI) which we have taken to be 0.2 m long.

The procedure was to track a number of rays (14) starting from a point source {Xo=Yo=0) through the system to the end (sf); then we fit the final coordinates to the expressions

rl2 X, = (x,|x;)x; + (x,|x;3)x;3 . (X,|X;Y;2) X;00Y (8a: ' (Xf|x;^)x;^ + (X,|X;3Y;2)X;3Y.2 , (X,|X'Y;;^)X;Y'1;+

Y, = (Y,|Y;)Y; + (Yf|Y;3)Y.3 , (Y,|X;2Y;)X;2Y; (8b) + (Y^IY;5)Y;5 , (Y^|x.2Y.3)x.2Y-3 . {Y^|x;n^)x;^Y;

In each case the six matrix elements were obtained from the fits of the final coordinates to the expressions (8a) and (8b), In Table VII we list the twelve matrix elements so obtained in both cases (a) and (b) (defined above). We also list the calculated contributions to the final coordinates using the extreme ray XQ = 10.2 x 10-3, Y^ = 7.26 x 10-3 fo^ the first, third, and fifth order separately. Note that the S functions (Xf|Xo) and (Yf|YQ) are small but non-zero; this is just due to the fact that realistic quadrupoles were used here rather than the ideal square-edged versions assumed in TRANS­ PORT. A small perturbation of the gradients given for the system in Table I would bring these matrix elements to zero.

Comparison of the data presented in Tables V and VII indicate good agreement in the third-order aberration coefficients calculated via linear fringe-field quadrupoles and the RAYTRACE assumed form; the listed third- order contributions to spot size AXf and AYf agree quite closely. We also note that with octupoles off the largest ratio of fifth-order to third-order contributions to Xf is 0.27 and 0.12 for Xf. When the octupoles are ener­ gized, the third-order aberrations are reduced to negligible values, but the fifth-order terms are enhanced slightly.

370 Finally, we have studied the effects of the octupoles in a true Monte- Carlo fashion: one hundred rays were generated according to a W distribution, 1 .e. &y ^ (^j ^ (y^ ^ fe)' <- ^ (9) and this represents a source with spatial extent. In Eq. (9) we have switch­ ed back to cm units for displacements and mr for angles. The 100 rays were tracked through the system using RAYTRACE and the Xf, Xf, Yf, and Yf values obtained. We removed the first-order angular contributions to size by com­ puting AXf = Xf - (XflXtl)) XJIJ and AYf = Y. - (YflY^) Yi;io then we defined the beam radius by

Ar^ = [(AXf)' + (AYf)']*^^ (10)

We have calculated the number of rays with Arf less than, e.g., 0.05 cm, 0.1 cm, and 0.15 cm. This procedure has been performed on both sides of the final focus (s = Sf) in order to locate the circle of least confusion; the beam size at the longitudinal distance AS = s-Sf from the final focus is given by Eq. (10) with AXf -> AXf + .001 X^ AS and AYf -> AYf + .001 Yf AS. In Fig. 3(a) we plot the Aa behavior of the fraction of rays with Arf ^ r^g^y^ with r^ax = O-O^ cm, 0.1 cm, and 0,15 cm, for the case where the octupoles are off. Figure 3(b) shows the results for the system with the octupoles energized. For rmax = 0-05 cm or 0.10 cm we gain a factor of 2.5 in the amount of useful flux when the octupoles are energized. In fact, we pass 85% of the beam through a 0.1 cm radius hole located 5 cm upstream of the "focus". These results are very encouraging since no corrections have been attempted for aberrations due to finite sources or fifth-order terms. Of course, the octupole gain factor (OGF) will depend upon the shape of the initial distri- btion (e.g., K-V, W, etc).

Conclusions

Using a less than ideal system we have achieved a sextupole gain factor (SGF) of 1.75 and octupole gain factor of 2,5 for the fraction of beam inci­ dent upon a 0.1 cm radius spot. Using the techniques listed at the end of the chromatic corrections section, we hope to boost the calculated SGF signif­ icantly. One should also use an improved octupole correcting system upstream of the final focusing lenses as suggested by Fenster.^ Finally, any system has to be carefully evaluated under "realistic" conditions as to the proper distribution function and space-charge effects.

Acknowledgements

People who have contributed to this work have been K. Brown (SLAC), D. Carey (FNAL), S. Fenster (ANL), S. Kowalski (MIT), and G. Magelssen (ANL).

371 References

1. K. Brown, "A Design Procedure for Correcting Second-Order Geometric and Chromatic Aberrations in a Beam Transport System", Brookhaven National Laboratory, report BNL-50769. p. 107 (1977).

2. S. Fenster, "Octupole Correction of Third-Order Aberrations", in these proceedings.

3. K. L. Brown, D. C. Carey, Ch. Iselin, and F. Rothacker, CERN 73-16 (1973).

4. K. L, Brown and Ch. Iselin, CERN 74-2 (1974).

5. D. Carey, Private Communication.

6. See e.g., K. Steffen, in "High Energy Beam Optics", p. 14, Wiley & Sons (1955).

7. The uncorrected beam sizes listed in Table III differ from the values quoted earlier because the present transport line includes 2+1 sections in addition to the final transport line shown in Fig. 1.

8. D. Neuffer, "Geometric Aberrations in Final Focusing for Hide", LBL HIF Note HI-FAN-36 (1978).

9. S. B. Kowalski (MIT), RAYTRACE (unpublished).

10. We still include first-order contributions from the finite source size, i.e., (Xf|X^) / 0 and (Yf|X^) f 0.

372 50 -

LO

-50 1 20 30 40 s (m) Fig. 1 - Beam transport envelopes for a 20 GeV Xe'''^ beam with normalized emittance En/ir = 2.0 Fig. 2 - s dependence of the indicated functions cm-mr and AP/P = ± 1.0%. Initial conditions in a +1 section; units are MKSA. The arrows drawn are XQ = YQ ± 3.36 cm, X^ = Y^ = ± 1.0 mr. at s values of 8.5, 16.5, 32.0, and 40.0 m Also shown are the locations of the six octupoles represent sextupole placement locations. used to correct third-order aberrations. xl.O _ (a) OCTUPOLES OFF

r^^j^=O.I5cm

UJ 4>

r^^j( = 0.05cm

-5 0 +5 -5 0 +5 As (cm) (a) As(cm) (b)

Fig. 3 - Fraction of 100 rays generated according to W distribution (see text), which pass through a hole of radius r^iax ^^^ *"niax ^ 0-05, 0.10, and 0.15 cm. The s dependence is shown near the final focus, (a) Triplet system without octupoles (b) Same, but with six octupoles (labeled 0-j in Fig. 1) energized to the strengths given in Table VI. + 3 TABLE I. Listing of 20 GeV Xe TRANSPORT Line

Effective Length Field Gradient Element (m) (T/m)

1. Drift 1.0 2. Quadrupole (HF) 1.0 30.0 3. Drift 0.25 Section 4. Quadrupole (HDF) 1.98 1 -30.0 5. Drift 0.25 6. Quadrupole (HF) 2.58 30.0 7. Drift 0.25

8. Drift 30.0 9. Quadrupole (HF) 1.2 18.5 10. Drift 0.6 Section 11. Quadrupole (HDF) 2.4 2 -16.2 12. Drift 0.6 13. Quadrupole (HF) 1.2 18,5 14. Drift 5.0

TABLE II. Basic 90^ FODO Cell

Effective Len :jth Field (T) or Element (m) Gradient (T/m)

1. Drift 1.94 2. Quadrupole (HDF) 2.0 -10.81 3. Drift 0.3 4. Dipole (11.25° bend 3.28 4.833 right) 5. Drift 0.3 6. Quadrupole (HF) 2.0 +11.028 7. Drift 1.94

375 TABLE III. Final Chromatic Aberrations and Envelopes

Case

Quantity (m) Sextupoles Off Sextupoles On

(X,|X^AP/P)^ -21.0 0

(Xf|x;^AP/p)^ -182.9 -77.9

(Xf|(AP/P)2)^ +3.365 -5.08

^f(env) ±0.0074 ±0.0015

(Y,|Y^AP/P)^ -29.9 0

(YflY^AP/P)^ 237.7 126.2

V(env) ±.0104 ±0.0017

TABLE IV. TURTLE Predictions

Case

Quantity Sextupoles Off Sextupoles On

No. of rays to end 4345 3347 No. of rays at end with r < 0.1 cm 872 1928 a^ (cm) 0.192 0,072

Oy (cm) 0.250 0.106

376 TABLE V. Third-Order Aberration Coefficients Calculated from TRANSPORT

Case Square-edge Linear-Fringe Function (m) Quadrupoles Field Quadrupoles

(Xf|x;3) -509 -5674

(^flW -1034 -39615

AX^* -0.0011 -0.0273

(Yf|Y;3) -4079 -36625

{Y,1Y;X^2) -727 -27787

AY^* -0.0021 -0.0350

Calculated from Eqs.(5a) and (5b) for the extreme rays X^ = 10.2 X 10-3, and Y' = 7.26 x 10-3

TA_BLE__V^I_. Octupoles to Correct ThiJ2d_-Order Aberrations

Location s(m) (T-m)

23.31 0.206 31.71 -0.465 38.91 0.390 40.7T -0.206 41.41 -0.390 41.81 0.465

377 TABLE VII. Matrix Elements From Fits to RAYTRACE Coordinates

Case Function (a) Octupoles Off (b) Octupoles On

0,923 0.924

(X^ X;3) -0.471 X 10^ +0.072 x 10"*

X;Y;2) -3,88 X 10^ -0.18 X 10^

(X. X-) -12,6 X 10^ -58.4 X 106

XA^Y„2) -94,4 X 10^ -14.1 X 106 0 0 X'Y"*} -10.8 X 10^ -22.1 X 106 0 0 ' X^ (first-order)* 0.0094 0.0094

AX^ (third-order)* -0.0259 -0.0002

AX^ (fifth-order)* -0.0070 -0.0079

(Y.iY;) 1.22 1.22

(Y,|Y;3) -2.73 X 10^ +0.14 X 10^

(Yf|X;2Y;) -2.53 X 10^ -0.055 X 10^

(Y,|Y;5) -113 X 106 -274 X 106

(Yf|X;2Y'3) -76.4 X 106 -39.0 X 106

(Yf|x;n;) +23.5 X 106 -20.7 X 106

Y^ (first-order)* 0.0089 0.0089

AY^ (third-order)* -0.0296 0.0001

AY^ (fifth-order)* -0.0035 -0.0087

* Calculated for the extreme rays with X' 10.2 X 10-3, and Y; = 7.26 x 10-3, 3^ started at s =°'7.3 1 m

378 G. PLASMA EFFECTS

FILAMENTATION AND TWO-STKEAM INSTABILITIES IN HEAVY ION FUSION TARGET CHAMBERS

R. F. Hubbard, D, S, Spicer, and D. A. Tidman Institute for Physical Science and Technology University of Maryland, College Park, Maryland 20742

Introduction

Heavy ion fusion systems require that the beam be focussed to a radius of a few mm in traversing the final 5-10 m from the wall of the target cham­ ber to the pellet. Classical transport models * ' indicate that these con­ ditions can be met for a "^ 30 GeV uranium beam with proper choice of system parameters. Classical scattering of the beam by the background gas limits the acceptable target chamber pressure p. For example the minimum beam radius exceeds 0,1 cm if p ^1-10 torr in air or >^ 100 torr in hydrogen. In addition, self-pinch effects arising from the net beam current degrade fo­ cussing by causing different segments of the pulse to focus at different points near the pellet. One strategy for dealing with this problem is to minimize pinch effects by pre-arranging a high background conductivity and current neutralization, injecting a large radius beam (> 20 cm), or by reduc­ ing the injected beam current and/or charge state. A second approach is to propagate the beam in a self-pinched mode by using a small ( '^'1 cm) initial beam radius.

Microinstabilities, which are excluded from classical models, may severe­ ly degrade focussing or disrupt beam propagation entirely. These deleterious effects arise from the eventual nonlinear evolution of the instabilities and are very difficult to predict for such a complicated system. Instead, we have attempted to find a range of parameters (pressure, beam current, etc.) for which the linear growth rates for the instabilities are collisionally damped or are acceptably small.

We present survey results for these different instabilities. The first, the electromagnetic filamentation instability, has been cited as a serious potential hazard because it can cause the,beam to break into self-pinched filaments which interfere with focussing. ' The direct two-stream (or e-b) mode arises from the interaction between the beam ions and the background electrons produced from ionizing the gas present in the target chamber. This instability severely disrupts propagation at low pressures in relativistic electron beams and,may lead to an "anti-pinch" effect in ion beams which de- focusses the beam. Finally, the return current (or e-i) mode is a two- stream instability generated by-^the return current drift between background electrons and background ions. It can lead to anomalous resistivity ef­ fects and may enhance defocussing from the e-b mode.

379 We find that all three instabilities can be controlled by a suitable choice of system parameters, Filamentation is most easily controlled by in^- jecting the beam with a large ( >10 cm) initial radius. Both of the two- stream instabilities can probably be eliminated (except for a small region near the head of the beam) by choosing p > 1 torr. All three instabilities are significantly easier to control if single beam power is kept below 100 TW by using a multiple beam system.

Filamentation Instability

We first summarize the analysis of the electromagnetic filamentation instability reported in Ref. 8 for transverse modes (^'^v ~ 0) in which the beam is assumed to be collis^or^less while the background plasma is collision- dominated. Oblique modes (1<^'V, 4 0) are discussed later in this section, Since the net current is small, the equilibrium state is effectively field free. The resulting dispersion relation is

4 TTi 0)0 0 = kc -w+tiT (1) 1-1-^1(1+ 5b^(5b> 1 _ ^"""it^JO 2 e Here (O and oi are the electron and beam plasma frequencies, w = (JJ + i.y is the complex wave frequency, V, and v, , are the beam^velocity and trans­ verse beam thermal velocity, O is the conductivity, ' ^ = a)//2kv^ and Z is the well-known plasma dispersion function. Unstable solutions (Y > 0) exist only for (0=0 and 0 < k < k^ ~^T,V ^^hX'^ ' If the group velocity Vg « V , the instability is effectively non- convective, and unstable growth at any position z along the beam trajectory begins when the^head of the beam arrives at z and ceases at a time !« later where Tp » 10 s is the pulse length. Hence, the number of e-foldings for these modes is Ny = Y(z)Tp where Y(Z) is the average growth rate. If Ny ^ 5 everywhere, filamentation defocussing will probably not occur.

The most important result reported in Ref, 8 was that focussed beams injected with a large initial rms radius RQ can easily meet this restric-' tion on Ny . Using the envelope equations of Lee and Cooper. one can show that the mean square perpendicular beam velocity vf = R^ + v, , is approxi­ mately constant and that v ,(z) = v ,RQ/R(Z) for an unpinched beam. In­ creasing RQ therefore increases -^ , near the pellet and substantially « reduces growth rates. This also increases vf since V? W R2 = (R V /s) , where s is the chamber radius, which makes pinch effects negligible for Ro >, 20 cm in most cases, The increase in v^ , near the pellet is usually sufficient to make |C, I « 1 . In this limit (neglecting displacement current), the growth rate is 2 2 2 kc (k - k ) Y(k) = ^z . (2) 47rka + Vy k c /v, j^

380 Note that k = %^h^^h-^^ -^^ approximately constant (except for charge stripping) because the R dependence of O) is balanced by the R dependence of v, , as R approaches its value R . at the pellet. The advantages of having a large initial radius are clearly reflected in Fig. 1 which plots Ny vs. R for a 10 ns, 34 GeV, 50 TW uranium beam fo­ cussed at a distance of 5 m and 10 m through air at 1 torr. The value v, ,(o) /V, = 2 X 10"^ was chosen so that R . = 0.10 at the pellet,"^^'-^^ and the charge state Z = 69 at s = 5 m. Fig. 1 overestimates the growth rate for R ,!< 5 cm because pinch effects increase v , somewhat.

Near the pellet,the second term in the denominator of (2) can usually be neglected. Maximum growth occurs at k = k /3 , and N can be written & & o * Y , T Z^T - • ' - -'- N = 1.5 X 10^ P ",-,^3/2^, 2, IU,(o) ^r-^h^\ ) •• (3) Av^re o ^ ' Here I is the beam particle current in amps, A is the beam atomic weight, JlnA ?5i 10 is the Coulomb logarithm, T is the background electron temperature in eV, and other quantities are in c.g.s. units. Strategies for reducing N are readily apparent from Eq. (3).

A complete j.nT^estigation of the filamentation instability must include oblique modes (l^'^u ^0). As k|| increases, the coupling to electrostatic two-stream modes becomes important, leading to a complicated dispersion re­ lation which must be solved numerically. However, for k"^ << kj_ and assuming zero parallel beam temperature the dispersion relation (1) is recovered with L = (CJJ - k||V )//2k,v , , Solutions with k|| ^ 0 will have U) =?^ 0 , and analytic solutions are possible only for a limited range of wavenumbers, 2 2 For |Ct I « 1 and ,k c « 1 , the lowest order solution is obtained from (1) with Z(^ ) == ITT^ . The real and imaginary parts of the dispersion relation decouple, and y is unchanged from its k|| = 0 value. The real frequency is

Note that the denominator is the same as in (2), Two distinct regimes are apparent. For n « Aira, the parallel group velocity v =8(JJ /9k|| << V^ , and the instability is effectively non-convective. Most cdses wnich we have investigated fall into this category. For n » ATVO , "Vg ^ ^^ » and perturbations are convected with the beam. Ny can be estimated by integ­ rating Y(z)/V, along the beam trajectory although the initial value approach proposed by the Livermore group may be better suited for such cases. The condition |^ | « 1 requires k|,/kj^ < 10-2 _ IQ-^ ^^ ^lost cases, so only small departures from 90° propagation can be studied using this approximation. Since k, may vary between 1 and 10^ cm ^, the parallel wavelength often ex­ ceeds the scale length of the beam. If the background plasma2is collision- less rather than resistive, the term AfTiaw is replaced by to in (1), and v = V, in all cases, e b

381 Direct Two-Stream Instability

The direct two-stream (or e-b) mode for a heavy ion fusion system has been investigated by Ottinger and Mosher and Jorna and Thompson.13 The in­ stability is stabilized by collisions with the stability boundary given byl3, 14

i^i^)c = \\^] ^Vb„ • ^^) This boundary is valid even when the collisionless growth rate Im(oj) = (/J/2)(uJ 0) )l/3 exceeds the collisional value Im(aj)p . The mode is sta-^ bllized 6y^increasing the collision frequency V (which is V = 3.9 x 10 n inA T-^/2(eY) for a fully ionized background plasma") or by increasing tSe paraile^ l beam thermal velocity v.b „= (Tbj /im b )^ A useful expression for the beam power at which the e-b mode first appears can be obtained by noting that maximum growth occurs at k;y ^e^^b ' For power P in TW and beam energy W in MeV, we have

2R 2 2 2 P = 2.8 X 10" WR w V v^ /V.Z, . (6) e b|| b b

Other quantities are in c.g.s. units.

If the direct two-stream instability does occur, its growth rate is generally larger than co . Since to :>, 10 s--*- in most cases near the pellet, nonlinear saturation is reached very quickly. It is clear from Eqs. (5) and (6) that increasing n is an effective strategy for eliminating the e-b mode. This is best accomplished by increasing the pressure p . Since (o2 % R , the region near the pellet is the most likely place for in­ stability to occur, except for a small region near the head of the beam where n is always small. Focussing considerations require v, ^ 0.02 V as an upper limit, but chromatic aberration effects in the final focussing lens may restrict v, to be less than 10"-^ V, . ^ b|i b Return Current Instability

The return current (e-i) mode was also studied by Ottinger and Mosher. The high degree of current neutralization expected in a heavy ion fusion system sets up a relative drift velocity between background electrons and ions given by V - Z.n.V,/n , Instability occurs when V exceeds a ^ -'ebb be ^ e critical velocity v . Ottinger and Mosher concentrated on the case T =T., for which v - v = IT /m )^, However classical transport code results2 cr e e e indicate that T >> T. in most cases. The critical drift velocity is thenl5 ^ ^

/mAig/T \^/^ /(* 2T^ "^ 2)\"1 /8m.\^ X v.. V = c 1 + cr J

382 1^ where c = (T /m.)^ is the ion-acoustic speed, X is the electron Debye s e i g _\. —3/2 length and V.. = 3.3 x lO" ink n (A/2) ^ T. is the ion-ion collision frequency.^ ^^ Collisional dampinf often raises v^^ by more than an order of magnitude over its collisionless value. As was the case for the e-b mode, the return current mode can be stabil­ ized by increasing the background gas pressure and hence n^ . This is doubly effective since it reduces V and increases v^^ , The rapid rise in n.b near the pellet increases the drift velocity and hence increases the pos' sibility of instability.

Search for "Stable" Propagation Window

We have seen that filamentation growth rates can probably be reduced to tolerable levels by proper choice of system paramaters (Fig, 1). Both of the two-stream modes can be eliminated if the chamber pressure is suffici­ ently high. However, if the pressure is too high, multiple scattering of the beam off background gas molecules can prevent the beam from being fo­ cussed to 0.1 cm. Also, increasing the collision frequency reduces two- stream growth rates but increases filamentation growth. Finally, all three modes can be destructive if the beam current (or power, if beam energy per particle is fixed) is sufficiently high.

From the above discussion, we expect that there may be a range of pres­ sures for which a high current heavy ion beam may propagate and be focussed across a 5-10 m chamber to a radius of a few mm without triggering two-stream instabilities and at the same time have sufficiently slow filamentation growth. A similar window is known to exist between 1 and 5 torr for pinched relativistic electron beams.^^ The rest of this paper will search for this window and will try to identify strategies for making it as large as possible

Figure 2 plots stability boundaries for a 34.5 GeV Uranium beam propa­ gating in air. Regions below the e-i and e-b curves are stable even at the minimum rms radius Rmin " 0*10 cm (edge radius ^xa.i.n ~ O-l^ cm for a radi­ ally uniform beam) . The filamentation boundaries are for Ny < 1 and "y < 5 assuming T = 5 nsec with the upper boundary being less conservative but more realistic. Other parameters are RQ = 14 cm, Tg = 10 eV, and T^ = 0.2 eV, and the background gas is assumed to be singly ionized. Multiple scat­ tering limits require p < 10 torr for a 5 m chamber and p < 1.2 for a 10 m chamber.8,10 Since a typical reactor might consist of eight 25 TW beams, a viable window probably exists between 2 and 10 torr for a 5 m chamber if ^bl(/^b ^ 0«005. The window is significantly less likely to exist if the chamber radius is 10 m or greater or if the parallel beam temperature is much lower. In addition, the self-pinch effects for a 25 TW beam propagat­ ing in air at pressures exceeding 1 torr will probably defocus the beam sig­ nificantly.

Figure 3 plots stability boundaries for the same beam propagating in hydrogen instead of air. There appears to be a spectacular increase in the size of the propagation window. The principal reason for this improvement is a factor of 3-5 reduction in Z^ at moderate pressures, leading to a similar reduction in [0^, . We have estimated Z^^ as a function of pressure

383 10 m cnambvr 5 m ctiambar limit limit 00 c r- 1000 c e-b : v^ •'/AV /v^-0.Q2): • >»?'' ^ // ~

•\:^ ,•;/ / -

100 — / r — / / - p : / / (TW) • ^' / - TlO" • x-' / - <•'' / . / 10 _- / _ • / ^ t / - a-b . - MO / /V|j" 0.005) , . y /

1 ' • r : .,[ 1 ' .-ll

p(torr)

Fig, 1. Filamentation growth rate y Fig. 2. Estimated stability boundaries (or,equivalently, number of e-fold­ (power P vs. pressure p) for uranium ings Ny) vs. RQ for a 10 nsec, 34 beam propagation in air. Parameters GeV, 50 TW uranium beam focussed to are: W=34 GeV, Ro=14 cm, Rniin=0-1 cm, 0.1 cm through 5 and 10 m of air at Tg=10 eV, T^=0.2 eV, T =5 nsec. Regions 1 torr. Control of filamentation below the e-1 and e-b curves are stable requires Ny ,^ 5 and can be achieved while Ny<5 is a reasonable criterion by increasing injection radius RQ. for control of filamentation. Pressure Note that Z^ = 69 after propagat­ limits are for R . ^ 0.1 cm. mm ing 5 m.

10 m cnombtf 10 m cnofflb*!- limit limit

' r' I I I I r'rr 1000 r / / / / ./ / 100 liVii/V^'Q-OOSl / \ . P .^ .-b ' (flv„/V^.O.OZ) / ' r (TW) / (TW) . / / y 10 r ^ IA»,/V^.O.OOS

p(torr) P(tort)

Fig. 3. Same as Fig. 2 except for Fig. 4. Same as Fig. 3 (hydrogen) propagation in hydrogen. Z is only except that T = 100 eV. 17 at 1 torr.

384 and propagation distance using the stripping length calculations of ^'u,et al-^ and note that stripping lengths in hydrogen are "^ 30 times longer than In air. In addition, multiple scattering is greatly reduced since the scat­ tering term in the envelope equation^*^^ is proportional to 2g(Zg + 1) with Z ~ 7.2 for air and.l for hydrogen. Hence, much higher pressures can be used without scattering the beam to a radius above 0.1 cm. This makes the control of two-stream modes considerably easier. With hydrogen in the tar­ get chamber, it appears likely that full power ( '^ 100 TW) beams could be used with pressures exceeding 100 torr. In addition, the relatively low values of Z^ at p "^ 1 torr would result in a substantial reduction in self-pinch defocussing.

The stability boundaries are sensitive to background plasma temperature and ionization fractions, both of which may change considerably as system parameters are varied. Figure 4 gives stability boundaries in hydrogen when Tg is 100 eV instead of 10 eV. The resulting decreases in V^^ leads to a reduction in filamentation (Ny < 1 at all pressures and powers shown), but two-stream modes are more difficult to eliminate. This points to the importance of model calculations which estimate Tg and n^ , such as the classical beam transport models now being developed.^j^ Such calculations can be coupled with our simple linear instability calculations to determine with greated confidence the existence of a stable propagation window.

Conclusions

We have discussed a number of strategies for controlling filamentation and two-stream instabilities in a heavy ion fusion target chamber. Trans­ verse beam heating, which arises naturally from the focussing process, is the principal stabilizing mechanism for filamentation instability if the beam is unpinched. Of several strategies for controlling filamentation, per­ haps the most effective is to raise the injection radius RQ to 20 cm or more. Other possibilities include increasing emittance, decreasing single beam power by using multiple beams, or reducing the beam charge state by reducing the pressure or the atomic number of the background gas. The two- stream modes can be eliminated entirely by raising background gas pressure although multiple scattering effects put an upper limit on allowable pres­ sures. A window of "stable" propagation for filamentation and two-stream instabilities is likely to exist between 1 and 10 torr for a -,< 50 TW beam propagating 5 m in air. This window is much more likely to exist for a chamber filled with hydrogen or helium, and a substantially wider range of beam power and background gas pressures appears possible.

References

1. Proceedings of the Heavy Ion Fusion Workshop, Brookhaven Nat, Lab, Report 50769 (1977).

2. D.S. Spicer, D.A. Tidman, and R.F, Hubbard, Bull. Am. Phys. Soc. 2^, 770 (1978).

3. S.S, Yu, H.L. Buchanan, F.W. Chambers, and E.P. Lee, Ref. 1, p. 55.

385 4. CG. Callen, Jr., R.F. Dashen, R,L. Garwin, R,A. Muller, B, Richter, and M.N. Rosenbluth, Heavy-Ion-Driven Inertial Fusion, SRI Internati­ onal Report, JSR-77-41 (1978).

5. R. Lee and M. Lampe, Phys. Rev. Lett. 3]^, 1390 (1973).

6. R.N. Sudan, Phys. Rev. Lett, 3]_, 1613 (1976),

7. P.F. Ottinger and D. Mosher, Ref. 1, p. 61.

8. R.F. Hubbard and D.A. Tidman, Phys. Rev. Lett. 41, 866 (1978).

9. S.I. Braginskii, in Reviews of Plasma Physics, edited by M.A. Leon- tovich (Consultants Bureau, New York, 1963), Vol. 5, p. 216.

10. E.P. Lee and R.K. Cooper, Particle Accelerators 7_, 83 (1976).

11. Note that a flat beam profile with radius r = v^R was assumed in Ref. 8. The beam propagation code in Ref. 2 assumes a truncated Bennett radial beam profile which we adopt throughout this paper.

12. F.W. Chambers, E.P. Lee, and S.S. Yu, Bull. Am, Phys. Soc. 23, 770 (1978).

13. S. Jorna and W.B. Thompson, J, Plasma Phys. j^, 97 (1978),

14. E.P. Lee, F.W. Chambers, L,L. Lodestro, and S,S. Yu, Lawrence Liver­ more Laboratory, Livermore, Cal., UCRL-79886 (1977).

15. W. Mannheimer, Phys. Fluids 20, 265 (1977).

386 Disruption of Geometric Focus by Self-Magnetic Fields

D. Mosher Naval Research Laboratory, Washington, D.C. 20375

and

Shyke A. Goldstein Science Applications, Inc., McLean, Virginia 22101

When injected into a reactor chamber with a background density in the

1 torr range, the ion beam strips to high ionization levels before propa­ gating 1 m. The resulting 50 kA or higher-current beam drives a plasma- return current which neutralizes nearly all of the primary beam current.

Here, the perturbation of ballistic ion orbits due to the azimathal magnetic field associated with incomplete current neutralization is inves­ tigated. It is shown that Vi current non-neutrallzati.-in is sufficient to disrupt the millimeter-radius focus desired for present reactor scenarios.

Implications of these results and directions for future research are discussed.

The calculational procedure is simple and not self-consistent but does provide a factor-of-two determination of the degree of current neutraliza­ tion required for successful geometric focussinp; onto the pellet. Single- particle equations of motion for characteristic ions are solved numerically assuming azimuthal magnetic fields of the form

B.(G) ~ (^r r

_L r > R(z) (1) 5r

387 where l(A) is the assumed constant net current in the beam channel and

R(z) is the envelope radius of the undeflected beam in cm.

R(z) = RQ(1-Z/L) (2)

In Eq. (2), R is the beam radius at Injection into the reactor chamber

and L is the distance to the pellet.

The exponent n allows various radial distributions of net current to

be chosen. The value n = 1 corresponds to a uniform current distribution

which might arise when a neutral gas background is rapidly ionized by

avalanche processes driven by the rising current near the beam front. In

that case, the magnetic field tends to focus ions to a single point on the

axis of symmetry. Values of n much greater than 1 correspond to net

currents which flow only near the radial boundary of the beam. The B-field

distribution then simulates the resistive-diffusion profile arising from

beam injection into a preionized plasma of finite electrical conductivity.

For these cases, only ions injected at large radius suffer large deflec­

tion from ballistic orbits.

The calculations performed are for 20 GeV Bismuth ions traversing an

L = 10 m focussing distance in a magnetic field characterized by n = 2.

Deflection of ion orbits is studied for various values of net current, for

injection radii in the 10-30 cm range, and for various beam-ion stripping

lengths X . The ionization level is assumed to vary with axial position s according to

Z(z) = 1 + (Z^-l)[l-exp(-z/X^)] . (3)

For the work presented here, Z„ = 50 is assumed.

388 The sample calculation displayed in the figure corresponds to

R = 10 cm, I = 500 A, and 30 cm (a value appropriate for a 1 torr o I s ~ gas fill). The figure shows orbits in the r-z plane for ions injected at i R , # R and R . The open dashed lines indicate the unperturbed beam channel in which the net current is assumed to flow. A major inconsistency in the calculation is the assunrption that current flows in the unperturbed channel even when ions Injected at the beam boundary cross the axis of symmetry. However, this procedure leads to large errors only near the end of the orbit unless n is much larger than 1,

In all cases, the inconsistency underestimates the perturbation in the in orbit since confining the total current to the interior of the orbit envelope always Increases the magnetic field strength.

The displayed parameter set illustrates defocussing at the pellet location to about 1 cm radius. It is important to note that a tight focus cannot be recovered by moving the pellet to the best-focus location indicated at about 9.2 m. Since the net current changes by a large factor from the front to the back of the beam, the best focus location will move by about 1 meter during the beam pulse. Thus, any given target location will experience a tightly-focussed beam only for a fraction of the beam duration.

Briefly summarizing the restilts of the parameter study:

• Tolerable net currents are proportional to the Injection

radius. A maximum deflection of 5 mm at z = 10 m corres­

ponds to 250, 500 and 750 A for R = 10, 20 and 30 cm.

These figures correspond to ,5^^, 1'^, and 1.5% nonneutrali-

zation for 1 kA of Injected ions subsequently stripped to

Zf - 50.

389 • Increase of / from 30 cm to the reactor chamber radius of s 10 m results in more than a factor-of-three relaxation in

required net current. This requires ambient background

pressures below ,1 torr.

If reactor chambers with very low pressure backgrounds cannot be

realized, the results presented here indicate that research concerned with the proper choice and preparation of the background to minimize

current non-neutralization should be carried out. In particular, pre-

ionization of the background should be Investigated, Reactor studies^

indicate that residual internal energy from the previous microexploslon

might be sufficient to maintain background ionization between pulses.

Additionally, electromagnetic waves or x-radiation propagating in front of the beam may be important.

In the event that sufficiently-complete current neutralization cannot be achieved,reducing the distance over which the beam is geometrically

focussed will greatly improve the quality of the focus. If transport over

an additional length is required because of reactor-chamber-size limitations,

consideration should be given to transport in a Z-pinch discharge as has

been proposed for light-ion fusion-reactor systems.^'^ For this transport technique, the heavy ion beam might be focussed over a length of 1-3 m

into a plasma channel carrying an externally-driven axial current. The

azimuthal magnetic field produced by thi3 current confines the ions to betatron oscillations within the channel. The channel current in amperes

required may be derived from conservation of single-particle energy and p cononical momentum'^ . v^(i-cose„) I . 10-3 A . ^ M. ^ l-(a/R^)^

390 where V (cm/s) is the ion velocity, 9 is the half-angle, a is the focus spot radius and R is the channel radius. For the case at hand, I can be of order 10^ A. The greatest uncertainties in this technique for heavy-ion transport are associated with the MHD response of the background plasma'* to beam passage. In particular, initial beam and channel radii of a few millimeters may expand by a factor of 2-3 near the tail of the beam, resulting in a time-dependent focus size similar to that associated with magnetic deflection of ballistic orbits.

REFERENCES

1. M. A. Sweeney and D. L, Cook, Bull, Am. Phys. Soc. 25, p. 800 (1978).

2. S. A. Goldstein, D. P. Bacon, G, Cooperstein and D- Mosher, Proc. 2nd

International Topical Conf. on High Power Electron and Ion Beam

Research and Technology, Oct. 3-5, 19YT, Ithaca, N.Y.

3. F. L. Sandel, G. Cooperstein, S. A. Goldstein, D. Mosher and S. J.

Stephanakis, Bullo Am. Phys. Soc, ^, p. 8l6 (1978). h. D. Mosher, D. G. Colombant, S. A. Goldstein, and R, Lee, I978 IEEE

Cat. No. 78CHI357-3 NFS, p. 113-

391 CHMIHEL RftDUIS IH CH X 18. CHANMEL CURRENT IN A : 989. VOLTAGE OF IONS IH U : 20.E9 TAPER-FOCUS DISTANCE IN CN : leea. TARGET DISTANCE IN CN : 999. CHARGE STATE : SO. ATONIC NURBER Z 289. STRIPPING LENGTH IN CN : 39. FIELD-SHAPE EXPONENT : 2.

RHAX-lO.e ZNAX- 998.9 FILAMENTATION DURING FINAL TRANSPORT IN A HIGH PRESSURE GAS

Edward P. Lee Lawrence Livermore Laboratory

The filamentation instability has been identified as a possible pathology afflicting final transport even when gas pressure is high enough to eliminate the two-stream mode.l This phenomenon is characterized by the spontaneous appearance of many narrow magnetic pinches within the pulse, with a corresponding increase in transverse temperature and emittance. If the time of flight of an ion exceeds one magnetic plasma period of the beam, then there is a danger of filamentation. However, large electrical conductivity (generated by the passage of the beam through the gas) inhibits mode growth for a pulse of finite duration. In addition, transverse thermal velocity damps perturbations of small transverse dimension, and therefore also acts to suppress mode growth. These ideas are developed here in a brief analytical treatment.

A simple model is adopted which contains the essential feature of the problem. Beam ions (mass M, charge q) propagate in the +z direction at constant velocity V2 = 3c, and the transverse velocities (vJ are small compared to V7. The effects of spherical convergence towards the pellet are not considered here; however, they do not appear to add any qualita­ tively new features.^ In the transverse direction the system is taken to be infinite and uniform (except for the filamentary disturbance), and the gas-plasma medium is characterized by constant scalar conductivity (o). As mentioned, the finite range and duration of the pulse are of some importance; the beam is injected at z = 0 and propagates a distance z^^^ = L. The time of injection of the pulse head at z = 0 is t = 0, and the tail is injected at t = Xp,

I. Model Equations

An adequate treatment of the electro-magnetic field is provided by the single component of magnetic potential A2:

B_j_ = V X A^e^ = -e^ x !-L A^ . (^^

3 A,

393 B, and E, being of negligible magnitude. Here , denotes the gradient in the x-y'"plane. Az satisfies Ampere's law, whicli in the present case reduces to

where Jh is the beam current density. The physical model is completed by the ion equations of motion in the transverse plane and the construction of Jb from the ion positions. We have, for a particle at {r_j_ , vJ:

= V. (4)

Scattering and energy loss are neglected. A statistical treatment of the ions is facilitated by defining a distribution function in the four dimension transverse phase space: let number of ions \ 2 2 I (per cm in d r_Ld V_L I , (6)

Then the beam current density is

Jj^(r_j_, z, t) = qBc d^. f , (7)

From eqs. (4) and (5) we construct the Vlasov equation satisfied by f:

|^-Bcg.v,.V,f.a^v,A^. V^^f = 0. (8)

Various approximations and assumptions are required to derive the model equations (1) - (8), the principal ones being: a. The paraxial approximation for ion motions (v_i_ « v^) is required for eqs. (4) - (8), This is justified since net current is low compared with the Alfven limit (I^ = ByMc^/q). b. High electrical conductivity is required for eqs. (1) - (3). We need 4TTa/k_j_c » 1, where k_^ is the transverse wave number of a disturbance.

394 c. Use of frequency-independent, scalar conductivity for the gas- plasma medium is valid if the electron-ion/neutral collision frequency is large compared with both the mode frequency (oj) and electron-cyclotron frequency.

d. Ion charge state (q) is constant. We assume here that the beam ions strip on the background gas, and the pressure is high enough that the process is nearly complete early in z.

e. a is assumed constant (~ lO^^ - 10^5 s-1). This is only a good approximation for a beam injected into a pre-existing hot plasma; for gas injection one finds o a t, requiring some modification of the results, Time-dependent o is readily incorporated in the formalism through transformation to the variable T: dT = dt/a(t).

It is found that it is very convenient to eliminate the time variable (t) in favor of (9)

This transformation simplifies the model equations and the variables (z, x) are natural for solving initial value problems. Note that a beam ion is characterized by a fixed value of x (the pulse head has x = 0 and the tail has X = Xp), Henceforth we drop the _i_ and z subscripts; using independent variables (r, v, z, x) the essential model equations are:

4TT V^A = - 0 M' (10) c ^b c \dT '2 .

Jjj(r, y, z, x) = q6c d V f(r, V, z, x) , (11)

VA = 0 (12) 3c (f) + V • Vf + YM !v^

II. Dispersion Relation

Let the unperturbed distribution function be

:i3) ^0 " "o ^^^^ "'"'' "'"^p ' ''' ' where n^ is the number density in real space, H(x) is the step function, and F(v) is normalized to unity. Then eqs. (10) - (12) give

395 J^o = qec n^ H(T) H(Tp - T) . (14]

(15a) % a bo '

VA^ = 0 . (15b)

The perturbed quantities satisfy the linearized equations

Ih- T rbi - c 3T / ' (16)

Obi = "ec d^fi . (17)

3f '^ ^^ • !^-^YM!^ • !v^o=° (18)

We consider a single mode of the form

(A J f ) cc pi{l<-r-fiz-a)T) (19)

Then eqs. (17) - (19) yield

f = !!!o , -^ • !v "^ 1 YM 1 Q6c - k . V (20)

2 2 « k . V F q 3^cn 2 ^ ^v 1 = 2. A d V ^1 YM '^l fiBc - k . V

q^3^cn k^F YM '^l d^V (21) (f^6c - k . v)^

396 Inserting expressions (19) and (21) into Eq. (16) we obtain the dispersion relation

0 4.a. .i,!A dS F ;22) k'^c'^ YMC^

It is useful to make the definitions

_ 4Tra (23; m ) kJ- c2

^Trq^n^ «b = 2 ) (24) YMC^

d^v F r(f2) = fi; (25) / k . V \'

Note that x^ is the magnetic decay time for mode number k and fi^ is the magnetic plasma frequency divided by 3c. Frequency to scales with xfri and ^ scales with ^b* ^^e physically interesting values of k"l occupy a broad range bounded above by beam radius (R) and below by the thermal spread (vt):

Using the definitions (23) - (25) the dispersion relation becomes (26; m ^ '

The function r(fi) is evaluated for several simple choices of F(y^): a. Cold Beam

F.(v) =6(v); F, =(4) • (27) b. Maxwellian

(28)

TT V.

397 (29) m 26'ox2- \^^^a^6 where thermal spread is represented in the quantity

k V. 6(k) = (30) /T f^3c and Z' is the derivitive of the plasma dispersion function;

.+00 « 1 -t lU) = dt ;3i; /if t - C * c) Lorentzian

f +CO v^/r2 dv.. F, = [321 '^ '^ 7T(VJ + v,^/2)

^L = [331 + i6

The r produced by this somewhat unphysical distribution is a single pole approximation of the Maxwellian (ffy,). The limits fi = 0 and fi -»• «> are the same for these functions and they are in fair agreement throughout the upper fi half plane.

III. Analysis of Dispersion Relation

Generally, initial conditions may be placed on f^ at z = 0 and on A^ at X = 0. A simple case is

ikx fl(z = 0, x) = f^e A^(z. X = 0) = 0 (34) with the Lorentzian distribution (eq. 32) assumed, After some analysis, one finds a perturbed amplitude

398 .+00 ^j^OfiZ . 1.- e--"^ • dfi (35) X = 271 (fi + is) where u(n) and r|_(fl) are given by eqs. (26) and (33). Defining the dimensions quantities

V=''' ^/^m=^'' + i6 = n' (36)

i(jjT„ = ioj' = 1 + —9 m ^ ,c we have

.+oo+Te ^-ifi'z' -ioj'x' -6z' 1 1 - e X = e dfi' 1 - (37) 2fT "IT" 10) .,2 J-00+i e

This expression differs from that obtained for a cold beam only in the outside multiplication factor e"^^ ,

When significant mode growth occurs, a good approximation for x is obtained by a saddle analysis centered on the factor

g-(ifi'z' + ioj'x' + 6z') ^ gg(fi',T',z') (38)

We drop the prime notation. Then the saddle is located at fiQ given by

(39)

we have:

1/3 "o-'(f^) (40)

g{n) -^+3(1^) -62 X = e = e (41)

399 The saddle analysis is valid if xz2 » l. Reinserting the dimensional factors, we have 2 2 , 1/3 'Tfib Z -^ + 3 - 6fihZ (421 log(x) 4T

Consider now the limits of x as z and T are varied (separately). Expression (42) may be maximized in each case, yielding

log X -1 exp(l - 6) fi^z (z fixed) , (431

1 X (x fixed] (44) log X 1 exp{^ ' ^^ f"

For given z and x the amplitude x (given by eq. (42)) lies somewhat below these bounds. Note that its maximum lies on the boundary of the (z, T) r-gion occupied by the pulse, e.g., X^ax ""^ located at z = L or x = -p for the case at hand. Also, mode is stable if 6 > 1.

For the heavy ion application, v-j- is very small since convergence to the pellet is required, i.e..

:45: 0 where E is emittance, RQ is initial radius and Rp is pellet radius, One finds ^

k V. kR t L [46]

Hence mode numbers k^ t^b^/Rp are stable. If fibL £ 1 there is no problem—this is the "safe" solution for filamentation. Most heavy ion scenarios end up with ^^L »1. An examination of eq. (44) then suggests "risky" method of stabilization. This is to introduce large enough v^ that p/"^"rn - 0(1). (Note that this expression does not depend on '" .) Large Vf causes the beam to go through a broad neck at the pellet. However, it appears possible that self-pinching will overcome this problem.-^ It is found that if v^ is adjusted such that the latter half of a pulse is pinched (while the front half blows up) then

^no *' = i? , (471 m

and growth is limited to

[48)

This approach is currently under investigation at LLL.

At first sight it appears that the preferred method of stabilization would be to make %l < 1 by the use of multiple beams. This may be difficult in practice as the following scaling indicates: VMao,(!l)(rf)>U)'tiS^)(# •

z-j = ion charge state

IQ = particle current

M^- = mass number

If IQ = 10 kA is split into 100 beams of initial radius RQ = 20 cm then ^bL = 1.

Acknowledgment

This work is performed under the auspices of the U. S. Department of Energy by the Lawrence Livermore Laboratory under contract number W-7405-Eng-48.

401 References

1. See review by W. Thompson in this report.

2. A paper containing a complete treatment of filamentation for a converging beam is being submitted to Physics of Fluids Journal by E. P, Lee, M, N. Rosenbluth, F, W. Chambers, S, S, Yu and H, L. Buchanan

3. See Appendix of S. Yu, H. L. Buchanan, E, P. Lee and F. W. Chambers in this report.

402 BEAM PROPAGATION THROUGH A GASEOUS REACTOR—CLASSICAL TRANSPORT

S. S. Yu, H. L. Buchanan, E. P. Lee, F. W. Chambers Lawrence Livermore Laboratory

Introduction

The following note deals specifically with classical beam transport through a gaseous reactor. The evolution of the ion beam together with the beam-generated plasma channel is followed in detail, but instability effects are not considered here.l

There are several reasons why classical transport studies are essential for understanding beam propagation. Instability analyses performed in the past several years have led to the elimination of some effects such as the firehose and the sausage mode as likely mechanisms for disrupting beam propagation,2 but have also brought to focus other possibly detrimental effects such as the two-stream mode,3 and in particular, the filamentation instability.1 These effects are marginal in the sense that the instabilities may be suppressed only under certain stringent operating conditions. This being the case, further refinements of the theories are called for. The growth rates of instabilities depend on initial conditions of the plasma characterized by various parameters such as the electrical conductivity, plasma temperature, and plasma density, as well as on various beam conditions such as the effective ion charge state and the r.m.s. radius. An accurate determination of these parameters from a classical transport calculation is therefore an essential prerequisite for instability analyses.

Even if an instability-free "propagation window" is found, a separate issue must be considered. The target size requirement is very stringent from the point of view of beam transport. The beam must not only be delivered to the target area, but must be delivered with sufficient intensity. The size of the beam as it hits the target is determined in these propagation models.

In addition to size considerations, target designs also favor certain pulse shapes. A significant amount of pulse shaping takes place automatically in the reactor chamber, and these effects must be taken into account in any meaningful attempt to control pulse shapes. In general, direct matching of beam parameters from the accelerator (such as beam quality) to target requirements without considering the beam development in the reactor is not justifiable.

403 The present calculations are applicable to any beam geometry with cylindrical synmetry, including the converging beam geometry (large entrance port with radius > 10 cm), as well as the pencil-shaped beam (small porthole with radius '^ mm)^ The small porthole is clearly advantageous from the reactor vessel design point of view. While the physics of the latter mode of propagation may be more complex, analyses up to this point have not revealed any detrimental instability effects that will inhibit propagation. In fact, the large perpendicular velocity Vj_ that the pinched mode can accommodate provides a mechanism for the quenching of filamentary instability. Furthermore, this mode of propagation can withstand more ion scattering and is not subject to the upper bound on pressure (p < 10 torr) which is imposed on the converging beam mode. However, a critical question that must be answered is whether the small beam will pinch or not i.e., whether the self-magnetic forces are large enough to keep the beam propagating at a small radius all the way.

Two sets of codes are being developed at LLL for these studies. The 1-D codes calculate all the beam and plasma quantities of interest as a function of z, the distance from the reactor porthole, and x, the distance from the head of the pulse. These codes are relatively fast, and are useful for parameter searches. However, to answer critical questions such as whether a beam will pinch or not, we found it necessary to employ a 2-D code. Here, the electromagnetic fields and the plasma parameters are calculated as functions of z and x, as well as a scaled radial variable u = r/R, where r is the radial distance from beam axis, and R is the r.m.s. radius of the beam. A key physical effect which makes the 2-D treatment necessary is electron cooling by thermal conduction in the radial direction. In order to determine the plasma temperature, and therefore, the electrical conductivity and the self-fields at small beam radii (R < 1 cm), this process must be included. The 2-D code development is still in progress, but we will report some new preliminary results from 2-D calculations which are essential for understanding beam propagation at small radii. Results from 1-D beam envelope calculations will also be presented.

Propagation Models

In our approach to transport studies (both 1-D and 2-D), beam motion is characterized by R(x, z), the r.m.s. radius of the beam. The development of the r.m.s. radius as the heavy ions traverse the reactor chamber is described by an envelope equation:^

2 k„ r 32R -^ = 0 (i; 3z2

The beam envelope evolves under two opposing effects: the emittance term, characterized bye, which causes the beamto expand, and the self-magnetic effects, characterized by the parameter kT^r^, which cause the beam to pinch. p

404 In free flight, the emittance e is an invariant of the motion. However, scattering of the beam by the background gas tends to increase the emittance. Anharmonic pinch effects lead to further changes. These changes are traced by an emittance equation:

oZ where ng is the gas density and the coefficient K contains the cross section information for gas-ion elastic scattering. The second term on the RHS gives a phenomenological description of anharmonic pinch effects.

k 32r2 represents the average betatron oscillation experienced by a beam particle. It is given as an integral over the radial dimension r:

k.V = (3)

where I^ and J^ are the beam current and current density respectively. Zf" is the z-dependent effective charge state of the ion, a model for which has been proposed earlier,2 M is the ion mass, and 8A/3r is the self-magnetic field.

To calculate kg2p2 ^^ |_p approximations, simple radial profiles are assumed for the plasma parameters and the fields, and the radial integration of Eq. (3) can be performed analytically. At the 1-D level, we have found it possible to improve on the results reported in last year's workshop proceedings with more realistic circuit equations. By assuming a parabolic profile for the beam current, the following equation for kgr2 could be derived

(4)

9 TTOR^3 ^m

To solve for ^o^r^ in the exact form of Eq. (3), the radial profiles of the magnetic field must be mapped out in detail. This is the procedure taken in 2-D calculations. The field equations are particularly simple in the very high conductivity regime which is relevant for the beam transport

405 problem. Complete charge neutrality may be assumed; the z-component of the vector potential A(u, x, z) is the only important field quantity, and is calculated by integrating the equation

9A = _i (5; 8x a3 where Jn is the plasma current density, and a is the electrical conductivity. Noting that current neutralization is almost complete, we can write

J_ = - JL 'p = •%('•!:) '" where x/x^ is a small correction term adopted from 1-D models. The shape of the beam current is assumed to remain unchanged throughout the problem (e.g. a Gaussian profile), although the r.m.s. radius R is variable. The calculation of A(u, x, z) from Eqs. (5) and (6) is straightforward if the electrical conductivity o is known. The electrical conductivity is beam-generated and is in general a function of the plasma temperature Tg, the plasma density ng, and the average charge state of the gas ions 2^^^, It is given by a=ei!le ,,^ m v„ m where

v^m = 2.0 X with e the average plasma energy in eV and v^^ the momentum transfer rate per neutral atom. An accurate determination of the plasma temperature is crucial for the calculation of a. When the beam radius is large (R > 1 cm), the plasma electrons, subsequent to their generation through ionization, are neither heated nor cooled very much. The plasma temperature corresponds therefore to the average energy of the secondary electrons as they emerge from the ionization process. Tg is typically a few eV. In this regime, Zfff^ 1. However, as the beam radius becomes small, the high beam concentration leads to strong direct ion heating. This process, together with strong

406 joule heating can bring the plasma temperature up to close to 1000 eV in some cases if there were no electron cooling. It turns out, however, that in these cases, there is also simultaneous electron cooling by thermal conduction in the radial direction, which helps to bring the plasma temperature, and therefore the electrical conductivity down. In addition, the gas ions now become multiply stripped, with Zg^'f » 1, which helps to lower the conductivity further. All the above effects must be included in determining the electrical conductivity at small beam radii, where self-pinch effects are most important.

The plasma temperature and plasma density are determined concurrently, using energy conservation and particle number conservation equations. An' independent electron model is employed for the gas atoms. With ny) defined to be the number density of electrons ionized from the iM level of the atom, the plasma density is given by

i) "'-e • ^E ^ "e" (8) 1 where ^^ is the occupation number of the ilt shell. A rate equation is now written for each shell

^= fe("g-"e^^'VlSn''^)^fe^-"e'^')"eVii^'(ri^'

The first term on the RHS describes the direct ionization by beam ions, while the second term corresponds to ionization by plasma electrons. The rate for ionization by plasma electrons is a function of the plasma average energy e.

The plasma energy is determined by the following energy balance equation

- 1 19 / n 9^ 3cR2 u 3irr^^

On the RHS, there are four terms. The first term is proportional to the Bethe stopping power s(3) and describes direct energy deposition by beam ions. The second term corresponds tp joule heating. The third term gives the energy lost as free energy, eJ.'^) being the binding energy for the iilL shell. The fourth term describes the effects of thermal conduction. The coefficient Q is proportional the the thermal conductivity. Equations

407 (9) and (10) are solved simultaneously for the plasma density and temperature. The charge state of the gas ions Z§" is related to the plasma density by a simple model

1/2 2 eff ;ii] g

With the plasma density, plasma temperature, and l^^^ determined by Eqs. (9), (10) and (11), the model for the electrical conductivity is complete.

Numerical Results

In Figures (1) to (5), we show some examples of radial profiles of plasma parameters and electromagnetic fields. In Figures (1) to (3), we show the plasma temperature Tg, plasma density ng, and electrical conductivity o respectively, while the electric field E^ and magnetic field BQ are shown in Figures (4) and (5). These plots are given as a function of the scaled radial dimension u for the entire beam, from head-to- tail (characterized by x). The distance into the reactor chamber z, is held fixed, and is fairly close to the target. At this point the 3 kA, 30 GeV U"*" beam has been stripped down to Z^"^' = 70. The beam radius is 1 cm at the beam head, and is pinched down to 1 mm at the tail. The reactor chamber is filled with 1 torr neon gas.

In Figure (1), we see the plasma temperature rising very quickly at the beam head due to strong joule heating. Fast thermal conduction is also taking place at the same time. Away from the beam head (at x '^ 20 cm) the buildup of electrical conductivity shorts out the field. The decreased field, combined with increased plasma density brings joule heating effects down, while thermal conduction continues to cool the plasma. The temperature drops to a valley. Beyond this point, as the beam continues to pinch, direct ion heating and joule heating (modified by continued thermal cooling) lead to a steady rise in plasma temperature all the way to the pulse tail.

In Figure (2), the plasma density ng is shown. As expected, the plasma density is higher on beam axis than along the wing, and continues to increase as one moves towards the back of the pulse. The plateau structure around the beam axis toward the tail of the pulse correspond to a saturation of the plasma density as the neon atom is totally stripped.

The electrical conductivity in Figure (3) has some rather interesting structures. As is evident from Eq. (7), the conductivity is determined by Tg and Zg", on beam axis, Tg is largest, but so is Zg^*. The net result is that the maximum in electrical conductivity can often occur away from the beam axis, at the point where Zg.f^ has its steepest drop. Towards the tail of the pulse, the conductivity shows a two-peak

408 structure, the first peak on beam axis, where Tg is highest, and a second peak somewhere on the wing, where Z^'' drops from its saturation point.

The electric field is shown on Figure (4). The field strength is generally strongest on axis. At the beam head, the field rises rapidly since the conductivity is low. Away from the head, the field drops as the conductivity is increased. The rise in field strength toward the pulse tail is due to the decreased beam radius because of beam pinching.

Figure (5) shows the magnetic field strength BQ . The field is small at beam head, and continues to build up towards the beam tail. The field is zero on beam axis, and rises to a peak around the r.m.s. radius of the beam. The magnitude of the field strength, which determines the degree of pinching, is critically dependent on the value of the electrical conductivity, particularly close to the beam axis.

In Figures (6) and (7), we show two examples of 1-D beam envelope calculations. The r.m.s. radius R of a beam are shown as a function of z, the distance into the target chamber, for various parts of the pulse (characterized by x, the distance from beam head). Figure (6) corresponds to a beam injected at small radius. The head of the pulse expands because of the finite emittance, while the tail pinches as the self-magnetic field builds up. In Figure (7), we show a converging beam injected at 15 cm radius. The beam propagation is ballistic over most of the beam path. But size and shape alterations take place close to the target where self-magnetic fields become more important. In both runs, 3.3 kA of 30 GeV U*^ with an initial emittance of 1 mrad-cm are injected into a vessel of 10 meter radius, filled with 1 torr of neon gas.

Acknowledgment

This work is performed under the auspices of the U. S. Department of Energy by the Lawrence Livermore Laboratory under contract number W-7405-Eng-48.

References

1. See paper by E. P. Lee, this report.

2. S. S. Yu, et.al., Proceedings of the Heavy Ion Fusion Workshop, Brookhaven, p. 55 (1977).

3. R, N, Sudan, Phys, Rev, Lett, 37, 1713 (1976).

4. E. P. Lee, and R. K. Cooper, Particle Accelerators 7, 83 (1976).

409 T^laswtaL Teyw^fir^arc/ \\e)\

"t

^-b>A py pu^e

a

UL=o

Figure 1

410 VW

- Wdwi Vd^l

LL CSCAW *aJi^\

Vacap*™AXt; i Fig. 2

r WsvNAa WvNAja<:^>0\-Vti (.(T")

Tau o\ paW

Fig. 3

411 E.\ec\«NC ^ve\Jl {^^

^ •WA olf PaW

k (.soaWJi vaiA»*\ (i^i^^s.mv ^ VJLOJ^ eJif PtjA% t Fig. 4

3^0^ p*A.v

Fig. 5

412 ^^^f ^ pu)s£ WaJi.

o4-&^ j^^^^^^5/ ,^'ftH^"--^-r^«-

h

WdVM I

Figure 6

413 aonOcrq 3^v ^ ^ Gawv (^wwwwfwawv yaci-uxs /v^ D.Z e>vv»- &^;\or \9». C^N^A Nw'\jcx\i

\5•.0o*^k

Figure 7

414 THE BEAM-TARGET INTERACTION IN HEAVY ION FUSION*

Roger 0. Bangerter Lawrence Livermore Laboratory Livermore, CA 94550

Abstract

The beam-target interaction in heavy ion fusion is theoretically understood, but experimental verification at appropriate beam intensities is not possible using existing accelerators. If fusion-intensity ion beams were to lose significantly less energy in passing through matter than calculated it would increase the cost of heavy ion fusion. In the worst case the cost scaling is such that a 25% decrease in energy loss would increase the cost of the accelerator by roughly 10%. In this paper we show that fundamental considerations place a lower bound on ion energy loss. The lower bound is not significantly less than the expected energy loss obtained from detailed calculations.

The beam-target interaction in laser fusion has proved to be a very challenging problem. It is therefore natural to be concerned about the beam-target interaction in heavy ion fusion. Much of this concern seems to arise from the feeling that a beam capable of target ignition is in some sense "intense" and thus qualitatively different than the low-intensity beams with which we are familiar in nuclear science. Intensl.ty must of course be quantified and by several measures heavy ion fusion beams are not truly intense. For example, we will show that for typical target and beam parameters the electron density in the target is roughly nine orders of magnitude larger than the density of beam ions. Furthermore there are about 1000 Debye lengths between beam ions in the target so that one might expect the beam ions to behave independently. These statements are simply a manifestation of the fact that for heavy ion fusion each beam particle carries a large energy ( ^10 GeV). This can be contrasted with light ion (proton) or electron beam fusion where the expected particle energy is 1 - 10 MeV or with laser fusion where each photon carries an energy of about 1 eV.

However, there are some ways in which heavy ion beams must be considered intense. Collective effects are important in the propagation of the beam in

*Work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore Laboratory under contract No. W-7405-ENG-48,

415 the accelerator and through the combustion chamber to the target. This is discussed extensively in other sections of this workshop report.

There are two classes of ion beam physics that must be considered: nuclear and electromagnetic. Recent accelerator design effort has been directed toward accelerating heavy ions to a maximum energy of about 20 GeV. At this energy the calculated range of a heavy ion is much less than a nuclear collision length so that only a small fraction of the incident ions will produce nuclear reactions.1 Furthermore, nuclear processes are unaffected by the state of matter in the target so that measurements of cross sections with low intensity beams are directly applicable. The only area of conceivable uncertainty involves electromagnetic phenomena.

The electromagnetic interaction of low intensity ion beams with ordinary matter has been reasonably well understood for about 60 years. The calculated energy loss of heavy ions in matter (or range) is in excellent agreement with experiments.2»3 However, experiments with heavy ion beams at the appropriate energies, intensities and matter temperatures have never been performed. Some additional relevant experiments might be performed at existing heavy ion accelerators, but it has not yet been possible to attain fusion-intensity beams. The continuing experiments in light ion fusion are also relevant to heavy ion energy deposition and may provide early verification of ion stopping predictions in hot matter.

In order to achieve fusion conditions, it is necessary to deposit > 2 x 107 J/g in the target.^ Thus for a given target size, less total energy is required if the range of the incident ions is short. On the other hand, there are significant accelerator design considerations that push one in the direction of high ion kinetic energy and therefore long range. Any anomalous effect that shortened the range of the ion would be welcome. Conversely, if the range of the ions were significantly larger than calculated it would increase the cost of the heavy ion accelerator. The estimates presented at this workshop show accelerator costs increasing as (output energy)~0.4, Thus if the range were 25% too long, one could compensate by increasing the output energy by 25% to achieve > 2 X 10' J/g. This would increase the cost of the accelerator by about 10%. This represents the worst case since it might be possible to redesign the target or accelerator to reduce the cost penalty. Fortunately, fundamental physical arguments indicate that the range will not be significantly larger than calculated.

As an ion passes through matter, it transfers energy to the ions and electrons in the matter through binary Coulomb collisions. It may also lose energy through excitation of plasma waves or other collective processes,^ In the following considerations, we will place an upper limit on the range of ions by making the pessimistic assumption that only binary Coulomb collisions with electrons contribute to the energy loss. As a by-product we will also obtain an expression for the spectrum of the energetic electrons produced by an ion beam and discuss preheat.

The cross section for scattering of electrons by ions with charge Z is given by the well-known Mott cross section.

416 ^2 4 da Z e dfi ,22.- 4p v sin 47i\ [^ - ^^ ^^"^ (f)] where p is the three-momentum of the incident particle, v is its velocity, and 6 is the scattering angle. The speed of light is set equal to unity. Assuming that the electron is initially at rest (or moving slowly), it is convenient to express this cross section in terms of the final kinetic energy of the electron in the laboratory, T = mP^'Y'^il - cos 0) where m is the electron mass, g is the ion velocity, and, as usual, y ~ (1 ~ B )~ '^. Making the transformation of variables, we obtain

O r,2 4 dJ ^ 2TrZ e [?- Note that the maximum electron kinetic energy, Tj^^j^, is given by setting cos 6 = - 1 so that T^^^ ~ 2m32Y2. For nonrelativistic ions, 2mY ^x » T^ so that the electron spectrum produced by nonrelativistic Ions is given by da/dT °^ 1/T^ . As usual, this diverges as T -• 0, corresponding to an infinite impact parameter, and it is necessary to impose some TJJJIJ^. Physically, Tjn^^ is determined by atomic binding energies or Debye screening, depending on the state of the stopping medium. In addition to the electrons having the l/T^ spectrum, there can also be a component associated with the incident ion if it is not fully stripped when it hits the targets. Since these electrons have about the same velocity as the incident ion, their kinetic energy is down by the ratio of the sum of their masses to the ion mass. Thus they contain only a negligible fraction of the beam energy and can be ignored.

Using the electron spectrum we have performed detailed Monte Carlo calculations of target preheat. These calculations are somewhat dependent on specific target designs and beam energies, but indicate that electron preheat is not a problem.

We now return to the question of energy loss. The energy loss of an ion per unit length is calculated by integrating da/dT between Tj^^^ and T^gx yielding. 2 dE/dx 0= Z^^^ |_ max min Jf

Note that we have replaced z2 by z2ff since the ion may not be fully stripped.

In order to obtain values for the parameters in this expression, we consider typical beam and target conditions. In particular, we will assume that a lOl^ watt, 20 GeV heavy ion beam (A - 200) is incident on a target having an electron density of n^ ^ 1023/cni3 ( ~ solid density) at a temperature of 200 eV. The beam radius is assumed to be > J ™°- With these values, the ion density in the beam is given by nfe < 2 x 10 /cm . The Debye length is AD -3 x lo"^ cm and the thermal speed of thetarget electrons is Be- 0.03. For the typical speed of an incident ion, we take

417 the value after it has lost one half of its initial energy, obtaining 3 "^ 0,3.

It has been experimentally established that Zgff is a function of ion velocity.^'^ As one might expect, an ion is stripped to the point that the orbital velocities of the remaining electrons are greater than or equal to the velocity of the ion. Brown and Moak' find that the experimental data for a variety of projectiles and targets are well approximated by Zgff/Z = 1 - 1.034 exp(-137 6/zO*69), xhus for g^0,3 even heavy ions are more than 80% ionized and the dependence of Zgff on 3 has become quite weak. Although the experiments have been performed in cold matter, the fact that Zgff depends only on g and not on other target characteristics implies that in the plasma case Zgff will depend on the relative velocity of the ion with respect to the target particles. In our case 3 is an order of magnitude larger than gg which is in turn 2 or 3 orders of magnitude larger than the thermal velocity of the target ions so that temperature effects on Zgff should be small. In fact, in the limiting case where B « 3g, Zgff is increased relative to cold matter by thermal ionization.

In obtaining dE/dx, we should also integrate over the appropriate thermal electron distribution. It can be shown that this is important only for 3< 3g.S

For 3 = 0.3, Tjnax 1® about 100 keV. In a plasma the electric field of the incident ion is expected to be screened at distances larger than Xp. Thus, for free electrons, T„ii„ is determined by setting the impact parameter equal to a Debye length. In this case,^

2Z^..e^ _^ T = —^— < 10 keV . min n2-, 2 ^ ni3 Aj)

Since ng ~ 1023/cm3 and Ajj ^ 3 x 10~° cm there are only a few electrons in Ap- For this reason collisions with impact parameters less than Aj) must be unscreened binary collisions. We can ignore 3 compared to ^n(T„ax/Tniin) since Tj^ax/Tmin ^ l^^- The energy loss due to plasma excitation' at impact parameters larger than Xjy has been calculated by Jackson.5 The net effect of this additional loss is equivalent to multiplying T^ax/Tmin ^V [l-123B/WpXjj]2 ^here ojp is the plasma frequency. For our assumed conditions this increases the value of Tmax/^inin ^7 ^ factor of 290. Thus even in the worst case where ^max ~ ^^ > binary collisions alone account for i;n(104)/5n(290 x 10^) = 62% of the total dE/dx. This represents a minimum energy loss rate that is independent of a detailed understanding of plasma physics.

Our ability to calculate this minimum energy loss rate depends on only three obvious or well-tested assumptions:

1. Validity of the Mott cross section. 2. Weak dependence of Zgff on target conditions for relevant beam and target parameters. 3. Binary nature of collisions for impact parameters less than a Debye length (especially since there are only a few electrons per A3.).

418 since the ions must lose energy through binary collisions that account for most of the energy loss, the only way the range can be significantly longer than calculated is for some mechanism to exist that accelerates the ions. To compete with the binary collisions, the accelerating field would have to add -- 20 GeV to a heavy ion in about 1 cm (range ~ 1 g/cm2 => 1 cm at density = 1 g/cm^). Assuming Zgff < 100, this would require a minimum electric field of 2 x 10° V/cm over a distance of about 1 cm.

Since the only source of energy is the ion beam this would require a chain of events whereby the ion beam could accelerate itself. In any case 2 X 10° V/cm fields are rather inconceivable. Joule heating results in a power dissipation per unit volume given by E^/i^ where E is the electric field and ri is the resistivity of the plasma. Following Spitzer° we calculate ri - 10~3 ohm cm for a high Z plasma and n — 10"^ ohm cm for a low Z plasma. Thus a 2 x 10° V/cm field produces >10^" W/cm3 in a high Z plasma and >1021 w/cm^ in a low Z plasma. Since the total power deposited by the beam is only about 3 x lOl^ W/cm3 the Spitzer resistivity would have to be wrong by more than 3 to 5 orders of magnitude before such fields become energetically possible.

In order to simplify the analysis we have considered only free electrons. For typical conditions high Z targets are only about 40% ionized so that there is also a contribution to dE/dx from bound electrons. Energy transfer to bound electrons is well understood from our experience with ordinary matter,2J3,5 but two modifications are required in the partially-ionized case. The average binding energy of the electrons is increased and impact parameters greater than Ap are excluded. Neither of these modifications fundamentally alters the physics of the situation.

If the beam strikes matter at all, it appears that it will stop as predicted. If the beam carried a large amount of momentum, it is conceivable that it could sweep the target material out of its way. Very simple calculations show that the effects of momentum deposition by a heavy ion beam are negligible compared to the thermal pressure developed by energy deposition.

In conclusion, it seems unlikely that fusion-intensity ion beams will have significantly less energy loss than predicted.

Acknowledgments

I am indebted to the members of the laser plasma theory group at Livermore for many valuable ideas and comments, and to John Nuckolls for support and encouragement. References

1. R. Silberberg and C- H. Tsao, Proceedings of the Heavy Ion Fusion Workshop, Brookhaven National Laboratory Report BNL 50769, p. 76 (1977). The calculations in this paper are for 63 GeV bismuth. The formulas can be used with range-energy information to obtain results at 20 GeV. Range-energy information for ions incident on lead is given in reference 4. For low Z targets the range is nearly a factor of two less.

419 2. G. Tarle and M. Solarz, Phys. Rev. Lett. 4a, 483(1978), This paper reports very small discrepancies between theory and experiment. For the purposes of heavy ion fusion the agreement is excellent. 3. For a review article see L. C Northcliffe Ann. Rev. Nucl. Sci. 13, 67(1963). ~ 4. R. 0. Bangerter, see reference 1, p. 78. 5. J. D. Jackson, Classical Electrodynamics, Chapter 13 (John Wiley and Sons 1962). 6. H. D. Betz, Rev. Mod. Phys. Uh_, 465 (1972). 7. M. D. Brown and C. D. Moak, Phys. Rev. B _6, 90 (1972). 8. L. Spitzer, Physics of Fully Ionized Gases, Chapter 5 (John Wiley and Sons 1962).

420 VII. PROGRAM

HEAVY ION FUSION WORKSHOP Argonne National Laboratory September 19-26, 1978

Date Time Topic 9/19 9:00 AM Welcome - R. G. Sachs (ANL) Workshop goals - R. L. Martin (ANL) Workshop program and arrangements - R. C. Arnold (ANL) Laboratory programs: Research progress reports and conceptual design presentations: 9:30 BNL - A. W. Maschke 11:00 ANL - R. L. Martin, R. J. Burke, and J. M. Watson Afternoon Session Chairman: J. Leiss (NBS) 1:30 PM LBL - D. Keefe, C. Kim, and D. Judd 3:15 Coffee 3:45 LLL - R, Bangerter, M. Monsler, and V. K. Neil

9/20 Morning Session Chairman: T. Kammash (U. Michigan) 9:00 AM Engineering development planning for ICF - T. Willke (Battelle N.W.) 10:00-11:00 Panel discussion: Scenarios for HIF development - A. W, Maschke, R. L. Martin, and D. Keefe 1:00-6:00 PM Parallel workshop sessions (chairmen): - Atomic and molecular cross sections (Macek) - Systems and cost analysis (Freytag) - Ion sources (Seliger/Clark) - Low beta linacs (Keane) - Beam manipulations and bunching (Khoe) - High current transport and final focus lenses (Garren) - Plasma effects (Thompson)

9/21 Morning Session Chairman: W. Herrmannsfeldt (SLAC) 9:00 AM Focussing experiments with light ion diodes - D. Johnson (SLA) 9:30 High current transport and linear acceleration of intermediate mass ions - S. Humphries (SLA) 10:30 Coffee 11:00 Diagnostics for pellet experiments - R. Johnson (KMSF) 1:00-6:00 PM Parallel workshop sessions

421 Date Time Topic 9/22 Morning Session Chairman: E. Lindman (LASL) 9:00 AM Beam target coupling and scaling laws: Comparison of laser and charged particle beam couplings - K. Brueckner (UCSD) 10:00 Review of the report of the Ad Hoc Fusion Experts Panel (Foster panel) - Major T. Johnson (DOE) 11:00 Progress in ionic and molecular cross section determinations - J. Macek (U. Nebraska) 1:00-6:00 PM Parallel workshop sessions

9/23 9:30-12:30 PM Reports of workshop chairmen: plasma effects, ion sources, low beta linacs, beam manipulations, transport and focus

9/25 Morning Session Chairman: D. Young (FNAL) Tutorial sessions on heavy ion fusion 9:00 AM Inertial confinement fusion principles - T. Godlove (DOE) 10:00 Targets for inertial confinement fusion - R. Bangerter (LLL) 11:00 Accelerator principles - L. Teng (FNAL) 1:00 PM Afternoon Session Chairman: I. Bohachevsky (LASL) 1:00 PM Existing accelerators - D. Sutter (DOE) 2:00 Description of conceptual heavy ion fusion driver designs: BNL - A. W. Maschke 2:30 ANL - R. C. Arnold 3:00 LBL - D. Judd 3:30 Coffee 4:00 Engineering development scenarios for heavy ion fusion (summary) - I. Bohachevsky (LASL) 4:30 Tour of ANL HIF experimental facilities

9/26 9:00 AM DOE program plans for inertial confinement fusion - R. Schrlever (DOE/OLF) 10:00 Summary of findings of workshop sessions - Report of Reference Design Committee - L. Teng (FNAL) 12:00 Closing remarks - DOE representatives 1:30 PM Meeting of DOE and laboratory heavy ion fusion program spokesmen [T. Godlove (DOE), D. Judd (LBL), R. Martin (ANL), A. Maschke (BNL), R. Schrlever (DOE), and L. Teng (FNAL)J with news representatives.

422 VIII. LIST OF PARTICIPANTS

ATTENDEES WORKSHOP ON HEAVY ION FUSION September 19-26, 1978 Argonne National Laboratory

Name Affiliation Adams, R. Brookhaven National Laboratory Angert, N. GSI (Darmstadt) Arnold, R. Argonne National Laboratory Baker. C. Argonne National Laboratory Bangerter, R. Lawrence Livermore Laboratory Barnett, C. Oak Ridge National Laboratory Blue, T. University of Illinois - Urbana Bock, R. GSI Bogaty, J. Argonne National Laboratory Bohachevsky, I. Los Alamos Scientific Laboratory Bohne, D. GSI Brueckner, K. University of California - San Diego Brumlik, G. The Slaner Foundation, Inc. Burke, R. Argonne National Laboratory Caird, J. Bechtel National, Inc. Chang, D. Occidental Research Corporation Cheng, K. Argonne National Laboratory Cho, Y. Argonne National Laboratory Choi, C. University of Illinois - Urbana Chupp, W. Lawrence Berkeley Laboratory Clark, D. Lawrence Berkeley Laboratory Clark, W. Maxwell Laboratories, Inc. Clauser, M. Sandia Laboratories Cole, F. Fermi National Accelerator Laboratory Colombant, D. Naval Research Laboratory Colton, E. Argonne National Laboratory Cooper, R. Los Alamos Scientific Laboratory Cron, A. W. J. Schafer Associates Curtis, C. Fermi National Accelerator Laboratory Danby, G. Brookhaven National Laboratory Das, G. Argonne National Laboratory Davis, M. Northwestern University Drobot, A. Science Applications, Inc. Drunmi, C. University of Michigan Edelstein, R. Carnegie-Mellon University Edwards, H. Fermi National Acceleratory Laboratory Faltens, A. Lawrence Berkeley Laboratory Farrell, J. Radiation Dynamics, Inc. Fenster, S. Argonne National Laboratory Foss, M. Argonne National Laboratory Foster, T. Westinghouse Electric Corporation Freytag, E. Lawrence Livermore Laboratory

423 Name Affiliation Gabbard, C. R&D Associates Gallup, G. University of Nebraska Gammel, G. Brookhaven National Laboratory Gardenghi, R. Westinghouse Electric Corporation Garren, A. Lawrence Berkeley Laboratory Gillespie, G. Physical Dynamics, Inc. Gilligan, J. University of Illinois - Urbana Gluckstern, R. University of Maryland Godlove, T, U, S. Department of Energy Golestaneh, A. Argonne National Laboratory Grammel, S. Argonne National Laboratory Guiragossian, Z. TRW Systems & Energy Gula, W. Los Alamos Scientific Laboratory Haber, I. Naval Research Laboratory Hammer, D. Cornell University Hammond, J. W, J. Schafer Associates Hartman, J, Battelle-Northwest Herrmannsfeldt, W. Stanford Linear Accelerator Center Hilland, C. U. S. Department of Energy Hoeberling, R. U. S. Air Force Hovingh, J. Lawrence Livermore Laboratory Hoyer, E. Lawrence Berkeley Laboratory Hubbard, R. University of Maryland Hummel, V. U. S. Department of Energy Humphries, S. Irani, A, Sandia Laboratories Johnson, D. Brookhaven National Laboratory Johnson, R. Sandia Laboratories Johnson, T, KMS Fusion, Inc. Jorna, S. U. S. Department of Energy Judd, D. Physical Dynamics Juhala, R. Lawrence Berkeley Laboratory Kammash, T. McDonnell Douglas Research Laboratories Keane, J. The University of Michigan Keefe, D. Brookhaven National Laboratory Kessler, G. Lawrence Berkeley Laboratory Khoe, T. Kemtors Chungs tent rum Kim, C. Argonne National Laboratory Kim, H. Lawrence Berkeley Laboratory Kim, K. Lawrence Berkeley Laboratory Kim, Y. University of Illinois - Urbana King, N. Argonne National Laboratory Klabunde, J. Rutherford Laboratory Klein, D. GSI Kulcinski, G. Westinghouse Electric Corporation Lampe, M. The University of Wisconsin Lapostolle, P. Naval Research Laboratory Lari, R. GANIL Laslett, J. Argonne National Laboratory Leiss, J. Lawrence Berkeley Laboratory Lindman, E. Jr. National Bureau of Standards Livingood, J. Los Alamos Scientific Laboratory Argonne National Laboratory

424 Name Affiliation Lofgren, E. Lawrence Berkeley Laboratory Long, H. State of Alaska McNally, J. Los Alamos Scientific Laboratory Macek, J. University of Nebraska Magelssen, G. Argonne National Laboratory Makowitz, H. Brookhaven National Laboratory Manley, 0. U. S. Department of Energy Martin, R. Argonne National Laboratory Maschke, A. Brookhaven National Laboratory Mazarakis, M. Argonne National Laboratory Miley, G. University of Illinois - Urbana Mills, F. Fermi National Accelerator Laboratory Mobley, R. Brookhaven National Laboratory Mochizuki, T. Osaka University Moenich, J. Argonne National Laboratory Monsler, M. Lawrence Livermore Laboratory Morettl, A. Argonne National Laboratory Nahemon, M. Westinghouse Research Laboratory Neil, V. Lawrence Livermore Laboratory Neuffer, D. Lawrence Berkeley Laboratory Nicholas, D. Rutherford Laboratory Olson, R. SRI International Pascolini, A. University of Padova Penner, S. National Bureau of Standards Perkins, R. Los Alamos Scientific Laboratory Pottmeyer, E. Westinghouse Hanford Raffenetti, R. Argonne National Laboratory Rambo, I. Westinghouse Electric Corporation Reiser, M. University of Maryland Rossi, C. U. S. Department of Energy Sachs, R. Argonne National Laboratory Sanders, R. Brookhaven National Laboratory Salisbury, W. Occidental Research Schultz, P. Argonne National Laboratory Seliger, R. Hughes Research Laboratories Sesol, N. Argonne National Laboratory Shiloh, J. Lawrence Berkeley Laboratory Shriever, R. U. S. Department of Energy Singh, S. Westinghouse Research Laboratories Smith, L. Lawrence Berkeley Laboratory Solomon, D. KMS Fusion Sramek, S. University of Nebraska Staples, J. Lawrence Berkeley Laboratory Steinhoff, J. Grumman Research Division Stekly, J. Magnetic Corporation of America Stokes, R. Los Alamos Scientific Laboratory Sucov, E. Westinghouse Fusion Sutter, D. U. S. Department of Energy Takeda, H. Argonne National Laboratory Teng, L. Fermi National Accelerator Laboratory Thompson, W. University of California - San Diego Tidman, D. University of Maryland Turnbull, R. University of Illinois - Urbana

425 Name Affiliation Vahrenkamp, R. Hughes Research Laboratories Wakalopulos, G. Hughes Aircraft Company Wallace, J. Los Alamos Scientific Laboratory Watson, J. Argonne National Laboratory Wilcox, T. R&D Associates Willke, T. Battelle - Northwest Wilson, J. University of Rochester Woodbury, E. Hughes Aircraft Company Young, D. Fermi National Accelerator Laboratory Yu, S. Lawrence Livermore Laboratory Zeiders, G. W. J, Schafer Associates

426 Distribution for ANL-79-41

Internal: R. C. Arnold (562) R. Lari C. Baker J. Livingood J, Bogaty G. Magelssen R. Burke R. L. Martin (20) K. Cheng M. Mazarakis Y. Cho A. Moretti E. Colton J. Moenich G. Das E. G. Pewitt R. Diebold R. Raffenetti S. Fenster Peter Schultz M. Foss N. Sesol A. Golestaneh H. Takeda S. Grammel J. Watson S. Harkness A. B. Krisciunas T. Khoe ANL Contract File Y. Kim ANL Libraries (5) R. V. Laney TIS Files (6)

External: DOE-TIC, for distribution per UC-21 (214) Manager, Chicago Operations and Regional Office, DOE Chief, Office of Patent Counsel, DOE-CORO President, Argonne Universities Association ZGS Complex Review Committee: M. Q. Barton, Brookhaven National Lab. J. D. Bjorken, Stanford Linear Accelerator Center R. L. Cool, Rockefeller U. V. W. Hughes, Yale U. W. Lee, Columbia U. F. J. Loeffler, Purdue U. L. G. Pondrom, U. Wisconsin, Madison R. Adams, Brookhaven National Lab. R. Bangerter, Lawrence Livermore Lab. (20) C. F. Barnett, Oak Ridge National Lab. T. Blue, U. Illinois, Urbana I. Bohachevsky, Los Alamos Scientific Lab. K. Brueckner, U. California, La Jolla G. Brumlik, The Slaner Foundation, Inc., New York M. Bullock, Continental Electronics, Dallas J. Caird, Bechtel National, Inc., San Francisco D. Chang, Occidental Research Corp., Irvine C. Choi, U. Illinois, Urbana W. W. Chupp, Lawrence Berkeley Lab. D. Clark, Lawrence Berkeley Lab. R. Clark, Maxwell Laboratories, San Diego M. Clauser, Sandia Laboratories, Albuquerque F. Cole, Fermi National Accelerator Lab. D. Colombant, Naval Research Lab. R. Cooper, Los Alamos Scientific Lab. A. Cron, W. J. Schafer Associates, Arlington, Va.

427 C. Curtis, Fermi National Accelerator Lab. G. Danby, Brookhaven National Lab. M, C. Davis, Northwestern U. A. Drobot, Naval Research Lab. C. Drumm, U. Michigan H. Edwards, Fermi National Accelerator Lab. A. Faltens, Lawrence Berkeley Lab. J. P. Farrell, Radiation Dynamics, Inc., Melville, N.Y. T. Foster, Westinghouse Electric Corp., Baltimore E. K. Freytag, Lawrence Livermore Lab. B. Gabbard, R&D Associates, Marina del Rey, Calif. G. Gallup, U, Nebraska G. Gammel, Brookhaven National Lab. R. Gardenghi, Westinghouse Electric Corp., Baltimore A. A. Garren, Lawrence Berkeley Lab. G. H. Gillespie, Physical Dynamics, Inc., LaJolla J. Gilligan, U. Illinois, Urbana R. L. Gluckstern, U. Maryland T. Godlove, Div. Laser Fusion, USDOE (20) Z. Guiragossian, TRW, Inc., Redondo Beach W. Gula, Los Alamos Scientific Lab. S. Gunn, Rocketdyne, Canoga Park I. Haber, Naval Research Lab. D. A. Hammer, Cornell U. J. Hammond, W. J. Schafer Associates, Arlington, Va. J. Hartman, Battelle Northwest Lab., Richland, WA W. Herrmannsfeldt, Stanford Linear Accelerator Center (20) C. Hilland, U. S. Department of Energy, Washington R. Hoeberling, U. S. Air Force, Kirtland AFB J. Hovingh, Lawrence Livermore Lab. E. H. Hoyer, Lawrence Berkeley Lab. R. Hubbard, U. Maryland V. Hummel, DOE-CORO S. Humphries, Sandia Laboratories, Albuquerque A. Irani, Brookhaven National Lab. D. Johnson, Sandia Laboratories, Albuquerque R. Johnson, KMS Fusion, Inc., Ann Arbor T. Johnson, United States Military Academy S. Jorna, Physical Dynamics, Inc., La Jolla D. Judd, Lawrence Berkeley Lab. R. Juhala, McDonnell-Douglas Research Lab., St. Louis T. Kammash, U. Michigan J. Keane, Brookhaven National Lab. D. Keefe, Lawrence Berkeley Lab. (50) C. Kim, Lawrence Berkeley Lab. H. Kim, Lawrence Berkeley Lab. K. Kim, U. Illinois, Urbana D. Klein, Westinghouse Electric Corp., Pittsburgh G. L. Kulcinski, U. Wisconsin, Madison M. Lampe, Naval Research Lab. L. J. Laslett, Lawrence Berkeley Lab. J. Leiss, National Bureau of Standards (20) E. Lindman, Los Alamos Scientific Lab. E. Lofgren, Lawrence Berkeley Lab.

428 H. Long, Anchorage J. H. Macek, U. Nebraska H. Makowitz, Brookhaven National Lab. 0. Manley, CTR Div., USDOE A. Maschke, Brookhaven National Lab. (50) J. McNally, Los Alamos Scientific Lab. G. Miley, U. Illinois, Urbana F. Mills, Fermi National Accelerator Lab. R. Mobley, Brookhaven National Lab. M. Monsler, Lawrence Livermore Lab. M. Nahemon, Westinghouse Electric Corp., Pittsburgh V. K. Neil, Lawrence Livermore Lab. D. Neuffer, Lawrence Berkeley Lab. R. Olson, Stanford Research Institute S. Penner, National Bureau of Standards R. Perkins, Los Alamos Scientific Lab. E. Pottmeyer, Westinghouse Hanford 1. Rambo, Westinghouse Research Labs., Pittsburgh M. Reiser, U. Maryland C. Rossi, Div. Laser Fusion, USDOE R. G. Sachs, U. Chicago W. Salisbury, Occidental, Irvine R. Sanders, Brookhaven National Lab. R. Schrlever, Div. Laser Fusion, USDOE R. L. Seliger, Hughes Research Labs., Malibu J. Shiloh, Lawrence Berkeley Lab. S. Singh, Westinghouse Research Labs., Pittsburgh L, Smith, Lawrence Berkeley Lab. D. Solomon. KMS Fusion, Ann Arbor S. Sramek, U. Nebraska J. Staples, Lawrence Berkeley Lab. J. Steinhoff, Grumman Aerospace Corp., Bethpage, N.Y. J. Stekly, Magnetic Corporation of America, Waltham, Mass. R. Stokes, Los Alamos Scientific Lab. E. Sucov, Westinghouse Electric Corp., Pittsburgh D, Sutter, Div. Physical Research, USDOE L. Teng, Fermi National Accelerator Lab. (20) P. Thiess, Catholic U. D. Tidman, U. Maryland (20) R. Turnbull, U. Illinois, Urbana W. B. Thompson, U. California, La Jolla R. Vahrenkamp, Hughes Research Laboratories, Malibu G. Wakalopulos, Hughes Aircraft Company, Culver City J. Wallace, Los Alamos Scientific Lab. T. Wangler, Los Alamos Scientific Lab. T. Wilcox, R&D Associates, Marina del Rey, Calif. H. Willenberg, Mathematical Sciences Northwest, Bellevue, Wash. T. Willkie, Battelle Northwest Lab. J. Wilson, U. Rochester E. J. Woodbury, Hughes Aircraft Company, Culver City D. Young, Fermi National Accelerator Lab. S. Yu, Lawrence Livermore Lab. G. Zeiders, W. J. Schafer Associates, Arlington, Va.

429 N. King, Rutherford Lab., Chilton, England D. Nicholas, Rutherford Lab,, Chilton, England P. Lapostolle, GANIL, Caen, France N. Angert, GSI, Darmstadt, West Germany R. Bock, GSI, Darmstadt, West Germany D. Bohne, GSI, Darmstadt, West Germany G. Kessler, Kernforschungszentrum, Karlsruhe, West Germany J. Klabunde, GSI, Darmstadt, West Germany N Marquardt, Institut fur Experimental-physik der Ruhr-Universitat, Bochum, West Germany J. Meyer-ter-Vehn, KFA Juelich, Juelich, West Germany D. Beriny, Magyar Tudomanyos Akademia, Debrecen, Hungary A. Pascolini, University de Padova, Italy Y. Itikawa, Nagoya U., Japan T. Mochizuki, Osaka U,, Japan T. Yamaki, Nagoya U., Japan J. P. Delahaye, CERN, Geneva, Switzerland

TiU.S. GOVERNMENT PRINTING OFFICE: 1979 — 650-066/09

430 ARGONNE NATIONAL LAB WEST