PREPRINT UCRL- 78204
Lawrence Uvermore Laboratory A Review of Direct Energy Conversion for Fusion Reactors
W. L. Barr and R. W. Hoir
September 20, 1976
This paper was prepared for submission to The Technology of Controlled Thermonuclear Fusion, Second ANS Topical Meeting, Sept. 21-23, 1976 Richland, Washington
This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint Is made available with the understanding that it will not be cited or reproduced without the permission of the author.
MEIER
W'nriK nt r'-.':s -r"!rii> r-.n- :-.r "".:|.ir.;!!TD A I'.LVIEW OF DIRECT ENERGY CONVERSION FOR FuSiOH REACTORS*
W L. barr and R. W. Hoir
LAURENCE LIVERMORE LABORATORY, LiVERMOR1 CALIFORNIA
The direct conversion to electrical energy of the energy carried by the leakage plasma from a fusion reactor and b' the ions that are not converted to neutrals in a neutral team inject r is discussed. The conversion process is electrostatic deceleration and direct mimil particle collection as distinct from plasma expansion against a time-varying magnetic field or conversion in an EXB ^uct (both MHD). 1 iji is Relatively sii.iple 1-stage plasma direct converters a- - discussed wnich can have efficiencies of about 50 . More compl / and costly li'ieasured in S/kW) 2-, 3-, 4-, and 22-stage concepts :e been tester at efficiencies approaching 90*. Beam direct converte > have been in tested at IS keV and 2 kW of power at 70 + 2 efficiency, and a test iKJillfiIf U of a 120-keV, 1-MU version is being prepared. Designs for a 120-keV. 4-MW unit are presented. The beam airect converter, besides saving or; power supplies and on beam dumps, should raise the efficiency of creating a neutral beam from 40 without direct conversion to 70 with direct conversion for a 120-keV deuterium beam. The technological limits determining power handling and lifetime such as space-charge effects, heat removal, electrode material, sputtering, blistering, voltage holding, and insulation design, are discussed. The application of plasma direct converters to toroidal plasma confinement concepts is also discussed.
INTRO.J-JCT I0;j Tne first significant fusion reactor application of electrostatic direct energy were separated from the ions by a transverse conversion was a concept put forth by magnetic field with the help of a negative Post to dpply the idea of a linear periodic electrical barrier (which is possible becaus» focused -accelerator in reverse. The the fan thickness is of order a Debye length). exhaust or leakage plasma from a mirror Next, the ions were decelerated and collected reactor was magnetically guided, expanded, on various electrodes (22 electrodes) at and transformed into a thin fan shape {see potentials near the kinetic energy of the Fig. 12). This process both reduced the ions. The electrons were collected at low plasma to a thickness of order one debye (ground) potential and formed the return length and converted random motion to current from the ion collector stage. This directed motion. Next, the electrons concept has been successfully tested at *Work performed under the auspices of the over 90' efficiency with a steady-state U.S.E.R.D.A. under Contract No.W-7405-Eng-48. plasma source. Simpler concepts based on
& triode, tetrode, etc, vacuum tubes have greater. It is therefore ne^es'-arv U> resulted in 1-, 2-, etc, stage concepts recover this power if the injector is to called Venetian blind direct converters1(2, ) be efficient. The ions can be magneticalW which have lower efficiency but also mucch deflected into a beam duiip from wnich power lower costs (S/kW). A 4-stage concept (3) can be recovered thermally, but the direct seems to have many of the advantages of recovery of electrical power is more effi the previous two. cient and can allow a nore compact design. More recently, attention is turning to The first bear direct converter concept the application of direct conversion to involved magnetic deflection and then neutral-beam injectors to increase their recovery in an imniersed-iyid direct con- 15) efficiency (i.e. to reduce power con verter. ' This converter type was tested sumed), to reduce the power supply re steady state at 20 keV and 200 W/cm2 in a (41 quirements, and to ease the design of the series of experiments in 1970. ' The charged particle beam dump. We have problem with the magnet was that the pack developed and tested a so-called in-line ing of a large array would be difficult. beam direct converter concept1 ' where A concept of immersed grids in an in-line the neutrals created from accelerated direct converter was developed by Fume1". ions in a charge-exchanged cell continue This in-line concept solved the packing through the "in-line" direct converter problem and resulted in a compact beam electrodes. The ions which are not con line, but beam interception on the grids verted to neutrals however are decelerated severely limited the beam power density and caught on these in-line electrodes. times pulse time, and for steady state In this paper, we discuss the beam the power was extremely limited (few direct converters, the plasma direct hundred W/cm In 1974, an in-line. converters, technological problems, and nonintercepting electrode converter was application of plasma direct converters proposed. (4) Designs and computer Simu to toroidal reactors (tokamak and reversed- lations using the DART code were then field mirror reactors). done1 ' and a comparative analysis of the BEAM DIRECT CONVERSION immersed-grid concept of Fumelli's and To efficiently produce neutral beams the nonintercepting concept was made. la) for fusion reactors, the energy carried Analytical and computer studies of both by the unneutrali.ed portion of the ion the immersed-grid and nonintercepting- beam may have to be recovered in a direct electrode concept were reported on in converter. Neutral beams are produced by 1975 by Raimbault.' ' The noninterceptinq passing an accelerated ion beam through a converter can handle much higher power gas cell where a fraction is neutralized densities than the immersed-grid concept, by charge exchange, but a significant but the product of beam thickness and fraction is not. When a beam of 100-keV current density is somewhat restricted as D is passed through the optimum thickness discussed below. To overcome this 1 imita of 0, gas, about half of the bam pow.-r tion, we propose to divide the beam into remains unneutralized. At higher energies, two blankets. Raimbault has recently' ' the unneutral!'zed fraction becomes even proposed an interesting concept employing aspects of both immersed-grids and non- cryopumps. Higher pressure than this intercepting electrodes that promises to would result in an unacceptably high den raise the beam thickness and power density sity of cold ions which would be acceler both. ated into the negative electrode. Principle of the Nonlnterceptlng Concept The negative electrode is water- The nonintercepting beam direct con- cooled and is held sufficiently negative (41 verter1 makes use of the fact that the (-15 kV) to prevent the electrons pro space charge of an unneutralized ion beam duced in the neutralizer cell from reach will cause the beam to diverge. By stop ing the positive electrodes. The positive ping the neutralizing electrons with an electrodes are also water cooled and are applied negative potential, most of the oriented so that they intercept as much ions can be caused to leave the fast- of the diverging ion beam as possible. atom part of the beam and be collected They ire held at high positive potential on appropriate electrodes. The neutral (about +110 kV here) that is adjusted to (atom) component of the beam is not maximize the recovered electrical power. affected. Figure 1 shows a cutaway view Another water-cooled negative electrode of an injector system1 ' with this type prevents backstreaming electrons from of direct converter, ions are extracted reaching the ion collectors. from the source, accelerated to 120 keV, There is a complication due to the and passed through a gas cell where 1\% fact that existing ion sources produce of the 0* ions are converted to D° atoms not only the desired ions (usually 0*), at 120 keV. (The neutralization would but "lso several other species (such as be 43* efficient if the cell were mry 0j, Oj) that break up in the neutrali2er. long). The gas cell is cooled to reduce The result 1s that at 120 keV, about 20;. the flow of gas into the direct converter of the ion current at the direct converter region where the gas pressure is kept (10S of the ion beam power} is in half- below 10"2 Pa (8 x 10"5 Torr) by baffled energy ions, and about 8% of the ion current (3* of the ion power) is in one- third energy ions. These fractional WWECT CONVf RTf.X i20hev KM SOURCE energy ions are turned back by the high positive potential in the collector region and are caught on the curved collector which is at ground potential. The purpose of the curved collector is
C»*O»*LPU««> to prevent the fractional energy ions from striking and heating the LN-cooled baffles near the cryopanels. Calculated Ion trajectories are shown in Fig. 2 for both full-energy (120-keV) ions and half-energy ions. The collector Fig. 1 A 120-keV neutral injector with in this case was held at 110 kV. The a beam direct converter to recover power from unneutralized ions. calculations were done in two dimensions produced at the positive ion «.olhrttor (a) arc induced everywhere with j '••'•-i\ ref erenced to the collector po*e»>* i secondary electrons lu-iit the t»u» Ia*-*t j I f o? ine potential rr-a .•. i r.-«:r, ir.side the collector to a few '*. I above U'lH'i.f.or Fig. 2 Computer simulation of a bean e direct converter at !7 A/* of !20-».eY vol "aye. ! or this reason, set. ondary L)+. Total length is 1.0 m: (a) full electrons alio-.-; the collection «t hi«|h energy, (bj half energy, and tc) equi- potential o* <*. c.uch higher density ion beam than would lie possible otherwise. with the 0ART*12* co&puter code, which Secondary electrons <\rv also produced calculates ion trajectories in the at the negative electrodes. I he space applied potential plus the self-consistent c ha rye of these enertp-tk electrons is space-charge potential of the ions and negligible, out their c-jrrent and power electrons. Vacuum potential due to the may not oe. Their trajectories are specified electrode geometry and voltages calculated to determine the loss in is first calculated using an over-relaxa direct converter efficiency. tion technique. Ion trajectories are then /ilthough a finite amount of space calculated for that potential in order to charge is necessary for efficient recovery, get a first approximation to the space too much space-char ' - -, - k(. )2(d/L). We have experimentally tested a beam 0 p fT31 ? 2 direct converter of this type. ' A Here. .< = nq /._M is the square of the steady-state MATS-II1 ion source was ion plasma frequency, d is the thickness masked to produce a slab beam 15-ran of the beam, and • is the time required thick and 60-mm wide consisting rosily for an ion to go a distance L. The scale of H ions. The ion energy was varied length I is defined by H- = qEL where Kg over the range from 10 keV to 15 keV, is the ion energy, and E is the applied and the full-energy ion current varied retarding electric field between the from about 50 mA to 130 mA. 5ince the collector and the neg-tive electrode. ion current from the source varies as Khen n, the central beam density in a 3/2 parabolic profile, is expressed in terms Wj. , we expected and found the same of beam current 1. the scaling displays 3/? efficiency at all beam energies. the expected ! • w. ' at constant ••.: A photograph of the direct converter is shown in Fig. 3. The device was con • - - •p(3\Fr M!!>±- 1 3/2 structed from molybdenum and was cooled " ° \%/ ** (Vc> ' by radiation only. When the voltages where h is the width of the beam and H is determined by trajectory calculations. The best fit to results at high current were •!„ * 1.0 and k = 0.11 for a flat- topped beam profile. Calculations have also been done for a Gaussian profile. In that case, -,0 is smaller than in the flat-topped case because more of the beam power is concentrated in the center of the beam where recovery is poor. For the Gaussian profile, ',„ =• 0.9 and we assume Fig. 3 Photograph of a scaled direct converter tested at 2 at of 15-keVH*. k * 0.11 as before, although k has not Efficiency is 70i. been studied in this case. are varied, the various electrodes range from warm up to white hot. At the optimum setting, the collector is only dull red since most of the power is recovered electrically. The efficiency was determined by measuring the currents and voltages at all electrodes and by measuring the ion tsam power with a calorimeter. The calori meter can be seen in its retracted position in the photo. By recording the total beam power transmitted through the direct con verter with no applied voltages and also with voltages set to stop all ions, th'»ent in half-energy protons. 6 kV in Fig. 4. Figurs * •>•• t% a plot of the measured A larger version of this direct con currents t.: ihe positive collector and to verter is being constructed and will be both nega-- : electrodes versus the tested on the Lawrence Berkeley Laboratory's voltage applied to the collector. The 120-keV test stand. The direct converter negative electrodes were both held at is designed to recover the 800-kW (6.75-A), -3 kV, the source voltage was 12 kV, and 1/2-s pulse of full-energy 0 ions. The the total ion beam power was 1150 W as direct converter will be located about measured with the calorimeter. At 11.8 kV, 5 m from the 10-cnt-square source, where the collected power reached a maximum of the beam profile is Gaussian with an 1050 W, and the drain on the negative elliptical cross section. The computer power supply was 48 W. Therefore, in calculations indicate that the highest this case the efficiency was heat load on the collector will occur when the collector is at; ground potential 1050 - 48 0.69. and the negative electrodes are -at their 1450 -15 kV operating potential. Then, most of the ions diverge and strike the collector with their full kinetic energy. The recovered power will net be used, The ion power will be distributed rather but will be dissipated in a variable uniformly over the collector surface, so resistor that, will be adjusted to give that the power density is calculated to the desired voltage at the collector. 2 be less than 200 W/cm everywhere on the All high-voltage caoles will be kept collector. The collector structure is short to reduce the stored energy that shown in Fig. 5. The electrodes are all could be dissipated in a spark. made of water-cooled copper and are Diagnostics will be electrical and also nickel plated to reduce sputtering. calorimetric. Testing is expected to All electrodes and apertures have begin in November of this year. elliptical cross sections to follow the In anticipation of favorable results contour of the beam power density. The from these tests, a preliminary design is first aperture is the smallest, with being developed for a direct converter to major and minor diameters of 36 cm and 9 be used on the injectors for the TFTR cm, respectively. At maximum power and (Tckamak Fusion Test Reactor). He are best focus, the beam power density strik- assuming that the ion sources will be 2 ing the aperture will be 500 w/cm . The 10-cm x 40-cm versions of the 10-cm square aperture has a tungsten insert to allow source being developed in Berkeley. The for less than optimum focus and alignment. power density at the direct converter will Total power density (neutrals plus ions) be higher on TFTR than in Berkeley because at the center of the beam will be 37 kW/ of the larger source. However, the more cm2. important difference is due to the shorter distance between the direct converter end the source on TFTR. There, the 4-HW beam of unneutralizea ions will have nearly a I i I I flat-topped profile and will be the full 0 10 20 30 10-cm thick. The space charge potential at the center of the beam after the electrons are removed will be more than 50 kV, requiring about 80-kV negative voltage on the negative electrode to penetrate in order to stop the electrons. Such * high negative potential is not practical because of the power loss and because of the danger from sparking. One possible solution is to reduce the beam height to 5 cm, which would reduce the required negative potential to about l-Aperture -20 kV. This, unfortunately, would reduce the output of each beam by a 1 ... factor of 2, which could be made up by j doubling the number of beams. Another Fiiy. 5 A direct, converter being built to recover 800 kW of 120-keV D+. possible solution to the problem is to magnetically deflected into the beam modify the source to produce a shadow down recovery unit. This concept has been the center of the beam. The negative discussed at some length in Ref. 4. where electrode in the direct converter could experiments done in 1970 at 20 keV and 2 then have a web in the shadow. This 200 W/cm were reported. Further analysis effectively halves the beam thickness and was presented in Ref. 8. In this refer reduces the space charge potential to ence, is developed a fairly fundamental one fourth of what it was. Figure 6 power limit. For example, with the in shows some trajectories run in this line immersed grid concept being pursued geometry. Those ions, especially the by Fumelli and Coworkers, the grids fractional-energy ions, that pass close are sufficiently small that for pulse to the web ire strongly deflected and durations of interest I 1 ms) the temper appear to be the most serious problem ature is uniform across tne grid diameter, with this scheme. in that case, for ribbons 0.1-imi by 1.0-mm made of molybdenum, a powev density times 2 pulse length of 500 W-s/cm will raise the grid from 300 K to 2200 K, where thermionic emission losses will exceed the recovered power. This value of 2 500 W-s/cm corresponds to a power den sity of 1 kW/cnf for O.t-s pulses, whereas the !20-keV converter at 4 Hi-; discussed above is designed to operate 2 at 10 kW/cm for 0.5 s, and quite possibly ould go to steady-state operation. At steady state the power density is either limited by thermionic emission from 2 immersed grids to about 50 W/cm or by Fig. 6 Calculated trajectories (a) and equipotentials (b) for 90 A/m of the convective cooling limit of possibly 120-keV D+ with central shadow. 2 as high as 2 kW/cm . The low limits on power densities and pulse lengths for Principle of the Imniersed-Grid Beam immersed grids are the effects which led Direct Converter us towards the nonintercepting-grid beam The idea is to direct the ion beam direct converter coirepts. through a rugged but sti11 tenuous grounded grid (cathode). To reFlect PLASMA DIRECT CONVERSION electrons with a similar grid which is Another type of direct converter is held at a potential about 3 kT /e nega required to recover the power from the tive (central grid) and to then decelerate ions that leak out from e magnetically the ions with a positive collector (plate) confined plasma. In a mirror fusicn at a potential approaching but somewhat reactor, only a small fraction of the below the beam energy. The grid set can injected beam power results in fusion either bt in-line or the ions can be before it escapes out the mirrors. It i'. thereto* t important to the overall is different in the two types of separa Mfii-ieii: .- to recover this power, just tion. With magnetic separation, the elec us it i^> ir.purtant to recover the un trons are removed from the beam and can neutral i^.-d ion power in the injectors. De collected, while an immersed negative "'it functions of the direct conversion grid simply reflects the electrons with process can be seen by following a typi out disposing of them. The sink for tne cal iiartjf le. A fuel ion will niove back electrons in this case is provided by a and forth between mirror points in the grounded grio which precedes the negative reactor until the particle diffuses hy grid in the beam line and establishes i'.ouloinb '.oil is ions into the loss cone ground potential. Thpn it masses over the ma/imuM- field I_rnmer_sed-c[r_id plasma direct converter ' I1- ";. where its erwryy is essentially The average energy of the electrons transverse to B. As it moves outwardly hitting the grounded grid is slightly in the e/nandfr, whose field may drop to less than kT . A numerical method usina e -i few hundred -jauss, the perpendicular a random-walk technique is being developed '•fiery; will drop linearly with B accord and can be used to calculate the electron ing to the principle of adiabaticity energy more precisely. The loss of the !W 'BJ const, so that, by the conserva : electron power is small if kT is much tion o' total energy, the velocity, which less than the mean energy of the escaping staged out perpendicular to B is now ions. nt-.irly parallel to G. Therefore, tne The simplest direct converter of the o/pander serves two purposes: it produces immersed-grid type has only one collector <: directed beai<: of ions, and it reduces stage. Figure 7 shows a 1 stage direct the current and power densities in the converter module. The first grid is be in-. grounded, and the second on? is held at Plasma direct converters can be a negative potential equal to about divided into two general types according -3 kT /e to stop nearly all (l-e~3 95 ) to whetntr the electrons are separated primary electrons. High-pressure helium out magnetically or electrostatically. at about 1000 K is used to cool the For magnetic separdtic.i, the plasma is grounded grid so that the electron and guided and expanded magnetically into a the intercepted ion power can be recovered thin slab from which the magnetic field, in a thermal cycle. The negative grid is and hence the electrons* can be abruptly water cooled to prevent thermionic emis diverted. The ions continue on with only sion and to keep the tube size small for a slight deflection if the expansion a minimum interception of ions. The ion resulted in a sufficiently weak field. collector is also helium cooled and For electrostatic separation, the plasma louvered so that it is opaque to the stream is expanded in two dimensions to directed ions but rather transparent for produce directed notion and to reduce the gas pumping. It is held at the positive 2 power flux to a level (100 W/cm ) where potential determined from the ion energy immersed grids can be used to reflect distribution to give the maximum recovered the electrons. The fate of the electrons power. For mirror machines, this potential is just equal to the parallel component ot charge e^cnartie bfiw-.vn '• >u\ .^.u (ja^ the minimum energy per unit of charge, so molecules, tconoiri; •. det"r:> M.;- the that all ions can reach the collector and optimun operating :iivr.s.iiv t'nr ,i r^LlO'1. none are reflected. This potential is Any number ot lutcrmediiiLf- st.-Mjc-. . aii given by be added to thic. basii. • tnjcti.re bv -.in<* the concept of the '.V-iet ian hli'-': direct V R cose/(R 1) converter. For that, the diro*i converter c0l.- 'O - is tilted at d slignt ami I*1 relative to where •; is the maximum angle between the the incoming bear vt that tr.<- nxr. velocity vectors and the .-•agnetic field fol low parabol if. tra jet tor i*-.. Iti*p--- lines, ;* is the embipolar potential, and niediate stages, cacn si'ilor t<, ,i R is the mirror ratio in the confining Venetian blind and each nfld at •*'.*!.< 5 kTfi/e. the slope of the individual pi«t*-s .;'J- The design shown in Fig 7 is for a justed for maximum transciss ion of" Lne mirror reactor^ ' for whicl. the minimum incoming ions. If an ion h.is insuffi energy of the escaping ions ij 96 keV, cient energy to reach lfv=- m-<* ni'jhf-r the average energy is 146 '.eV, and potential, it will be turnc ; :,di !• , but - = 0.20 radians. After allowing for with the wrong slope to got through ihf the Qc of the incident power that is plates. Consequently, tne ions tend to carri J by electrons, the efficiency be caught on the collector tvjt ic. at the of the direct converter is 52 . highest potential that the ion ran rtvich. Behind the ion collector is a cryopunip Since the ions are collected on the hacks with a water-cooled and an LN-cooled of the collectors, an electro'- -,iinpross,or baffle. The pressure in the expander grid is located directly behind e^:'-. must be kept below about 10 Pa {8 x 10 intermediate collector stage to control Torr) to reduce the losses caused by secondary electrons. Figure 3 shows a three-stage direct converter module designed for a rirrnr 114 1 frsion reactov ' for whicn tne leakage ions have a mean energy of 178 keV and a minimum of 100 keV. With that energy distribution, the efficiency of the direct converter is 60 after allowing for the 8 of the incident power which was carried by electrons. The Cryopump module is 2,6-m square and the inter- electrode spacings are each 1.0 m. The 1.0-m spacings are slightly less than the maximum allowed by space charge for the given power flux and energy distribution. Fig. 7 A single-stage direct converter Since the average power flux into the module designed to handle 1.75 MW/mS 2 Mean energy is 96 keV. Efficiency is 52". direct converter is only 45 W/cm , the increased interception on early stages. Figure 9 shows possible locations of the two direct converters discussed above (141 -M on a mirror fusion reactor. ' The single-starje direct converter at the bottom in the figure was kept small so that the lower half of the reactor r'n be lowered to allow access to the blanket. Only 20? of the power was allowed to go to the l-staqe unit, while 80" goes upward to the 3-stage converter. One of the 2-stage modules is shown being replaced. We have experimentally tested a 2- stage version of the Venetian blind direct (15) converter1 ' using an ion source and later using a plasma source, at the end of a magnetic expander. The measured efficiency varied with the energy of the incident ions in good agreement with the calculated efficiency. The measured efficiency of 65° was only slightly less Fig. 8 A three-stage module of a Venetian blind direct converter. At than the calculated 69%. 0.5 KW/m2, the efficiency is 60%. negative grid and the two intermediate MCCULE CAR electrodes with their suppressor grids are made of carbon fiber and are cooled by radiation. The third stage is made up of a chevron pattern to allow gas pump ing without transmitting either ions or radiation. It and the walls are cooled by 1000 K helium to allow thermal recovery of the excess ion energy and the radiated heat. A water-cooled baffle, a liquid- nitrogen cooled baffle, and then the BLANKET SECTOR cryopump follow the third stage. The support posts are water cooled in order to keep the high-voltage insulators cool. -r 2 This design can handle up to 100 W/cm Fig. 9 Showing possible locatiors of of incident ions, and more intermediate the two direct converters on a mirror stages could be added. There is little fusion reactor, with one nodule being replaced. to be gained by adding more than about five stages, however, because of the V ' Slab-Geometry Plasma Direct Converter distribution. We have studied two different direct Optimization was done using the DART converters of the slab-geometry type. computer code to calculate ion trajec Both depend on a magnetic expander to tories in the applied electric field plus form the plasma stream into a slab of the self-consistent space-charge field. well directed ions. The magnetic field The efficiency depends on the energy dis deviates abruptly at the entrance to the tribution and on che amount of space direct converter. Electrons, behaving charge. Lower space charge allows higher adiabatically, are guided away, while applied voltages, and hence greater energetic ions cross the field lines recovered power. An ansiysis shows that and enter the direct converter. for a given energy distribution, the The simplest of the two direct con efficiency scales by the same expression verters is the space-charge dominated, as for the beam direct converter, but 4-stage device' ' shown in Fig. 10. It with different coefficients. For a is similar to the beam direct converter triangular-shaped distribution (to discussed above. The first electrode approximate the efflux from a mirror is an electron repeller to stop any reactor) and for a 300-to-l expansion electrons that are not magnetically into a thin slab, wo find diverted. Without the electrons to neutralize their space charge, the ions n = 0.80 - 0.10 ( The DART computer code was used to _ = r + _ sin (-j-) cosh (-j-j + optimize the efficiency by varying the parameters. Individual trajectories 2? s'n (—;sinh IT-; • were followed in ion beams with a specified energy distribution and current density. The cosh term gives weak focusing, whereas Certain qualitative features emerge from the sinh term gives strong focusing, which this parameter search. For C greater allows higher densities to be handled in than optimum, efficiency declines because the presence of space-charge blowup. of particles being collected too soon (at nti;3r potential functions could be in too low a potential). On the other hand, vestigated in order to optimise the for C less than optimum, efficiency loss collection process. However, we take the is mainly caused by so-called "retrograde" same form but with A = 0. In this case, particles, those particles that turn there are three parameters (Vg, L, and C) around and escape without being collected. whose values can be adjusted in searching In this type of direct converter, space for the most efficient collection com charge has a deleterious effect. The patible with practical dimensions and electric field due to space ciiarge in the electric field values. In Fig. 11, a beam tends to defccus the beam. Increasing collector is located every L/2, whereas C partially counteracts this effect since for the cosh term a collector is located the focusing field is proportional to C. every L; thus, the direct converter The condition that the applied perpendi overall length is effectively halved by cular field, Ei = 3V/3Z, be stronger than the use of strong focusing for the same the field due to space charge everywhere number of collectors. in the beam reduces to In Fig. 11, the curved electrodes and the plane parallel electrodes lie on (u T) < C, where u ii the ion plasma frequency and T = L/v as before, but now L is the spacial period in the periodic structure. Thus, as the power density is increased C must •.iso be increased, with the penalty described above. By optimizing the parameters in our numerical simulation studies of beams with different densities, we find ' that the efficiency, n, varies as 2 2 n = nn - k(u.px) (d/L) . "0 Fig. 12 A mirror fusion reactor with This relation was also predicted by a fan-shaped expander and periodic f 181 focusing direct converter. Marcus and Watson/ ' When restated in terms of the linear power density. P, the expressions discussed above. The (watts per metre of periphery around the experimental results agree with those expander), the efficiency becomes from numerical simulation. Z Alternate Concepts for Plasma Direct n - n0 -k- Pl W- , Energy Conversion where W is the mean ion energy. Beam Several other concepts have been thickness, d, is assumed to be propor proposed. tional to W ' here. For a flat-topped Parabolic Trajectory Concept: The idea energy distribution with W = 600-keV D is to form the plasma stream into a and P. = 3 MW/m, we find numerically that narrow, well directed slab and remove the n = 0.85 if nQ = 0.85. We have included electrons by electric and/or magnetic all non-space-charge-related losses in r,.. fields. Then the ions enter a region of In the design of a reactor, a compromise uniform electric field whose direction is must be made between a large expander giv nearly but not quite directed against the ing a low PJJ and hence a high n, and a ion flow direction. The ion will slow small expander that is less expensive. down and bend following a parabolic Figure 12 shows a drawinq of a conceptual trajectory. Since different energy ions (19) design of a reactor* equipped with have different trajectories, the slowing a fan-shaped expander and a periodic- down progress leads to spacial separa'ion focusing direct converter. The overall of the different energy groups and allows diameter is 275 m, and the output from collection on many electrodes whose the direct converter is 1 GW in this voltages nearly match the initial ion design. energy. The concept was independently The periodic focusing concept was conceived by a Soviet group' ' and by tested in a series of scaled experi Barr.' ' The idea was analyzed and ments.'16, ' Physical size scales shown to be very efficient (98%). How- (22) with orbit size in the expander, and ever, the concept has been shown' ' to space-charge effects scale according to be sensitive to space-charge effects; nc-i.ce, the concept seems uninteresting tion occurs, then deceleration by imcerse fron. (i cost per unit of power standpoint. grids can be done. This concept has not EXB Concepts: The idea is to use the been studied sufficiently to determine different F. x B/LT drifts of different its limitations, but it is expected to energy particles to produce energy be about 70;'. efficient and to handle separation. Two different concepts were about as much power as the 22-stage proposed,' * ' but neither seemed very concept. promising and were not pursued. Cost Anajysis and Comparison Cj/clotrcn Resonance: The concept due to The choice of a particular type of 'orrester " is to form a slab beam as plasma direct converter will depend on in the case of the 22-stage concept but the economics of the particular applica have ri magnetic field continue through tion. For a fusion power reactor, the trie deceleration region. A periodic parameter to be minimized will probably transverse electric or magnetic field is be the total cost per unit of net suneriiiico^ed so that spatial cyclotron electrical power output (S/kWe). Other resonance occurs for particles as they considerations, such as the effect of slow down. Once near resonance, the waste heat on the environment, may how partici'? energy transverse to the guide ever, require high efficiency even if field increases rapidly with a correspond that means an increased cost. In the ing increase in gyroradius. Collectors case of a D-T fueled mirror reactor, the dre arranged to catch these slowed down output from the direct converter accounts ions. A netailed evaluation of this for r,ughly half of the gross electrical coiv-ept has net been made nor has a com output. Therefore, the efficiency of the parison to the 22-stage periodic focus direct converter has a strong effect on ing cuncept been made. the net electrical output. An expensive Traveljnt| Wave: An electrostatic wave direct converter may produce the lowest is inposed with electrodes such that the S/kWe even if it is only slightly more amplitude increases with distance and efficient than any less-expensive one. the wave velocity slows down. The This situation also exists in an advanced f 251 idea is to Tap ions in the wave fuel reactor, since the direct converter and then slow these trapped ions down. will handle most of the power. On D-T The concept is space-charge limited to fueled tokamaks and on fusion-fission about the same power as the 22-stage hybrids, the direct converter handles concept and appears to be limited to only a small fraction of the total power, about 50'. efficiency. Good coupling or and its choice will be dictated by other loading of the electrical circuit by the considerations such as magnetic field beam may be a problem. geometry and pumping requirements. Electric Field Deflection„ _ : This concept, Cost estimates can be scaled from the due to Hamilton, ; is based on the idea various conceptual designs that have been that an electrostatic deflection of a published on different direct converters. beam results in a larger-angle deflection In comparing the costs, it must be kept for lower-energy (momentum) ions than for in mind that the assumptions that were higher-energy ions. Once energy separa used in making the different cost esti- mates were not all the same. However, at 200 keV must be roughly the same as the following examples demonstrate the for the periodic focus oevice at 600 keV main differences: and the same power density because the Venetian Blind: In Ref. 14, a 3-stage expander would be nearly the same in Venetian blind direct converter for ions both cases. However, at 200 keV the with 170-keV mean energy (See Figs. 8 and cost of the cryopump is significantly 9) was estimated to cost S260 per kilo greater than at 600 keV. At 200 keV and watt handled. Of this, $90/kW was due at 6 MW/m the net cost would be approxi to the cryopump. Since the efficiency mately S280/kWe for a 55 efficient was about 603;, the cost amounts to S430/ direct converter. The cost would increase kWe. It appears that a minimum of about rapidly as the energy is decreased because S290/kWe would be obtained (but the of the planar expansion and because of the efficiency would drop to 53%) if the greater pumping area that would be needed. number of stages were reduced to two and Technology if the area of the cryopump was reduced. The design of a direct converter must The decrease in efficiency is due mostly offer solutions to the technological to the loss of ions by charge exchange problems associated with heat removal and because of the reduced pumping. Pumping voltage holding in the presence of 1 MW/ 2 costs dominate at lower ion energy. At m of incident energetic ions and electrons. 80 keV, the minimum cost would be about Heat Removal: Because direct converters S460/kWe, and 154 of the ions would are not 100" efficient, a significant charge exchange before reaching the fraction of the incident power is con direct converter. verted to heat. This heat must ne removed Periodic Electrostatic Focusing: In Ref. to limit the temperature of the various 19, an estimate of S280 per kilowatt surfaces, yet it must be removed at as handled (1976 dollars) was obtained for high a teoiperature as possible to allow a 22-stage direct converter and a large its use in a thermal bottoming cycle. fan-shaped expander (Fig. 12). That In the case of immersed-grid direct con design was for ions with a mean energy verters, the problem is complicated h/ of 600 keV and for a power density of the fact that most of the structure must 3 MW/m. Since the efficiency was about be kept highly transparent to the in- ident 73%, the net cost was S380/kWe. At lower ions. For this reason, both conceptual energy, the cost would be much higher, designs of Venetian blind direct con varying roughly in proportion to the verters that have been done used radi- inverse fourth power of the energy. atively cooled intermediate stages. Ihe This is because of the planar expansion walls and the last stage receive the and the sensitivity of the efficiency radiated heat and dre convectively cooled to the power per linear metre, while the with high-temperature ( I00fl K) helium. cost varies approximately as the surface The grids can be radiative!/ cooled if area. the total incident power flux is less than 2 Space-charge Dominated Four-Stage: No about 1 MW/m . At higher power flux, the cost estimate has been made for this grids become hot enough to emit thermionic type of direct converter, but the cost electrons that seriously degrade the efficiency. Up to about 5 MW/m , con- 10 cm" is reached in 8 hours. vectively cooled tubes can be used if the Voltage-holding tests on tungsten and loss due to interception on the tubes niobium electrodes that were blistered and the manifolds can be tolerated. with a 300-keV He beam showed a signi Convective cooling at higher tempera ficant voltage-holding degradation, but ture and hence high pressure is complicated proper conditioning such as high-temper by the different high voltages. Either ature operation allowed voltage to be heat exchangers designed to stand off held as high as with unbombarded elec- (29) high voltage, or insulators designed to trodes. Sputtering may also lead to confine high pressures at high tempera roughening of the surfaces, but again at ture, may be used. elevated temperatures the voltage-holding properties may not be degraded. Choice of Materials: Those structures that are cooled by radiation must be The long-term damage problem will be made of conducting materials that can the erosion of electrodes due to sputter withstand high temperatures (up to ing and build up of sputtered material. 1800 K). The choices are the refractory This process will set replacement times metals or carbon. Either woven or for electrodes and will be most severe monolithic structures made of carbon have for the thin radiation-cooled grids of interesting possibilities. One objection the immersed-grid concept. Present to the use of carbon is that the sputtered estimates give an erosion rate of 0.02 carbon could cause the embrittlement of mm/yr for tungsten wires and a consider nearby hot, refractory metals. ably faster rate for carbon fibers. Convectively cooled grids require Chemical Compatibility: One material materials that have high tensile strength under consideration for electrode to withstand the hoop stress and the material is graphite due to its good thermal stress in small, thin-walled tubes. high-temperature properties and low cost. The alloy Ta-10 W was chosen as a superior One potential problem is chemical sput material under similar conditions in the tering due to formation of methane. first wall of the Fusion Engineering Another potential problem is the tritium Research Facility (FERF) design.'2 ' holdup that is not possible to predict because of the lack of experimental data. Electrode Damage and Voltaqe Holding: Electrodes will be bombarded by ions Another problem' ' is the chemical causing both short-term and long-term reaction with metals at high temperatures. problems. The short-term problem is For example, one concept called for expected to be a degradation of voltage graphite platelets strung on tensioned holding due to roughening of the surface tungsten wires. The tungsten wires will due to blistering produced primarily quickly form a carbide layer which is so by He bombardment. This problem is brittle as to be unusable. Present concepts discussed in ftef. 28. For typical that use graphite electrodes use metals only power levels (-100 W/cn ), the dose of at relatively low temperatures MOOO K). Insulators: Insulators used in direct I 50 keV) and the plasma wanting to converters wi11 have to be very wel1 operate at lower energies ( 50 keV) due designed to stand up to the harsh environ to power-density related costs. The ment. , radiation will have to be kept reason the direct converter wants to down to a certain level to prevent the operate at relatively high energies is insulator from becoming a semiconductor that the ions can be lost due to charge with a catastrophic breakdown. exchange in the flight path from the Replacement will be set by neutron- divertor to the collector, i.e., in the induced damage and possibly surface magnetic expander. The probability of deteriortion due to neutron and charged charge exchange drops rapidly as the particle sputtering. The insulators will energy is increased. For example, we have to be well shielded from sputtering. find the direct converter efficiency is Special cooling will be required to pre halved if the mean energy drops from above vent the insulator properties from being 100 keV to 50 keV in one particular seriously degraded by high temperatures. case. We find a very encouraging The whole question of insulator require effect that tends to alleviate this ments and an assessment of the technology problem: the edge (separatrix) of the of insulators for mirror fusion reactors toroidal plasma is at a fairly high has recently been reviewed. ' positive potential due to ambipolar Application of Plasma Direct Converters plasma flow to the grounded wall (first to Toroidal Reactors direct converter electrode). The plasma A number of problems arise when ions have a mean energy of order 3/2 kT. applying plasma direct converters to when they leave the toroidal region, but toroidal reactors. A divertor must be gain an energy e-i. where ; is some as yet designed which will lead or guide plasma undetermined multiple of T . A deleteri leakage ions and electrons out of the ous effect is that the temperature of the toroidal confinement region to the leaking ions will tend to be lower than magnetic expander before cross-field the bulk of the contained ions because diffusion to the walls can cause plasma of a number of effects such as radiation cooling due to wall reflux. In the cooling of the outer layers, and cooling reversed-field mirror reactor, an axial due to wall reflux. diverter is part of the equilibrium The technological and economic aspects configuration itself and is not expected of the converter design are not expected to be a problem. In the case of the to be different for toroidal application tokamak, poloidal and toroidal (bundle) than for mirror application except as diverters are being investigated, and noted above. difficult technological problems are CONCLUSION in evidence. Once the plasma is diverted A number of different concepts for and guided past the toroidal coils, direct energy converting plasma end magnetic expansion is not difficult. losses and ion beams in neutral-beam The next problem appears to be the injectors have been proposed and experi conflict between the direct converter mentally verified. Theoretical analysis operating efficiently at higher energies aided by computer simulation has resulted in design scaling laws that have been a steady plasma, a 2-stage Venetian blind tested at relatively low voltages and low plasma converter at 65* + 2% with a plasma powers; now we are in the process of source, and a 15-keV, 2-kW ion beam at 70 + going from the scientific feasibility 2% efficiency. We are preparing a 120-keV stage to the development stage. We are 1-MW ion beam recovery test and a 100-keV, 2 preparing tests at over 100 keV and 0.5-MW/m Venetian blind plasma converter powers exceeding 1 MW (0.5 MW/m for the test. For the future, we plan to integ plasma direct converter). Past accomp rate the beam direct converter into the lishments include a 22-stage plasma con neutral-beam injector for the TFTR. verter tested at 91% + 2% efficiency with REFERENCES 1. R. F. Post, In Proc. British Nuclear Engery Soc. Conf. on Nuclear Fusion Reactors (Culham Laboratory, Culham, England, 1969), pp. 88-111. 2. R. W. Moir, and W. L. Barr, Nucl. Fusion 13, 35 (1973). 3. S. J. Gitomer, W. L. Barr, and R. W. Moir, Bui. Am. Phys, 5oc. 19, 878 (1974). 4. R. M. Moir, First Topical Meeting Tech. Contr. Nucl. Fusion (Proc. Conf. 740402-P1, San Diego, 1974) 1, 432. 5. R. F. Post (Chairman), Preliminary Report of Direct Recovery Study, Lawrence Livermort Laboratory Rept., UCID-15650 (1970). 6. M. Fumelli, and F. P. G. Valckx, "The Annular Duopigatron and Direct Recovery of the Charged Beam Fraction, " Proceedings Second Symposium on Ion Sources and Formation of Ion Beams, Berkeley, California, 1975 (LBL-3399, 1974.) 7. R. W. Moir, W. L. Barr, and G. A. Carlson, "Direct Conversion of Plasma Energy to Electricity for Mirror Fusion Reactors," in Proc. Fifth Conf. Plasma Phys. and Controlled Nuclear Fusion Research, Tokyo, Japan, 1974 (IAEA, 1975) _3, P- MM 8. D. J. Bender, W. L. Barr, and R. W. Moir, "Performance Analysis of In-line Direct Converters for Neutral Beam Sources", in Proceedings of Sixth Symposium on Engineer ing Problems of Fusion Research, San Diego, Calif., 1975, also Lawrence Livermore Laboratory, Rept. UCRL-77239 (19751. 9. P. Raimbault, Etude Numerique de Certaines Methodes de Recuperation d'Enerqie dans les Injecteurs'de Neutres, LURATOM Rept. EUR-CEA-FC-780 (1975). 10. P. Raimbault, In-Line Electrostatic Energy Recovery System for Fast Neutral Particle Injectors without Beam Interception, EURAT0M Rept. EUR-CEA-FC-823 (1976). 11. J. H. Fink, W. L. Barr and G. W. Hamilton, A 225-MH Neutral In.iection System for a Mirror Fusion-Fission Hybrid Reactor, Lawrence Livermore Laboratory, Rept. UCRL-76704 (1975). 12. B. C. Hoviard, W. L. Barr and R. w. Moir, DART: A Simulation Code for a Oirect Energy Converter for Fusion-Reactors, Lawrence Livermore Laboratory, Rept. UCRL-51557 (1974). "> 13. W. L. Barr and R. W. Moir, "Direct Conversion for Neutral Beam Injectors", in Proc. 1976 IEEE International Conference on Plasma Science, Austin. Texas (1976). 14. G. A. Carlson and R. W. Moir, "Mirror Machine Reactors", Session V this meeting. REFERENCES 15. See Ref. 7 or R. W. Hoir, and W. L. Barr, Experimental Results on the Two-Stage Venetian Blind Direct Energy Converter, Lawrence Livermore Laboratory, Rept. UCID-16429 (1:1/4). 16. R. W. Moir, W. L. Barr, R. P. Freis, and R. F. Post in Proc. Conf. Plasma Physics and Controlled Nuclear Fusion Research (International Atomic Energy Agency, Vienna, 1971), pp. 315-328. 17. W. L. Barr, 8. C. Howard, and R. W. Moir, Computer Simulation of the Periodic Electrostatic Focusing Converter, Lawrence Livermore Laboratory, Rept. UCRL-51593 (1974). 18. F. B. Marcus and C. J. H. Watson, in Sixth Eur. Conf. Controlled Fusion and Plasma Physics (Moscow, USSR, July-Aug. 1973T1 ' " " ~— 19. B. H. Smith, R. H. Burleigh, W. L. Dexter, and L. I. Reginato, in Proc. Texas Symposium on the Technology of Controlled Thermonuclear Fusion Experiments and The Engineering Aspects of Fusion Reactors Austin, Texas (1972). 20. W. L. Barr and R. W. Moir, Experimental Results on Direct Energy Conversion for Mirror Fusion Reactors, Lawrence Livermore Laboratory, Rept. UCRL-76278 (1974). 21. 0. A. Vinogradova, S. K. Dimitrov, A. M. Zhitlukhin, A. I. Igritskii, V. M. Smirnov, and I. G. Tel'kovskii, Consultants Bureau translation UDC 621.36 .Translated from Atomnaya Energiya, Vol. 33, No. 1, pp. 586-589, July, 1972. 22. W. L. Barr, Direct Energy Recovery from a Beam of Charged Particles using Parabolic Ion Trajectories, Lawrence Livermore Laboratory, Rept. UCRL-51147 (1971). 23. G. H. Miley, "Fusion Energy Conversion", published by American Nuclear Society (1976), p. 113. 24. A. T. Forrester, J. Busnardo-Neto, and J. T. Crow, A Corrugated Mirror-Cyclotron Freguency Direct Conversion System. ReDt. PPG-196, University of California, Los Angeles, (CUMI-CYFER) (1974). 25. H. I. Mirkin and R. J. Briggs, Phys. Fluids 16_, 929 (1973). 26. G. W. Hamilton, A Simple Energy Recovery System Using an Energy-Spread Beam Passed through a Transverse Electric Field, Lawrence Radiation Laboratory Rept. UCrD-15638 (1970). 27. T. H. Batzer, et.al.. Conceptual Design of a Mirror Reactor for a Fusion Engineer ing Research Facility (FERF), Lawrence Livermore Laboratory, Rept. UCRL-51617 (T§74). 28. R. H. Moir, U. L. Barr, and G. H. Miley, J. Nuc. Mater. 53, 86 (1974). 29. G. H. Miley, Voltage Holding Considerations for Direct Collection Units. Lawrence Livermore Laboratory, Rept. UCRL-51482 (1973). 30. R. W. Werner, Lawrence Livermore Laboratory, private communication (1976). 31. R. H. Condit and R. A. Van Konyneburg, Electrical Insulator Reguirements for Mirror Fusion Reactors. Lawrence Livermore Laboratory, Rept. In preparation. NOTICE "•til, fepoel Ma, ntcpated a, MI account ul n-otk .ponvorcd hy the United Suit, Government. Nciinct Ike United Stele, are the United stele, Encipy Rceafcli eY l>c*ehpmcnt AdmHihlralion, nnr any ul IneM employee*, nor any of IheH runt! :clim. uiffconiia.lsir,. m Hwlf employee make, any avatranty. e«nfo tit implied, ••( anunm any tela! liebHily or tcipomimliiy l"t the accuracy, cttfflplcleneu at uteTulncu of en-, tnlafmalmff. apparalui. peoduct of pirn..:,. diKlmed, «e fcpirycOl, that It, uic vti.uld not •nftlnfc prrtelelyowned eifhl."