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CIC-14REPORTCOLLECTION LA=6044-PR ProgressReport REPRODUCTION UC-20 Cmy Issued: Awust 1975

LASL Controlled Thermonuclear Research Program

January —December 1974

Compiled by

F. L. Ribe

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h J ! IosiQ4a Iamos k scientific laboratory of the University of California LOS ALAMOS. NEW MEXICO 87545

4 “b An AffirmativeActian/EqualOpportunityEmplayer

UNITED STATES ENERGY RESEARCH AND DEvELOPMENT ADMINISTRATION CONTRACT W-7405 -ENG. 36 The four most recent reports in this series, unclassified, are LA-4585-MS, LA-4888-PR, LA-5250-PR, and LA-5656-PR. In the interest of prompt distribution, this report was not edited by the Technical Information staff.

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PrintedintheUnitedStatesofAmerica.Availablefrom NationalTechnicalInformationService U.S.DepartmentofCommerce S265 PortRoyalRoad Springfield,VA 22151 Price:PrintedCopy$7.60Microfiche$2.25 .

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. . \ -— ~===%.—- SUMMARY AND INTRODUCTION ,.— .- .— F. L. Ribe and G. A. Sawyer

Since the last Annual Progress Report (LA-5656- In the case of the Scylla I-B and I-C experiments. PR, .July 1974) Scyllac has been rearranged into its detailed studies of the plasma implosion were com- final, complete toroidal configuration with 4-meter pleted and the device has been rebuilt for lower- radius. The equilibrium and m = 1 instability temperature, higher density plasma operation ap- properties of the 4-meter-radius sector were found to propriate to heating and scattering experiments us- be unchanged, i.e., plasma confinement was ter- ing a 1OO-.J, 4 X 1010 W/cm2 C02 laser furnished by minated by the m = 1 instability with a growth rate Group L-1. y = 0.7 MHz at a compression field of 40 kG and an The implcwion-heating experiment (Chapter VII) / = 1,0 wavelength of 33 cm. The full-torus con- has been in operation for some months after I@rat ion allowed the toroidal mode structure of the successfully (wercoming numerous problems of high- m = 1 instability to be measured. It follows the wjltage technology. The data are yieldin~ a consis- theory with a cutoff minimum wavelength of about 4 tent picture of’ the irnplosi(m process. meters. No m = 2 or higher m instabilities were In the ZT-1 diffuse toroidal pinch experiment, ion observed. These results were reported at the 1974 temperatures of 140 eV at c(mfinement times of 10 — IAEA Fusion Conference in Tokyo. psec have heen obtained. Detailed studies of Since the Tok.vo Conference the main attention of magnet ic-i’ield structure show that stahilitv is the Scyllac group has been to closing the gap limited by diffusion of the poloidal and toroidal” between the plasma dynamics of the instabilities fields. A new configuration (ZT-S) with 50”( larger and the current risetime (gain-bandwidth) minor radius and more closelv matched poloidal and characteristic of the feedback circuit (see Chapter III toroidal lield risetimes is being set up to lengthen the below). Bv lengthening the / = 1,0 wavelength to 63 cfmfinement by raising the fielci-diffusi(m times. A cm and decreasing the compression field to 18 kG parameter study of a Z-pinch fusion reactor has been the growth rate has decreased to 0.3 MHz in accord made. wit h theory. The plasma confinement time has been In the realm of plasma diagnostics HF-laser. side- correspondingly increased from 10 to 25 psec. Im- on holography has been successfully applied to provements in the feedback circuit have decreased Scyllac, yielding results of primary importance. In its risetime from 1.5 to 1.1 Ksec and raised its current addition the basic plasma-beta and coupled-cavity capability from 700 to 1100 A. At this writing interferometer measurements have been com- manipulation of the plasma column by programmed puterized with large savings in data-reduction time. currents in / = O feedback coils is proceeding to test Tw(~-dimensional displays of Thompson scattering the theoretical finding that the plasma response will data are being developed. be excessive. i = 2 feedback coils are being elec- The Experimental Plasma Physics group con- trically tested and will probably be used, since they t inued to extend its studies of the electrical resistivi- have the virtue of instantaneous plasma response ty by utilizing the detailed information about the and produce three to four times greater force on the threshold for parametric instabilities or anomalous plasma. With the new plasma characteristics, im- absorption that was obtained by them in previous proved circuit, response and I = 2 coils, we are years. A particularly important demonstration of cautiously optimistic that the next year will see the these precision measurements is this group’s recent purpose of Scyllac accomplished—the production of * observation that intense ac electric fields can plasmas with staged heating and low compression produce a fundamental change in the electron-ion rat ios (b/a z 2.5) appropriate for wall stabilization collision rate. of’the m = 1 mode. Much significant new technology The Theoretical Physics Program has continued of high-voltage, high-charge capability, low- strong programs in magnetohydrodynamic (MHD) inductance spark gaps have been developed for this theory including diffuse plasma and field profiles, experiment. Vlasov analysis of stability properties of plasmas, A capability of conventional, long linear theta and computer modeling of plasmas. pinches is being restwed with the nearing comple- tion of’ the 5-meter Scylla IV-P experiment. Engineering support of the CTR program includes of superconducting wire, high-current interrupters, . mechanical design development of specialized elec- and fabrication of a 300-k.J storage coil. trical components, such as spark gaps, construction Fusion Technology and Reactor Design have con- of new experiments, and engineering support of the tinued in the areas of reactor system studies, ● major confinement devices. neutronics data assessment, and insulator and struc- Magnet ic Energy Transfer and Storage (METS) t ural alloy research and development of conceptual studies are progressing in the areas of development design of a Scyllac Fusion Test Reactor (SFTR).

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2 II. SCYLLAC FULL TORUS EXPERIMENTS

E.L. Cantrell, W. R. Ellis, B.L. Freeman, K.B. Freese, H. W. Harris, F. C. Jahoda, R. Kristal, M.D. Machalek, J. R. McConnell, W. E. Quinn, A.S. Rawcliffe, R. E. Siemon

A. Introduction MHD theory to within -5%. The unstable m = 1 plasma motion follows the predictions of both the The main objective of the Scyllac experiment is to old-ordering6’7 and Freidberg’s generalized theory8 study methods of producing stable high-beta plasma to within 15ri both in absolute value and the equilibria and confinement in a high-beta, relative scaling of the growth rate from the 5- and 8- stellarator, toroidal geometry. The long range goal is m sector experiments. Furthermore, conditions in the development of a toroidal fusion reactor based on both the sectors and the torus satisfied Freidberg’s the theta-pinch principle. Preliminary Scyllac stabilization criterion for m=2 modes. 9 These experimental were performed in 5-m (R=2.4 m) and studies provide no indication of higher order poloidal 8-m (R=4.O m) toroidal sectors to study the plasma mode structure than m =1, supporting experimental- equilibrium and stability and their scaling. The 5-m ly the validity of the finite gyroradius stabilization sector experiments, which demonstrated the ex- criteria. istence of the high-beta, Q= 1,0 toroidal equilibrium, Experimental evidence gives a strong indication were completed in 1972. Conversion to the Scyllac that the unstable plasma motion lies in the plane of full torus with a major radius of 4.0 m began in early the torus. Theory predicts a toroidal mode structure 1973 and was completed, including device checkout, for the m= 1 instability with a cut-off at a minimum in April 1974. wavelength which is dependent on the major radius From April to November 1974, experimental con- and the bending of the magnetic field lines. An finement studiesz on the Scyllac full torus were analysis of the mode structure in Scyllac gives performed without the aid of the planned feedback further credence to the theoretically predicted scal- system. The results on the full torus characterize the ing of the absolute magnitude of the m =1 instability y confined plasma by the following parameters: growth rates. Measurements of the toroidal mode $=0.8; a=l.O cm; n=2.7X1016 cm-3; Te=500 eV; Ti numbers have been made up to 5, and the =0.8 keV; and Iz = 1.3 kA. A toroidal helical plasma measurements reveal the theoretically expected fall- equilibrium is achieved as predicted by them-y.3i4’5 off of the unstable displacement amplitude past The stably confined plasma is terminated after 6 to n =3. Theory also predicts that the maximum un- 8 PS by an m = 1 unstable motion of the column, stable mode number, n, which can exist in the whose pro erties are those of the theoretically Scyllac torus is 6. ? predicted6 S8m = 1 instability y and coincide with the Toroidal currents exhibiting peak values as high observations on the 8-m sector experiment. Streak as 1.3 kA have been observed in the Scyllac dis- photographs give an m = 1 instability growth rate of charges. Currents of this magnitude exceed the 0.7+0.3 MHz and indicate a toroidal mode structure Kruskal-Shafranov limit for Scyllac, but apparently in agreement with theory. Comparison of the do not influence the plasma stability on the measured plasma parameters and magnetic fields available time scales. This conclusion is based on with MI-ID sharp-boundary theory confirm the the experimental observations that the unstable plasma equilibrium and instability growth rate and plasma motion is predominantly planar, whereas their scaling. kink modes would produce plasma motion out of the The plasma exhibits an ini~ial 6 to 8 ps stable plane, and the observed growth rates are a factor of 5 phase during which equilibrium conditions are greater than the predicted values of the Kruskal- achieved. This stable period is consistent with the 8 Shat’ranuv kink-mode growth rates, whereas the to 10 ps plasma behavior observed in the studies per- measured values agree quite well with the formed in the torwidal sectors. 1 The equilibrium theoretical m= 1 growth rate. In addition, no obser- conditions for force balance along the major radius vable difference in the plasma behavior results when in the plane oft he torus follow the predictions of the the net toroidal current is reduced to zero or even

3 reversed by an externally induced counter current. where R is the major radius, a is the plasma radius The major divergence of the observed plasma and @ is the ratio of plasma pressure to the external behavior from theoretical predict ions is in the period magnetic-field pressure. The super-position of the of quiescent equilibrium in the initial stages of the small !2= 1 and Q=0 fields on the main theta-pinch discharge. Sharp-boundary MHD theory of an over- field produces first-order distortions in the plasma compressed toroidally-structured Q=l or Q=O surface of the form plasma predicts the onset of the instability at the in- itiat ion of the discharge. The dispersion relation, 5 r=a[ 1+61cos(0 - hz) - cijcos hz], (2) derived in sharp-boundary theory, and even the generalized treatment of Freidberg8 for where h=2irlA is the common Q = 1 and Q = O overcompressed plasmas, shows that destabilizing wavenumber, z is the toroidal coordinate and 0 is the terms due to the helical and bumpy plasma distor- azimuthal coordinate. Figure II-1 shows a perspec- tions dominate the wall-stabilization term. Accor- tive view of the plasma column in its helically ding to MHD predictions, the plasma should move shifted equilibrium position, together with the right- toward the walls immediately with the e-folding handed coordinate system used. time exhibited in the experiments. This experimen- The plasma column distortions 61 and 80 are t al observation of stable plasma confinement, related to the applied fields by alt bough not completely understood, gives an en- I;(s) couraging indication that high-beta toroidal 2%=1’B0 a ‘M’=o 151=y (3) equilibrium can be achieved and maintained. l+E~ll(E)K;(E) c(l-f3/2)‘ [ 1 The Scyllac full torus experiments, including a brief summary of the theory, the experimental and arrangements, and the results, are presented below. 1; (&) The preparations for the feedback stabilization of ‘k=o’Bo ‘E=o’Bo the m = 1 instability on Scyllac are presented in Sec- C5=y ~ (4) o l+Ef310(&)K:(e) 2(1-!3) tion HI. [ 1 where I and K are the modified Bessel functions B. Summary of Scyllac Theory and c = ha. The applied field ratios, B ~. fi 0 and B =o/Bo,are defined as coefficients in the expression The fundamental idea behind Scyllac is to bend a for the vacuum magnetic field, theta pinch into a toroidal configuration as nearly similar to a linear theta pinch as possible, in order to retain the advantages of the straight geometry, i.e., neutral stability and a proven method of plasma where ~Z is a unit vector in the direction of the minor heating, while eliminating particle end loss. In toroidal axis, and ~ is the vacuum magnetic scalar Scyllac a high-~ toroidal equilibrium is achieved by potential: superimposing a small Q= 1 helical field and a small f!=O axisymmetric bum ~ field on th e main toroidal theta-pinch field, 3.4,5..7 where Q describes the O=(B =1/h) [211(lN)/hl sin(O - hz) + (B =@.) [L(hr)/ h] sin hz + (B./Bo)r sin O + perturbation fields which vary as sine ( Q 0 - hz). (B1,JBJ[11(2hr)/h] sin (0–2hz). This Q= 1,0 configuration has the advantage that to (6) leading order in the helical field quantities the The two small components, B., and B 1,2 (B, is a plasma column is stable to the m= 1 mode, which vertical field, perpendicular to the plasma of the has an exp(im~) dependence. In the theoretical torus, and B1,z is a helical field with twice the sharp-boundary model, the equilibrium is described periodicity of the main Q= 1 field) are required by a constant-pressure plasma contained by currents theoretically, 3 to produce vacuum flux surfaces flowing only on its surface. which are centered on the torus minor axis. Their theoretical amplitude is 1. Equilibrium. In the Scyllac torus the combination of plasma pressure and the gradient of Bv/Bo=B1,2/BO=B Q.IB Q.0/4B20. the main compression field BO results in the outward (7) toroidal drift force per unit length of the plasma The asymmetry in the sum of the impressed column given by plasma excursions 61 and 60 results in the Z- independent equilibrating force FR =flB~/4R, (1)

4 The first term in Eq. (II) is a dipole wall- stabilization term due to the induced J?= 1 plasma currents. However, because of the strong fourth- power dependence on the ratio of plasma radius to wall, a/b, this term is negligible in the present Scyllac experiments. The second term in Eq. (11) represents a weak instability driven by the Q = 1 field and the last term an instability driven by the Q =0 field. The highest unstable mode, which has the minimum toroidal wavelength, is given by the max- imum n value in Eq. (10) for which ~(n} is real. StIt - ting y(n)=O gives

R Fig. II- 1 n .— Y@. max (12) Perspective view of the = 1 helical and =0 (2-f3)1’2 ‘A bumpy, high-b plasma column in the Scyllac toroidal equilibrium configuration. C. Experimental Arrangement. The Scyllac torus has a major radius of 4.0 m and a cir- = h2a3@B~[l+ (1 - 13)IO(C)/I~(E)]&160/8 (8) ‘1,0 cumference of 25.13 m. The compression coil, whose inner surface is shaped to generate the Q = 1 helical and Q=() bumpy equilibrium fields, has an average Equating the outward toroidal force F, to the Fl,o bore of 14.2 cm. The toroidal quartz discharge tube force gives the toroidal equilibrium condition, has an inside diameter of 88 mm. The primary energy storage system consists of a 1O.5-MJ fi160=2/h2aR [1+(1 - /3)Io(t)fI’l (c)] = 2/(3 - 2i3)h2aR. capacitor bank of 3,150 1.85-~F, 60-kV capacitors. (9) The energy storage system and the compression coil The amplitudes of the Q = 1,0 equilibrium fields, are divided into 15 independent sections termed BQ=lB,~ and BQ=o/B[,, are determined by this racks. The fifteen energy. storage racks are equilibrium relation. Figure II-2 shows graphs of the symmetrically arranged around the central torus Fl,o/FR force ratio, from Eqs. (8) and ( 1), as a func- and are tangent to the walls of the experimental area tion of the plasma (3 for various plasma radii. at four points. A three-level platform structure fills the central core of the torus. The upper or coil level is 2. Stability. Although MHD theory shows that situated 7.6 m above the basement floor and 1.3 m the leading order m = 1 destabilizing term vanishes below the horizontal plane of the torus. A for the !2= 1,0 equilibrium system, higher order photograph of the torus is shown in Fig. 11-3. terms indicate the plasma column is unstable to dis- Each rack of the Scyllac energy storage system placements of the form ~(n) =~o exp i(mfl-nzfR).5 feeds a single collector plate assembly which in turn The instability growth rate -y(n) is given by4 feeds a 1.67-m arc-length of the toroidal compression coil termed a coil-sector. Each of the fifteen collector ~2(n) = 72(0) – v~ (2–@)n2/R2, - (lo) plates are cabled with 1,260 coaxial load cables from the 210 capacitor-spark gap units of the main bank . Alfven speed, and the growth rate -y(o) of the fun- in one rack and with 24 cables from the two 0.7-~F damental mode is given by4’8 capacitors of the preionization bank. Figure H-4 shows a plan view of the torus with its collector plate current feeds and the various diagnostic viewing 4 slots in the coil-sectors. y2(o)=h2v: -62: 62 + 6(4-3f3)(2-6) ~2a262 1 8(1-0) 1 [() 1. Parameters of the Scyllac Torus. ,The + 6(3-2!3)(1-8) electrical and mechanical parameters of the Scyllac (2-(3) (11) full torus are listed in Table I. These are discussed further in Section XI. fjO- -& I;(@Io’(f=) 1+(1-/3)10(d/I; (d l/{l+@Il k) K;(G)]~/{l+eBIo(e)K~(c)] ‘Z= OBZ=I [ FR a 1[ 1 602 I

%4=%=0~=0.064; h=O.15 cm-’ 1.2- B.

1.0-- a= 1.0 I < 0.8- - 0_. L 0.6- -

0.4-

1 1 I I I I 1 I ! I ! I 1 { 0.6 0.65 0.7 0.75 0.8 0.85 0.9

P

Fig. II-2 Rotio of the FI,o equilibrium force to the outward toroidal force FRas a function of the plasma d for ~Ym-iousplasma radii a and the indicated Scyllac parameters.

2. Scyllac Control and Monitor Systems. The designed by calculating the shape of the magnetic Scyllac control system includes the monitoring of flux surfaces for the required vacuum fields given by the various bank voltages during the charge phase by Eqs. (5) and (6). Figure 11-5 shows plots of the flux the Scyllac computer which has an abort control surfaces at four z positions: hz=O, center of a land over the overall system. region where B,, is a maximum; hz=~/2, between a A spark-gap monitor system based on magnetic land and groove region; hz=~, center of a groove probes is used to monitor the firing times of the main region where BZ is a minimum; and hz=3x/2, bank start gaps, the crowbar trigger gaps, and the between a groove and land region. The annular crowbar’ gaps. This function assists in the cross-hatched areas of Fig. II-5 indicate the location maintenance and trouble-shooting of the 6800 spark of the quartz discharge tube. The outer flux surfaces gap switches in the Scyllac energy storage system. give the coil-bore cross sections at the indicated Z posit ions. 3. Q= 1,0 Toroidal Equilibrium Fields. The Figure 11-5 shows that the inner flux surfaces are experiments on the 8-m toroidal sector resulted in a circular in cross section and as a set are centered choice of 41.9 cm for the Q= 1 and J?=0 wavelength about the minor axis of the torus. The helical shift of and equilibrium plasma column excursions of the flux surfaces about the minor axis is produced by 61=0.71 and 6.= 0.21 for the full torus. The the Q= 1 field. Magnetic probe results obtained on magnitudes of the Q= 1 helical and the Q=0 bumpy the toroidal minor axis in the shaped compression fields were determined through the toroidal coil show that the Q= 1 and Q=O fields are in agree- equilibrium condition, Eq. (9), and the expressions ment with the design values. for the plasma distortions, Eqs. (3) and (4), to be: (B Q. IfBo) = (BQ=o/B,, = 0.064 and (BJB,,) = 5. Toroidal Discharge Tube and Pump-Out B1.fi.) = 0.001024. Ports. The discharge tube for the 8-m diameter torus consisted of 10 quartz tube sections, each with 4.Q= 1,0 Shaped Compression Coil. The an arc length of 2.5 m. These quartz sections were compression coil, whose inner surface was shaped to joined by O-ring seals to short ceramic sections of generate the Q= 1 and Q=0 equilibrium fields, was 99°; alumina, which had an oval shaped pump-out

6 TABLE II-I design of the pump-out ports was to achieve suf- ficient pumping speed while minimizing pertur- SCYLLACFULL TORUS PARAMETERS bations in the magnetic field and in the initial plasma sheath formation. PARAMETER VALUE The ceramic pump-out stubs terminated ina9-cm . PreionizationBank diameter cera”mic tube after partial penetration Bank capacitance 21 lJF through the compression coil wall. The cylindrical Bank operatingvoltage 50 kV ceramic tubes, which had a metal valve near the center of their l-m length, provided appropriate Bank energystorage 26 k.1 voltage insulation. These tubes connected into a Ringingfrequency 400 kaz common toroidal manifold below the torus. Peak current 2.4 NA 6. Magnetic Field Variations Between Coil- Maximummagneticfield 1.2 kG Rack Sections. In the toroidal geometry, it is important that the plasma have the same properties PrimaryBank Bank capacitance 5828 PF all around the torus, other than for variations within Q=l,O wavelengths, in order to satisfy the re- Bank voltage 60 kV quirements for toroidal plasma equilibrium. Since Bank energystorage 10.5 FIJ the parameters ofthe plasma are dependent onboth Normaloperating 40-55 kV the implosion and compression phases of the dis- voltagerange charge, there has been concern about possible variations in the magnitude and waveforms of the Major radius 4.0 m magnetic field between coil sections. Torus circumference 25.13m The Scyllac energy storage systemis divided into Averagecoil bore radius 7.1 cm fifteen capacitor racks. As mentioned above, each rack feeds asingle collector-plate assembly whichin Dischargetube wall radius4.4 cm turn drivesa 1.67-m arc length ofthe 25-m compres- Sourceinductance 0.17 nH sion coil. The racks are independent of each other Coil inductance 0.80 nH except for conducting ties near the compression coil which have relatively high inductance and a com- Transferefficiency 0.82 mon trigger source. Bank voltage variations were Rise time 3.6 ~S largely eliminated by connecting the charging supp- ly systems together through 2-kfl resistors to give an L/R decay time 250 US RC time of 0.4 s between adjacent capacitor racks. Peak current 110 MA Field variations of -0.5% can result from 50kV) (at variations in the resistance of the liquid resistors Maximummagneticfield 55 kG used to isolate various sections of the capacitor (at 50 kV) bank. Variations in the crowbar trigger system and Azimuthalelectric 0.57 kV/cm in the crowbar spark gaps can also produce signifi- field (at 4.4 cm and cant differences in the magnetic field during the 50 kV) crowbarred phase of the discharge.

L=l,Owavelength 41.89 cm 7. Magnetic Field Measurements. Magnetic -1 field measurements were made around the torus to 1=1,0wavenumber 0.15 cm determine if significant field variations existed from No. of !L=l,Owavelengths 60 coil-sector to coil-sector. This was accomplished after the power supplies were connected together as B~=l/Bo=Bg=O/Bo 0.064 described above. Bv/Bo=Bl2/B. 0.001024 Measurements were made with a standard B ~ s probe, RC integrator, and oscilloscope. The standard probe was moved from coil-sector to coil-sector while stub extending downward through the compression fixed probes were maintained to record shot-to-shot coil as shown in Fig. II-6. The wall ofthe cylindrical variations. To assure reproducibility, the output of portion of the ceramic section was semi-continuous, the standard probe versus penetration depth into the being perforated with 10, 5-mm diameter holes coil was investigated. It was found the probe could above the pump-out stub. The objective in the

7 .

“

Fig. II-3 Photograph of the Scyllac full torus.

8 1

\ 2

I O“N \T Feedback pxition’ Y “O. detector slots(D) M o:. ‘ \F MF’O ‘o 14 o“~ M TT/Y -Y ,0 >0 Compression coil ,0 I 0<”” \ Mognetic P o \ probe slots(M) K---- \T % n I ‘C%%’S’”’S-51

u- ... ,F I o 05 0. +M 0; .D F12 Y‘

Fig. II-4 Plan vieio of the Scyllac torus showing the various diagnostic viewing slots, the vacuum pump-out ports and the collector plate current feeds.

be moved 6.5 mm with no measurable change in the The probe was positioned in one coil for 21 shots to . groove regions in which measurements were made. obtain data on shot-to-shot variations resulting in Position was easily maintained within 2 mm for all + Ici at peak field and +2% at 7 KS. The ratio of measurements. fields for each coil at peak field and at crowbar time . Comparative measurements of B, were made at should be the same for all coils, but it ranges from peak field and also in the crowbarred phase, 3.6 gs 0.77 to 0.84. The magnitude of the variations and 7 gs respectively, after firing the main bank. between coil-sectors, at peak field, with the power The results are shown in Fig. II-7 as a plot of [B. – supplies connected together and with relatively large (BJ~.1/)BA~, as a function of coil-sector number. induct ive ties between collector plates, suggests that The variations at peak field time are larger than ex- in the coil-sectors with lower fields a fraction of the pected and are observed to further increase during crowbar gaps are firing early andlor some of the start the crowbarred phase. gaps are not triggering. The largest variations during .

Y w

x

t — t hz=O( Land) hz=_m/2

~Y

hz = T (Groove) L

Fig. II-5 Plots of the vacuum magnetic flux surfaces generated by the shaped inner surface of the com- pression coil at four toroidal z positions. The annular cross-hatched areas indicated the dis- charge tube.

10 pression coil, which allowed an area of approximate- ly 320 cm2 between collector plates for coupling of the driven-I. flux around the plasma column.

9. Plasma Diagnostic Apparatus. Figure II-4 shows a plan view of the torus with its various diagnostic viewing slots. The following measurements are being used to study the high-~ toroidal plasma: (a) As many as seven high-speed streak cameras are used to record the transverse motions of the plasma column at various locations around the torus; (b) A coupled-cavity He-Ne laser interferometer is used to measure the time-history of the plasma electron density integrated along a chord of the plasma cross section. This diagnostic, which has a fully automated data acquisition system, is also used routinely for determining preionization discharge tube levels during machine operation; (c) A ten-channel luminosity experiment provides self-luminous profiles of the plasma column. These luminosity Ceramic pump-out tube profiles give the plasma radius and, in conjunction with the coupled-cavity interferometer data, give absolute density profiles; (d) A balanced magnetic I loop and probe arrangement measures the magnetic To vacuum manifald flux excluded by the plasma column. Combined with the relative density profiles from the luminosity Fig. II-6 measurement, the excluded flux can be expressed in Perspective view of the discharge tube and terms of the plasma 8; (e) Scintillation and silver- vacuum pump-out port in the Scyllac compres- foil activation counters measure the neutron sion coil. emissions; and (f) Thomson scattering of laser light the crow-barred phase occurred in the older is used to determine the plasma electron capacitor racks (which have many more discharges temperature with a unique three-grating on the gaps), indicating those gaps might be firing polvchrometer. improperly due to wear. Data were not taken in coil- Additional new diagnostics on the full torus in- sectors 7 and 14 as excluded flux measurements were clude: “(a) A side-on holographic interferometer gives being made there. spatially and time resolved absolute plasma electron density profiles. Radiation at 2.87 pm from a 8. Driven Iz-Current Arrangement. Two hydrogen-fluoride laser is used as the interferometer different arrangements have been used to induce an light source in order to maximize sensitivity with a 1, current in the plasma column: (a) a single-turn wavelength transmittable through the quartz dis- loop around the inner face of the compression coil charge tube; (b) Net toroidal currents are measured (-24-m circumference) was driven by a 14-I.LF, 10-kV with an 81 -turn Rogowski coil mounted around the capacitor to induce a plasma current of -1.5 kA with quartz tube inside the theta-pinch compression coil. . a risetime of 15 WS;and (b) a fast-rising IdT/4-2 As) An extraneous component of B, pickup is nulled-out was produced by breaking the single-turn loop into in vacuum using a differencing circuit of the exclud- five sections and driving these in a parallel arrange- ed flux, loop-probe type and a small B, probe; and (c) A fast, 360° optical system on the torus main axis 9 ment with a 1.85-#F, 60-kV capacitor. The fast 1. had a variable amplitude of 1 to 2 kA. Effective images eleven top coil slits in grooves, almost un- coupling of the IZ flux to the toroidal plasma column iformly distributed around the torus, onto a single required the removal of electrical conducting ties image-converter framing camera. This arrangement between collector plates near the compression coil. provides a determination, at one instant in time, of New conducting ties were installed between collector the toroidal mode structure of gross plasma column plates approximately one meter back from the com- displacement away from the discharge tube axis.

11 tI . - t Bz (Bz)av vs coil-sector (Bz)ov Bz number “ 0.10 I At peak field (3.6Ps)- 0.08 0246810 ----- At 7.0PS f (/As) 0.06 ~--= No Data ?and 14 - i I ‘- -- I I 1 0.04 – [--; 1 I FI > 1I I‘i’L,-- I I 0 I I r--- . I > 0.02 ---~ : I I mN 0 -N I m 0 1- L J 1 — ; ‘- I I -. I I -0.02 “ L --- -- 3 : -0.04 – u ;y I I -0.06 – L1~-- I I 1I — -0.08 - I L;-. -0.10 ‘ 1234567891011 12131415 Coil-Sector Number

Fig. II- 7 [;raph.s oj magnetic field variations around the torus as a function of coil-sector number at peak field time (3.6 PS) and during the crowbar phase (7.0 PS).

D. Plasma Measurements and Parameters. TABLE ~1-2 The plasma parameters in the Scyllac full torus experiment with the bank operating at 40 kV (B,,x40 PULL-TORUSPLASMAPARAMETERS kG) are summarized in Table H-2. Radius (a) -1.0 cm The plasma radius was determined from the luminosity profiles (cf. section E2) and confirmed Beta (f3) -0.8 by absolute profile measurements in the groove Density(n) 2.5-2.8x1016cm-’ regions with the side-on, HF-laser, holographic in- Temperature(T) 1,2-1.4keV . terferometer (cf. Sections II-F-5 and IX-B- 1). The plasma beta on axis was determined from the com- Te 0.5-0.6keV bined excluded flux and luminosity profile 0.7-0.8keV measurements (cf. Section II-E-2). The plasma ‘i ● Neutronemissions -lo51cm density was derived independently from (a) the coupled-cavity interferometer measurements (cf. 61 -0.71 Sec. IX-C-3) and (b) the side-on HF interferometer 6 ‘0.16 measurements (cf. Sections II-F-5 and IX-B-1 ). The 0 1= 1.0-1.5M total plasma temperature (T= Te+Ti) was calculated from pressure balance using the plasma Y(o) ().7* 0.3 ~~ beta, density, and magnetic field measurements.

12 The electron temperature was determined from 90° such data sets have been analyzed, and they reveal . Thomson scattering (cf. Section H-F-3) and the ion the following general characteristics: (a) there is lit- temperature is inferred from Ti =T - Te. The neutron tle or no systematic difference between equivalent emissions were measured by the Ag activation positions on opposite sides of the torus; (b) land counters. positions and groove positions on opposite sides of . The 61 and 60 values in the table were calculated the torus are equally reproducible in this regard, from Eqs. (3) and (4) using measured values of~ and within experimental error; (c) land data differs from a, and design values of B Q. l/BO and B Q.fi O(Table groove data in significant and characteristic ways, H-1 ). The luminosity profile data, by contrast, these differences being much larger than either shot- provided a direct measurement of 80: 6.= (a C-a L)/ to-shot variations in a given location, or opposite (~+aL)~ ().22 (see Fig. 11-9). effects in a given location. Data from racks 7 and 14, The axial current Iz was measured by the such as represented in Fig. II-9, have therefore been Rogowski loop (cf. Section II-F-4). Them= 1 growth used with confidence to analyze the characteristics rate was determined by fitting an exponential curve of the plasma equilibrium in the Scyllac full torus. to the plasma column trajectories from the streak Further discussion of these parameters is given in photographs. Sec. II-E-2.

1. Plasma Beta Measurements. Measurements 2. HF Interferometry of the plasma “beta parameters” (excluded flux and external magnetic field from the loop-probe system a. A4casurernents. A technique has been and plasma radius from the luminosity apparatus) developed for side-on holographic inter ferometry of have been made, and these data have been com- Scyllac at 2.9-pm wavelength using an HF laser. The bined to yield the plasma beta on axisl as a function method is described in Section IX-B. The of time in the Scyllac ftdl torus experiments. In order background or reference fringe pattern is arranged to compare measurements with theory, the beta with straight fringes perpendicular to the plasma parameters should be measured in both land and column with the laser beam passing through the groove positions (axial positions of maximum and plasma perpendicular to the plane of the torus. minimum magnetic field, respectively, cf. Fig. H-l). A typical data interferogram is shown in Fig. 11-10. In contrast to the sector- experiments, however, The several fringes shown provide a redundant which required measurements to be made essentially measurement of the electron density profile. This in one restricted place, namely near the center of the results from the fact that the viewing slit in the com- sector, in the full torus there were 60 nominally iden- pression coil ( 1.5-cm width) is only a small fraction t ical Q = 1,0 wavelengths available for study. In (4”;) of the Q=1,0 wavelength (41.9 cm), and the order for plasma measurements at one or two variation in plasma position and profile is therefore locations to be valid for “global” equilibrium studies negligible across the slit width. Averaging the involving the entire plasma ring, it was necessary to nominally identical fringes together helps to im- establish that land positions around the torus were prove the fringe resolution. indistinguishable from one another, and similarly for An analysis of the fringe data vs position is also grooves. shown in Fig. 11-10. The solid line, labeled “data”, is In order to test this hypothesis, simultaneous a free-hand average of several fringes. The peak measurements of the beta parameters were made on fringe shift is -0.8, corresponding to a particle area roughly diametrically-opposite sides of the torus, in density of 6X 1016 cm’2 and a peak number density racks 7 and 14 (see Fig. H-4). Typical results for the on axis of 3X1016 cm–3. “raw data” are shown in Fig. II-8, all obtained in this For comparison a Gaussian profile is also shown, . case from a groove in rack 7. Data from four with the same peak and I/e point as the data curve. nominally identical discharges (12-15 mtorr DZ The data appear to be somewhat less diffuse than filling pressure and 40-kV charging voltage) taken Gaussian, although the Gaussian fit is everywhere ● close together in time have been superimposed in better than 0.1 fringe. In either case, the plasma Fig. H-8 to. illustrate normal shot-to-shot data radius (l/e point) is about 1 cm (at 3.1 KS in a groove scatter. The reproducibility of the data is seen to be region). A comparison of plasma radius determined good, allowing meaningful coverages to be obtained. from holographic profiles (e.g., Fig. II-10) and from Figure II-9 compares average data curves derived in conventional luminosity profiles (e.g., Fig. II-9) has this fashion from land and groove positions in racks 7 been made. Agreement in I/e point obtained by the and 14. Data curves derived from Fig. H-8 appear in two methods (at the time of the holographic ex- Fig. II-9 as the solid curves labeled “G”. A series of posure) is better than 5’%o.

13 50 I00 r . 40 “ ~: 80 30 - w 20 -

10 - ;- 8 o I I I I J ) 246810 Time (p) Time (ps)

) [ Rack 7-groove data I 2.5 ~ 2.0 ~ 1.5 F .: 1.0

g o~ (jo- 0246810 (L 10 Time(ps) Time(ps)

“Fig. II-8 observed time variations of the magnetic field, excluded magnetic flux, plasma radius from luminosity profiles, and computed plasma B on axis in a groove region of coil-sector No. 7.

For the analysis of the luminosity data, a Gaus- If we assume a plasma density n which is uniform in sian profile is nearly always assumed. Inversion to z and a plasma radius given by ~=a( 1–60 cos hz) radial coordinates then yields a Gaussian of the [Eq. (2)1, the average line density N over a complete same radius. Figure 11-11 shows the result of fitting wavelength should be both a Gaussian and a 9= 1 rigid-rotor profile to the Abel-inverted side-on inter ferometry data. It ~=n7ra2(l+6{/2) (13) appears that a high-/3 rigid-rotor profile is a better fit to the data than a Gaussian for the conditions of this whereas the line density NG in a groove should be discharge (Groove Region, 3.1 ps). No data were ob- tained in a land position due to the lack of an ap- NG=nTa2 (1+ 60)2. (14) propriate viewing window (see Section IX-B). Equating ~ to w~b2 where no is the atom filling . b. Line Density Analysis. The plasma line density and b is the tube radius, gives, density results from integrating over the density profile. Comparison of the side-on interferometry NG =~rb2(l+ 60)2/( l+r52~2). (15) data with the initial deuterium filling density in- . dicates that most of the plasma resides in a groove Using the luminosity-measured 60 of 0.22 and a region. This observation is supported by the filling pressure of 15 mtorr (no= 1.1x1015 cm–3), Eq. “enhanced” 60 measurements derived from the (15) gives NG=9.7 X 1016cm-*, vs the measured luminosity radius (cf. Sec. II-D). The measured line value of -1.2x 1017cm–1 from Fig. II-10. Thus the density from the data curve in Fig. II-10, for exam- observed line density in a groove is -259’0 larger than ple, is - 1.2x 1017cm – 1. The expected line density a uniform plasma density would imply. A 25’% excess can also be computed from the known filling density. of particles in a groove would imply a -6070 deficit

14 lool-

IL g’OLl_LIJ— I I [ I J Eio2 8 10 00 2 4 6 8 IO +ime &s) Time (p)

2.5 4 lScyllac AT-40 seriesl ~ 2.0 g 1.5

g J——_LiJ oo~o n 0246810 u Time (p) Time(p)

Fig. II-9 observed time variations of the magnetic field, excluded magnetic flux, plasma radius from luminosity profiles, and computed plasma /3 on axis in groove and land regions of coil-sector Nos. 7 and 14. of particles in a land due to the ratio of areas, the scattered signal, and fluctuations in the (1+6.)2/(1–60)2 , corresponding to a density luminosity were the limiting noise sources in the ex- differential of a factor of -3. As mentioned above. no periment. Seven channels recorded the intensity of line density measurements in a land position were the Thomson-scattered laser light. The spectral made. If such a large density gradient does exist, it width of each channel was made progressively wider could create transient longitudinal particle flows as the separation from the incident wavelength in- possibly affecting both the plasma equilibrium and creased. The fitting of the data to a Gaussian, taking stability. In fact the comparison of the plasma @ into account the spectral widths of the detector data with theory (Section II-E-2) indicates that an channels and corrections for relativistic effects, gave axial pressure readjustment occurs between land plasma electron temperatures in the range of 500 to - and groove regions, which corresponds to a net 600 eV, with T, having the same value in land ~d. transfer of energy density from grooves to lands dur- groove positions within experimental err! rl’ ing the first few microseconds of the discharge. Measurements were made at the time of peak field.

3. Electron Temperature. The electron 4. Integrated Neutron Measurements. Fifteen temperature was measured by Thomson scattering LASL Ag act ivat ion detectors 11 were installed on using a special polychrometer to reject stray light. 10 the Scyllac torus and calibrated with a known A 1O-J, 30-ns Q-switched ruby laser beam was pass- source, PuBe (2.23X 106n/see), in situ . These ed side-on through the 8-mm-diameter quartz dis- detect ors use Victoreen 1B85 Thyrode counter t ubes charge tube without special entrance and exit ports for the active element in the electronic circuit. and focused at the center of the plasma column. The Integrated neutron-yield information was ob- plasma luminosity was comparable in intensity to tained for each of the fifteen Scyllac coil-sectors on

i ,5 .

u

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. ●

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(N I

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.

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.

17 . each discharge. An average of 1.33x107 neutrons per detector was measured in a series of thirty-five 40-kV . discharges. It is estimated that each detector observ- A.emgeneutron ytekt 24 x107 ed approximately one meter of the plasma column, II .ersusc.31. sector mjtier -1 implying a neutron yield of -1.3x 105 n/cm. Even k ?2 though the various detectors around the torus had different relative locations with respect to lands and 20 - grooves, no differences in neutron yield due to this g .9 18 - geometric effect were observed, probably due to the > relatively long length of plasma column being z . 16 - observed. Average results from three different series 5 of discharges, thirty-five discharges at bank voltage s 14 – of 40 kV, eight discharges at 45 kV, and eight dis- charges at 40 kV after the 45-kV series, are displayed 12 – in Fig. 11-12. In all three series, coil-sectors 5 and 3 lo- were consistently the highest neutron-producing racks. On the average, coil-sectors 11 through 15 08 – produced lower yields than coil-sectors 1 t hmugh 10. 0,6 X,c170~ In the 45-kV series, the smallest variation in yield around the toru< was observed. Coil - Sectw Number

E. Plasma Equilibrium and Stability Fig. II- 1.2 A l’eragc neutron yields from Ag act iuat ion In the experiments on the full torus the Q= 1 and COUIIt ens around the torus for the indicated Q = O equilibrium fields were generated by shaping bank voltages as a function of toroidal position the inner surface of the compression coil. The or coil-sector. plasma equilibrium was achieved by adjusting the initial deuterium filling pressure to give a balance ed m = 1 motions appear to have a tor(jidal mode between the Fl,o force [Eq. (8)] and the outward structure, i.e., a Fourier decomposition into various toroidal force FR[ Eq. (1) ] through their fl wavelengths (k > O) around the torus. dependence, as shown in Fig. II-2. With the main The streak photographs of Fig. 11-15 show energy-storage bank operating at 40 kV [B,,=40 kG 1, variations in the terminating m = 1 motion of the the plasma equilibrium was achieved with a plasma column. Discharge 2224 shows the plasma deuterium filling pressure in the range of 9 to 14 going outward in the plane of the torus at various cir- mtorr. It was observed experimentally that the force cumferential locations, while discharge 22!26 shows ratio F1,o/FR decreases with increasing filling the column going out ward in two regions ( 1410 and pressure in the range of 8 to 100 mtorr. Since F l,,@R 174°) and inward at another (273°). Such streak increases with @ (Fig. II-2), this implies that @ camera observations suggest that the m = 1 plasma decreases with increasing pressure over this range. motion has a toroidal mode structure. The streak photographs show that when the 1. Transverse Plasma Motions. The streak plasma beta is approximately that required for photographs of Fig. II-13 show transverse plasma equilibrium, i.e., when the plasma column is in ap- motions in the full torus. The top views show the proximate equilibrium, the terminating m= 1 mo- plasma motions in the plane of the torus in two tion usually carries the plasma to the inside wall at . groove regions as indicated. The front views show the some locations and to the outside wall at others. motion in the vertical plane between land and This plasma behavior indicates that m= 1 instabili- groove regions. Figure 11-14 compares streak ty, which is predicted by MHD theory, is occurring . photographs taken in the full torus with those of the and terminating the discharge rather than a loss of 8-m sector. In both the sector and the full torus, the equilibrium. When the plasma B is slightly below plasma forms a well defined column, comes into an that required for equilibrium, the plasma strikes the equilibrium position, and the stable confinement is outer wall at many points and if the /3 is too high for terminated by an m = 1 sideward motion of the equilibrium the plasma hits the inner wall at many column to the wall. The terminating motion general- points. ly occurs in the horizontal plane of the torus. The The streak photographs in the full torus show general plasma behavior is similar to the behavior in that: (a) The plasma forms a well defined column previous sector experiments except that the observ- and comes into a helical equilibrium position; (b)

18 1268

Top (55.5°) Groove

Front (270°) ,

Top (307. 5°1 Groove

mTorr Bz= 40 kG PD = 9.0 2

Fig. II- 13 Strcah photographs of the full-torus plasma, showing the plasma motion in the plane of the torus (upper and lower photographs) and perpendicular to the toroidal plane at the indicated toroidal angle.

19 . 7 .

1?

3. ml —

J .

b

20 r’OPsT r’07 Top (141°) Groove mm

Top (174°) Land

Top (273°) Groove

= [1.4 mTorr; BO=40kG; = 11.8 mTorr . ‘D2 ‘D2 2224 2226 d

Fig. II- 15 Streak photographs comparing plasma motions in the plane of the torus at the indicated toroidal locations on two separate discharges (2224 and 2226).

21 The stable confined plasma period of 6 to 8 ps is ter- The measured field ratio, (B G/BL) 2~~~~, is seen 10 minated by an m = 1 sideward motion of the column; agree with the vacuum design value, (c) The m= 1 motion is predominantly in the plane (BG/BL)~esim(VAC), within a few Percent. The ex- of the torus; (d) The plasma observations indicate perimental beta ratio is also close to the magnetic that the m = 1 motion has a toroidal mode structure; field ratio for times greater than 4-6 ps, indicating (e) The plasma confinement times are 6 to 10 ps; and that 4 -6 AS is the time required for axial pressure (f’) Assuming the m= 1 motion is an instability, the readjustment to take place. The direction of change fit t ing of an exponential to the m= 1 trajectories give in both the 8-m sector experiment and the full torus an experimental growth rate of 0.7+0.3 MHz, in is to increase beta in a land relative to beta in a agreement with the predictions of MHD sharp- groove during the period of pressure readjustment. boundary theory [Eq. ( 11) gives ~(o) =0.705MHz]. The average plasma betas measured in the various toroidal sectors and full torus experiments can be 2. Comparison of the Q=1,0 Plasma compared in a different way with the theoretical Equilibrium with Theory. In addition to the use of values required for toroidal equilibrium. Using the streak photographs, plasma equilibrium and force expressions for the plasma excursions 6I and 60 [Eqs. balance have been studied parametrically in the full (3) and (4)1, in the f! = 1,0 equilibrium relation [Eq. torus by means of the measured plasma beta, (9) ] gives a relationship between the Q = 1,0 plasma radius, and external magnetic field as dis- wavenumber, the torus major radius, the cussed in Sec. II-D-1. Typical time variations of equilibrium fields, and the plasma beta, as these parameters have been plotted in Fig. II-9. In order to compare experimental measurements in ~ ‘I=lBL=O . 2(2-6)(l-B) (18) lands and grooves to the predictions of sharp- (3-26) boundary theory, it is convenient to define the B: average, or unperturbed, measured radius as or

-%+’G (16) mess 2 .—1 S_hR‘E=lBE=O 2 B: where aL and ac are themselves averages over I several nominally identical discharges in lands and grooves, respectively. This quantity is plotted as the 112 _ ~R ‘L=lBI=O + ~ top set of curves in Fig. 11-16 for both the 8-m sector (19) and full-torus experiments. The error bars give the B2 ‘[ o standard deviation from the mean due to shot-to- 1[ shot data scatter. This relationship is plotted in Fig. H-17. The solid The middle set of curves in Fig. H-16 relate to the curve gives the theoretical value of the plasma f? re- toroidal, or horizontal-plane, force balance. Accor- quired for toroidal equilibrium as a function of the ding to sharp-boundary theory (see, e.g., Fig. II-l), quantity hR B Q.1 BQ .o/13\. In this approximation for each value of the plasma radius a there cor- the equilibrium beta value is independent of plasma responds a unique value of beta for which FR = F 1,0. radius. The theoretical beta curve in Fig. 11-16 is derived With the equilibrium fields generated by the assuming FR =F1,o and a= mess from the shaped inner surface of the compression coil, the experiment. The actual measured beta curve, shown quantity hR Bg.1 B Q.o/B”% is fixed for a given for comparison, is labeled <$> ~ea., and is defined experiment as indicated by the vertical dashed lines analogous to Eq. (16). of Fig. II-17. The experimental points for the average The lower set of curves in Fig. II-16 refers to axial measured plasma beta are plotted together with pressure equilibrium along the plasma column. The error bars to indicate the observed shot-to-shot condition that nkT be independent of axial position spread (note the suppressed zero). It can be seen leads to the requirement that that theory and experiment agree quite well for all three basic Scyllac configurations studied to date. These results confirm quantitatively that the $L BG 2 —. same basic type of Q =1,0 equilibrium has been (17) successfully achieved in the closed torus as was ‘G ~“ () earlier achieved in the open-ended toroidal sector

22 8-m sector Full Torus . I 1 1 I I ! I 1.6– g . ~ 1.2— .- U !: ; S-40: f 0.8– al’ 0 m 0 0 A & (0 .,O,= %+% S!0.4— ~ 0.4 – 2 al I

I I I I I T I I

~r$ oo~ * !

Time (/Ls)

Fig. II-16 Graphs of measured and theoretical parameters as functions of time describing the Scyllac plasma equilibrium in the 8-m sector and full torus experiments. Data points are averaged over four or more discharges.

devices. The Q = 1,0 plasma equilibrium and its field. The direction of the toroidal current is opposite scaling have been verified according to sharp boun- to the main field and can be interpreted as resulting dary theory, and the equilibrium plasma and from changes in the magnetic flux of the main field magnetic field parameters agree with sharp boun- which link the helical plasma column. . dary theoretical predictions to within 10%. The IZ current exceeds the Kruskal-Shafranov limiting current of approximately 500 A for 40 kG 3. Toroidal I. Current. A net toroidal plasma and one-cm radius, indicating instability to current- current of 1-1.5 kA peak amplitude has been driven kink modes. However the streak photographs 4 measured in the Scyllac torus by means of a nulled show little evidence of plasma motion out of the Rogoswki coil (cf. Section II-C-8) mounted around toroidal plane and the theoretical growth rate is 0.1 the discharge tube in a groove region. The lower os- to 0.2 MHz which is smaller than the observed m = 1 cilloscope trace of Fig. II-18 (1796) shows the growth rate [y(o) =0.7+ 0.3 MHz]. waveform of the IZ displayed with the main toroidal Similar 1, currents were observed previously in the field (upper trace). The current rises in two stages, plasma experiments with Q = 1 fields in the linear -50% in the first few hundred ns during the plasma 3-m Scylla IV-3 device when electrodes were placed implosion phase, and the remainder in the following at the ends of the discharge tube and a current -3.5 gs during the risetime of the main compression return was connected externally. 12. With a linear Q

23 1.0 .

8-m Sector . -,5-m’Sector 0.9 I

() ~R B~=l B#=()= 2 (2-/3) (1-~) ( 0.8 (3-2/3) FulI Torus ~ Q I I

0.7 I I I

0.6

“1 I 0.5 : 1 1 # , I 1 1 t 1 1 I , 1 d 0 0.1 02 0.3 0.4 0.5 0.6 c1? hR B2=I B#=0\Bo2

Fig. II-1 7 Comparison of the measured plasma beta required experimentally for toroidal plasma equilibrium (experimental points) with that predicted by sharp-boundary theory (solid line).

= 1 shaped compression coil (Bg.@~ = 0.11), the 1, the amplitude of the net axial current remained ap- current was - 1 kA with a risetime comparable to proximately constant during the rise of the main the main B. field and in a direction opposite to that magnetic field. These results with the applied slow I Z of the B. field, as in the present torus experiments. indicate a tendency for the plasma to carry a cons- With driven ! = 1 windings in Scylla IV-3 tant current. A fast rising IZ(T/4-2. PS) was induced in the (BQ .,/Bo %0.067), Iz was smaller (-100-300 A) and plasma by breaking the single primary loop into parallel to Bo. Also, in the latter case, the magnitude parallel sections and driving them with a low capaci- of Iz decreased with increasing delay of the Q = 1 ty, high-voltage capacitor. The fast Iz was usually fields relative to the main field. applied 0.3-0.6 IM after the application of the main A slowly rising axial current (r/4-15 ps) was in- compression field, i.e., near the end of the implosion duced in the full-torus plasma by a single-turn, phase of the discharge. Figure II-18 shows t he results capacitor-driven loop mounted on the inner face of with a fast-rising current: the lower left oscillogram b the toroidal compression coil (R-3.8 m). This exter- shows an axial current of -1.1 kA generated in the nally driven IZ was applied to the preionized plasma plasma in the absence of an applied i,; the lower such that its maximum was achieved at the time the right oscillogram shows the successful cancellation main compression field was applied. This current of the net axial current by the applied Iz; the upper had a variable amplitude of 0.8-1.5 kA and was left oscillogram shows the applied IZ waveform in the applied either opposing or aiding 1,. With the primary circuit; and the upper right oscillogram applied axial current opposed to 1, a reduction of shows the approximately nulled-out BZ pickup in the approximately one-third in the amplitude of Iz was 81-turn Rogowski coil on a vacuum shot in the observed. However, wit h the driven current aiding I Z absence of plasma.

24 m, ,,...... 7, . . “1he Cancellation 01 the net 1, dlcinot have a noticeable effect on the plasma behavior. Obviously, (a) inducing a canceling current cannot guarantee that toroidal currents are not distributed in such a manner as to produce a zero net toroidal current and locally violate the Kruskal-Shafranov limit. However, the fact that the plasma behavior is the same whether or not it is under the influence of an opposing current, coupled with the observed planar plasma motion and growth rate, shows that the in- stability is not a kink mode.

4. Toroidal Mode Structure

a. Introduction. Sharp boundary MHD theory predicts a growth rate for the m = I instability y given by

( b) y2(n)=~2(0) – v~(2–/3)n2fR2

where VA is the Alfv6n velocity, and R is the torus major radius. The axial mode number, n, is defined by the number of wavelengths around the torus, and Y(O), Eq. ( 11), the growth rate for an infinite wavelength, is calculated to be 0.7 MHz for the Scyllac torus parameters. Streak cameras initially indicated the existence of a tomidal mode structure. In order to determine the plasma structure more precisely at one instant of time, a 360° framing camera system was devised that eventually had 11 viewing slits distributed 13 almost uniformly around the circumference. Randomness of phase between modes caused non- reproducibility of the plasma motion from discharge (A to discharge, and required (2n+ 1) simultaneous data points to measure n harmonics (a constant dis- placement term for zero order, and displacement and phase for each n> O).

b. Experimental Arrangement. The experimental arrangement is indicated in Fig. 11-19. A single image-converter framing camera located at the geometrical center of the torus had 11 horizontal viewing slits, almost uniformity spread in angle over 360°, imaged on its photocathode. The light from each slit was relayed by two plane mirrors, one directly above the slit, and the second a member of a multi-facet pyramid structure also centered on the Fig. II- 18 toroidal axis, to a Cassegranian telescope (f/l .8, Top trace, axial magnetic field (2 ps/div). Bot- focal length 41 cm), which imaged the slits at 10:1 tom trace, axial current (O.7 kA/div): (a) reduction in an approximately circular array onto typical I. current generatedin torus with (IJ the 2.5-cm diameter photocathode. applied = O;(b) I=current applied in primary Iz In order to measure the plasma location within circuit; and (c) net IZ plasma current with an each slit, the slit ends had to be well defined in the applied IZ.

25 was the weighted variance of the fit, i.e., the square

column Mulls-segmenl root of the sum oft he squares of the deviations oft he mirror /’ foldinq tirror data points from the curve divided by the number of degrees of freedom. Figure 11-21 illustrates a succes- sion, of curves with an increasing number of modes, . n, fitted to the data of one particular discharge. Over a collection of 15 such discharges, the weighted variance was a minimum either at n=3 or n=4, with Tog view almost the same number of times for each. This / ,. \ means that three modes fit the data pretty well, with k--———a\/~ the 4th harmonic generally of smaller amplitude aiding the fit by a small amount. On the other hand, Cossegroin using only 2 harmonics, the fit was definitely worse. Otsch.afge tube colleclor It should also be noted that using 5 harmonics forced

Franing camera an exact fit to the 11 data points, and was therefore plasma .3 ps exp statistically meaningless, since the curve was forced to pass precisely through the data points, which S!de view themselves were determined with less than absolute pregision. It is significant, nonetheless, that when 5 Fig. II- 19 harmonics were fitted, the amplitude of the 5th har- Schematic of 360° framing camera arrange- monic on average was only slightly larger than the ment on Scyl[ac. The plasma is viewed 4th, and smaller than the first three, in support of simultaneously at eleven different cir- the conclusion that there is a rapid fall-off in cumferential locations in the toroidai plane. amplitude with increasing mode number. As a consequence of the above results, a fitting image. This was accomplished by a separate long- procedure including all mode numbers n=() to n=4 time exposure of reflecting tape on the slit ends il- was selected as the best representation of the data. luminated by individual flood lamps. The tabulated chi-square distribution of 2 degrees of An example of the raw data is shown on the left of freedom fit the distribution obtained from the sums Fig. 11-20. The circular arrangement is the somewhat of squares of the deviations if the experimental ac- arbitrary result of the alignment procedure, and curacy c was chosen to be 0.35 cm. Repeated while it evokes a mental image of the toroidal readings of the data indicated that this relatively geometry, in fact, the images are inverted, so that large uncertainty was not unreasonable. The phase the ends nearest the center are actually toward the anglesf the modes appeared to be randomly dis- outside, and the large aspect ratio of the torus is tributed, and the relative amplitudes also varied completely distorted. from discharge-to-discharge. In consequence, the plasma column assumed a different shape et’ery ciis- c. Data Analysis. Numerical values of the charge, as illustrated by comparing the -l-harmonics plasma displacement from the discharge tube axis at case in Fig. II-21 with the right side of Fig. 11-20. each angular position were obtained with the Graf- This is just what would be expected for a superpfJsi - Pen digitizer under the control of a computer ticm of several instability modes, and all further in- program which then proceeded to a curve fitting ferences must be of a statistical nature. routine. The analytical form of the fitting function The amplitudes of the various modes, n=O was chosen to be through n =4, were averaged over 15 discharges and are plotted in the lower half of Fig. II-22. We use the n calculated growth rate of 0.7 MHz for the n=O mode d=ao + COS h$ + bg Sin ~ . (21) x( a% ) and the relative growth rates for the other n *1 numbers, as indicated by the upper half of Fig. H-22, b as well as the actual time, t =4.6 YS, when the fram- The inputs are the 11 values of displacement d at ing pictures were obtained. The relative dis- the 11 different angular positions o and, for a placements of the various modes were then specified n S 4, the (2n+ 1) a and b coefficients were calculated on the “white noise” assumption of equal determined in a least-squares fit with 2(5–n) initial amplitudes. The absolute scaIe value was degrees of freedom. The results were di;~~ayed in determined by fitting to the observed data point for terms of a mode amplitude, (aQ +bQ ) , and a n= 1. This set the coefficient of the growing exponen- mode phase angle, tan–l (b~ la Q ). Also computed tial x=xoeyt at XO=O.023 cm. The resultant

26 ●

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I I

o In co—. (N

.

● 8) m m

o

8 —

27 calculated displacements are plotted as crosses in generalized theory to within 15%, both in absolute the lower half of Fig. II-22 and are connected by the value and in the relative scaling of the growth rate . solid line. from the previous sector experiments. The scale was not fitted to n=O because this is a somewhat special case which is only a constant shift (g) Measurements of the toroidal mode structure of term in position vs angle and can be confused with the m = 1 instability show the existence of at least . small errors in setting up the correct equilibrium five toroidal modes (theory predicts a maximum of conditions due, for instance, to slightly incorrect in- six) and confirm the t heretically expected fall-off of itial fill pressure. There should, in fact, be an initial the unstable displacement amplitude past n=3. 6-mm inward equilibrium shift since all the viewing These measurements give further credence to the slits were in groove locations, and using this or some theoretically predicted scaling of the absolute other value instead of the discharge tube center magnitude of the m = 1 instability growth rates. would slightly change the observed value for n =0. (h) These experiments provide no indication of d. Conclusions. The data presented here are higher order poloidal instability modes than m= 1, entirely consistent with sharp boundary calculations supporting experimentally the validity of the finite for the expected m= 1 instability modes. A priori, gyroradius stabilization criteria.8 instability might be expected to develop with equal likelihood in the vertical plane. Streak camera pic- (i) The major divergence of the observed plasma tures, however, indicate much less vertical than behavior from theoretical predictions is the period of horizontal motion. This could well be explained by quiescent equilibrium in the initial stages of the dis- slight force imbalances in the horizontal plane charge. Recent Nihon University experiments, 14 providing the initial set from which the instability indicate that the time variation of the plasma radii grows primarily in the toroidal plane. These could between the minima and maxima of the Q=0 field arise from variations in the magnetic field around regions in Scyllac is providing dynamic stabilization the torus (cf. Fig. II-7). We must then distinguish of the m= 1 instability according to the Haas- instability motion resulting from an initial set, due Wesson theory. 15 to force imbalance, from the total motion being the result of the longer term action of this force im- References balance. Simple arguments can be evolved to show that a 1. W.R. Ellis, F.C. Jahoda, R. Kristal, W.E. Quinn, force imbalance of only 2!; can establish the initial F.L. Ribe, G.A. Sawyer and R.E. Siemon, “Plasma set of 0.02 cm in about 0.4 As, i.e., a time short com- Equilibrium and Stability in the Scyllac Toroidal pared to when the position determination was made, Sector Experiments,” Nuclear Fusion 14, 841 so that the instability calculation can actually be (1974). applied from essentially t =0. On the other hand, the same 2(i force imbalance continuing to act in the 2. E.L. Cantrell, W.R. Ellis, H.W. Harris, F.C. absence of instability would give a trajectory which Jahoda, R. Kristal, M.D. Machalek, J.R. is too slow to explain the observed limit on plasma McConnell, W.E. Quinn, F.L. Ribe, G.A. Sawyer, confinement. This reinforces our interpretation of F.T. Seibel, and R.E. Siemon, “Plasma Ex- the data. periments in the Scyllac Toroidal Theta Pinch, ” This argument breaks down if the force imbalance Fifth IAEA Conf. on Plasma Phys. and Controlled is assumed appreciably larger. A significant experi- Nuclear Fusion, Tokyo, Japan, Nov. 1974, Paper ment would have been to measure at two instants of CN-33/El-2. time, during the same discharge, to determine whet her the separate n modes grow at different 3. F.L. Ribe, “Free-Boundary Solution for High- rates. Neither the available light level nor the ex- Beta Stellarators of Large Aspect Ratio,” Los perimental schedule permitted such a measurement. Alamos Scientific Laboratory Report, LA-4098 (1969). (e) The experiments confirm further the scaling of the toroidal equilibrium from the previous toroidal 4. F.L. Ribe and M.N. Rosenbluth, “Feedback sector experiments (R=2.4 m and 4.0 m) to the full Stabilization of a High-p, Sharp-Boundaries torus. Plasma Column with Helical Fields,” Phys. Fluids 13, 2572 (1970). (f) The unstable m= 1 plasma motion follows the predict ions of both the old-ordering and Freidberg’s

28 ? 2: ‘–7 ~ 2539 2 Harmonics ● :1 !-’ t /:’>

:o~e / \ , la \ 1-)

; :2 ‘T:’:’? “’* ?L–.-o I .---i o“ ’00° 200” 300” 400” 0“ 00” 201+ — 300” 400” Toroidol Angle ‘oro,dal Angle

2r —-T —-p .- .~ 2539 3 Harmomcs ●

/4”- \a

o ● \ b’ -1 ● -—= w ● % / =- / -2 ● -._l_— o“ 100” 200” 300” 400” 0“ 100” Zo(r 300” 400° LYJ.!Y‘1--ToroldaI AngIe I Toroldol Angle

Fig. II-21 Rodinl pknma displacement versus toroidal angle for one discharge successively fitted with an increasing number of harmonic terms.

F. Conclusions

Plasma experiments on the Scyllac full torus have shown the following: \ (a) The theta-pinch plasma heating by “shock” im- plosion and subsequent adiabatic compression is un- affected by the toroidal curvature and the presence of the !2= 1 and Q=O equilibrium fields during the implosion. 0 ‘+- ““----- ”--+ -“1 (b) The plasma column takes up a helical, bumpy toroidal shape and comes into an equilibrium posi- tion as predicted by theory, and remains stably con- fined for 6 to 8 us. . x ‘alculated WJ FIf N’ ; :: 4.6 S 06 _ -m 7(0)= Cf.7MH? (c) The period of stable confinement is terminated xO = 0.02 cm J =X 1 by an m= 1 unstable motion of the plasma column, u _’\\. (XS L A. whose properties are those of the theoretically f ‘ . . predicted m= 1 instability and coincide with the ~ ‘~, -j 0/ ‘x. observations on the 8~m sector experiment. The un- t i stable motion usually develops in the plane of the ___ 01 ‘ ’”>- ] torus. -! ! 7 3 4 567d Fig. II-22 (d) Measurements of the magnetic field, plasma Spectrum of theoretical growth rate (upper) beta, plasma radius, and relative density profile con- and average displacement as a function of firm in detail the theoretical predictions of a high-~ toroidal mode number (lower). toroidal equilibrium for the Scyllac plasma.

29 5. J.P. Freidberg, “Survey of Scyllac Theory,” 11. R.J. Lanter and D.E. Bannerman, “The Silver Plasma Physics and Controlled Nuclear Fusion Counter, A Detector for Bursts of Neutrons,” Los . Research (Proc. 4th Int. Conf., Madison, 1971) Alamos Scientific Laboratory Report LA-3498-C IAEA, Vienna, 3, !?15 (1971). (July 1966). . 6. M.N. Rosenbluth, J.L. Johnson, J.M. Greene, 12. K.S. Thomas, C.R. Harder, W.E. Quinn, and and K.E. Weimer, “Stability Limitations for R.E. Siemon, “Helical Field Experiments on a Stellerators with Sharp Surfaces,” Phys. Fluids 12, Three-Meter Theta Pinch,” Phys. Fluids 15, 1658 726 (1969). (1972).

7. H. Grad and H. Weitzner, “Critical /3 from 13. F.C. Jahoda, R. Kristal and W.E. Quinn, St ellarator and Scyllac Expansions, ” Phys. Fluids “Toroidal Mode Structure in the Scyllac Full 12, 1725 (1969). Torus,” Los Alamos Scientific Laboratory Report LA-5853-MS (1975). 8. J.P. Freidberg, “Stability of the Straight Q=1 Scyllac Configuration,” Phys. Fluids 14, 2454 14. T. Itagaki, T. Karakizawa, K. Suite, S. Shiina, (1971). J. Jodoroki, “Stability and Toroidal Equilibrium Conditions of Theta-Pinch Plasma in a Multiple- 9. J.P. Freidberg, “Vlasov-Fluid Model for Studying Mirror Field, ” Fifth IAEA Conf. on Plasma Phys. Gross Stability of High-/3 Plasmas,” Phys. Fluids and Controlled Nuclear Fusion, Tokyo, Japan, Nov. 15, 1102 (1972). 1974, Paper CN-33/E7-3.

10. R.E. Siemon, “Polychrometer with Extreme 15. J.A. Wesson and F.A. Haas, “Dynamic Rejection of Stray Light,” Appl. Optics 13, 697 Stabilization of the Theta Pinch,” Phys. Fluids 12, (1974). 1271 (1969).

.

.

30 III. FEEDBACK STABILIZATION OF SCYLLAC

D. L. Call, K.J. Kutac, G. Miller, W.E. Quinn

A. Introduction system should be able to demonstrate control of the plasma instabilities, provided other end effects are The Scyllac full torus experiment as well as the absent. The derated parameters will be in a plasma previous sector and Q= 1 linear experiments indicate re~ime which will yield addititmal information on that the observed m = 1 plasma motion is due to the the Freidberg criterion for the finite-Larmor-radius instability predicted by sharp-boundary MHD (FLR) stabilization of the m > 2 modes. In the theory. The growth rate -y from the MHD theory (for derated plasma regime, the criterion for the m= 2 long wavelength modes) is given by may be violated. Hencq there is a possibility for comparing the theoretical predictions for the FLR criterion and the m =2 growth rates with experiment. 4 2+ 4-36) (2-8) ~2a262 The preparation for feedback stabilization ex- Y =hvA -8 ~ 6; +8( [() 8(1-L3) 1 periments on the derated Scyllac sector are describ- q 1/2 ed below. The selection of the derated plasma + !3(3-26) (1-6) 62 (1) parameters and the capabilities of the feedback (2+3) o 1 system are also discussed. A detailed analysis of the feedback loop with the conditions expected in the Two methods of stabilization have been proposed, Scyllac feedback experiment has been carried out feedback 1 and wall stabilization. z Since in the and projects a generally favorable result. present Scyllac experiments the ratio a/b of plasma to wall radius is too small (-O. 1) for wall stabiliza- B. Experimental Arrangement. tion, feedback control has been chosen for plasma stabilization. In the MHD feedback stahilizati(m system 2’3’4’5 The results from the toroidal sectors and the full for Scyllac, the feedback force is generated by small torus have established the relationship between the c(mtrollable =0 field which produces a plasma per- required specifications of the feedback system and turbation the plasma parameters. An assessment of the feed- back system based on this knowledge showed that *FB = -B;:o/2Bo(l - $) the time response of the existing feedback amplifier o (2) system is insufficient to control the unstable motion in the Scyllac torus. Modeling studies indicate that This plasma perturbation produces a feedback 7T <0.5 (Y7 is the product of instability growth rate and the feedback delay -risetime) is required for con- restoring force trolling the instability, while Scyllac has -p = 1. These considerations have led to a re-evaluation of FB = f3(3-28)B~h2a3& 16~/8 (3) the plasma regime in which the initial feedback ex- ‘1,0 . periments will be conducted. In order to reduce the instability growth rates to values which are compati- in opposit i(m to the m = 1 destabilizing force, ble with the response time of the present feedback . system, the main compression field will be reduced to -15 kG and plasma parameters derated accor- (4) ‘ dingly. Feedback studies utilizing the derated plasma will be carried out in a new series of 120°, 8- m sector experiments. The objective of these ex- where l) is the mass density of the plasma column periments is to clearly establish the principles of and f the displacement from its equilibrium posi- feedback stabilization in Scyllac. t ion. The derated plasma parameters will allow a Equating the feedback force to the destabilizing relatively long end-loss time in which the feedback force gives the !2=0 feedback field required for plasma stabilization,

31 In order to accommodate the capability of the feed- FB back system, it was decided to reduce the plasma . B (5) 1=0 4(.3(3-26)(1-6) ~2av2*y2EB0 parameters. To achieve YTFB=0.5 and to reduce the Al required feedback field, the Alfv6n speed will be reduced by lowering the main toroidal field to 15 kG. . The feedback field is produced by four 9=0 feedback With the milder implosion-compression conditions it coils per Q= 1,0 wavelength inside the main compres- is estimated that the plasma /3 will be lowered to ap- sion coil with alternate pairs connected in opposition proximately 0.65. to the feedback power amplifiers. In order to reduce T17B,the output inductance will The feedback stabilization system, shown be halved by using each module to drive only a single schematically in Fig. III-1, consists of four basic pair of feedback coils, which requires 2 modules per components: (a) the plasma posit ion detectors, Q= 1,0 waveiengt h. This decreases Jhe L/R risetime silicon quad-cell photodiodes desi~med to detect to 0.6 PS and the overall dela TFB to 1.5 KS (cf. Fig. $’ plasma motion up to I cm away from the III-z). The feedback field B{= ~ will be increased by equilibrium position; (b) signal processing units, enlarging the clearance between the Q=0 coils and which produce an output proportional to the sum of the compression coil wall from the previously plann- plasma position and velocity with separate position ed 2 cm to 6 cm, thereby reducing image currents and velocity gain controls (the principal “knobs” of effects. Figure HI-3 is a photograph of the new sector the feedback system); (c) wwr amplifier modules. compression coil with an average diameter of 24 cm. each of which consists of three separate stages of The inner surface of the coil is shaped to generate amplification ending in the push-pull operation of the Q= 1 helical and Q=O bumpy equilibrium fields. two ML-8618 power vacuum tubes operating at 35- Since the device and plasma parameters are being kV plate voltage; and (d) Q=0 feedback coils driven considerably changed to accommodate the feedback by the power module output transformer. capability, the initial feedback experiments on Initial feedback plans for Scyllac used 60 feedback Scyllac will be carried out in an 8-m sector (120°) us- modules with each module driving two pairs of Q=(l ing Racks 6 through 10. feedback coils (one module per Q= 1,0 wavelength). It was planned to remachine the compression coil to C. Parameters of the Derated Sector with Feed- a mean inner radius of 8 cm, corresponding to a com- back pression field of approximately 35 kG with a clearance of 2 cm between the feedback coils and 1. Scaling of Scyllac to Lower Magnetic compression coil inner surface. Modeling Fields. Simple scaling of the plasma temperature measurements showed that the feedback modules in the implosion phase and subsequent compression could generate a feedback field of 230 G in this con- and neglect ing inertia and expansion effects follow- figurate ion. More important, the total time delay. ing the implosion give VR, from optical position detector to the feedback 114= U2B coils in a realistic mock-up was found to be 2.1 PS. A m eo (6) large fraction of the 2.1 PS was the L/R risetime T. 314 ‘ ( -1.2’ KS) of the output current from the feedback n o modules, arising because two pairs of feedback coils were driven by each module. This arrangement was where ~, isthe initialfillingdensityand m the ion planned in order that the available 60 modules mass. Using thistemperaturescaling,conservation would cover the 60 Q= 1,0 wavelengths of the 25-m of particlesand the plasma beta relationgivesa circumference. . plasma radiusscaling, In order to feedback stabilize we must simultaneously have sufficient 13~B0 to restore the plasma from reasonable displacement (ap- 1/4 ~ = ~llamllab ‘e . proximately one cm) and a growth rate small enough (7) 0 t #2B112 to be followed after the risetime delay of the feed- o back system (YTFB

32 ~ .- -- SUM —-- SIGNAL PROCESSING Iov @ Iv UNIT .- DIFFERENCE --

LOW LEVEL AMPLIFIER

ML8618

VACUUM TUBE 2 STAGE ~ DRIVER TRANSISTOR .4?=0 AMPLIFIER I ST STAGE 2 ND STAGE COILS AND PHASE 2 2 SPLITTER = 4CX600J 3-1000Z

T

POWER AMPLIFIER “’w=-=’ ‘35kv L ‘3 FEEDBACK AMPLIFIER AND LOGIC SYSTEM

Fig. III- 1 Schematic of feedback stabilization system

3/4 n~ 8B FEEDBACK SYSTEM TIME DELAYS fD.LCALL] o (8) n = ~1/4El/2 “ 7004 MAX .0 — ~ Wl 5,, I ‘~h fosmcsd SIGNAL DRIVER OETECTOR PRCCESSIW AWLIFER The Alfven speed scaling is obtained by using the L= uNIT b ‘-- h density scaling, (.0 -!7’ 35 kV COIL ~ ~~ 114B112 3/.ls OELAY 6~s CIELAY .6 ~s(90%) R13E TIME ‘e, o (9) ‘A “ 3/8m31861f2 “ n o

Using these scalings and assuming the initial fill-

1.0 TIME in: density remains constant the parameters in Table 111-1 for a field of 15 kG have been scaled from the listed parameters in the present torus ex- Fig. III-2 periments. Block diagram (upper) of feedback system sh(jt[ting the s>stem time delays and the feed- 2. Feedback Parameters. The growth rate y back output current response (lower) to a step and the required feedback field B~B ~ can be input at t=O. minimized with respect to the J?= 1,0 wavelength

33 .

.

.

.

Fig. III-3 A photograph of a section of the shaped com- prcs.sitm coil for the derated sector.

34 TABLE III-1 where the wall-stabilization term has been neglected, and SCYLLAC PARAMETERS

Full Torus Sector Feedback *rB~+- ~ h~l+2(1-6)2(2-s)2> ~B. (12) Parameter Experiment Experiment __ [ (3-20)2 hR2B: 1 0 B.(kG) 40 15 The growth rate -y, Eq. (11), is plotted as a function of$ for h=O.10 cm–* and B] = 0.09459 in Fig. III-4 Ee(v/cm) 445 170 and as a fuilction of B1 for @ = 0.65 in Fig. III-5 for Alfv6n velocities in the range of 1.5 to 3.5x107 cmls. T/4 (lls) 3.7 3.5 The feedback field BFBQ. o , E~. (12), required for stabilization of the m= 1 mode M plotted as a func- s 0.8 0.65 tionof$ forh=O.10 cm-’ and BI =0.09459 in Fig. III- a (CM) 1.0 1.42 6 and as a function of B1 for P=O.65 for ~B. values in the range of 10 to 30 kG-cm in Fig. III-7. -3 n(cm ) *.,x& 1.33X1016 Minimization of the required feedback field, Eq. (12) [which is proportional to ~ 2, Eq. (11)] with T (eV) 1177 272 respect to BI gives

vA(cm/see) 37.55X106 20.04x106

(13) A~ o (cm) 41.89 62.83 * h(cm-l) 0.15 0.10 The optimum values of h from Eq. (10) and Eq. (13) 61 0.71 0.98 for $-0.65 and B1 -0.09 are in the vicinity of 0.1, which corresponds to an !2= 1,0 wavelength of 62.8 6 0.16 0.21 cm. Pratt ical considerations such as an integral 0 number of Q=1,0 wavelengths around the torus and the machining of the inner surface of the coil lead to Y (VS-l) 0.705 0.318 a choice of Al,o =62.83185 cm and a corresponding 1.1 - 1.5 0.48 h =0.10 cm – 1. This choice consists of 3 coil sections ‘~FB per wavelength. BFB(G) 620 342 Taking h=O.10 cm ‘1 the optimum B1 field can be determined from E s.’ (10) and (13) for h, which (~=1.O cm) %B minimizes -Y and BQ = o , respectively. Table m-z lists the resulting feedback parameters for a Bo field A1.0=2~jh, where h is the Q=l,O wavenumber. of 15 kG. Freidberg has done a theoretical optimization to The parameters in the first row of Table IN-2, i.e., minimize y which gives an optimum wavenumber, with @=0.65 and BI =0.09459, have been selected for the sector experiments. The ~ =0.7 and B 1 = 0.08774 -116 case is a better selection from a feedback point of %miny)- view, however, there is some question about making . [(‘-’’TV’-’)’] Fur”- ‘1”) a plasma j3 of 0.7 with the reduced Ee and BO. Secondly there is concern about the separation of the It is convenient to express -Y,Eq. (1), and BIB o , helical plasma from the discharge tube wall, which . Eq. (5), in terms of the Q= 1 helical equilibrium field, would be smaller with 61= 1.08. B] = BQ.1/B. using 61 = 2B1/ha(l-(3) and the The selected parameters are listed in Table III-1 equilibrium relation, 60 = 2/(3 -2P)h2aR61, to obtain with the Scyllac full-torus parameters.

D. Analysis of the Feedback Loop 112 S(4-3B) ~2B2 + 5(1-8) (2-8) & . (11) y - ‘A 2(1-6) (2-5) 1 (3-26) it2B2 The Scyllac experiment has shown the m= 1 [ 1 1 growth rate and toroidal mode structure to be

35 1/2 13FB.0.1206 ~K,8006 ~lo-4 I BO y.7.4529 x 10-3 8 (4-3~1 .10.1285 J9(l-i3] [2-81 “A 110 [ [2-8) ( I-B) [3-2?3) 1 [ Bo - 1 ‘O-r w . R=400 Cfll; h. 0.10cm4; +:0,0%59 o.6-- 90+ ~ R.400cM, h. O.lOcm+; &O.65

C!6- - . 0.4- ~ 20 1.5 02- :

08 i 100 ! I 0.3 0.4 0.5 0,6 o? 0.8 0,9 007 0.08 0.09 0.10 0.1 I 0,12 B %.l/Bo

Fig. III-4 (iraph.s of the m = 1grou~th rate as a function of Fig. 111-7 the p la.sma e for various Aflven speeds. I’1(/ts of the feedback fic[d required for S(Obilizo! i(m of the m = 1 instability as a func - titm of th c ~ = 1 h ~lical equilibrium field for the indicated l~o[uesof ( B,,.

0.7 “o”’” [(WV-;I”2”A generally in line with those predicted by sharp boun- R=400 cm, h=o.l~~m-’; p.o.~ ,A=3.5X ,07 0.6 dary MHD theory. Also in the past year a less ., + marginal configuration of the feedback system has been decided upon, and the relevant parameters measured. With these updated inputs analysis of the feedback loop has been carried out taking into ac- L ~ 0.3 -!- ‘count delay and risetime of the feedback controlled f- 1.5 Q= O field, plasma dynamics, toroidal mode struc- 02+-— — 1 ture, and feedback amplifier saturation and 007 008 009 0,10 0,11 0.12 threshold characteristics. The result is a generally favorable prognosis for the upcoming Scyllac feed- back experiment, although a previously ignored ad- Fig [11..5 ditional delay, the time for plasma axial flow, l’lt~ts of the m = 1 groioth rate as a function of reduces the capability of the system. th [’ P = I field for the indicated A lfue speeds. 1. Feedback Model. As a starting point the simplest case of m =1, n= O plasma motion (rigid

091 K21 Bf4.3,91 101285 PI;::2:)BI ~80 sideways motion) will be considered. With a linear %3”05’0 —[—”s ( 3-281 (’-s1 I 1-81 1 position and velocity control algorithm6 The R,,aw c“, 11.o.!ocln? L&w,, 2.0m-- equation of motion is

l,m -

~ ,,@Q_ _ i(t) =y2<(t) - Fmx@Ut- -r)+ e?(t - T)) s (14) ? . =– sOO- - .

0 Q3 04 0.5 0.6 0.7 0.8 0.9 where $ is the plasma displacement from its P equilibrium position, y 2 the growth rate squared of . the unstable m= 1, n=O plasma displacement from sharp boundary MHD theory, 7 the time delay in the Fig. III-6 feedback system, and F~,. the maximum feedback (iraphs of the feedback field required for F1,o “force” corresponding to the maximum Q=0 s[abilizotion of the m = 1 instability as a func- field produced by the feedback system. Under the tion of the plasma O for the indicated values of conditions expected for the Scyllac feedback experi-

36 TABLE III-2 . OPTIMIZED FEEDBACK PARAMETERS FOR B = 15 kG 0 BFB

P (sl 6 h (G) _l__— (~m) ‘1 (myz) 0

h 0.65 1.42 0.09459 0.318 342 0.986 0.210 FB ‘in ‘9=0

0.65 1.42 0.07955 0.329 432 0.829 0.250 ‘(rein y)

h 0,7 1.37 0.08774 0.317 313 1.079 0.211 FB ‘in ‘R=o

0.7 1.37 0.07478 0.330 386 0.92 0.248 ‘(rein y)

The position and velocity gains are a and B with This indicates that velocity control (B # O) is essen- 1/(( and 1/$ the plasma displacement and velocity tial when time delay is present. that produce maximum (saturated) output of the In the general case Eq. (15) has more than two feedback amplifier. roots so that there are more than two linearly in- dependent solutions of Eq. (14) and the motion is 2. Frequency Response Analysis. Neglecting not specified by the initial position and velocity saturation Eq. (14) is a linear equation with alone. solutions of the form e ‘i~t. The frequencies w are

roots of the following equation obtained by express- a. YT Limitation. The transcendental equation, ing ~(t) in terms of its Fourier components, Eq. (15) has well defined roots even when time delay is not small. It seems to be the case that as ~T -1, it is impossible to keep these roots out of the upper half (15) -(fAI/y)2= 1- E_(a - i@) eh , of the complex u plane by adjusting the gains a and @. This is illustrated in Fig. 111-8 which shows the variation in growth rate produced by varying the where ~~~X is F~~X/2y , the plasma displacement that gains from O to some final values, keeping velocity leads to an unstable force equal to the maximum gain ~ proportional to position gain a. By suitably feedback force. choosing the ratio of 8 to a it is possible to make the With the assumption of small time delay (uT

37 GROWTH RATE AS FUNCTION OF GAIN SETTING for $ not too near O or 1. In both limiting cases o-O a (POSITION) AND @ (VELOCITY) (equilibrium response) and U-CIJ (instantaneous . PIJSMA DISPLACEMENT w EXP(-icd) response) Eq. (20) can be derived from elementary ,B=2.5a IMAGINARY considerations, constant pressure along the column a,fl=o -,1.: in the former case, and local adiabatic compression UNSTABLE GROWING MODE . or expansion in the latter case. \ The consequences of inserting the frequency response function obtained from Eq. (19) and l?q. i—— ‘ (20) into Eq. (15) are that new weakly damped or -1.5 -LO -0.5 0.5 1.5 growing oscillation frequencies are obtained, related \ ---; L------‘“0 =.___—- --- , ------v, to the natural frequency w= hv.. However because ~ +a i 1 FEEDBACK STABLE, 7Ts0.5 the bounciness, due to the lack of any damping, of I the plasma described by Eq. (20) seems unphysical, we concluude only that plasma dynamics may be responsible for an additional delay. Fig. III-8 This delay is equal to the propagation time over a Pl{jtscJf them= lgroulth rate as a function of quart er wavelength, r/(2h), at the velocity v,,, which the pt~.sition (N) and velocity (@) gains of the is roughly the thermal velocity. For the conditions of fecdlmch s.ystem u]ith ~ =2.5 n for the indicated the feedback experiment the numerical value is Jr lwlul?s. rP =1.61.Is, or -yTp = 0.5. The ratio of instantaneous response to equilibrium response from Eq. (20) is given by c. Plasma Dynamics. In deriving the feedback (1 –$)/(7$/2+ 1–$). For the expected @ of the feed- equation of motion Eq. (14) it is assumed that the back experiment (8= .65) this is about 0.4. Thus a time scale is such that 6,, takes on an equilibrium fair fraction of the feedback force is applied without value. with negligible delay, corresponding to the any delay. applied feedback 5!=0 field. This assumption will now be examined more closely. 3. Integration of the Equations of Motion. A The feedback F1,0 force in the case of non- more straightforward approach to Eq. ( 14) is to in- equilibrium is given by7 tegrate it numerically to obtain the plasma displace- ment as a function of time and check that the mo- tion remains within the confines of the discharge :160( 2-B) -2(1 -6)~0 11(2-6).41 ] ( ), tube. This method has the advantage that toroidal ?-F (19) ~0:16(3-2f0 mode structure and nonlinear effects may be includ- ed. The disadvantage is that only a pure time delay can be assumed. where the bars denote equilibrium values. In the case of high $, with al =~1, this means that the force a. Toroidal Modes. It appears that the plasma is roughly pmport ional to 60. instability in the Scyllac torus is characterized by a Using sharp boundary MHD theorya it can be number of modes along the toroidal axis, generally shown that the plasma response as a function of fre- consistent with sharp boundary MHD theory, which quency w to an applied !2=0 field is predicts the following relation between growth rate and n, ~(t-o) 1 . 6u-~— &s?l (20) 2(1-B) 2 0 (hc)z (hvO) 2+2 Y: - Y:.. - (2+3) (): “: , (22) . where fidisthe Fouriercomponent of d,,(t),h isthe wavenumher of the applied field,c is the sound where R is the major radius of the torus. The feed- velocitygiven by c= ~~VA, and vu isthe group back system is thus faced with the task of stabilizing velocityof an m=O disturbance,given by a plasma displacement which is a function of toroidal angle @ as well as time,

(21) C($.t) - ~ [an(t)cos Iw + bn(t)s,n n+] . (23)

38 The generalization of the equation of motion, Eq. ~max= 1.0 cm . ( 14) for higher n modes is a physically reasonable ex- tension of the Fl,o body force concept. The n ‘h n,~aX = 5 Fourier component of the feedback force considered where n~aX refers to the maximum unstable n value. s as a function of @is assumed to act on the nth mode amplitude together with the unstable force e.g., an = The series given by Eq. (23) was truncated at n = 7 -y~a~ -F*. neglecting the effect of higher order stable modes. Two slightly different feedback algorithms were The differential equation of motion was integrated considered, both generalizations of the linear posi- for various choices of gains, a and ~, and initial con- tion and velocity control given by Eq. ( 14). In the ditions. In Fig. 111-10 are shown the plasma positi(m first, each position detector station was used to drive versus time trajectories at one point on the torus equally the power amplifiers and !2= O coils nearest (/,=0) calculated for various gain settings. The dam- to it. In the refined algorithm, illustrated in Fig. III- ping effect of velocity gain is illustrated. The initial 9, the position detector signals are interpolated conditions are a uniform (n=O) 3-mm displacement between stations, as might be accomplished with at t = O and each a. and b. having a random initial simple voltage divider networks. In the numerical velocity in the range + 0.05 cm/~s. The refined feed- work the following parameters were assumed: back algorithm illustrated in Fig. HI-9 is used; however, only a small difference is caused by use of y,.o = .33 ps–1 the simpler algorithm. The range of gain settings that stabilized the mo-

T = 1.5 lfS tion with the initial conditions as stated was ap- proximately 2< ~ <5, 3< (3 <20, and 1.5< a <~,

Location Of Position Detect~s

— — — —

n f Relative ,Current J Output From 40 Modules n \ J-

— — — — 1 r Toroidal Angle

Fig. III-9 Computer simulation of the plasma position and the feedback output current as a function of tcjroidal angle with multiple position detectors.

39 I

—.. Powtmn Gain = 2 cm-’ I I I Feedback Ampllf,er Response Veloaty Gain A 00 cm-’ JLS 0 3.3 cm-’ PS 50 furatson1 c 5.0 cm-’ /Is 0 10.0 cm”’ ps

z al 15 Feedback ?40tt.ans : nr= 5 Unstable Modm “,.:33 ~,-t : % a ; o

Threshold Fig. III- 10 Graphs of the plasma position versus time tra- o \ jectories at a fixed toroidal position (~= O) for o l’arious velocity gain settings. Inpul Voltage in qualitative agreement with the gain limitations given by Eq. (17). This range is comparable to that Mtwsurcd output current response of the fced- obtained when only one mode was allowed with the hoct? omplifier ,systcm as a function of input

initial velocity increased to compensate for fewer ldt (lAr(’. degrees of freedom. The number of feedback stations required for n ~~~ —– 5 is greater than ten so that the distance between E. Status of the Feedback Stabilization Ex- detector stations is less than the smallest unstable periments half-wavelength. The computer studies indicated that 15 stations was a workable number. A con- Following the Scyllac full torus experiments, figuration wit h 11 or 12 stations was unable to hold which were completed in late November 1974, the the plasma with the same initial conditions. modification of a 120° sector (8.4-m arc length) of the torus and the installation of the feedback cmn- ponents were begun. The Scyllac compression coils b. Amplifier Non-.Linearity. Feedback amplifier were bored out and their inner surfaces machined to saturation was included in the computations leading the new design of the Q = 1 and Q= O equilibrium to Fig. 111-10. The split phase design of the fields as given in Table HI-1. The sector bank has amplifiers seems to result in an unavoidable I been modified to operate at one-half capacity for the threshold type non-linearity as well. This is il- derated experiments. The assembly of the compres- lustrated in Fig. 111-11. A 20% threshold, that il- sion coils with the discharge tube and the device lustrated in the figure, was incorporated into the check out should be completed by mid-February computer calculation with surprisingly little 1975. The initial experiments will determine the deleterious effect. The range of gain settings for derated plasma behavior and parameters in the stability quoted above was only slightly diminished. absence of the Q= O feedback coils, which will be in- . Thresholds of 30 — 40%, however, led to loss of stalled in March 1975. stability.

References . 4. Conclusions. Feedback stabilization of the m = 1 instability looks feasible on the basis of these 1. F. I.. Ribe and M.N. Rosenbluth, “Feedback modeling exercises. Realistic time delays, toroidal Stabilization of a High-$, Sharp-Boundaried mode structure (with a sufficient number of position Plasma Column with Helical Fields,” Phys. Fluids detector stations), and amplifier nonlinearity are all 13, 2571 (1970). surmountable obstacles. The time required for axial flow of the plasma is a significant additional delay 2. .J.P. Freidberg, “Stability of the Straight =1 and may be a serious problem if the estimates of its Scyllac Configuration,” Phys. Fluids 14, 2454 magnitude are correct. (1971).

40 3. “Annual Progress Report LASL Controlled Ther- 6. K .1. Thomassen, “Feedback Systems on Linear O . mrmuclear Research Program, ” Los Alamos Scien- Pinches with Helical Fields,” Los Alamos Scientific t ific Laboratory Report, LA-5656-PR (July, 1974). Laboratory Report LA-4598-MS.

4. R.F. Gribble, S.C. Burnett, and C.R. Harder, 7. G. Miller, “Motion of a Plasma Column in a Per- . “Feedback Stabilization of an Q= 1 Theta-Pinch turbing Magnetic Field, ” Phys. Fluids, to be Plasma Column, ” Proc. Second Topical Conf. on published. Pulsed, High-Beta Plasmas, Garching, W. Ger- many, July 1972, p. 229, Garching Report IPP-1/127 (1972).

5. W.R. Ellis, R.F. Gribble, and C.R. Harder, “Preliminary Q1,0 Feedback Force Experiments on Scylla IV-3, ” Los Alamos Scientific Laboratory Report LA-5788-MS (November 1974).

41 .

IV. STAGED THETA PINCH PROGRAM . K. Thomas, W. Borkenhagen, D. Call. R. Dike, J. LAmtning, R. Cribble, C. Harem er, A. Jacobson, R. Kewish, R. Linford, E. Little, M. McKinstry, A. Rawc[iffe, (7. Sherwood, T. Zaugg

A. Introduction ponents of the same design as the new components used in the 4.5 m STP experiment as well as parts Previous theta pinches have performed initial from the 0.9 m STP prototype. This experiment will implosion heating of the ions and subsequent be useds to test new circuits and components for adiabatic compression with a single capacitor bank possible use on the 4.5 m STP. power supply. Projected theta pinch feasibility ex- periments and fusion reactors, however, will require B. Resonant Heating Concept separation of the two functions to achieve greater implosion heating and less adiabatic compression. Resonant heating is the name given to a new The Staged Theta Pinch (STP) program is designed method of implosion heating which involves the to study the technological and physics problems “tuning” of a simple circuit to the plasma dynamics associated wit h separating the two funct i(ms. resulting in a “fat” plasma, i.e., a plasma with a The principal experiment in the program is the relatively large ratio of plasma radius to implosion 4..5-m-long linear STP. It will use a relatively low coil radius. This process could be used in future energy, high-voltage capacitor bank to produce the theta pinch feasibility experiments where it would theta pinch plasma. A lower voltage, higher energy be followed by an adiabatic compression. Because capacitor bank will be used to contain the plasma the resonant heating creates a hot fat plasma, the and provide a variable amount of adiabatic compres- adiabatic compression can raise the plasma to ther- sion. The experiment will be capable of producing monuclear temperatures without making the plasma high temperature plasmas with a much larger ratio radius too small for wall stabilization as mentioned of plasma radius to discharge tube radius than is in Section A. possil)le in conventional theta pinches. Plasma ex- Other implosion heating methods have been periments will study the effect of magnetic field proposed for producing fat plasmas. Freidberg, amplitude and time history on plasma formation, M(~rse, and Ribe * presented three concepts the properties of the plasma formed, and later, the indicated in Fig. IV-1 which was taken from their effect of helical magnetic fields on plasma stability. paper.* No specific circuits were proposed to If the ratio of plasma radius to coil radius can be produce these precise waveforms, but the plasma made large enough, the effect of plasma stabilization dynamics were analyzed for each case. Since the free by image currents in the coil walls will be obser- expansion case appeared most promising, R. Gribble vable. designed a circuit which simulates the field behavior In addition, two smaller experiments were con- in Fig. IV-lb. The resulting circuit, shown in Fig. IV- structed to support the main program. The first, the 4. is being used in the STP experiment described in ().9 m long STP prototype, was operated from May to Section C. Octoher 1974. It was used to obtain experience in the The resonant heating process theoretically design and operation of high voltage experiments produces plasma parameters very similar to those and to conduct initial studies of the effect of time resulting from the STP circuit. The advantage of . varying magnet ic fields on plasma behavior. The ex- resonant heating is the efficiency and simplicity of periment was operated in the corner of the STP ex- perimental area and was closed down to allow com- *The paperl contains an error in the calculation of pletion of the 4.5 m experiment. The Resonant the relative size of the two pulses of implosion field Heating Experiment was constructed in another for the “free expansion” case, but the numerical fac- area during the last four months of 1974. It uses com- tor has been corrected in Fig. IV-lb.

42 Le L~

~ Lp(t) A A I I CAN I I crowbar implosion Load I Switch Bank Coil /, I r~ l--

B B

I I

I I

c

c

Time —

Fig. IV-2 R,.v(mant heating circuit showing the temporal Iji’holjifv i~f the B-field and the plasma.

J Figs. IV-2a and IV-2C. This allows the field to decay TIME— to a specified value at t~ when the crowbar switch is closed. The B-field value at ti is chosen so that the Fig. IV- 1 field at k is barelv sufficient to prevent the l)riving fiekfs assumed by Freidberg, Morse, expanding plasma from touching the wall. Following (Itld Ribe’ for (a) simple implosion heating, (b) te the oscillations of the field and the plasma radius fr,’(-expansion heating and (c) programmed Eo decay as shown schematically in Fig. IV-2. The field h~ating of a theta-pinch plasma. decays exponentially on a much longer time scale, which would allow the slowly rising compression the circuit shown in Fig. IV-2a. The circuit is field of future experiments to take over. Since this topologically the same as the circuits used in present simple crowbar is sufficient, the power crowbar used theta pinches such as Scyllac, but the component in the STP experiment appears to be unnecessary in sizes are chosen so that the peak field is reached these future experiments. before the time tc at minimum radius as shown in

43 The field profile of the resonant heating system The circuit design is shown in Fig. IV--$. The 22.5- (Fig. IV-lb) is somewhat similar to the free- cm-i.d. compression coil is fed from both sides and . expansion case in Fig. IV-2b since the plasma is Fig. IV-4 represents a 0.9-m-lcmg section. There are allowed to reexpand against a field which is less than five such sections on each side of the machine. The opposite sides will operate at different electrical the initial implosion field. This feature reduces the . work done by the expanding plasma on the field. In polarities, which requires the insulating of the elec- the STP circuit, this field programming is ac- trical components from ground potential. The high complished by properly tuning the resonant frequen- voltage (125 kV) part of the circuit is rlit’ided into cies of the two circuit loops containing the implosion two parts with independent trigger systems. banks, and by closing the switches at the ap- Figures IV-5 and IV-6 are photographs of Ihe ex- propriate times. In the resonant heating case, the periment as it existed in mid-December 1974. Figure natural resonance of the imploding and expanding IV-5 is an end view of the coil and irnplosi(m circuit plasma is used as the second “resonant loop” thus part of the experiment and Fig. IV-6 is a top view of necessitating only one properly tuned implosion the same area. bank. The actual design of the circuit and numerical 2. Construction. Engineering design of the STI’ comparison with the STP circuit requires the use of was started during the summer of 1973 and construc- a model for the plasma dynamics which strongly t ion started in August oft hat year. The platform and affects the circuit behavior through the load induc- cap~citor racks were installed during .January 1974. tance ~,. Several analytic and numerical simulation The staging bank capacitors were installed in codes are being used at the present time. * February 1974. Assembly of. the Pulse Forming Preliminary results indicate that the plasma Network (PFN) charging Marxes was completed by characteristics are similar for the STP and resonant August 1974. The installation of the PFN gaps, heating circuits, as previously mentioned, but the ef- capacitors and collector plates was completed by Oc- ficiency of transfer of stored capacitor energy to tober 1974. Construction of the experiment should plasma energy is about 3 times higher for the reso- be complete by late January 1975. Preliminary elec- nant heating circuit than for the STP circuit. This trical checkout of the new trigger systems started in efficiency and simplicity makes the resonant system December 1974. easier and less costly to build and operate. In addition to the theoretical comparisons now be- 3. Engineering. The STP has a 4.5-m-long load ing worked on, a Resonant Heating Experiment coil and collector plate system. The collector plate (RHX) described in Section E is being constructed system consists of five individual assemblies at each so that experimental results can be compared with oft wo feed points. It is arranged so that a fault in the STP and the theoretical models. collector plate insulation can be repaired without disassembling the entire collector plate. The discharge tube consists of two 2.75-m-long C. 4.5 m STP quartz sections, with 21-cm o.d. The sections are jointed together using a nylon-Pyrex slip joint, Fig. 1. Description. The layout of the STP IV-7. This joint is similar to the one used to join the experiment in the old Scylla IV experimental area is Scyllac torus. shown in Fig. 3. The staging bank, which is the The experiment is designed so that energy is fed Scvlla IV 50 kV main bank, is located on a plat form from two 125-kV capacitor banks to the load coil above the high voltage implosion circuit. The start through two feedpoints. one positive and the ot her switches for the staging bank have been moved down negative. The electric field around the discharge . to the collector plate in order to isolate the load tube is approximately 2 kV/cm. The system consists cables from the high voltage circuit. This of a number of’energy storage banks shown in Table necessitated the replacement of the start switch in IV-7-I. . the Scylla IV capacitor gaps with a shorting column. The trigger system for the preionizat ion and crowbar The crowbar system was left intact. The high voltage is identical to that used in Scyllac. The preioniza- gaps are connected directly into the collector plates. ti(~n has a master gap for each polarity. The crowbar trigger consists of two masters for each polarity, which are completely independent. In the event of a *The principal models and codes have been single fault, this design will ensure the operation of developed by F. Freidberg, R. Gribble, R. Linford, the crowbar system and thus prevent the breakage of C. Nielson, and T. Oliphant. the discharge tube.

44 STAGED THETA PINCH .

t. r ,STAGINGBANK\ 44 J! . ‘+ I

1

1,1 1 1

v I tiARX BANK ‘IMPLOSION BANK 0123 SCALE METRES

Fig. IV-3

Layout of Staged Theta-Pinch experiment.

/4 L4 17 IIH L2 2 nH

. . . .

Fig. IV-4 (’ircuit diagram of 0.9 m section of Staged Theta-Pinch experiment.

45 ●

✎

.

.

46 *

.

47 the same fast biasing characteristics. In addition it is capable of handling the large amounts of energy from the staging bank. Both of these gaps must mul - t ichannel to operate correctly. In order that they multichannel, it is necessary that they receive a very-fast (10- 15 kV/ns), very- high-voltage (200 kV t trigger voltage. Producing this type of a trigger voltage in a large system is very difficult, and may be the largest engineering problem in the future operation of the experiment.

D. 0.9 m STP Prototype Fig. IV- 7 \’acuum joint used to connect two sections of The 0.9 m STP Prototype operated with plasma discharge tube in Staged Theta-Pinch experi- from .June to October 1974. The experiment had a ment. 22-cm-id. compressi(m coil with a 20-cm-i.d. quartz discharge tube. Each of the two feed points was The trigger system for PFN 1, PFN 2, and the driven by a capacitor bank consisting of three 125 kV staging bank are all basically the same and consist of capacitors, each capacitor having its own spark gap. a master which in turn triggers sub-masters (two) The spark gaps used were modified Scyllac gaps. which in turn trigger the main gaps (15 PFN or 20 Because of the high inductance of the spark gaps the staging gaps). These systems use RG-19 source and transfer efficiency without plasma was only about trigger cable; the source cables are pulse charged to 40ci. (The new gaps to be used on the 4.5 m experi- 200 kV by a small trigger Marx unit. ment will lower the source inductance by a factor of The STP experiment uses two completely new almost two. ) The experiment was operated initially spark gaps. The PFN gap is shown in Fig. IV-8. It is with 0.2 gF capacitors. With these capacitors the a 125 kV field distortion gap with fast biasing magnetic field waveform without plasma was a characteristics so that half the PFN capacitors may slightly damped L-C discharge with a half period of be fired without prefiring the other gaps. The staging 0.6 ps. With plasma the magnetic field waveform in rail gap (Fig. IV-9) is also a field distortion gap with the first half cycle was a slightly distorted sine wave

TABLE IV- 1

SUMMARY OF STAGED THETA-PINCH ENERGY STORAGE BANKS

Bank . Type Capacitor Number Stored Energy (kJ)

P.I. 0.7 ~F/75 kv 10 20

PFN {/1 0.2 PF/125 kV 30 47

PFN #2 0.4 LIF/125 kv 30 94 . Staging Bank 2 ~F/50 kV 320 800

Crowbar (Staging Bank) 0.7 pF/75 kV 32 63 . Maxi-Marx Assemblies* 15 IJF/20 kV 80 240 (To charge PFN system)

TOTAL 502 1264

*TheS~ assemblies consist of eight capacitors connected in a Marx configuration with a voltage output of 160 kV maximum.

48 a. Two different plasma regimes were observed. The initial conditions for the two cases differed tmly in initial fill density or in the size of the preioniza- tion bank. The difference in plasma behavior was probably a result of different preionizatitm levels. Similar results have been observed in Scylla IB. For low preirmization levels rapid magnetic field penetration occurs and a plasma with a relatively low $($<0.6) is formed. At higher preicmizati(m levels magnetic field penetration is about a factor of 2 slower and a high-$(~= 1) plasma is created.

b. During the implosion two luminous rings are observed. Figure IV-10 shows end-on streak camera pictures for four different plasma conditions. Of the four cases shown, the case with 8 mtorr fill and 0.5 k.J preionization capacitor had rapid magnetic field penetrati(m. The other cases correspond to slower field penetration.

c. During the initial implosion, magnetic field gradients extend all the way to the discharge tube wall. Similar results were obtained in Scylla lB Fig. IV-8 showing that the field gradients existed even in the l)FN spark gap. region where the plasma density was below the sen- sit ivity limit of the holographic interferometer ( -3 with a half period of 0.5 p.s. Because of the higher X 1014 cm ‘:3). Figure IV- 11 shows magnetic field source impedance the dL/dt term due to the im- profiles for the case of 123 kV main bank voltage, 13 ploding plasma did not cause as large a change in the mtorr initial fill. Figure IV- I la is the external magnetic field waveform as had been observed in the ma~metic field. Figures IV-1 lB, IV-n C, and IV-1 Id Scylla lB experiment. Because of this fact, the im- show B. vs radius for different times after main plosion velocities in the 0.9 m experiment and in discharge initiation. Scylla IB were similar, allowing a close comparison The magnetic field just inside the discharge tube of the results of the two experiments. wall is the same as the external magnetic field until The 0.9 m experiment was first operated with 0.2 approximately halfway through the second quarter pF capacitors up to a voltage of 95 kV. The cycle. At this time a strong breakdown at the wall capacitors were then changed to 0.4 KF. This in- (discussed below) occurs. This great ly reduces the creased the time of the first half period with plasma rate at which flux can diffuse into or out of the region to 0.8 psec. When the main bank was charged to 125 inside the discharge tube. Because of this effect the kV, operating conditions were close to those desired expansion of the plasma after the initial implosion for optimum magnetic field programming, i.e., the compresses the magnetic flux outside the main maximum of the magnetic field occurred slightly plasma column against the discharge tube wall. This before the time of maximum plasma compression ( - leads to a magnetic field time history at a point 0.5 . 650 ns). cm inside the discharge tube which is similar to the Preionization of the plasma was accomplished by time history desired for optimum magnetic field a Z-pinch discharge. The preionization bank was in- programming; the magnetic field external to the . itially a 0.7 pF capacitor. This was later increased to main plasma column decreases as the plasma ex- 1.5 pF to determine the effect of increased preioniza- pands after its initial maximum compression and tion levels on plasma performance. then rises again to prevent the plasma column from Plasma diagnostics consisted of an excluded tlux contacting the discharge tube wall. This effect is apparatus, an internal magnetic probe inserted ax- shown in Figs. IV-1 Ic and IV-lld. Although the ially and an end-on streak camera. plasma is still in the dynamic phase, the pressure The results of the plasma studies were: profiles at the later times in Fig. IV-1 Id show that if

49 I

+

+

+

+

+ — J

L11 Slss Ssss

the field near the wall could be held constant the Fifth Cfmference on Plasma Phvsics and Controlled plasma would probably settle down to a radius of Nuclear Fusion Research, Toky~, Japan, November about 7 cm. 11-15, 1974. The plasma results obtained on the 0.9 m experi- d. Secondary breakdown at the quartz discharge me~t lead to several conclusions. First, the mode of tube wall occurs about 600-700 ns after discharge in- magnetic field programming where the magnetic itiation. The cause of the formation of the current field in the first half cycle is in the opposite direction . sheath at the wall is unknown. The process may from the magnetic field at later times will not work start at the time when the plasma is in contact with due to the large amount of magnetic flux locked into the discharge tube and take some time to develop, or the plasma column. Secondly, a better understan- . it may be due to low density plasma being carried to ding of the origin and parameters of the low density the wall because of the decrease of magnetic flux in- plasma which causes the magnetic pressure side the discharge tube. gradients outside the main plasma column is need- The above results were presented, along with im- ed. Also more information should be obtained on the plosion studies on other experiments in the paper causes of’ wall breakdown and its dependence on dis- “Implosion Heating Studies in the Scylla IB, Implo- charge tube material. sion Heating, and Staged Theta Pinch Ex- pediments, ” by R. F. Gribble et aL presented at the

50 .

*

Q > 0 (9 0

.

.

51 E. 0.9 m Resonant Heating Experiment References . The 0.9 m Resonant Heating Experiment (RHX) 1. F.P. Friedberg, R.L. Morse, and F.L. Ribe, was designed and constructed during the last four “Staged Theta Pinches with Implosion Heating,” months of 1974. In its initial configuration it is the Technology of Controlled Thermonuclear Fusion Ex- * same as a 0.9 m PFN section of the STP experiment. periments and Engineering Aspects of Fusion Reac- After initial checkout and operation, it will be con- tors, Austin, TX, ( 1974), USAEC Report CONF verted to a configuration where each side of the ex- 721111. periment will have four 0.2 gF capacitors with PFN gaps. The other two gaps will be converted to crow- bar gaps to st udy the resonant heating concepts out- lined in Section B. Later it will be used to test new components such as new spark gaps and end-fed im- plosion coils which will be needed for future ex- periments on the STP experiment.

52 .

●

$

u .

*

53 .

V. SCYLLA IV-P THETA PINCH

● W. E. Quinn, A. G. Bailey, G.I. Chandler, L.D. I{nn.vb(m)uqh, .J. W. Li[lberg, M.D. Machalek, F. T. .S(>ihci

A. Introduction basic physics prohlerns relevant to h[)th approaches are being addressed in the Scylla IV-P device am-l in Scylla IV-P is a flexible, linear experiment to laser heating experiments of plasmas with magnetic sIlplxJrt the toroidal Scyllac experiments and to in- confinement. The Scylla IC experiment rlescrihed in vest igate high-density, linear t beta-pinch concepts. Secti(m VI addresses the question of laser heating of The Scvlla IV-P device was proposed 1’2 and dense theta-pinch plasmas. al)t)r[wed in FY 1974. It is a conventional linear The experiments planned for Scylla IV-P include theta pinch with a 5-m length that is energized by a the ft]l]owing: (a) Experiments to measure end fW-k\r. 2-M.] capacitor hank of”the Scyllac type. The effects including end-loss rates and associated design. f’abricati(m, procurement and c(mst ruct i(m of” phenomena such as “area waves”, the variat i(m of S(vlla IV-P began in early FY 1975 and is scheduled the plasma beta with time and axial positi(m. end ~[)r (.om])let ion in August 1975. short ing effects, and electron thermal conducti(m. I.inear theta pinches have demonstrated stable These experiments will assist in quantitative inter- I)lasma confinement and intense heating throughout pret at i(m of end effects; (b) Invest igat i(m of t he wall- the history of their exploration. In the micf-1960s, the stahilizat i(m phenornen(m is planned hy means (d’an Scvlla IV experiment at LASI, routinely produced inject i(m experiment.5 In the inject i(m procedure a ion heating to thermonuclear igniti(m temperatures theta-pinch coil is energized with quasi-steady in a straight theta-pinch geometry. In the linear helical magnetic fields which will ultimately contain systems the limiting factor on confinement is the a wall-stabilized helical column. Two adjacent I(JSSof plasma from the ends of’ the theta pinch and linear theta-pinch coils are operated in such a way not MHD stability (n- radial diffusi(m. However, the that their final pulsed field is of the same magnitude part icle losses through the ends at c(mvent i(mal rlen- as the quasi-steady helical field. The axial pressure sities (a few times 10 IGcm-:{) w(mld require a theta gradient created in their plasmas should drive pinch of several kilometers length to achieve plasma from each end into the helical region. The ec(m[]mical fusion power product i(m. diameter of the region into which plasma is injected The applicati(m of’ uranium (w thorium blankets can he made small enough to permit wall stabiliza- surrounding the plasma for the purpose of breeding tion. Fluid codes are now being developed to I)redict fissi(mahle materials gives iml)etus to the applica- the plasma behavior: (c) “V:iriahle-epsil(m” ex- tion of linear theta pinches as neutr(m s(mrces for periments are planned to study the Q= 1 and Q= O hyl)riri fusi(m-fissi(m.:] Therefore a c[)mpeilin~ scaling. and m = I growth rates relevan[ to the reas[m for pursuing high-density. linear theta-pinch Scyllac t(woicfal configuration.” An important aslwct research to larger systems is to breed fuel and of”these experiments will be the investigation of the pr(wirle power in combination with fission reactors. tlnite-I,arnlor-radius (FLR) stahilizati(m of m ~ 2 The linear theta pinch with its established plasma modes; (d) The application of’ the linear theta pinch . heating and stability properties may pr(wide such a to high I)lasma densities ( I-5X 1017cm–3) and high fusi(m-fissi(m hybrid system on a time scale com- magnetic fields (200-300 kG) will be invest igated. (; parable to that (d’ the first fusion test reactors. The These include high-density plasma formation and . .Sc.ylla IV. P linear t beta-pinch program stems f’rorn heating, particle and thermal-conducti(m end 10SS, approximately 20 years of world-wide research on and other end effects (line-tying, end shorting, the theta-pinch systems. It is a test bed for lon~er, “wohhle” effect, impurities, etc.). These ex- denser svstems aimed at a fusion-fission hybrid periments will provide important information for the system. There are two approaches to the linear linear fusion-fission hybrid reactor; (e) Various end- fusion-fission hybrid system: (a) a theta-pinch stoppering techniques, such as multiple mirrors, shock-heating and compression system; and (b) a cusps, etc., will be investigated to reduce the end- combination of laser heating and compression. 4 The 10SSrates; (f) The sustained theta pinch may also be

54 investigated providing studies indicate its feasibili- . C. Construction Status tv. A ctmstant dc magnetic field is generated by an outer coil and an inner pulsed coil is energized to br- Scvlla IV-P is approaching its period of maximum ing the dc field to zero in the plasma region to allow act ivitv relative to component assembly and in- a the initial plasma production and shock heating; (g) st allat ion. The skilled crafts have now essentially Laser-heating experiments will be performed using a completed their work of modificati(m of utilit ies and 1-k.J CO? laser furnished by the LASL Laser installation of’ new steel support structures in the Division: and (h) The device will also be used in the Pit. development of plasma diagnostic techniques. The PRIME computer and its attendant hardware have been set up in the Scyllac area. The system has B. Experimental Arrangement been debugged and at present software development is proceeding. As soon as the new screened r(wm has The Scvlla IV-P device is being constructed in the been erected and wired for power, the computer will Pit room. which has a floor area of 256 square meters be m(wecl to the Pit. and a ceiling height of 8 m. The 5-m long compres- The following” items are in progress in early 1975: si(m coil will be energized by a 60-kV, 2-MJ (’ollect(m plate fabrication, coil machining, cable capacitor bank of the Scyllac type. Figure V-1 shows dressing. vacuum system assembly, shorting ball an elevation view of the device. The arrangement of assembly, trigger system construct i(m,, and cable the energy storage system is unique in that the trav installation. capacitor-spark gap units are arranged in clusters on Delivery of load capacitors is essentially C(lmplete, a three level platform structure rather than in con- \vith less than two cifwen vet to be delivered. These vent i(mal racks. This will provide for more con- final units should be shipped along with venient access to the bank. The collector plates and rel)lacen]ents Ii)r defective units discovered during compression coil are situated on the middle or ex- testing. perimental platform level. Another feature of” the device is a computer control system.

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‘..,, ., ,, [m ‘/j,1 :, ., ,. ,1 :’ Liquid Ill I , resstct n,

r-+!!l’. L- PIm m

Fig. V-1 Elevation View of Scylla IV-P Experimental Area,

55 Sl)ark gap components have been steadily :Irriving 3. (J.E. %sler, D..J. Dudziak. and W.R. Ellis. “A . and presently enough C[)mpfments are ~\’ililal)lC to Preliminary Appraisal of a Fusi(m-Fissi(m Hyl)ri(l asseml)le shout -1oo” gaps. C(jnsidt’ral)le sLlh - Reactt]r Based on the Linear Theta Pinch.” l)roc. ;IssetI)l)ly work on sl)ark -gap com]xments has Ix$(tn Ninth Intersocietv Energy Conversi(m Engineering . (x~nll)lrtcd. Actual, complete assembly (Jfsl)ark gal)s C(nltkrence [IJ?CE(’). San Francisco (August 1971). hiis lxIctn p(wtlxmerl (!ntil spring 1975, at which time several new technicians are to l)e available Ii)rwxjrk. -1. \V. R. Ellis and G.A. S;lwyer. “St’sling I,tiws li~r Scvlla I\r-l) is now in an excellent Ixwition to (he l.il~ear Theta Pinch 1: A C[)ml)aris(m [)fMagnetic l)r(wced at I’1111spew] toward assernhlv. l+ilrring anv and I,asc*r Heat ing. ” 1,[)s Alamos S(icntil”ic

I“:lilllrt’ tore’ceivet ll(’llecc’ssary arlditi(mal I’[inrtstlnd l.iit)()]~t(]r\, Report I, A-54: {4-MS (C)ctol)er 197:{). ln:lnlxnver. conll)leti(m ot’the capacitor h:lnk system for S(’ylla IV-P hy mid-summer 1975 at present 5. B.M. Marder and R.E. Sierm)n, “A I.(mg (’(mline- ment Experiment (LC’E) Proposal.’” IAM Alamos :11)1)~’ilrsto he a very realistic goa]. Scientific Laboratory R(’p(rt I, A-5399-P (September References 1. W.R. Ellis. W.B. Riesel~feld, and 1973). (;.A. Sawyer. “l)roposal for the C(mstructi(m of a Scylla IV-P C(mfinemeni Studies Theta Pinch. ” Los 6. W.R. Ellis, “CTR Applications of the High- Alamos Scientific Laboratory Report LA-.5474-P J)ensitv Linear Thela Pinch.” Nuclear Fusi(m 15, (11[’cemher 1973). (1975).

?. W.R. Ellis, ,J.P. Freidberg, and W.E. Quinn, 6’Supplement to the Proposal for the C~mstruction of a Scylla IV-P Confinement Studies Theta Pinch, ” 1,os Alamos Scientific Laboratory Report LA-5474- P. Suppl. (May 1974).

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56 i

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57 VI. SCYLLA I-B/C

● K. F. McKenna, K. B. Freese, F. C. Jahoda, T.M. York, E. L. Zimmerman

A. Implosion Heating Experiments in Scylla I-B End-on photographs of the imploding plasma self- Iuminosity were made with a Beckman Whitley 1. Introduction. Future toroidal theta-pinch image-converter camera. The framing camera had devices will use fast implosion heating in order to an exposure time of 10-ns and a spectral response of generate high-~ thermonuclear plasmas of low com- 3500~-6500?L pression rat io (ratio of coil radius to plasma radius). The preionized plasma density distribution was Theoryl predicts that such plasmas can be wall studied using a 3.4-~m He-Ne laser interferometer stabilized against the m = 1 instability. The object of operating in the coupled cavity mode. The time the Scylla I-B implosion heating experiment was to resolved measurements were made end-on, with the study the implosion process over a range of Eo’s and laser beam parallel to the tube axis. Data were initial fill densities characteristic of past and present collected in l-cm radial increments. Scylla type theta pinches. 4. Preionization Studies. Preionization of the 2. Apparatus. The Scylla I-B O-pinch apparatus 10-mtorr Dz fill gas was accomplished with a single capacitor discharge through the compression coil. is described in the 1973 annual report. 2 Fifty-four Three different PI capacitors were used to generate 0.7 ALF capacitors provided a maximum energy the initial plasma; 1.8 KF, 0.7 pF and 0.25 KF storage of 106 kJ at a charging voltage of 75 kV. The capacitors charged to 55 kV. The total fractional 100-cm long, 22-cm-diameter compression coil con- ionization produced for each PI system was obtained sisted of two half-turn sections, each section being by numerical integration of the radial electron densi- fed by half the capacitor bank. Main bank operation ty profiles3 obtained from the coupled cavity from 40 kV to 70 kV generated vacuum Eo’s from interferometer data. At the time of main bank initia- about 0.7 kV/cm to 1.2 kV/cm at the inner wall of the tion the percent ionization of the fill gas was ~ 60% 20-cm id. discharge tube and corresponding peak with the 1.8 gF capacitor, =15% with the 0.7 PF un- crowbarred compression fields of approximately 9.5 it, and S5T0 for the 0.25 pF unit. kG and 17 kG were obtained 1.25 KS after main bank Internal magnetic field robe data taken during initiation. the preionization discharge’ ? indicated that after gas breakdown the external ringing magnetic field was principal plasma 3. Diagnostics. The effectively shielded from radial positions r S 6 cm. diagnostics consisted of magnetic field probes, a Within this radius the direction (negative field refers laser interferometer and a plasma luminosity detec- to BZ opposite to the direction of the main tor. The magnetic field probe contained three iden- compression field) and magnitude of the slowly tical ten-turn B, coils with a 2-cm separation decaying and spatially uniform trapped PI field was bet ween coils. The O.16-cm-diameter coils were 10-14 cm ‘3) giving an interferometer sensitivity of the magnet ic field penetration rate was about a fac- =3 X1014cm–3. One interferogram was obtained per tor of two slower, and a piston sheath thickness of plasma discharge.

58 about 2 cm was observed at 40 kV main bank a few radial oscillations the plasma column settled voltage. In the latter case, compression of the initial to a mean I/e radius of 4.5 cm with a peak density of . ( –60 G) trapped preionization field was observed on about 5X1015 cm–3 and attained an average axis. In the following only the results obtained with compressed-plasma kinetic temperature (Te+T i) of the high preionization level (15%, 0.7 ~F PI approximately 0.8 keV, as determined from pressure ● capacitor) will be discussed. balance. Scylla I-B implosion phase results for operation at The implosion phase results presented for 55 kV 40 kV main bank voltage, 10 mtorr initial fill main bank voltage are characteristic of those ob- pressure and preionnization level X1014 cm’3 have tained over the entire range of operating voltages, been published.4 Figures IV-1 and VI-2 present only the time scale of the implosion event and final results for 55 kV main bank voltage. Figure VI-1 column temperature changes, the implosion being shows end-on inter ferograms taken at six different more rapid and final temperatures greater at higher times during the implosion. The entire 20 cm diam initial E 0’s. of the discharge tube was illuminated by the laser During the implosion, magnetic field gradients are light. The tip oft he magnetic field probe, seen in the observed in the region external to the imploding inter ferograms, was located 5 cm from the discharge plasma density distribution, indicating the presence tube axis. At early times during the implosion (t s of a low density ( <3x10*4 cm–3, the holographic 200 ns, Fig. VI-I) a relatively smooth density dis- interferometer sensitivity) high temperature tribution is observed. At later times a well defined plasma. The magnetic field gradients, being nearly structure develops. Macroscopic flute like in- negligible at 40 kV main bank voltage, increase stabilities can be seen on the trailing edge of the den- significantly with increasing operating voltage. 5 sity distribution. Interferograms obtained at higher, Very similar behavior has been observed in the 70 kV, and lower, 40 kV, main bank charging Garchin high voltage, fast magnetic compression 0- voltages display an identical density structure dur- pinch, ing the implosion phase, with the inward radial density ~~?~~~~c~:~ ~~!#~l?I-~?~?~?@ velocity of the plasma being greater at higher bank cm ‘3 ). In the Garching experiment the external voltages. field gradients are believed to be supported by an Interferograms of the compressed plasma column observed low density plasma halo, n~-O.5X 1014 were also taken.3 Spatial integration of the reduced cm ‘3, caused by flute instabilities which develop plasma column density profiles n,(r) indicated that during the implosion. Flute-1ike instabilities, dis- all of the initial fill gas was swept up by the magnetic cussed below, have also been identified during the piston field. Although only 15% of the fill gas was Scylla I-B implosion. However, the existence of a low ionized at the time of main bank discharge, the density plasma region surrounding the plasma remaining neutral particles were ionized and swept column in the Scylla I-B experiment could not be up during the implosion process. Total sweep up was measured due to the sensitivity limitation of the in- indicated at all operating voltages. terferometer. It should be noted that the external Profiles of n,(r) and B.(r) at various times during magnetic field gradients indicated from the the implosion, derived from the interferograms (Fig. magnetic field probe data at the higher main bank VI- 1) and internal magnetic field probe data ob- voltages could possibly result from inaccuracies in tained at 55 kV main bank voltage, 5 are presented in the probe measurements resulting from probe in- Fig. VI-2. The implosion is characterized by an in- teractions with the hostile plasma environment. itial period, 100-150 ns, of fast penetration of the ex- ternal magnetic field, implying a plasma resistivity 6. Plasma Implosion with Applied Bias Field. during this time which is greater than classical. The The implosion process was studied with a reversed plasma resistivity drops rapidly with time as in- bias field applied. At the time of main bank initia- . dicated by the fact that the –60 G trapped tion the bias field had a magnitude of –400 G (op- preionization field is compressed by the imploding posite to direction of the main magnetic field). With plasma. Halfway through the implosion (t~200 the bias field, data were collected at 40 kV main nsec) the plasma density front begins to separate bank voltage and 10 mtorr Dz fill pressure. . and accelerate away from the magnetic piston field. Holographic interferograms taken with and The front attains a xpaximum velocity of about without the applied bias field are shown in Fig. VI-3. 3.5x107 cm/s, nearly 1.8 times as large as the The main bank voltage and fill pressure are the same magnetic piston velocity. The density front collapses in both interferograms. The structure of the im- on the discharge tube axis at t~410 ns. The piston ploding plasma is significantly altered by the in- field decelerates during the formation of the plasma troduction of the bias field. With no applied bias column and is finally stopped by the kinetic pressure field (Fig. VI-3a) the fully developed density profiles .of the /3x 1 compressed plasma at about 500 ns. After (plasma at mid-radius) are characterized by (a) an

59 .

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t= 100nsec t=335nsec

t=200nsec t=360nsec

.

t=275nsec t=410nsec . 55kVMain Bank Voltage, 10mTorr D2 Fill Pressure

Fig. W-l Plasma implosion inter ferograms.

60 I I I I I I I I I 6 I I I I I I I I I

J I 55 kV, 10 m torr t = 335 nsec 4 – t=155 nsec – 4_ B,

2 – Bz n~ o / L I I I I I I I 1 I I I I I I I 1 024 8 10 R(cmf I I I I I I I I I I I t = 215 nsec t = 360 nsec

n~

I I I I I I

I I I

t = 275 nsec B,

L I I I I I I I I I

Fig. VI-2 Implosion profiles of n,(r) and B.(r) at fixed times, reduced from inter ferograms and magnetic field probe data obtained at 55 kV main bank voltage.

61 .

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—u a) ● - IL

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62 initial density rise and plateau, interpreted as a photographs, was located 5 cm from the discharge shock region containing plasma moving ahead of the . tube axis. Immediately after discharge initiation a magnetic piston field, (b) a density peak correspon- single uniformly luminous structure, indicative of ding to the magnetic piston region and (c) a region of current sheath formation, is observed near the dis- electron density decay which supports flute-like charge tube wall. As the current sheath accelerates . macroinstabilities. Conversely, in the presence of radially inward, striations in the outer luminous the bias field (Fig. VI-3b) a relatively smooth densi- boundary appear. These striations indicate the ty profile is observed for the entire duration of the growth of Rayleigh-Taylor flute-like instabilities, 9 implosion event. The development of flute-like in- generated during the inward acceleration of the stabilities on the trailing edge of the imploding den- plasma-magnetic field interface. For an incom- sity distribution is not affected by the bias field as pressible fluid the growth time for the flutes is given can be seen from inspections of Figs. VI-3a and VI- by T= (gk) -1’2, where g is the interface acceleration 3b. In addition to altering the imploding plasma and k the wave number (k= 2xIA, where A is the structure, the bias field also increased the time re- wavelength). This formulation is extended to the quired for the plasma to arrive at the discharge tube present case only to indicate expected order of axis, an expected result. The pinch time with the magnitude values. At t% 175 ns the instability m applied bias field is about 525 ns compared to 435 ns number (total number of striations), determined without the bias field. from the luminosity photographs and laser in- At the termination of the implosion a “density terferograms, discussed below, is approximately 90 well” is observed on axis in the bias field case. The at a“ mean radius r=9 cm, yielding a wavelength density minimum is attributed to trapping of the A=2rr/m of 0.63 cm. Estimating the interface reverse bias field during the implosion. The density acceleration from the trajectory of the density profile minimum on axis persists for the duration of the ex- peak to be about 7X1013 cm/s2, the predicted growth periment, -1500 ns, indicating that the compressed time is then -40 ns. This is within an order of trapped field is not annihilated within the plasma magnitude of the observed time of appearance of the column, a result substantiated from the internal striations, about 150 ns after discharge initiation. magnetic field probe measurements. 5 Spatial The instability wavelength increases linearly with integration of the plasma column density profiles in- time attaining a maximum value of 1.2 cm at t ~500 dicated, as in the case without applied bias field, ns. that all the initial fill gas was swept up during the As the implosion progesses a structureless inner implosion. luminous front develops and moves ahead of the striated region, the front being separated from the 7. Imploding Plasma Self-Luminosity striations by a relatively dim ring (t =210 ns, Fig. VI- Patterns. In weakly compressed (a/b-l/3) high-~ 4). The dim ring moves inward with the magnetic plasmas at low O-pinch fill densities nO<1014 cm ‘3, piston velocity, while the inner luminous front Rayleigh-Taylor flute instabilities which surround travels inward at the velocity of the imploding the implosion-heated plasma column and extend to plasma density front. Approximately 100 ns after the the discharge tube wall have been identified luminous front collapses on the discharge tube axis, photographically. The question of the existence of the striations in the outer luminous region can no such macroinstabilities disrupting the stabilization longer be photographically observed. of confined ~lasmas m“ planned, 8 higher density (~-1015cm - ), wall stabilization experiments has The evolution of the flute instabilities was also observable from end-on interferograms. Figure VI-5 been posed. 7 In Scylla I-B the evolution of these instabilities was observed, both photographically shows interferograms taken during the implosion and by interferometer density measurements. The (t =325 ns) and after formation of the plasma column . flutes only occupy a fraction of the plasma self- (t =640 ns) for 40 kV main bank voltage and 10 mtorr Iuminosity pattern. Details of the total self- fill pressure. The flutes appear as ripples on the luminosity patterns have been directly associated trailing edge of the density distribution (t =325 ns, . with the dominant structural features of the tran- Fig. VI-5). The time varying instability wavelengths sient plasma density and magnetic field distribu- obtained from the interferograms are identical to tion. those determined from the luminosity photographs. The time development of the plasma self- Of major significance here is the fact that the in- luminosity, obtained with a 10-ns exposure time stability disappears (n, <3X10*4 cm–3 , the end-on framing camera is shown in Fig. VI-4. The interferometer sensitivity) after the plasma column photographs were taken at 40 kV main bank voltage is formed. This is seen from inspection of the in- and 10 mtorr fill pressure and are typical of those ob- terferogram taken t =640 ns, Fig. VI-5. As previously tained at higher operating voltages. The tip of the noted this occurs about 100 ns after collapse of the magnetic field probe, visible in some of the luminous front onto the discharge tube axis. Such

63 .

t=80nsec t=290nsec t=440nsec

t=175nsec t=350nsec t=500nsec

.

. t=210nsec t=415nsec t=670nsec

Fig. VI-4

Tim e scquencc of framing camera photographs taken during the plasma implosion.

64 .

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65 behavior indicates the interaction of either a the -2-cm-thick plasma front region. The ionization reflected shock wave with the region of instability, or cross section is about 6X 10–17 cm–z and with an . radially imploding deuterons passing through the elect ron density of -1X 1015, the ionization time is center of the tube and interacting with the piston on the order of 50 ns. In the plasma frame a neutral field. The exact mechanism causing the flute dis- travels -1.6 cm during the 50-ns time interval, in- . appearance is unknown. In either case, the ex- dicating significant ionization phenomena in the perimental results demonstrate that macroscopic piston, which could account for the density increase flute instabilities do not surround the implosion- in this region. heated plasma in 1015 cm’3 fill density O-pinches. From the known framing camera and film spectral Accordingly, such instabilities would not be ex- sensitivity, phototube gain, and geometry of the op- pected to influence the stability of the plasma tical setup the power density of the emitted plasma column in planned wall stabilization experiments. a self-luminosity was determined within an accuracy Figure VI-6 shows profiles of nC(r) and Bz(r) at of about a factor of two. A comparison of the t =385 ns derived from the inter ferograms and measured power density wit h that predicted for magnetic-field-probe records obtained at 40 kV main Bremsstrahlung emission (PB cc n~T,– 1/2), over the bank voltage. The reduced data illustrate the struc- spectral range of the phototube, indicated that the ture of the plasma halfway through the implosion, radiation observed from region I could result solely where initial effects (rapid tield diffusion and piston from continuum emission, assuming a reasonable sheath formation) no longer dominate the flow and electron temperature on the order of 25 eV. 10 To the general characteristics of the imploding plasma supphrt this result, various light filters were used in are fully developed. Also shown in Fig. VI-6 are the order to identify the spectral distribution of the boundaries of the self-luminous regiims, obtained emitted radiation. Results of the filter studies again from reduction of many luminosity photographs. demonstrated that Bremsstrahlung radiation could Region I corresponds to the boundaries of the inner account for the observed emission. From these uniform luminous front and is identified with the results it can thus be inferred that the dim ring plasma which travels ahead of the piston field and (region 11) identifies a region of rapid electron interacts with the partially ionized background gas. heating, probably turbulent, in which the electron The dim ring, region H, coincides with the magnetic temperature increases significantly, decreasing the piston, defined by the maximum B, gradient and intenstiy of the continuum radiation. Such rapid corresponding to the electron density peak. Region elect ron heating in the magnetic piston region agrees HI identifies the trailing edge of the detectable elec- with previous experimental results.6.10 tron density profile where the flute instabilities generated during the early stage oft he implosion are observed. B. Plasma Experiments in Scylla I-C The ions in the plasma front interact with the neutral background throu h char e exchange with a 1. Introduction. The Scylla I-C theta pinch is -1% cm-f cross section ax 2X1O For the neutral being used in conjunction with a CO1 cold cathode density of -6X 1014 cm ‘3, the ion mean-free path is laser, supplied by the L-1 group of the Laser -0.8 cm, indicative of some collisional processes in Research and Technology Division, to study the in- teraction of axially directed long wavelen th laser light (10.5 ym) with the dense (n,> 10 *!’ cm-3) %@---- 3 - - 5 theta pinch plasma column. Initially, the ex- + I ---+ll-+m/~-” perimental investigation will be directed toward ~- E studying (a) containment or diffraction of the laser “2 - ul beam as it traverses the meter-long plasma column, . -0 = ne (b) heating of the plasma column by laser energy ab- - 2 cm I - sorption and (c) instability induced anomalous backscatter of the incident laser light. . Construction of the C02 laser has been completed 0 56789 and electrical testing of the laser power supply r (cm) system is in progress. Operation with plasma of the Scylla I-C theta pinch began in ,July 1974. The elec- Fig. VI-6 trical characteristics of Scylla I-C and the properties Profiles of nc(r) and Bz(r) and the plasma self of the theta-pinch generated dense plasma are dis- luminosity boundaries half-way through the cussed below. implosion.

66 2. Experimental Arrangement. A schematic of Fig. VI-9. Spatial integration of the reduced density the Scylla I-C linear O-pinch is shown in Fig. VI-7. profiles m(r) indicated that for the 100 mtorr fill . Scylla I-C has a maximum capacitor energy storage pressure case, 50% of the fill gas was ionized by the of 175 kJ at 60-kV main bank voltage. Fifty-four 1.8- time the pinched plasma column had expanded to KF capacitors feed the 100-cm long, 10.5-cm discharge tube wall. With 500 mtorr fill pressure, . diameter single turn compression coil. Main bank about 20% of the gas was ionized at this time. operation at 40 kV generates a vacuum Ee of 0.26 kV/cm at the inner wall of the 3.6-cm id. quartz dis- 4. Main Discharge Luminosity Measurements. charge tube and a peak crowbarred compression Side-on streak photographs of the main discharge field of 33 kG is obtained 2.0 PS after discharge in- plasma were taken at the coil midplane. Figure VI- itiat ion. Plasma experiments, conducted at 40-kV 10 shows typical streak pictures obtained with main bank voltages, have been carried out over a PO= 100 mt err. These streaks are characteristic of range of fill pressure, PO, from 100-mtorr to 500- those taken at higher fill pressures.** mtorr Dz. The dynamics of the plasma during the implosion and plasma column formation phase can be observ- ed in Fig. VI-ha. The initial radial shock wave and subsequent plasma oscillations can be clearly iden- tified. The radial oscillations damp out ap-

I 39 nH 106nH proximately 1 KS after termination of the implosion. T/4 = 2,0~sec il i The quiescent plasma column is highly stable and L St,rt ~ Crowbar spflr~. qaps spark gaps reproducible for a period of approximately 9 AN,Figs. T 972/.lf VI- 10b and VI-1OC. The compressed column breaks “50 kV O{scharge tube , up into filaments (m =2) after this time, probably as 122 kJ d!om 3Gcm(, d) COII 4=IM a result of classical Rayleigh-Taylor flute-like in- T auortz“ “Pdlom :105 ~m T 1 stabilities characteristic of high-density O-pinch 54 spark gao 54 crowbar CompressIon capOcItoC m)ts spark qop un,ts Coil operation .12

Fig. VI- 7 5. Plasma Density Measurements. The time .%>[la I-C theta pinch schematic. and spatial evolution of the main discharge plasma density distribution was determined using a 30-ns pulsed holographic ruby laser interferometer. A limited number of interferograms were taken with 3. Preionization Studies. Gas preionization is the laser beam transverse to the plasma column. In accomplished with a specially designed Z-pinch order to obtain details of the plasma density dis- preionizer. The Z-pinch system consists of a 0.7-KF, tribution near the column axis, the majority of the 75-kV capacitor, a crowbar spark gap modified to ac- interferograms were taken with the laser beam commodate five varistors, eight RG -14/59 load parallel to the tube axis. cables, and the Z-pinch electrodes. A schematic of Figure VI- 11 presents a sequence of end-on in- the Z-pinch is shown in Fig. VI-8a. The current terferograms obtained with an initial fill pressure of waveform generated by this system, at a capacitor 100 mtorr. The plasma column formation phase voltage of 60 kV, is presented in Fig. VI-8b. A side-on (t=O.7 gs, Fig. VI-11) is dominated by high m- streak camera photograph of the preionized plasma renumber (m>6) flutes, with some of the flutes exten- for 100-mtorr fill pressure is presented in Fig. VI-8C. ding from the plasma column to the discharge tube . A sufficiently rapid rising current, of -18-kA peak, wall. At later times, t>l.4 Ks, the flutes disappear is supplied to the static fill gas to cause pinching of and a well confined high density plasma column is the plasma under the jZBti force interaction. At the observed for several microseconds. The beginning of . termination of the pinch the plasma expands and the plasma column break up and filamentation uniformly fills the discharge tube. (m=2) is evidenced at t=10 As. The density of the preionization plasma was Figure VI- 12a presents a plasma column in- measured by means of a 30 ns pulsed holographic terferogram obtained at 300 mtorr fill pressure and is ruby laser interferometer. A single pass end-on typical of the high fill pressure data. The plasma system with a sensitivity of -1 x 1014 cm’3 was electron density profile, derived from the in- used. A typical preionization plasma inter ferogram, terferogram of Fig. VI-12a is shown in Fig. VI-12b. obtained wit h 100 mtorr fill pressure, is presented in The density profile is non-Gaussian and exhibits a

67 ELECTRODE \ 8, RG-14/59 + 1 I CABLES e— \ J!!5 5 VARISTORS \ DISCHARGE TUBE \ . SPARK GAP> 9 loon L

I 0.7 pf T n

a) Z-PINCH CIRCUIT SCHEMATIC

b) CURRENT WAVEFORM

l—-- w--l

.

.

C) STREAK PHOTOGRAPH

Fig. Vi-8

X-pinch preionization system.

68 .

.

. . -q-.—-’-”---q!!.—

,/

.

. t= L25pec

Fig. VI-9

Inter ferogram of preionization plasma obtained with 100 mtorr fill pressure.

69 .

. a)

c)

.

. -1 1- 10 flsec

Fig. VI-10

Streak photographs of the main plasma discharge obtained at 100 mtorr fill pressure.

70 .

.

0,7psec 2.5psec 6.Op.sec

1.4~sec 3.Op.sec w8.Opsec

2. Opsec 4.Opsec 10.O~sec

Fig. VI-II

Time sequence of plasma column inter ferograms obtained at 100 mtorr fill pressure.

71 .

.

a)

L5

\ . \ ‘o \ \ GAUSSIAN \ \ 1.0 . d \\ \ b) \

n \ 0.5 . \

. \ \ \\ .

I 1 1 I w 0 1 .

TUBE RADIUS (cm)

Fig. VI-12

Plasma column inter ferogram and reduced density profile forp 0=300 mtorr, t =2. 7ps.

72 long tail which, at high fill pressure, extends to the 1.8 . discharge tube wall (r= 1.8 cm). Extracting an exact plasma density profile from the interferograms taken 1.6 - at fill pressures greater than 300 mtorr is difficult * due tot he large number of closely spaced fringes. At P,, =500 mtorr t he total number of fringes was x77 at I.4 - maximum compression, t=2.O ps. The peak density on axis could be estimated from simple fringe coun- ting and the peak density determined from the end- 12 - on interferograms at 500 mtorr fill agreed within 20% with the values derived from the side-on in- z 1.0 - terferograms. .S = From analysis of many interferograms, the ~. average plasma density at maximum compression, 0.8 - t=2.O ~s, was estimated to be 1.05x 1017 cm–3 at P. =100 mtorr, 1.45x1017 cm–3 at PO=250 mtorr, and 0.6 - 1 2.33x 10*7 cm–3 at 500 mtorr fill. Spatial integration over the reduced density profiles, obtained at 100 mtorr and 250 mtorr fill, indicated that 100’L of the 0.4 - fill gas was ionized and contained within the obser- vable plasma density distribution at the time of 0.2- maximum compression; approximately 70% ioniza- tion was indicated from both end-on and side-on data at Po = 500 mtorr. 01 , ! 0 [ 2 3 4 5 t (~sec) 6. Excluded Flux Measurements. The effective radius r~fl at which magnetic flux is excluded from the compressed plasma was determined from stan- Fig. VI- 13 dard differential magnetic loop probe Excluded flux radius obtained at 100 mtorr fill measurements. The excluded flux data, when ap- pressure. propriately combined with the known plasma densi- ty distribution, is used to determine the plasma 6 duration is also observed. The minimum value of r ~cf (ratio of plasma pressure to magnetic field pressure). is almost insensitive to fill pressure, changing only From the $ measurement an estimate of the plasma 15% between 100 mtorr fill (0.22 cm) and 500 mtorr kinetic temperature can be made. fill (().19 cm). The excluded flux radius derived from the loop probe data is presented in Fig. VI-13 for the 100 mtorr fill pressure case. The implosion phase, 7. Determination of Plasma ~. From the damped oscillation phase and quiescent plasm a definitions of excluded flux and the pressure balance column phase observed in the streak photographs of equation it can be shown 13 that the area of excluded Fig. VI-10, can also be identified from the excluded flux rr%r is related to the plasma 6 through the flux data of Fig. VI-13. Of primary interest to the expression C02 laser-plasma interaction experiment is the m 2 quiescent plasma column period immediately w (1) . eff = f [1-=]2~rdr following the damped plasma oscillation phase. Dur- o ing this period the plasma density is maximum, the Assuming that the plasma temperature is indepen- plasma column is well defined and the end losses . dent of radius, pressure balance yields minimal. From Fig. VI-13 it can be seen that rel~ remains relatively constant at a minimum value of (2) 0.22 cm for a period of approximately 1 KS centered about the time of maximum compression, t=2.O Ps. It is during this time interval that the CO z laser where nA and PA are the plasma density and ~ on beam will be fired. The excluded flux data of Fig. VI- axis. For a Gaussian density distribution, substitu- 13 is typical of that obtained at higher fill pressures, tion of Eq. (2) into Eq. (1) yields an exact solution where a period of constant r~ff of at least 1-KS for P,4 as a function of refr and the I/e plasma radius.

73 For a non-Gaussian profile such as shown in Fig. VI- IX IO’8 100 .0 12b, n(r)/nA must be det ermined graphically and t he . result substituted into Eq. ( 1) which can then be numerically integrated to determine 8A. For the Scylla I-C density profiles at maximum . compression, t=2.O ps, the fiA determined by 5X10’7 50 ).5 numerical techniques were; 9,4=().45 with PO= 100 H mtorr and @A=0.33 with PO=250 mtorr. The value of t- !- @A obtained assuming a Gaussian profile (Fig. 12b) and calculating the l/e radius using the peak density value were; $A =().63 for 100 mtorr fill and PA =().37 1 for 250 mtorr fill. The difference between the PA m- ‘E BA determined numerically and that calculated assum- 0 ing a Gaussian profile decreases as the fill pressure c< increases, being - 2996 at 100 mtorr and 11!; at 250 mtorr. The convergence of the PA values generated by the two techniques indicates that the density profiles more closely approximate a Gaussian shape as the fill pressure is increased. Assuming that the IXIC17- Ic ).1 profile at P. =500 mtorr is Gaussian, the calculated @Ak then @.17.

8. Determination of Plasma Electron Temperature. The compressed plasma ._..__ . &05 temperature is determined from the measured io’o 2&I 3;0 400 500 values of plasma density on axis n& the measured ~ (mtorr) external magnetic field B., and the calculated values of bA. From pressure balance, Fig. VI- 14 B: Scylla I-C plasma parameters at the time of B — x nAk(Te+Ti ) (3) A 8Tr maximum compression, t =2. O p.s.

In the high density plasma column the thermal channeling of the laser beam along the large aspect equilibration time between electrons and ions is ratio (L/D =-100) plasma column, (b)plasma heating small (<< 1 ys) so that k(Te+Ti)~2kTe. The plasma by laser energy absorption and, (c) anomalous electron temperature can then be determined direct- backscatter of laser light. ly from Eq. (3). The properties of the dense plasma column Figure VI-14 summarizes the Scylla I-C plasma generated in Scylla I-C have been discussed in the parameters nA, Te and PA obtained at maximum previous section. Final electrical testing of the C02 compression over the investigated range of fill laser system is currently in progress. The design pressure, Po, from 100 mtorr to 500 mtorr. The error characteristics of the C02 laser and a discussion of bars displayed on the plasma density data reflect the the expected results of the laser-plasma interaction, assumed uncertainty in the data reduction and in- based on preliminary analysis, is given below. dicate the error associated with the calculated value . of Te and PA. 2. C02 Laser Parameters. The CO? cold cathode laser was designed and constructed by the C. Laser-Plasma Interaction in Scylla I-C L-1 group of the Laser Research and Technology . Division. A modification of the A-3 amplifier14 oft he 1. Introduction. The concept of heating high LASL C 02 laser system was chosen as a source for density magnetically confined plasma with long the 50-100 J requirement of the laser-plasma interac- wavelength laser light is of considerable interest for tion experiment. A photograph of the completed fusion applications. The Scylla I-C experiment was laser system of the Scylla I-C experiment is shown in initiated in order to investigate the interaction of a Fig. VI- 15. The C02 laser design characteristics are 10 Km C02 laser beam with a high density (n,> 10*7 given in Table VI-I. cm-s) fl-pinch plasma column. Initial experiments will be directed toward the investigation of (a)

74 TABLE VI-1

C09 Laser Parameters L

Optical aperature : 50 cm2

Laser length . I 00 cm

Beam diameter 8 cm

Short pulse ou- put : 80~20 J in (j(j ns (ZX 09W, peak)

Focusing mirror : R=6m for post-pinch heating radius of curvature : R=8m for laser preheating

Focused beam diameter : 2 mm

Laser power density : ~x~ol”w/cm2(nominal average)

The 8-cm diameter beam will defocused onto the I/2 I .03x1035(T )3’2 n end of the plasma column by one of two possible e !?, = l-~ (4) spherical reflecting mirrors. A mirror with radius of ab n2 ,.19 e kh(l .39 Te)3’2 curvature, R=6 m, will focus the beam to a -2-mm om spot at the near end of the plasma column. This mirror is intended for heating of the compressed where Te is in eV and ne in cm ‘3: This length plasma column. A second mirror with a radius O! represents the distance at which the power in the curvature of 8 m will be available for future ex- C02 laser beam, traversing a uniform plasma of periments where laser heating of the preionized temperature T, and density n,, will be reduced to I/e plasma, followed by main field compression, will be (37’;6) of its initial value. The absorption length is invest igated. The R= 8 m mirror would focus the plotted in Fig. VI-16 for the experimentally deter- beam at the far end of the plasma column. mined plasma parameters of the Scylla I-C theta pinch. 3. Laser Heating of the Plasma Column. The The rate of energy absorption by the electron plasma column generated in the Scylla I-C theta population as a result of the inverse bremsstrahlung pinch has a density maximum on axis. A fundamen- mechanism, assuming that the electron-ion ther- tal objective of the present experiment is to deter- malization time teq is greater than the laser pulse mine if the laser beam will “drill” a hole into this width t ~ and neglect in ~ thermal heat conduction density maximum and channel down the entire losses, can be written as 1< length of the plasma column. Channeling of the aT beam will be considered in a later section. For the $ Nok $ = W/9. (5) discussion given below it will be assumed that the ab incident laser beam does remain contained within . the compressed plasma column. where No is the particle line density (N O=fill density In the fully ionized plasma column the energy of x discharge tube area) and W is the CO~ laser the incident C02 laser light is absorbed through the power. Neglecting scattering and emission, the spatial rate of change of the incident laser power is . process of inverse bremsstrahlung by which the elec- trons are accelerated in the electric field of the focus- given by ed light. The plasma ions are heated as a result of W — = -w/lab subsequent elect ron-ion collisions. For CO ~ laser dz (6) radiation, the inverse bremsstrahlung power absorp- where z =0 defines the vacuum-plasma interface at tion length in an underdense plasma (n~<

75 .

.

Fig. VI- 15

C(I2 laser constructed for the Scylla I- C laser-plasma interaction experiment.

76 -.

I 1 I 1 1 % = ,.7)(,03”- ab (7) e

where fn( 1.39T,)3’2 = Qn .i has been taken as 6. As the electron temperature increases the local plasma expands. Assuming that pressure balance is maintained and that /3 does not vary significantly during the expansion, the electron density can be written as

n = 2.5X,0’O @2 e (8) ()Te + T: where T? is the plasma ion temperature prior to laser heating in eV and B is in gauss. The laser beam is assumed to expand at the same rate as the local plasma. Substituting Eqs. (7) and (8) into (5) with W=WO

n~=2.33x10’7cm-3 yields,

~=loev 3Te _ E ~6B2)2(T ~-3/2(T ●To)-2 —- [.5XI05 f (9) a+ a ei o 10’0 I 1 I I t () 1AI00 200 300 400 500 600 where E ~(J) is the total laser energy. Integrating the ~ (mtorr) above equation over the laser pulse width tQ and neglecting any changes in the ion temperature gives, Fig. VI-16

Coj laser beam absorption length for the + (Te) “2 + ; (~)7’2 (~) + ; (Te)5’2 (~)2 cxperimentall.y determined plasma parameters

in the Scylla I-C theta pinch. E = ~ 45 ~To)9/2 + 1.5XI05 (f3B2)2 : (lo) e path. Substituting this solution for W(z) into Eq. () o (5), the change in electron temperature can be ob- tained by integrating Eq. (5) over the duration of the where T: is the plasma electron .temperature prior to laser pulse. This procedure provides an approximate laser heating. value for the laser induced change in electron For the Scylla I-C experiment where B=33 kG (at temperature when the absorbed laser energy results peak compression, t=2.O MS) and E0=80 J, the in only a small perturbation on the total plasma expected electron temperatures at the laser input energy. end of the plasma column calculated from Eq. ( 10) When the absorbed laser energy becomes a signifi- and the final heated region density, estimated from cant fraction of the initial plasma energy, nonlinear Eq. (8), are given in Table VI-II. absorption, referred to as “bleaching”, results. Since From a more detailed analysis of the nonlinear laser R ● ab - T#2, local laser heating of the electron plasma absorption process 16 it can be shown that, for the continually increases the absorption length over the measured Scylla I-C plasma parameters and COZ laser pulse duration, rendering the plasma in- laser energy, the laser induced electron temperatures creasingly more transparent to the incident radia- at the laser beam exit end of the plasma column are . tion. In this case Eqs. (5) and (6) must be solved within 10% of the values calculated for the input wit h !2~b as a function of the local electron end, indicating a relatively uniform heating of the temperature and density. entire plasma column. For nonlinear absorption, the governing equations In the above analysis only electron heating was can be simplified by considering only the electron considered, the electron-ion thermalization time was temperature change at the laser input end (z =0) of assumed to be long compared to the laser pulse the plasma column. In this case W in Eq. (5) can be width, t~ =60 ns. From Spitzer17 the thermalization replaced by Wo, the incident laser power. From Eq. time between the laser heated electrons and the (4) the absorption length can be approximated as,

77 TABLE VI-11 density minimum (and thus channel) even if a den- sity maximum is initially present on axis of the con- Initial plasma , temperature, plasma temperature fined plasma column. It would thus appear that a increase after iaser heatfng and final heated piasma density as a function of fiitial fiil laser power density “self-channeling” threshold ex- ists, above which the laser beam will “drill” its own pressure . density minimum through the plasma regardless of P. (m+orr) Te (eV) ATe (eV) he (1017 cm_3) the on-axis density conditions. It might be expected that such a threshold would coincide with the initia- I00 66 8 i .02 tion of the “bleaching” phenomena discussed earlier. It should be noted that in Hoffman’s 250 42 II 1.19 experiment 20’21 the plasma column leng-t h was an 500 2e i8 i .22 order of magnitude smaller (10 cm) than the column produced in Scylla 1-C (100 cm). Accordingly, the plasma ions is =425 nsec at P,,=1OO mtorr and investigation of beam channeling in the present ex- bQ=llOnsat 500 mtorr. Thus, the ion temperature periment, and the possible identification of a “self- significantly lags the electron temperature over the channeling” threshold, is of primary interest. time scale of the laser pulse. Assuming that the laser beam forms its own densi- A possible energy loss mechanism, not included in ty minimum during the early stages of the laser the simple analysis presented above, is radial heat pulse (an assumption consistent with the bleaching conduction. Since ~Ci Li0, converging diffraction of for radial heat diffusion L = ~D7 , where D1 is the the incident laser light is indicated. Further, the cross field thermal diffusivity5 is determined to be analysls “ 16 predicts that at sufficiently large axial approximately 0.013 cm, which is nearly an order of positions, point focusing of the channeling laser magnitude less than the radius (>0.1 cm) of the beam will occur. The axial position, fP at which all heated plasma region. Accordingly, radial heat of the internal laser beam is focused to a point can be losses during the laser heating time are insignificant. obtained from the calculated ray trajectories. (It Since the plasma column is expected to be heated should be noted that total focusing of the laser beam relatively uniformly along its length, axial heat con- will not occur since, in any real plasma, the density duct ion is unimportant. gradient (dn/dr) goes to zero as r - O). For the Scylla I-C plasma parameters it can be shown 4 that Q~1, 4. Laser Beam Refraction-Channeling and < 0 should result in fusion applications. These effects will be in- channeling of the beam down the column axis, and vestigated in detail in the present experiment. possible beam self-focusing. Conversely, the laser . beam would be expected to refract away from the ax- 5. Laser Light Scattering Instabilities. The is, and thus out of the plasma column, if the plasma irradiation of plasma with laser light of sufficient density has an on-axis maximum. Experimentally, it power level can cause “laser driven instabilities” to has been established 19 that channeling of the laser occur which result in anomalous absorpticm22 or . beam does result when the plasma has a density backscatterm of the laser light. Anomalous absorp- minimum on axis, and for low power density laser tion instabilities are effective for laser radiation near beams ( - 107 W/cm2), refraction of the beam out of the plasma frequency or twice the plasma frequency. the plasma has been observed 19 fort he case of an on- In the Scylla I-C experiment uo<

78 be important. However laser light scattering in- 3. K.F. McKenna, R. Kristal, F. Jahoda, R. Grib- . stabilities, which occur in underdense plasmas, ble. K. Thomas, E. Zimmerman, F. Seibel, S. could result in the reflection of a significant fraction Linzey, R. Deaton, R. Amsden, J. Smith, CTR-3 of the incident laser radiation. Quarterly Report, July-September 1973. . The set of coupled wave equations which describe the evolution of the scattering instabilities are ob- 4. K.F. McKenna, R. Kristal and K.S. Thomas, tained by combining the fluid equations for ions and “Measurements of Plasma Density Distribution and electrons with Maxwell’s equations. It can be Current-Sheath Structure in the Implosion Phase of shown23 that the solution of this set of equations is a Theta-Pinch Discharge,” Phys. Rev. Lett. 32, 409 completely described in terms of three waves excited (1974). by the incident laser light. Two of the excited waves are electromagnetic, the backscattered wave and a 5. K.F. McKenna, E. Zimmerman, S. Linzey, forward traveling nonresonant wave. The forward port, ,Jiinuary-March 1974. scattered “Stokes” wave, not being in resonance, can be neglected. The remaining excited wave is 6. F. Soldner, “Investigation of Fast Magnetic electrostatic, being either an ion wave, Brillouin Plasma Compression as a Method for Generating scattering, or an electron plasma wave, Raman High Temperature with Weak Compression, ” Max- scattering. Planck-Institut fur Plasmaphysik Garching bei The power density thresholds for the scattering in- Munchen Report IPP-1/141, 1974. stabilities are obtained from balancing the wave growth rate with the damping rate. For the Raman 7. M. Keilhacker, M. Kornherr, H. Niedermeyer, F. and Brillouin instabilities the linear thresholds can S61der, and K.H. Steuer, “Flute Instabilities during be written as,23 Fast Magnetic Compression of Collisionless /3=1 Plasmas,” Phys. Rev. Lett. 32, 1044 (1974). I (I?aman ) > J#J- nemec3 (11) a pe 8. F.L. Ribe, cd., “Proposed Experiments on Heating, Staging, and Stabilization of Theta Pinches,” Los Alamos Scientific Laboratory report ‘Lve i 2 2 l(Bril louin) > 4 — vekonemec (12) LA-5026-P, ( 1972). u Uz s pe 9. T.S. Green and G.B.F. Niblett, “Rayleigh-Taylor where yP = (-y + ~ei ) is the damping rate for the Instabilities of a Magnetically Accelerated Plasma, ” electron wave, y the Landau damping rate, ~ei the Nucl. Fusion 1, 42 (1960). electron-ion collision frequency, uPe the plasma frequency, u, the ion wave frequency, WOand k. the 10. M. Keilhacker, M. Kornherr and K.H. Steuer, incident light frequency and wave number, respec- “Observation of Collissionless Plasma Heating by tively and v, is the electron thermal velocity. Strong Shock Waves,” Z. Physik 223, 385(1969). In the Scylla I-C experiment the C02 laser power density is expected to be IX4X 1010 W/cm2 . The 11. K.F. McKenna, E.L. Zimmerman, S. Linzey, instability thresholds for the plasma parameters at R. Kristal CTR-3 Quarterly Report, July-September p,) = 250 mtorr (Fig. VI-2) are 1974. I(Raman)~I(Brillouin)x 3X108 Wlcrn2. Accordingly, strong backscatter of the incident laser 12. H.A.B. Btjdin, T.S. Green, G.B.F. Niblett, N.J. light could be expected in the present experiment. Peacock, .J. M.P. Quinn, J.A. Reynolds, “The Influence of Trapped Field on the Characteristics of References a Magnetically Compressed Plasma, ” Nucl. Fusion, . 2, 521 (1961). 1. J.p. Freidbergand B.M.Marder, “Stability of Two-Dimensional Magnet ohydrodynamic 13. W.R. Ellis, J.P. Freidberg, R.E. Siemon, E.L. Equilibria,” Phys. Fluids 16,247 (1973). Zimmermann, in Progress Report LASL Controlled Thermonuclear Research Program, Los Alamos 2. M.J. Katz, compiler, Progress Report LASL Con- Scientific Laboratory Report LA-5250-PR, 38 (1972). trolled Thermonuclear Research Program, Los Alamos Scientific Laboratory Report, LA-5656-PR (July 1974).

79 14. W.H. Reichelt, E.E. Stark and E.O. Swickard, 19. N.A. Amherd and G.C. Vlases, “COz Laser “Gigawatt Pulses from a 3 Atmosphere C02 Electron Heating of a Small 0-Pinch,” Proc. 2nd APS Topical . Beam Controlled Laser,” Los Alamos Scientific Conf. on Pulsed High-s Plasmas, Garching, Paper Laboratory internal report (1973). G4, July 1972. . 15. A.L. Hoffman, “Laser Heating of Magnetically 20. A.L. Hoffman, Mathematical Sciences Confined Plasmas for X-Ray Production, ” Northwest, Inc., personal communication, 1975. Mathematical Sciences Northwest, Inc., Report MSNW74-118-1 (1974). 21. A.L. Hoffman, “Strong Axial Laser Heating of a Theta-Pinch Plasma,” Appl. Phys. Lett., 23, 693 16.T.M.York and K.F. McKenna, “Laser-Plasma (1973). Interactions in the Scylla 1-C Experiment: Preliminary Analysis, ” Los Alamos Scientific 22. E. Fabre and C. Steng, “COZ-Laser-Beam Laboratory report LA-5957-MS (1975). Absorption by a Dense Plasma,” Phys. Rev. Lett.,32 , 823 (1974). 17. L. Spitzer, Physics of Fully Ionized Gases, 2nd Ed. Interscience Pub., New York (1962). 23. D.W. Forslund, ,J. M. Kindel and E.L. Lindman, “The Theory of Stimulated Scattering Processes in 18. L.C. Steinhauer and H.G. Ahlstrom, “Propaga- Laser Irradiated Plasmas, I,” submitted to Phys. tion of Coherent Radiation in a Cylindrical Plasma Fluids ( 1974). Column,” Phys. Fluids, 14,1109 (1971).

80 VII. IMPLOSION HEATING EXPERIMENT

J.E. Hammel, I. Henins, T. R. Jarboe, J. Marshall, A.R. Sherwood

A. Introduction plasma. Here at standard LASL theta pinch density, the plasma appears as an inconveniently low im- The Implosion Heating Experiment (IHX) was pedance (0.3 fl) and in order to achieve 250 kV ac- completed toward the end of this year and now is in tually applied during the implosion, a very low im- routine operation, although not yet at full design pedance generator is required. The generators of the level. IHX has two basic purposes, one scientific and various collisionless shock experiments have all had the other technological. Its scientific purpose is the impedances amounting to several ohms. The effec- study of the implosion process, the initial heating tive impedance of IHX is approximately 0.3 Q, equal ~echanism in fast theta pinches. It is hoped in the to the plasma impedance, and thus a total emf of 500 future to develop theta pinches with enhanced im- kV is required in the circuit. plosion heating and, in order to do this intelligently, After considering a number of different types of more must be known about the physics of the generators it was decided to use pulse forming process, and the requirements and effects of the networks (PFN’s) built up out of capacitors and in- preionization process preceding it. The technical ductances. The final system drives the coil at four objective is the development of high voltage feed slots, the PFN capacitors being fast Marx technology. This has been necessary in order to build charged to 125 kV, so as to add up to a total of 500 IHX, and is expected to be applicable to future kV. The PFN’s are connected to the feed slots machines. The technical objective has now been through field distortion rail gaps, and the switching largely accomplished; IHX is in operation, and some is done near Marx current maximum so as to add elements of the technology developed have been in- transfer capacitor characteristics to the system. The corporated in the Staging Experiment, now nearing charging current, since it is already flowing at completion. A general view of the experiment is switching time, can be added to the load current, shown in Fig. VII-1. and need not build up in the capacitor inductances. In order to facilitate the study of the implosion Thus a larger current and faster rise are produced process, IHX is designed as a relatively short (one than would be possible if the PFN’s were slow charg- meter) linear theta pinch of unusually large ed. The PFN capacitors are modified Scyllac di?meter (40 cm). The coil is long enough so that the preionization capacitors, having substantially implosion process at the center should be unaffected smaller capacity (0.2 and 0.4 PF instead of 0.7 PF as by the ends. The large diameter gives enhanced in the original). This allows the ringing frequency of space and time for diagnostics. One object of IHX is the capacitors to be considerably higher, and makes to extend the implosion to larger velocities thus re- a fast risetime possible. The PFN circuit was design- quiring more driving magnetic field strength during ed, with the help of computer modeling, to have a the implosion than has been customary. A large im- fast rise to 800 kA, followed by nearly constant plosion field stren th at standard theta pinch filling current for about 500 ns. A model had to be assumed 5 * density (10 15cm – ) with faster implosion implies a for the plasma in order to do this, since the plasma more rapid flow of magnetic flux into the discharge has a large effect on the waveform. The plasma was tube and therefore a larger azimuthal electric field assumed to be surrounded by a thin inward moving . strength. IHX is designed to achieve a field of 2 current sheath, originating at the wall and reflecting kV/cm, approximately twice the value used in ions by an elastic bounce process, so that the previous LASL theta pinches. All of this requires a deuterons move radially inward ahead of the sheath large total voltage applied around the tube, 250 kV at twice its speed. No accounting was taken of the during the implosion. Systems resembling IHX have same particles interacting more than once with the been built in the past for the so-called collisionless sheath. This produces a small error during current shock experiments. The voltage around the tube in rise, but a very large effect when deuterons from the some of them exceeded the requirement for this ex- other side meet the sheath at about one-third its in- periment, but was applied to a much lower density itial radius. For purposes of computation the plasma

81 .-

“’: *.

i *

Y

./

82 was assumed to stop its motion at that time. The B. Final Construction and Initial Operation . final circuit design is shown in Fig. VII-2. In order to design the PFN circuit it was necessary It had been planned to bring IHX into preliminary to know the circuit parameters of its various com- operation early in 1974 with two feed slots instead of % ponents. These included the pinch itself, with its four, the idea being that the less complicated system connections. The capacitor headers were developed would be easier to operate, and that valuable ex- to use silicone rubber voltage gaskets, the original perience would be obtained for operation of the full capacitor insulators having been cut down so as to system. This plan was dropped when it began to be allow smaller inductance. The capacitors were apparent that the two-feed-slot system would be assumed to have internal inductances equal to the radically different in symmetry, requiring special Scyllac preionization prototype. The coil connection arrangements for triggering, diagnostics and groun- design depended on the development of adequate ding. In addition, operation of a half system would surface flashover protection, as did the cable connec- interfere seriously with construction and would tions from the Marx generators to the PFN ‘s. The delay completion of the full machine. Accordingly rail gaps were commerical from Physics Inter- construction of the second pair of PFN’s was con- national, having been adapted from a design intend- tinued in place. ed to be used at higher voltage and lower current un- der water. It turned out that reliable voltage hold off against flashover at Los Alamos altitude required 1. Capacitor Failures. The second pair of the addition of conducting plastic to the rail gaps for PFN’s, being on the other side of the coil from the voltage grading. The preionization system was first, had to have negative high voltage on the bot- designed to use four standard Scyllac preionization tom side instead of the top. It was desired however to capacitors, each with a spark gap, feeding one of the operate the capacitors right side up on both sides four feed slots through two 50 Q cables in parallel for because of problems of bubbles in the impregnating inductive isolation. oil. This meant that these PFN capacitors had to be positively charged instead of negatively, as were

22nH /

o.53@i 10 nH 7.5 nH 15 nH

C2 cl [“‘2.45AF ;!8.5fi .-v1.2NF =o.8JlF luo.05JL

Plasma load bl

Fig. VII-2 The IHX electrical circuit for one feed slot. The parameters given here are representative of those obtained from the computer by matching the observed voltage and current waveforms. Some of these values are somewhat different from the original design, but they probably represent closer to what has actually been achieved.

.. 83 those in the first two PFN’s. In fact, what was done gap behavior might be obtained with a different gas, was to ground the capacitor terminals and charge 92% Ar, 8% SF6. The mixture has breakdown . the cans to negative high voltage. When the positive- characteristics resembling Nz, but presumably has ly charged PFN’s were tested, a number of chemical behavior like SFG. In any case it does not capacitors failed on first charge. Apparently the produce insulator surface contamination resulting in capacitors had a polarity dependent failure mode. spark gap flashover. The new gas mixture came after Postmortem investigation showed that failure was in a decision had been made to abandon the commer- the same place in all capacitors, across the surface of cial gap, however. the insulating paper where it was folded at the top, near the terminal. Fortunately a second batch of 4. Failure of Commercial Gaps. Single channel capacitors had been procured from a competing breakdowns at high energy resulted in the fracture of manufacturer and these have given no trouble of this the plastic envelopes of several of the commercial sort. Capacitors from both manufacturers had gas rail gaps. It is probable that under ideal conditions bubbles at the top. The failure appears to have the gaps could have been made to work. It appeared, something to do with the precise way in which the however, that ideal conditions might be a long time paper is folded. The capacitors, of the type which coming, and that to get the machine running failed on positive charge, have given no trouble in reliably, it would be advisable to have a more robust long operation on negative charge. main switch, which would be easier to service if that were necessary. Two simultaneous programs were in- 2. First Operation. IHX was finally completed itiated for the development of such a switch. One in- and brought into initial operation in May 1974. volved the use of solid dielectric switches, and the Almost immediately difficulty was encountered with other was to build rail gaps capable of high energy the main switch rail gaps. The difficulty was the single channel operation without damage. The solid result of a complex of small problems which led to dielectric switch was the less attractive alternative, mechanical failure of the acrylic plastic gap but appeared at the time to be the more nearly cer- envelopes. The gaps were adapted by the manufac- tain of success. Its disadvantages were the time re- turer from a switch built for service under water at quired for replacing switches on every shot and the -400 kV with much less charge transfer. SFsgas had large amount of material which would be used up. been used at -15 bars pressure. SF does not perform The rail gap alternative turned out to be not too dif- well at low enough pressure to break down at 125 kV, ficult, so the solid dielectric switch development was but it was found that Nz behaved quite well. Air did dropped. not produce good multichannel breakdown so it could not be used. N2 led to surface contamination 5. New Rail Gap. A cross section of the new rail and single channel untriggered surface breakdown. gap is shown in Fig. VII-3. In some of its features it This made it necessary to clean the gaps, and this resembles the rail gaps developed by Llnford et al., turned out to be time consuming, particularly in for staging gaps. It differs from the commercial gap readjusting the electrode positions. Additional in having much heavier, stronger electrodes, a much troubles were initiated by cross talk in trigger stronger plastic envelope with much larger internal systems aggravated by the very complicated circuit. volume, better access for maintenance of the in- One typical trouble was failure of one of the terior, and more accessible terminals for making cir- preionization (PI) gaps to fire when triggered. Since cuit connections. It has been modified from the all four PI capacitors and gaps were effectively in original design by the addition of acrylic flashover series, this tended to put 400 kV across one of the coil shields glued to the top of the switch. These were feed slots, and therefore across one of the rail gaps. added when it was found that under unusual, but . The rail gap would then break down single channel, not vanishingly rare circumstances a flashover could and break down in the same channel again when the occur between trigger electrode terminal and the voltage came up on the PFN’s. Enough energy might more distant main electrode terminal along the sur- thus be dissipated locally to cause mechanical face of the lid to a bolt head and from the bolt under . failure of the gap. This particular cause of” single the edge of the lid and round the side of the switch to channel breakdown has been circumvented by con- the terminal. The discharge under the edge of the lid necting all four PI capacitors in parallel, using one tended to crack it although no lid was ruined beyond rail gap to switch them on to the coil through four use, since they are made of polycarbonate plastic. In pairs of 50 fl cables as before. order to maintain accurate electrode spacing the lids are keyed into slots machined in the switch 3. New Spark Gap Gas Mixture. At this point envelope. news came from Physics International that better

84 d=l AA

)

o 5 10 15 20 25

SCALE-cm

Fig. VII-3 A cross section of the new rail gap switch body of of fiber glass reinforced epoxy. The elec- trodes are approximately 40 cm long.

6. Optical Trigger Links. Problems were also of 1.0 T) is matched by a reduced filling density, so encountered with cross talk in the trigger systems. as to produce the design implosion velocity. This These were caused partly by the difficulty of main- allows the current waveform to take approximately taining a simply connected electrical system in a its design shape, with a fast rise followed by nearly complicated circuit in a limited space. Inevitably, it constant current for about 500 ns. Operation at seems, ground loops develop. Different amounts of reduced current allows the development of return flux from the coil, threading through the diagnostics and debugging of the control system un- different loops, cause currents to flow in cable der conditions where component failures are less braids, and produce extraneous emfs. This problem likely and less destructive than at design current. A has been attacked frontally in IHX by the develop- good fraction of the failures encountered until now ment of optically triggered high voltage pulsers. The have been associated with control system or trigger master timer is in the screen room where it triggers system malfunction. As the systems are improved . solid state injection lasers in the near infra red. The the chance of failures decreases and operation at light pulses from these are transmitted through fiber high voltages becomes less hazardous. optics to electrically isolated high voltage pulsers at the required places around the machine. C. Diagnostics . 7. Routine Operation. The new rail gaps were The diagnostics in use until now include magnetic completed, the optical trigger system installed, and probes, image converter photography, both framing the machine put back into operation in November and streak, fractional fringe interferometry, flux 1974. Since then IHX has been in operation, so far at measurements including excluded flux and of course reduced current, and data are being taken on the im- voltage and current measurements. Problems re- plosion. The reduced level at which the machine is main in several of these diagnostics, mostly being operated, (-0.6 T instead of the design value associated with the high implosion velocity, the

85 complicated circuit, the high voltage and the large dominated by a series of luminous fronts moving in- tube diameter. As a result no completely consistent ward from the wall on every successive current ex- . picture has yet been obtained of magnetic field and cursion. The main implosion shows a luminous front plasma density as a function of time and radius. coming in at about sheath velocity, but no dark

space behind it, as would be expected with a plasma- 4 1. Probes. The only probes used so far have been free magnetic piston. Photography with the camera magnetic probes consisting of small coils enclosed in off axis shows high luminosity near the wall beyond fused quartz or ceramic envelopes. Plans are being the ends of the coil. This is presumably due to made for electric probing in the near future for the plasma flowing out through the ends of the coil along measurement of radial ambipolar and azimuthal in- field lines during the implosion. Whether all of the ductive electric fields. Magnetic probes have yielded luminosity outside of the current sheath is due to questionable results in previous LASL theta this is not known as yet. pinches, because of the energetic plasma surroun- ding them, which tends to destroy probes and to 3. Flux Measurements. Excluded flux ablate the probe surface, producing a secondary measurements have become a standard diagnostic local plasma and thus a locally reduced magnetic on most theta pinches at LASL. They are performed field. Preliminary results are that these problems are by comparing the total flux inside the tube with a still with us, but that probe surfaces tend to clean up flux obtained by multiplying the magnetic field just after many discharges. Some indication of the ac- inside the coil by the area of the tube. The difference curacy of probe measurements can be obtained by of the two is the flux excluded by the plasma. The integrating the results over the area of the discharge total flux is the time integral of the voltage around tube and comparing it with flux measurements (see the tube obtained with a wire loop. The subtraction below). If nothing else the probes appear to give a of the two fluxes is done automatically by a resistor correct qualitative picture of the motion of the network. In the case of IHX the flux measurement is magnetic piston during the implosion. Results till much more difficult than in standard theta pinches now are that the current sheath is about 2 cm thick because of the high voltage. The wire loop would with a velocity roughly what would be expected from have to be insulated for -500 kV, and it would have the bounce model. A large part of the current sheath to be between the coil and the tube, a place where thickness appears to be built in during the first rise there is not overmuch room. The solution of this of the coil current, and may be associated more with problem which has been applied to IHX is to replace degree of preionization than with plasma resistivity. the wire loop around the tube with a resistive loop Azimuthal inductive electric field measurements connected around the tube, a small portion being with double probes may give a valuable alternative tapped off to provide the signal. The resistive loop is measurement of magnetic fields. Such probes have made of fine resistance wire glued to the glass of the given physically believable results in the past under tube in a zigzag pattern to provide enough length. much more severe plasma energy flux conditions in The resistive loop has performed well functionally in gun plasmas. They measure the radial flow of that no high voltage arcs have occurred in its magnetic flux (VXB), and with velocity information” neighborhood. Problems remain however which obtained from other measurements can give values appear to be associated with the RC behavior of the for B. Radial electric fields are expected during the loop-coil system and the effects of one rail gap firing implosion, because the current driving the plasma slightly out of synchronism with the others. There is inward is carried mostly by electrons. The electrons not yet a reliable comparison of the flux measure- are then driven ahead of the ions, producing partial ment with the probe measurement although charge separation and electric fields such as to drag preliminary comparisons have supported the view . the ions along. These probing programs are only that the probes indicate a lower magnetic field than beginning, but are expected to consume a con- is actually there. siderable part of the effort during the next year. . 4. Fractional Fringe Interferometry. A 2. Image Converter Photography. The fractional fringe interferometer is used to obtain a information available so far from image converter time-resolved measurement of electron density along photography is incomplete and primarily a line parallel to, and at various distances from, the qualitative. Partly this is because no image con- axis of IHX. It uses the red light from a He Ne laser verter camera is available full time. Streak (6328A) arranged in approximately a Mach-Zehnder photography of the preionization phase fits well with interferometer configuration, one beam passing once probe measurements, giving a general picture of the through the plasma and being then combined with a preionization process discussed below. The picture is reference beam passing outside the coil. The light is

86 detected by a PIN diode and displayed on an os- diminishing because of resistive diffusion, and/or . cilloscope. A discriminator, on the output of the because of outward plasma motion. The ionizati(m detector, fires the machine when the detector output of the gas during the PI discharge is the result of a is halfway between extrema. Fringes are passing by series of mag-netosonic waves propagating inward b relatively slowly all of the time, of course, because of from the wall, one starting each time the magnitude room vibrations or because of the motion of a driven of the field at the wall exceeds the magnetic field in- mirror in the interferometer. An auxiliary measure- side the plasma appreciably. These waves can be ment gives the voltage difference between extrema, observed with magnetic probes and with image cun - and, by comparing the observed signal during a shot verter streak photographs, where they appear as in- with this, the phase shift introduced by the plasma ward moving luminescence. The prei(mization dis- can be calculated. Room vibrations are much slower charge is followed -40 gs later by the main implo- than the effect of the plasma, and produce only a sion, at which time the ionization is about 25?i, in the slight error over the time from preionization to the outer half of the discharge tube, falling off to lower end of implosion. Various difficulties with the values at the center. Occasionally there is a shot on system such as electrical noise, plasma light and which the preionization is lower than usual, such subtle effects of frequency response in the electronics that the implosion current waveform is noticeably have prevented the accumulation of interferometer affected, having a more or less sinusoidal shape in- data which can be reliably correlated with other stead of the usual more or less square wave. The diagnostics. These difficulties are much less severe reasons for this are not well understood. Increase of in the preionization phase than in the implosion, so preicmization voltage raises the ionization fraction that relatively trustworthy results have been ob- rapidly. The general subject of preionization, its tained for the preionization electron density. mechanism and its effects, will be studied during the coming year. D. Preionization E. Implosion The preionization system uses four Scyllac preionization capacitors in parallel (2.8 PF As mentioned above there is as yet no internally altogether) switched into cables which provide in- consistent picture of the main implosion. The ductive isolation from the coil feed slots. Each feed diagnostics are plagued by a set of difficulties which slot is fed by two 50 Q cables in parallel. This circuit lead to inaccuracies in each measurement. Probes has a natural frequency of -200 kHz but the actual are strongly affected by plasma bombardment. behavior of the system is strongly affected by the Interferometry suffers from the necessity of looking charging system of the capacitors. The capacitors through plasma which is escaping from the ends of are pulse charged by means of a Marx generator to a the coil. Side-on inter ferometry has not yet been potential of up to 125 kV. Slow charging is avoided tried because of high voltage problems, but has its because the capacitors are rated to only 70 kV dc, difficulties too. The general features of the implosion although, because of peculiarities of the $cyllac cir- are roughly as expected from the bounce model. The cuit, they may be exposed thereto pulses of up to 120 current sheath is about 2 cm thick, with the kV, and were so designed. The Marx generator and thickness determined during initial formation. the connection cables are inductive, giving the Strong luminescence appears on the wall beyond the charging system a ringing frequency of -100 kHz. ends of the coil rather early during the implosion, The resulting closely coupled systems then produce presumably because of plasma flowing outward a complicated waveform for the preionization along field lines. A strong crowbar effect is found on . current in the coil, with successive current peaks the wall at the end of the flat-topped current pulse varying considerably in amplitude. Typically the which traps magnetic flux inside the tube. This is first half cycle of preionization current fills the accompanied by strong luminescence on the wall . volume of the coil with magnetic field as though near the middle of the coil. The study of implosion there were no gas present but produces a small phenomena is being carried out intensively initially amount of ionization. As the magnetic flux flows out at less than design values of density (5x 10’4 instead at the end of the first half cycle, it carries plasma of 1015 cm ‘3) magnetic field (-0.6 T instead of 1.0 with it, depositing it on the surface of the discharge T) and Ed (- 1.2 kV/cm instead of 2 kV/cm). These tube, and finally accumulating enough plasma there numbers will be pushed up after sufficient data have to amount to a crowbar current. This traps magnetic been collected to give a more or less complete picture field inside the plasma, and this magnetic field from at initial conditions, and after system shakedown the first half cycle of the PI discharge remains inside and debugging. the plasma until implosion time, gradually

87 .

VIII. THE Z-PINCH PROGRAM

D.A. Baker, L.C. Burkhardt, J.N. DiMarco, P. R. Forman, A. Haberstich, R.B. Howell, H.J. Karr, J.A. Phillips, A. E. Schofield

A. Summary A parameter study of ion temperature for various values of toroidal bias field, peak current, rate of The past year has been spent studying the change of current, and filling pressure has been characteristics of the toroidal reversed field Z-pinch made. At the lower toroidal bias fields the mean T i experiment ZT- 1 between 1010 A/s and 2X1011 A/s. values range up to -140 eV for 90 kA peak current. In this derated mode of operation improved As one might expect, the higher temperatures are stability is obtained with reversed field program- achieved at the higher compression ratios which ming. A pinch which would normally strike the wall locate the plasma farther from the wall and are in 2-3 FS without reversed field, contacts the wall harder to stabilize. The lengthy optimization of between 10 and 15 KS, when appropriate reversed stable times has not been done at these higher field programming is used. Best results are obtained temperatures. The exact nature of the ion heating when the reversed field is programmed early in the mechanisms is not known. The Ti values increase discharge, The discharge exhibits fast poloidal field both with I and dIfdt. Strong shock fronts were look- diffusion and loses part of its positive toroidal flux so ed for but not observed. that an initially favorable profile will diffuse to an A combination of numerical linear MHD stability unstable one having a fast growth rate. The studies analyses of magnetic field data with the results of a on ZT-1 have been concentrated in two major areas: one dimensional time dependent MHD computer (a) the physics of setting up stable profiles and (b) code has proven to be a powerful tool in determining the processes involved in the loss of stable con- the nature of the unstable modes expected as the figurations. plasma profiles evolve due to diffusion. These Detailed studies of the pitch of the field lines and analyses give evidence that the anomalous resistivi- the poloidal flux surfaces from magnetic probe data ty is indeed responsible for the loss of a portion of the show that the setting up of given pitch profiles in the initially trapped toroidal flux and lead to narrower pinch, assuming a perfectly conducting plasma, is unstable profiles. Calculations indicate that the not a viable technique. As the field diffusion plasma has an anisotropic conductivity, nearly proceeds the loss of positive toroidal flux and the classical near the pinch center but anomalously high shortening of the pitch of the field lines in the at the larger radii. neighborhood of the magnetic axis lead to very un- Studies have continued on the restrictions for set- stable profiles. ting up stable equilibria that are imposed by the re- In order to decrease the field diffusion time, steps quirements of global energy and pressure balance. were taken to increase the electron temperature by The concern is that for very fast rising currents the increasing the preionization currents. Thomson pressure due to compression and diffusion heating scattering data showed that these measures were may become too large for the poloidal field to con- able to increase the interior T~ value before the main tain without first having plasma-wall contact. . compression from -1 eV to at most 8 eV. Although Further calculations indicate that if the full diffu- the rate of poloidal field diffusion was slowed for ear- sion of the toroidal current to a uniform current ly times in the pinch, T, after -3 I.LSwas -20 eV and channel can be prevented for containment times of was nearly the same as previously obtained so that interest, then the requirements for equilibrium can little was gained in the long time diffusion and be established without the requirement of energy stable times. losses or plasma pressure at the walls. Measurements of the electron density indicate The above studies point to the need of a larger that the plasma has a hollow profile and is well con- bore discharge tube in order to increase diffusion and fined away from the walls. Integration of the density stability times. The ZT-S device, which involves a profiles indicates that essentially all of the filling gas modification of ZT-1 to replace the 10 cm diameter is brought into the pinched column and that the con- tube with a 15 cm diameter one, is planned to come tribution of gas from the walls is small.

88 on line in a few months. ZT-S should give informa- Results obtained from the slow and fast modes . tion on the scaling of diffusion and ion temperature have been previously reported. This report will ex- with size. pand on the intermediate mode. Preliminary Z-pinch fusion reactor calculations The intermediate mode is broken down into have been made and indicate that the lower limits b categories called Derate 1 through 5, which progress on burning time are critically dependent upon the through increasing 1. and dI/dt. The electron and ion neutron damage at the first wall. temperature, and formation of a stable plasma are Experiments on the peaking capacitor circuit us- investigated over as wide a parameter range as possi- ing a constant inductance load have reached dI/dt ble. values of 3X1012 AIs with --40 nh inductance in the Table VIII-II summarizes the Derate operation. load circuit. If favorable results can be obtained with The parameter values in Table VIII-II reflect the in- the varying inductance of a linear Z-pinch this cir- itial stage of operation with the circuit and are-not cuit will be used to energize a larger device, ZT-P. the maximum attainable values. This would eliminate the need of fuses to obtain fast rising currents. C. Formation of Reversed Field Profiles

B. Modes of Machine Operation The formation and time evolution of the reversed field profiles in ZT-1 were investigated by varying The Z-pinch experiment has been operated in the rate of change of the reversing field and its tim- three modes: the fast (fuse) mode, the intermediate ing with respect to the start of the IZ current. The (resistor) mode, and the slow mode. Each gives a experiment was set up to operate in the mode different range of the amplitude and rise time of the “Derate 4“, with a gas filling of 20% He, 80% Dz at toroidal current. The different modes may be ex- -40 mtorr. The maximum rate of change of the plained by referring to Fig. VIII-1. The toroidal poloidal magnetic field was 4.7x105 T/s. current is inductively coupled into the plasma from The rate of reversal of the toroidal magnetic field a coaxial aluminum primary that is divided into was controlled by the initial voltage on the reversed quadrants. Each quadrant is energized by a pair of field capacitor bank. The rate of change of the parallel feed plates connected to the power supply, toroidal magnetic field depends on the plasma being as indicated in the figure. In order to prevent elec- present; with no plasma, 12 kV on the reverse bank trical imbalance the storage inductor L, is common is equivalent to 0.6x 105 T/s. With plasma, a rate of to each quadrant. However, in the equivalent cir- change of 1.3X105 T/s was measured. cuits of Fig. VIII-1 it is represented as an inductance All data presented were obtained from magnetic per quadrant. The highest currents and shortest rise field probes which are inserted into the plasma at 1 times are obtained with the fuse circuit. The fuses cm intervals; five probes measured Be and an open near the time of peak current and the transfer additional five probes measured BZ. From these switches close, resulting in a high voltage pulse of up magnetic field profiles the motion of flux tubes and to 70 kV per quadrant. the time behavior of the pitch of the magnetic field The intermediate mode which involves lower lines were obtained. Figure VIII-2 shows the flux currents and lower rates of rise is obtained by remov- tubes for the reversed field pinch. The motion of the ing the fuse and replacing the transfer switch with a poloidal and toroidal flux tubes with respect to one series resistance F&, as shown in Fig. VIII-1. This another can be seen from the plots. This nullifies one resistance is made large compared to the remaining concept of pitch programming based on the idea of circuit impedance to give an overdamped current the flux tubes being “locked” to the plasma. waveform. The value of & and L~ can be varied to The evolution of constant values of the pitch is . control both the rise time and the peak current. shown in Fig. VIII-3. The value of pitch is specified The slow mode is obtained by shorting the series for each curve and the dashed lines to the right resistor; a slow rate of rise, governed by the natural represent the location of the ceramic discharge tube. . period of the circuit, is then obtained. The pitch can be seen to disappear on axis, an effect Typical rates of rise, magnitudes of the toroidal that can only result from diffusion of the magnetic current and corresponding electron and ion field. temperatures for these three modes of operation with These data are combined with data from the other plasma densities of -3x 1015are shown in Table discharge conditions and replotted to show the time VIII-I. behavior of values of constant pitch as presented in Figs. VIII-4, VIII-5 and VIII-6. Figure VIII-7 shows a comparison of the toroidal flux measured with a flux loop with the integral of the toroidal magnetic field measured with probes.

89 Fuse Transfer . Switch \ A L~ B * k ‘Y Tc /7

Series Resistor

B Rs

Fig. VIII- 1 Iliagram showing the four quadrant feed p~int arrangement in ZT-1 and the circuits used to obtain fast and intermediate rise times by means of fuses and series resistors, respectively.

TABLE VII1-1

MODES OF ZT-1 OPERATION

● T i ‘i Mode of Operation (A/s) &l—_ (e;) (eV)

slow , x @ 130 -15 ~ 60

Intermediate (Resistor) 2 x & 120 -20 ~ 80

Fast (Fuse) 1.5 XI(312 200 ’40 ’800 .

.

90 TA8LE VIII-11 . DERATEMODES

Per Quadrant i I Derate Resistance Capacitance Inductance z z Mode Q PF PH x 10I1 A/s Id

1 0.45 150 280 0.6 40

2 0.45 150 140 1.2 40

3 0.355 150 140 1.2 60

4 0.2 150 140 1.2 75

5a 0.094 45 -200 2.0 110

aDerate #5 uses a modification of the fuse circuit, in that, the fuse is replaced by a resistor designed to heat up but not vaporize.

Back bias + 50 kV

Main marx charging voltage - 72 kV

Total voltage swing during shot 122 kV

Maximum ~ in peaking charge circuit 8 X # V,s

Average ~ during peaking capacftor charge cycle 2.4 X # V,s

Input charging circuit current 80.3 U Ontput current into inductive load 227 kA 12 Maximum i 2.8 X lo A/see

Percentage of voltage appearing across the 25X inductive load coil

Total inductance of load circuit ’40 nH

The flux loopis aloopofwire placed on the outside combination of initial conditions and programming, ofthe aluminum primary. Circled data points repre- the profile eventually evolves toone having values of sent the positive flux in the discharge. A pitch on the axis approximately equal to the paramagnetic effect can be seenat- ljiswhenBZ=O diameter of the discharge tube; (e) The loss of atthe wallof the discharge tube. Annihilation of the positive BZ flux results inaovercompression of the positive flux with time is noted here aswellas in Fig. pinch; (f) For favorable programming, the rates of VLII-2, butwhen the crowbarisapplied theannihila- chahge of the poloidal and toroidal magnetic field tion stops, and in some cases at high forward bias must be comparable, at least within a factor of ap- field, the positive flux increases in time. proximately four. Some conclusions based on this investigation are One way to reduce the rate of diffusion by in- as follows: (a) Pitch programming by assuming that creasing the initial electron temperature is con- flux tubes move with the plasma cannot reapplied sidered in section D. to the present mode of operation; (b) Pitch values longer than 0.1 m are unaffected by programming D. Experiments to Increase the Electron and must be set up by initial conditions; (c) Pitch Temperature During the Preionization Phase of values shorter than 0.1 m can be modified ‘by ZT- 1 programming; (d) Diffusion of the magnetic field results in a continued evolution of the pitch profile, This work was motivated bythe results obtained sothatevenif astable profile canbe achieved bythe from the programming experiments which showed that the pinch becomes unstable as the magnetic

91 *Z Wb( X 10-3) .

01 lnoNm u)mJo m 08 Wb/m (x IO-2) N’ IQlxqq III?? w & 0000 000 o“ 4.0 1 I I I . ‘ *loll 3.5 -

3.0 -

2.5 - ~ [.2 ~ @ 2.0 “ .-E 0.8 1- 1.5 - 0.4 I ! I 0.2, I 1.0 - I 0“’ I I 0.5 - I II I I I I I II i 0.01 0.02 0.03 0.04 0.05 Reverse Radius (m) Radius (m) Fiz. VIII-2 Radial time dependence of toroidal and p;loida[ flux tubes for a reversed field pinch. The magnitude of each flux tube is shown ‘on the plot.

21rr Bz P:— (ml El.

40, 1 1 r 11lolls \ —Reverse Applied \ I \ Ii 0.05- P= O.2(m)

0.04- FEZ Rf3z kV kV E e 3.0 0.0 . .0 u :0.03- x 3.0 7.8 .: ● 3.0 12.0 z 5.a 12.0 . i !’ 0.02- ‘&J \ 0‘-x( I \ I .

I \ I a“O’tY2\.1.0 2.0 ‘Y,+3.0 . 1 Time (PC) R.adaus(m: Fig. VIII-4 Fig. VIII-3 Radial time dependence for a pitch value of 0.2 Radial time depen~ence of specified values of m, under different conditions of rate of toroidal the pitch for a reversed field pinch. The value field reversal and the time at which the reverse of pitch is specified for each curve. field is applied.

92 2.0 I 1 I

PsO. I (m) #tloll!

0.05 - F8Z RB~ ! kV W

0.04 - \ e 3.0 0.0 \ x 3.0 ~ \ ● \ -.a.o .-% - 6.0 12.0 .$0.03 - z K 1.5 \ 0.02 - \

0.01 - <2.5x104m/s>A, b I 1 I 1.0 2.0 3.0 4.0 Time (PS)

Fig. VIII-5 1.0 Radial time dependence for a pitch value of 0.1 m, under different conditions of rate of toroidal field reversal and the time at which the reverse field is applied.

1 I , 0.5 I Ii‘.- Reverse Applied 0.05 P. O.O(m) -i F8z Rfkz kV kV 0.04 ‘b x 3.0 7.0 Crowbar ~ --.s0 12,0 ~ i “~ 0.03 ● 3.0 12.0 a ~% 1 I I 1.0 2.0 3.0 4.0 0.02 Time (ps)

0.01 Fig. VIII-7 Time dependence of the toroidal flux for a I 1 t , J reversed field pinch. 0 1.0 2.0 3.0 4.0 Tim* (PS) fields diffuse in time. If the time scale for diffusion could be changed by increasing the conductivity, ex- tended stable periods should result. Fig. VIII-6’ Four approaches were tried in the attempt to in- Radial time dependence for a pitch value of crease the initial electron temperature using existing zero, under different conditions of rate of systems. The first approach was to increase the toroidal field reversal and the time at which the voltage on the preionization bank. This was limited reverse field is applied. to about 12 kV by prefiring of the main bank switches. The second approach was to match the im- pedance of the preionization bank to the Z-pinch by transformer coupling through the fast magnetic core.

93 A third approach was to increase thepreionization 810345 bank from its present 60 PF to 150 gF total 20, I I 1 I 1 . capacitance. The fourth technique was called screw pinch preionization (SPP). The timing of the Iz preionization bank was adjusted as early as possible . during the rise time of the toroidal B. magnetic field. In this way energy from the B. bank was also coupled into the plasma. The two banks could not be fired Time (ps) simultaneously because a finite B, is required (-60 mT) before ionization of the 20T0 He, 80’%0D2 gas mix will take place. This technique is to be contrasted with the standard mode of preionization (SMP), where the preionization timing was adjusted so that the variation of the B, field during the preionization was reduced to a minimum of approximately 590. Electron temperature was measured by Thomson scattering at a position 1 cm from the axis of the dis- 4 i charge tube. The polychromator’s limit of resolution t was -1 eV. The density was obtained from a coupled-cavity interferometer using a He-Ne gas laser. Sine-cosine coils were used to detect the onset of an instability during the preionization period. The coils respond to a displacement of the centroid of the L current from the axis of the discharge tube. Time (PS) All of the results reported here are obtained with 40 mtorr of 20% He, 80% D2 gas mix and the toroidal Fig. VIII-8 bias field is 0.15 T. Toroidal current and electron temperature us The time dependence of the plasma current and time for the SA4P with a 60 pF capacitor bank. electron temperature are shown in Figs. VIII-8 and VIII-9. The SPP mode gives a substantial improvement E. Plasma Density in electron temperature and it appears that temperatures of -4.6 eV can be achieved with small The coupled-cavity interferometry technique has toroidal shift as determined from the sine-cosine been used to measure the electron line density across coil. Higher temperatures can be achieved; however, chords of the toroidal discharge region. An Abel in- the sine-cosine coil indicates that a helical distribu- version of the fringe shift data for a set of chords tion of current is established. Driving more current gives the radial density profile. The resulting dis- to achieve still higher temperature produces a kink tributions of electron density at five different times instability. Figure VIII-10 shows the line density ob- after pinch current onset are shown in Fig. VIII-12. tained from the coupled-cavity interferometer com- The results indicate the existence. of a minimum in pared to the initial filling line density. This general density on the axis of the pinch. The dotted line behavior is the same for all conditions investigated; represents the symmetry axis of the density distribu- higher power inputs result in the peak occurring tion which agrees with the toroidal shift obtained . earlier. These data are interpreted as indicating the from equilibrium calculations. 1 After 8 PS the 100% ionization is achieved. column becomes unstable. The effect of increasing the initial electron Integrations of the density profiles yield essentially . temperature on the poloidal field diffusion is shown constant values for the total number of electrons pre- in Fig. VIII-11. A faster diffusion rate of the main sent during the stab le period of the discharge. The pinch current is observed for the case of a low initial value agrees within - 15?4 of that deduced assuming electron temperature. However, for times greater full ionization of the initial filling gas. One concludes than -3 ps the electron temperature for both trials is that essentially all of the initial gas is brought into approximately the same at -20 eV, so that further the pinched column and that the contribution due to diffusion of the magnetic fields proceeds at nearly gas from the wall is small. the same rate and the stable times are essentially unchanged.

94 810426 0.3 * 10285 1 1 I I # 10460 20 - t 0.8ps ~ 0.2 - /-. 10- / . / N / u o 10 20 30 40 0.1 - / 50\ / I -lo - Time (ps) 00 --+/0: 9* I I I 1

8 - /-\ 1.6ps 0.3 - \ 7 - 0 0 \\ 0 // \ 6 - c 5 - -~ 0.2 - /’ q=; m 4 - 00 0 0 3 - o. I “ // 2 - “/ I - I I I I 0 10 20 30 40 50 Time (p) /–-,2.4% /’ \ 0.3 - \ Fig. VIII-9 Toroidal current and electron temperature us time for SPP with a 60 pF capacitor bank and 0.2 - // transformer coupling. #10389 o 0.1 -/ “/’

0.01 0.020.0.30.040.05 Radius (m) 0.6- Y- Fig. VIII- 11 S Plioidal magnetic field profiles of the main .: 0.4- pinch current at three times, comparing the z 10U1preionization case (dashed curve) to a high preionization case (solid curve). 0.2- F. Plasma Ion Temperature

[ To obtain the plasma ion temperature, 00 10 20 30 40 50 measurements were made of the Doppler broadening Time (#s) of spectral lines from impurity ions added in known Fig. VIII- 10 amounts to the plasma. The results reported here Typical electron line density (in terms of in- were obtained with the HeII 468.6 nm line with a terferometer fringe shift) us time. Initiul filling 20% He and 80’% Dz mixture. The addition of helium refers to a calculation that assumes 100’%oun- to the deuterium filling did not observably alter the iform ionization acrossthe discharge tube.

95 4, , I , , 1 t 1 , . I 240 -

220 - 0 -0.06T Ti Ooppler o -0. I05T “ Broodeninq A -0.150T 200 - Results / 10/.6 X - Probe Results 180 - /

160 -

140 - T s

E 120- : c s 100-

8 0- I I 6 0- F’”-Y’s 4 0- / / 01 2 34 5 Radius (cm) , t , t , 100 20 30 40 50 60 70 Bo 90 Fig. VIII- 12 O#%chO,qP I UC*PI :, * - Electron density profiles obtained from in- Fig. VIII- 13 terferometer measurements. Temperature in ZT- 1 as a function 00 current u]ith the initial toroidal bias field as a plasma dynamics as indicated by magnetic probe parameter. and electron temperature measurements. The spec- tral line broadening was determined with a seven classic Bennett relation (for a zero bias field) is also channel polychromator. Since the recent addition of shown in the figure along with values of Te + Ti Biomation analog to digital converters and connec- obtained from magnetic field probe measurements tions to the SDS Sigma II computer, the signals are at 0.06 T. fed directly to the computer for analysis. To obtain the results shown in Fig. VIII-14, five The ion temperature obtained with the ZT-1 derated modes of increasing current and current rise system depends on several parameters — the main time were used so that the increase in Ti shown is the ones being discharge current, current rise time, result of both increasing IZ and dIfdt. Figure VIII-14 stabilizing magnetic field, and gas filling pressure. shows the increase in Ti with Iz for constant values In the fuse mode of operation ion temperatures of -1 of the parameter 00 (where 00 =BOWaU/BZO). These keV have been observed. To facilitate observations results show that both IZ and dI/dt are important of the plasma stability behavior, the system has factors in determining the ion temperature. . been operated in a derated or intermediate mode Measurements of the ion temperature distribution during the last year with the current and current rise over the cross section of the plasma column were time reduced by a series resistor. made through small holes in the metal primary and The increase in ion temperature with discharge a quartz window in the ceramic discharge tube. The . current in the derated mode is shown in Fig. VIII-13. holes defined parallel chords through the plasma. The measured values of ion temperature increase Results indicate that Ti is somewhat lower on the monotonically with current up to 130 eV at -95 kA axis of the pinch. The mean value of Ti is found to be with a stabilizing toroidal bias field BZO of 0.06 T. higher than the Te obtained from Thomson The ion temperature is reduced with increasing scattering 1 cm from the tube axis. stabilizing fields as shown in Fig. VIII-13. The sum The precise mechanism for the ion heating is not of ion and electron temperatures predicted by the presently known. For the intermediate mode of operation, a search was made for the existence of a shock using a figure eight magnetic field probe. (See

96 15(a) is calculated with an anomalous perpendicular resistivit y of the form ~1= 1.25 B/(ne). The result is 100 - essentially an anomalous shock driven by an x 60=40=%3w011/f% O 8.=32 anomalous pinch. Figure VTII-15(b) is obtained with

● 8.= 2.6 x a quasi-classical resistivity of the form ~1=~~ ndn, where PS is the Spitzer resistivity at 4 eV, no is the /“. initial and n the instantaneous local electron densi- ty. This version produces a classical shock with an anomalous pinch effect. The measurement at 30 mtorr indicates that if the & field gradient extends over a distance greater than the spatial resolution of the probes, it must be no greater than 1.2 T/m. If, on the other hand, the B. front is very steep, then the change in magnetic field ‘:( ;o~: ❑ does not exceed 0.0034 T. Thus, the result of the ex- ● periment is closest to the theoretical result of Fig. VHI-15(a) obtained with the anomalous resistivity. The measurement at 10 mtorr gave a similar result. , 1 , 20 I 1 03 0.5 0.7 0.9 1.1 1.3 I.5 1.7 1.9 An alternate explanation for the weakness of the ~,xlO-ll (A/see) & front might be an anomalously high viscosity or a combination of high resistivity and viscosity. There also remains the possibility that the differential Fig. VIII- 14 Dependence of ion temperature on the rate of probes are being shielded by the plasma and do not rise of current with the compression factor 00as see the true gradient of the magnetic field. a parameter. H. MHD Stability and Diffusion Sec. G.) No strong shocks were observed. Also preliminary measurements made of the Doppler 1. MHD Stability. Magnetic field profiles have broadening of radiation from high Z impurity ions do been measured and analyzed for MHD stability un- not show the mass dependence that would be ex- der the following Derate 4 (see Sec. B) discharge con- pected if the ions had a common velocity distribu- ditions. The filling gas was 40 or 120 mtorr of 80% tion rather than an equal thermal energy distribu- D2, 20% He. The preionization (PI) current was set tion. Calculations made with a time dependent at 13 or 22 kA. The experiment was run without B, MHD code suggest that a large anomalous resistivity reversal, or with prompt or delayed B. reversal. or viscosity may explain the observed temperatures. The results are stability diagrams such as those shown in Fig. VIII-16. These plots are completely G. Field Gradient Measurement computer produced, under the assumptions of cylin- drical symmetry, ideal incompressible MHD, and The gradient aB,/& of the axial magnetic field equilibrium. Only the fastest growing m = 1 modes has been measured as a function of time and radius are considered. The lines crossing the diagram by means of two differential magnetic probes. The horizontally are unstable axial wavenumbers k.. probes were inserted in a 6.5 mm outer diameter Five of the unstable kz’s are analyzed for normal ceramic tube which was mounted across a minor modes. The width and location of these modes are . diameter of the discharge tube. The spatial resolu- indicated by heavy horizontal bars and their growth tion of the probes was of the order of 6 mm. The pur- times are shown on the right hand side of the pose of the measurement was to see whether there diagram. The remaining curve in the diagram is the . was a shock present during the imploding phase of locus of – I/P, where P is the pitch length rBfio. the pinch. The experiment was run in the Derate 4 The stability diagrams in Figs. VIII- ~6(a) and mode of operation (see Sec. B), at i’5’%0 D2, 25~0 He VIII- 16(b) have been obtained at 3 and 5 KS respec- filling pressures of 10 and 30 mtorr. tively, at 40 mtorr, low PI, and delayed B, reversal. A shock should manifest itself by a compression of Unstable modes are concentrated at the edge of the the initial BZ bias field and, therefore, by the inward plasma column, that is in the region of steepest motion of a positive gradient tlB~&. Figure VIII-15 pressure gradient. As time goes on, this region shows one-dimensional MHD simulations of the gradually shifts toward the axis of the discharge and pinch at a filling pressure of 30 mtorr. Figure JTH- the calculated growth times become shorter. This

97 !00 # ,(),()~ r 3ps Wall 50 1

— 0.3 I 1 I I k q U-1

N x — . Lk----——. 1..— .-‘– 1- -50 73’h 0.2 7.2 9. I 0.9 -1oo 12.7 (a)

0.1

,i 1 0 I I I I 1 I I I I ‘Tn3”’I l— 0 0.02 0.04 0.06

L RADIUS (m) - I I -T (0)

0.3 I I I I I I I I I I I

: /-x3 ““’(~’): I I I .;6 1.1 k .b2 .;4 0.2 Radius (m) 0.9 (b) 0.7 I Fig. VIII- 16 Stability diagram of a 40 mtorr discharge with

0.1 I low PI and delayed BZ reversal, kz is the axial wave number, and y ‘1 the growth time of the \& ‘1 unstable m = 1 modes.

I behavior correlates with a gradual loss of the trapped 1 . n I I I I I I I I Ii positive Bz flux in the central region of the pinch and “o 0.02 0.04 0.06 with a slow increase of the axial current density. Both effects appear to be due to diffusion. RADIUS (m) The trend of the calculated growth times and of (b) the loss of trapped BZ flux is shown in Figs. VIII- 17(a) and VIII-17(b), respectively. Growth times and Fig. VIII- 15 trapped fluxes are plotted for three 40 mtorr, low PI one-dimensional A4HD simulation of the im- discharges: without BZ reversal, with prompt plosion phase of (a) an anomalous 30 mtorr dis- reversal and with delayed reversal. Delaying the charge (b) a quasi-classical 30 mtorr discharge. reversal by about 2 gs reduces the loss of trapped flux and improves the stability of the pinch. The

98 The magnetic field profiles at 120 mtorr, and low PI give calculated growth times which are roughly,10 times longer than the 40 mtorr low PI results. In- creasing the PI current tends to eliminate the in- stabilities at the edge of the plasma column while creating some unstable axial modes. These modes could be fortuitous, since they are caused by a narrow central peak in the calculated pressure profiles. They are not visible on the streak photographs. The higher PI current clearly reduces the loss of trapped BZ flux, and the observed stable times exceed 8 VS. The 40 mtorr, high PI discharges show some slight improvements on their low PI counterparts. The calculated growth times are increased by ap- 0 .L_JLJ_l proximately a factor of 2 and the loss of Bz flux is 01234567 only very slight with delayed reversal. The shortest T]me(ps) observed stable times are of the order of 6 Ks. (a) 2. “Diffusion. The preceding results indicate

1.8 I I I I I I fairly good initial MHD stability followed by a gradual deterioration of the stability conditions in _ 1.6 the Derate 4 mode of operation. This late behavior has been tentatively attributed to diffusion. n ,/’’;0104 ~ 14 To test this hypothesis, the magnetic field profiles measured at 3 AS in the 40 mtorr, low PI, delayed ; 1.2 reversal case have been entered as initial conditions in our one-dimensional hydromagnetic code. The IT code was then run for 2 PS discharge time, and the 10 eN resulting profiles compared with the profiles measured at 5 p.s. The initial radial dependence of .—: 08 the ion and electron temperatures were assumed to .— be parabolic, with Ti =T. = 20 eV on axis, and ~ 06 Ti=Te= 10 eV at the wall. The initial density profile L followed from pressure balance. The expression for 04 the electrical resistivity tensor was varied until the calculated profiles agreed with the profiles measured 02 at 5 KS. Finally, the calculated magnetic field profiles were analyzed for stability, as if they had n I 1 1 I I I u been measured on the experiment. ‘01234567 The resulting stability diagram at 5 ps is shown in Time (ps) Fig. WI- 18. It is seen to be almost identical to that obt~ined experimentally in Fig. VIII-16(b). The (b) comparison shows that the slow change in the stability of the pinch can be interpreted on the basis Fig. VIII-17 of a simple MHD model; that is diffusion, heating and plasma motion. Growth time of the fastest m=l modes and trapped Bz flux as functions of time for three 40 The value of the electrical resistivity necessary to mtorr, low PI discharges: without Bz reversal duplicate the experiment is essentially classical on axis with a 100-fold exponential increase toward the (dashed line), with prompt reversal (dotted wall of the discharge tube. A comparison of the line), and with delayed reversal (solid line). measured parallel and perpendicular curent den- arrows indicate the earliest time at which the dis- sities at the intermediate time of 4 ys shows that the charge is observed to go unstable. The instability parallel current is much larger than the perpen- becomes visible 1-2 e-folding times after having been dicular current over most of the interior of the dis- predicted by the analysis. charge. If the increased resistivity toward the wall is

99 J. Plasma Resistivity from MHD ’00~ 4“2 5 p Wall Using the MHD code, the parallel and perpendicular resistivities have been calculated 50 between zero and 1.6 ps for shot number 11678. Radial heat transport was included in the calcula- t n tion. The thermal conductivity was assumed to scale from its classical value by the ratio q Il/q IIC1,S.These are analyzed to find what part can be described by I I ‘ik classical resistivity and what part can be described - by anomalous resistivity. The radial profiles of %n 11.3 ‘- resistivity which give the correct magnetic field profiles in the MHD code from O to 0.9 ps are shown in Fig. VIII-19 and profiles from 1.0 to 1.3 WSas are .loo~l.g shown in Fig. VIII-20. The inner region corresponds 1111 0 .02 .04 .06 ‘x’o”’~ Radius(m) 9 , <,. , z“. I ! ,,.04 8.,,.1a2..lL,lol,, , ,,,, ., 5,,, Fig. VIII- 18 Stability diagram of the discharge shown in Fig. VIII- 16(a) following a 2 ps simulation with the one-dimensional A4HD code. the result of some anomalous effect, and if this effect is related to a threshold in the electron drift velocity, IX IO-5 , it appears, therefore, that this threshold must be 1 2345 Radws(cm] related to the perpendicular component of the elec- tron drift velocity rather than to the parallel compo- Fig. VIII- 19 nent. An accurate measurement of the electron den- Radial resistivity profiles for the time interval sity profile, and if possible of the electron up to 0.9 ps after the onset of the main pinch temperature profile, would help clarify this point. current. WI and ?lL are the parallel and perpendicular resistivities. I. Calculation of Parallel Plasma Resistivity

IXIO-3 The parallel plasma resistivity can be calculated I I # , I from the time varying signals of B. and Bo measured ,ls1.3, qL.2q,l -z ● at several radial positions. The limitations of this L--Lll/ t”U VA*%, f 1.2,vA.IOVII k I*1.0,,A.5,1, calculation are that a given Be signal can range over : ------several decades in the time duration of the implosion :: IXIO-4- and thus cannot be properly measured from one os- .-z 3 cilloscope trace. There are also inherent errors in the u amplitude and timing of the measured signals. However, measurements have been made of the Ixlo-sl , 0 , , I parallel resistivity at five radial probe positions as a I 234s function of time. The measured values of the parallel Rodiw km) resistivity on the outside region of the discharge tube (greater than 2.6 cm from center) are between Fig. VHI-20 2.5x10–4 ohm-m and 5.0x10–4 ohm-m for times Radial resistiuity profiles for the time interval between 0.4 and 0.9 ps into the discharge. The values 1.0to 1.3 p.s. in the inside region are considered highly inaccurate because the Bo field is below the resolution of the to a classical parallel resistivity of 5 eV which fits digitizing apparatus. well with the measured electron temperature of 6 eV. Assuming no other losses than thermal heat conduc- tion, it is found that a perpendicular resistivity of

100 five times larger than the parallel is required in the – 100 kV. Triggering has not been in the self- outside region. It corresponds to an effective collision triggered bootstrap mode, as before, but initiated . frequency of 0.2 to 0.3 ~pi.If the other losses are with a (–) 90 kV fast rising pulse derived from shor- negligible, the outside region has to be anomalous. ting a length of coaxial cable charged to (+) 45 kV. Another interpretation is that T, is reduced in the With a voltage on the Marx bank charging circuit of 3 outer region of the pinch. Radial electron the order of 80 kV, trigger delay times of about 30 ns temperature profiles are required to resolve these are observed, with jitter being less than +30 ns. questions. The anomalous resistivity which may be The limitations inherent in the field distortion gap present is related to the various processes such as are being studied in terms of trigger jitter and delay turbulence which may be taking place in the plasma. time. The requirements of switching several peaking These processes may in turn be responsible for the capacitor sources into one load will be unusually high ion temperature that we observe. stringent. The fasi-rising peaking capacitor currents are K. Energy and Pressure Balance Calculations about 2.5x 105 A and modifications are in progress to provide more current in the Marx charging circuit to The previous work2’3 has shown that for fast give the desired approximation to a constant current rising currents (i.e. rise time << field diffusion and source having a fast rise with a relatively flat top of plasma compression times) equilibrium pressure 10 KS. Components for this phase are in the assembly balance can be reached, after the current has dif- stage. After the psuedo squme wave-shape is proven fused to a uniform column, only with losses or with the aluminum inductive load, a plasma will be kinetic pressure at the wall. This consideration substituted as the dynamic, pinching load. becomes particularly important for short rise times When this phase is successful, the peaking with fast diffusion where radiation and ionization capacitor circuit should be able to replace the induc- losses during the pinch formation may become low tive storage system which is switched by explosive and wall contact may be required before equilibrium switches on ZT- 1 type toroidal pinch experiments. is attainable. Even if the equilibrium is accessible The convenience of the peaking capacitor method the combined diffusion and compression heating will increase the rep-rate and hence improve the may give rise to poloidal beta values too high to be data acquisition rate. compatible with MHD stability. The present ex- During the interval of this report, typical of the periments are directed at determining the optimum 1748 shots, are the conditions tabulated here: rise times and currents for attaining stable profiles Beck bias +SOkV with Ti as high as possible. Since diffusion rates and Mm marx charging voltage 72 W losses are not predictable the conditions must be es- - Tot-l kV tablished experimentally. voltage sting during shot 122 Mu.fmtm V In n.akinu charge circuit ~ x # “,, More recent calculations (to be published) in- dicate that if a pinch can be formed in which the Average ~ durfng. peaking capacitor charge cycle 2.4 x 1011 Vfs current layer does not diffuse to the axis in confine- Input cha?giog circuit current 20.3 kA ment times of interest, the above limitations implied Outputcurrent into fnductfve load 227 M by global energy and pressure balance can be relax- XdMW i 2.8 x ,0” A/.,. ed. Thus the current layer scaling with minor Percentageof voltage appearing acroas the 2s% diameter becomes important. If, as has been inductive load coil evidenced by earlier Perhapsatron experiments, the Total inductance of load circuit -40 IIS diffusion of the poloidal field occurs at a slower rate, . the heating due to poloidal field diffusion will be M. Z Pinch Fusion Reactor Studies reduced, resulting in lower beta values and making the achievement of stable profiles easier. Elementary calculations have been made to study the nature of a toroidal reversed-field Z-pinch fusion . L. Transfer Capacitor Prototype Circuit reactor. The main constraint considered is that the device must produce more electrical power than it In the past year, the size of the peaking capacitor consumes. To simplify the calculations, idealized has been increased a factor of four to 0.32 ~F. The field distributions are assumed. The reversed value of dI/dt has increased from 1.5x1012 to toroidal field configuration and limited radial com- 3X1012. More than 1000 shots have been fired in the pression features of a stable reversed field pinch are high-energy, high voltage mode, extending the life retained. The energy losses associated with main- test of the components. The header insulation has taining the appropriate currents, both within the held off routinely, +40 kV and then was reversed to plasma and in the external windings, are assumed to

101 correspond to those of copper windings at room MOOEL REVERSED FIELD WNCH REACTOR Cowr F,*U Rogrommq Cdl temperature. All the energies are recovered with a ?-.. COPP*V pf,mary .+ thermal-conversion efficiency. No direct conversion Seqnmnwd Bbok.t /“”~’” \,. of plasma energy to electrical energy is assumed. The basic energy balance equation considered is

((wn+we+wb+ wp+wb,)=M(wp+we +Wb +Wt),) where

E Is the thermodynamic efficiency with which the heat energy is converted to electrical energy Wn is the energy from nuclear fusion reactions . . We is the resistive loss in the conductors which

establish and maintain the appropriate fields Suparcord.cmq 0.s Cd<

Wb is the total magnetic field energy Fig. VIII-21

Wp is the plasma energy (’mss-section ofareversed-field Z-pinch reac- tor. w~r is the energy lost by the plasma due to bremsstrahlung radiation The energy balance equation then gives a relation M is a multiplication factor. between~, I&, and Tb forvalues K, @#, 6P, drand @I. The field energy formula for Wb is based on a All quantities are considered perunit length around uniform current sharp boundary pinch. the major circumference. These quantities are then Shown as solid lines in Fig. VIII-22 are plots of I ~ expressed (in MKS units) in terms of the following versus& fortwovalues of the burn time7B (l sand variables: the total toroidal current 10 as deduced 10 s). The following values for the adjustable from the generalized Bennet relation, 3 the poloidal parameters were assumed beta Po, the time of burn TB, the radius of the conducting wall L, the compression ratio k,i.e., the /30=0.5, K=2.5, M=1O, 6=0.4, 6P=df=0.1 m radius of the wall divided by the radius of the plasma, and6P and &which are the thicknesses of These values of (?oand K are chosen to be consistent the primary and reversed field windings (ct. Fig. with the requirements of plasma stability. The value VIII-21 ). These substitutions lead to of c=0.4 represents a typical thermal efficiency and an M of 10 yields a circulating-power fraction = lfM of 10To. Also plotted on this graph are two curves labeled A=20 and A= 10 where A is the aspect ratio of the torus R~fRW where R~ is the mean major where anion temperature oflOkeV has been assure- radius. These curves are a result of the requirement ed and the extra energy due to the lithium reactions that the area inside the torus is sufficient to provide in the blanket has been included. the volt -see to drive the toroidal current. It is assum- ed that the flux is supplied by a magnetic core, which itself has a packing fraction fl of 0.85. The fraction fz of the area which is available for iron is . u=- 2#Rw ‘-’x’ra’’[:+~l%P assumed to be 0.75. f The flux in the core is given by . S@+’ [4..+:)+(2-6,)(1+34] @C=@m-Rw)2flfzB,

where BS is the saturation magnetic field. This equation and the curves of Fig. VIII-22 are for no 10‘8 f3812 up - 7.5 x back biasing of the iron. The flux needed to establish the current in the plasma is

~=47rx10-7R~( Q nK+ 1/2)10

102 -3s, an aspect ratio of >20, a current of -4 MA and a density of n~ x 2.5x 1015 cm’3. A larger bore wall with a minor radius of -1 m would have a minimum burning time of -7 s, an aspect ratio of 210, a current of 10 MA and n~3)(1014 cm–3 . A whole spectrum of reactor sizes is possible, but with the constraints imposed here, a burning time of tens of milliseconds could only be achieved with a small bore (few cm) high density device. To achieve such ~=loz~m short burning times with larger bore reactors re- quires either a more neutron-damage resistant first wall or a more frequent replacement of the first wall than once every two years. Since a large range of reactor sizes is admitted by the above analysis, it is evident that the actual size of a working reactor depends primarily upon the physics and scaling of confinement time and field diffusion.

w N=IO’g/m References

Rw(m) 1. D.A. Baker, L.C. Burkhardt, J.N. DiMarco, P.R. Forman, A. Haberstich, H.J. Karr, L.W. Mann, J.A. Fig. VIII-22 Phillips, and A.E. Schofield, “Z-Pinch Experiments Solution of the energy equation (solid lines) for with Schock Heating, ” Proc. Fourth Int. Conf. tuw burn times (1 and 10 s). Assumed Plasma Phys. and Controlled Nuclear Fusion, parameters are 13=0.5, K=2.5, ~=0.4, M= 10. Madison 1971, Vol. I (IAEA, Vienna, 1971) 203. These lines represent upper limits. A [so shown are uolt-second constraints on the aspect ratio 2. M .J. Katz (Compiler) LASL Controlled Ther- (bold-dashed lines) and a first wall constraint monuclear Research Program, Los Alamos Scientitlc due to total neutron fluence. Laboratory Report LA-5656-PR, (July 1974), p. 120.

the requirement then is 3. D.A. Baker and J.A. Phillips, “Pressure Balance Limitations in Z-Pinches with Diffusion Heating, ” 47rx10-7 R~ (Qn K+l/2)I*SPi (R~–R,)2 flfzl B. Phys. Rev. Lett. 32, (February 1974) 202.

The curves of Fig. VIII-22 use a value of B,= 1.2 T. The loss of poloidal flux due to plasma resistance is assumed small enough to be handled with the safety factor provided by the use of back biasing of the iron. The limitation of 10 due to neutron bombardment of the first wall has also been plotted on Fig. VIII-22. It is assumed that the total allowable number of neutrons incident on the first wall of the device is 3X 1021/cm 2. A duty cycle of 0.1 is assumed for the . reactor and the requirement is made that the first wall last for two years. With ~e=O.5 and K=2.5, and these assumptions the curve labeled Max 10 . (neutron flux) results. These simple considerations indicate that a crucial constraint on the maximum current and hence on the minimum burning time of a Z-pinch reactor, with a given first wall diameter, is imposed by the limited lifetime of the first wall as a result of neutron damage. For the neutron fluence of 3X 1021 cm –2 assumed here, a reactor with a first wall radius of -12 cm would have a minimum burning time of

103 .

IX. PLASMA DIAGNOSTICS

F. C. Jahoda, R. C. Amsden, G.I. Chandler, A. DeSilva, W. R. Ellis, K.B. Freese, P.R. Forman, R. Kristal, J. W. Lillberg, F. T. Seibel, R.E. Siemon

A. Summary Group have all been given computerized data ac- quisition capability with access to on-line analysis The primary responsibility of the Diagnostics and programs (Section D-1). Computer Applications Group is to aid the toroidal Computer control of all operational functions on and linear theta-pinch experiments in all aspects of Scylla IV-P, except hard-wire fail-safes for personnel plasma measurements. Some diagnostic support is safety and equipment protection, is being im- given other CTR groups, particularly in automated plemented (Section D-2). data processing functions. The start-gap and crowbar-gap monitoring Side-on holographic interferograms with a system, which was adequate on the previous sector hydrogen fluoride laser (A= 2.9 ~m) have given experiments, has never worked satisfactorily in the detailed spatial density profiles in a groove location more extreme noise environment of the full torus on Scyllac, overcoming the sensitivity limitation of operation. Great effort has gone into understanding ruby laser holography. Preparations are underway to the source of noise, and curative measures are being utilize two of the output wavelengths from the same explored (Section E). laser for simultaneous interferograms at adjacent Development of spatially resolved Thomson land and groove locations in order to quantify axial scattering measurements of Te with a digitally flow measurements (Section B). controlled S.I.T. tube television camera is well along A 360° multiple-slit framing camera (11 viewing (Section F). slits) has shown that the Scyllac toroidal mode A plasma motion simulator was built by acousto- structure is consistent in a statistical sense with the optic deflection modulation of a laser beam to enable m = 1 instability predictions of the sharp-boundary complete check-out of the feedback system (Section . . model. The first few modes of finite wavelength G). around the torus have growth rates comparable to Some further infrared laser developments, either the k= O mode, and the developed plasma mode achieved, in progress, or contemplated are outlined structure approaches a cutoff at the theoretical (Section H). value given by magnetic field line-bending effects (Section C). B. HF Laser Side-On Holographic During the past year, all diagnostic measurements Interferometry on Scyllac with analog electronic signal output (i.e., suitable for oscilloscope display) have been fully 1. Introduction. With side-on interferomet ry at automated. Analyzed results in graphical form on a the ruby laser wavelength of 0.694 pm, only - 1/4 TV screen are available to the machine operator fringe shift maximum would result through the upon push-button command. In particular, this in- Scyllac plasma. Since the sensitivity limit of “ cludes preionization density vs time from the coupl- holographic inter ferometry is - 1/10 fringe, the ruby ed cavity laser interferometer, electron temperature wavelength is insufficient to give a spatial distribu- from ruby laser scattering, and, most significantly, P tion wit h adequate resolution. While sensitivity . vs time from the combination of plasma luminosity scales linearly with wavelength, the 10.6 Km CO z and excluded magnetic flux (Section D-3). The com- laser wavelength is not transmitted by the quartz puter also performs various monitoring functions discharge tube. A hydrogen fluoride laser during the charge cycle and has abort control upon holographic interferometer operating at 2.9 ~m has fault indication (Section D-2). therefore been developed. A preliminary report of Through time sharing of our second Sigma 2 com- the laser and interferometer design appeared in the puter, the Z-Pinch Experiment, the Staged Theta last Annual Report, LA-5656-PR, p. 49. Pinch Experiment, and the Basic Plasma Physics

104 Good inter ferograms at 2.9 ~m have been obtained . on the Scyllac full torus. Measurements were made in a groove region of the coil which directly yield the k plasma fringe profile. Integration of the fringe profile gives plasma line density, and inversion of the data . . {R::! from the cylindrical observation geometry to radial coordinates gives local plasma electron density. The Scyllac results. are given in Section II-D. GrrJting ~:kJo;ge Bkmuth 2. Method. The layout on the machine is shown %-l plonor 1 detector in Fig. IX-1. The laser beam comes up through the floor to the diagnostic level. All subsequent beam handling is done by elements mounted on a single vertical base plate in close proximity to the Scyllac compression coil. The beam is first filtered to select . a single wavelength out of the several emitted by the laser. Line selection is accomplished with a grating, lens, and pinhole combination. Either of 2 strong lines near 2.9 pm may be used. These are the most intense lines available that are transmitted by quartz between the absorption band at 2.7 ~m and the IR cutoff at -3.6 ym. Reference After the single wavelength beam passes the beom pinhole, it is allowed to expand to the size needed to [ cover the plasma before being collected by a lens. This lens also converges the beam to compensate for the diverging lens effect of the discharge tube. After the lens, a beamsplitter directs part of the beam to the reference arm of the interferometer. From this Fig. IX-1 point on, scene and reference beams pass through Layout of HF holo~raphic interferometer on nominally identical optical paths. The imaging Scyllac coil. lenses give about a 6:1 reduction in size of the plasma image on the 200~ thick bismuth film detec- permitted this change in a g-move region where the tor. This reduction is needed in order to have enough coil here was large. For future experiments, two such energy density for evaporation of the bismuth. The sections have been fused into the toroidal tube in reference arm also contains a p;ece of discharge tube ad,jacent land and groove regions. to help equalize the two patterns on the bismuth Further details on the system may be found film. The beams are incident on the detector plate elsewhere. 1 from opposite sides. Reference fringes are introduced by tilting the 3. Results. Results are discussed in Sec. II-D bismuth plate between the first and second ex- along with other Scyllac data. Figure IX-2 shows a posure. The direction of tilt is about an axis parallel typical inter ferogram and the density profile derived to the torus major radius vector passing through the from it. For comparison a Gaussian profile is shown. . point of observation. In this way, the reference The experimental profile is somewhat less diffuse fringes are produced perpendicular to the plasma than Gaussian although the Gaussian is everywhere axis and parallel to the long direction of the slit. In better than 0.1 fringe. A detailed analysis of the . the presence of a diffuse plasma column, the fringes profile and comparison with luminosity data has are distorted by the total phase contribution (= ,f been made. nd Q ) along the various chords through the plasma. The quality of the inter ferograms was found to be 4. Plans. The questions raised by the high line strongly affected by the optical quality of the dis- density in the grooves (Sec. II-D) point out the need charge tube. In fact, it was necessary to replace a for simultaneous side-on interferometry in adjacent small section ( -6 cm) of the standard Scyllac tube land and groove regions. A system for doing this is presently being assembled for Scyllac. Essentially with a more highly polished cylindrical section to ob- two interferometers are required. In order to use the tain the data shown below. The O-ring seal used only

105 . w .— . . Lo ● N .. . . . ,

E o I 0. .- (/) 0 . . Q

u)

* -cl) N 16 I “E!. “.((2 ,: ,,::.

..” . 4.! ..= ...... ,...

.

— -,

.

——— . ..

106 one laser source and not suffer a 10ss of laser energy preionization, are logged for use by analysis programs. Data from individual shots are archived . in the double measurement, we are planning to use two of the wavelengths emitted by the HF system, on the disk (capacity -100 shots) until removed to one at each location. magnetic tape storage. The multiplexed A/D conversion of stored charge . The land and groove measurements will also per- mit determination of 60 and 61. Further, this on -6000 capacitors for the gap monitor system has technique could be used to measure particle end loss been described previously (LA-5656-PR, p. 53). rate in sector experiments. A higher energy amplifier section for the laser is b. Other experiments. The Z-Pinch, Staged under development. \ Theta Pinch, and Basic Plasma Physics experiments have all been put on-line for data acquisition on a C. Toroidal Mode Structure Framing Camera multiplexed basis on the second CTR Sigma 2 com- puter. The first two experiments use Biornation A special framing camera with a 360° field of view transient recorders while the third experiment has has been developed. The optical system, located on its own highly multiplexed A/D converter (Phoenix the torus main axis, images 11 top slits, almost un- Data System). Light coupling units were installed at iformly distributed around the torus, onto a single both ends of the lines between the computer and the image-converter framing camera. This camera per- Z-Pinch to prevent ground loops between ex- mits precise determination, at one instant of time, of perimental areas. the toroidal mode stucture of the Scyllac plasma All three experiments are equipped with column. keyboards which allow command and data entry to The toroidal mode structure framing camera and on-line analysis programs. its use on Scyllac are described in Sec. II-4. In the future, it is planned to incorporate micro~channel 2. Computer Control Functions plate image intensification to permit image beam splitting after the telescope lens in order to obtain a. Scyllac. While Scyllac remains under the more than one exposure per discharge. This should control of hardwired relay logic for most functions, also allow more viewing slits. the high speed response of the computer has been utilized in the design of a protection scheme to pre- D. Automated Data Processing and Computer vent a full-bank discharge subsequent to a pre-fired Control or otherwise disabled crowbar circuit. This involves physically inhibiting the clock in the Scyllac timing 1. Data Acquisition circuit during the charge cycle, thus preventing any premature firing due to noise transients into the cir- a. Scyllac. Direct data acquisition by computer cuit. When “charge complete” has been reached and with the submicrosecond time resolution required by the charging circuits are quiescent, the clock is pulsed high density experiments is limited by the restored and the trigger input is enabled. If at any capability of buffered A/D conversion between the time any crowbar voltage falls below a preset value, data accumulation rate and the Scyllac Sigma 2 the trigger input is disabled. If the timer has not computer acceptance rate. been triggered, then the relay logic is activated to There are currently 64 Biomation 610 transient discharge the bank through dump resistors. recorders in use on Scyllac, with 256 sequential 100 ns (minimum) 6-bit time bins each. In early 1975, 32 b. Sty/la IV-P. The Scylla IV-P experiment will . more units will be installed. Besides recording be completely computer controlled, except for plasma diagnostic physics data, these are widely h,ardwired “fail-safe” interlocks for personnel safety used for monitoring bank voltage waveforms, trigger and equipment protection. This is to be a learning . signals, feedback module operational parameters, experience for large future experiments. A Prime 300 etc., that can then be called for display on a TV con- computer has been delivered. Interfacing will be sole or for hardcopy reproduction. One special done with CAMAC components for purposes of Biomation (10 ns sample time, 8 bit X 2048 words) future standardization. System design is proceeding records data from the coupled cavity interferometer. rapidly. Eight gated integrators store Thomson scattering data. 3. Data Processing (Scyllac). A push-button Shot number, date and time, digital pressure panel at the Scyllac control console currently offers a gauge reading, and shot type, e.g., main bank or selection of data analysis programs. A brief descrip- tion of four of these follows:

107 a. Luminosity. The 10 channel side-on plasma software sophistication, this procedure is now also luminosity recorded cm Biomations is a quantitative automated to give results within three minutes after analog of a streak camera picture. Each channel is a shot. normalized to a strobe light calibration pulse at the Results of the new program, as displayed on the start of the charge cycle. The data are assembled CRT consoles are shown in Fig. IX-3. The output into intensity vs position plots (least square Gaus- beta plot also alerts the operator to fault conditions sian fits) at discrete time intervals; plasma radius, on signal levels and calibrations that should be cor- position, and profile information can be displayed in rected for acquiring better data on subsequent shots. a variety of graphical forms. These data are also one The results are identical with the older means of input to the on-line beta analysis. analysis.

b. Laser Scattering. The outputs of t he 7 channel 4. Programming. The computer code that polvchrometer and a laser monitor pulse are stored traces flux surfaces for fields with specified on-axis on a LeCroy Model 227 gated integrator; a 100 ns components has been converted to run interactively wide gate pulse is synchronized to the 40 ns laser under LTSS (a time sharing system) on a remote ter- pulse. Read-out through an A/D converter (Fifth minal for more rapid Scyllac coil design. After Dimension) follows a computer command ap- repeated iterations achieve a design that fulfills the proximately 5 ms after the shot. A least square fit- physical constraints, a more precise calculation ting procedure of a Gaussian distribution to the produces coordinates to drive a numerically con- channel signals results in a display of the best fit and trolled milling machine to produce the templates of the associated electron temperature with error es- non-circular cross section used on the boring lathe timation with 45 seconds. for the coil manufacture. Programming aid was given to several groups for c. Coupled Cavity Interferometer. The time file handling and data analysis, and a User’s Hand- history of density integrated along a 3.4 Am He-Ne book for the Sigma 2 was written. CW laser line-of-sight is obtained from phase shifts due to plasma changes. The plasma effects are E. Gap Monitor Maintenance superimposed on an externally generated periodic modulation. The output waveform is sampled by the The same spark gap monitor system which was fast Biomation transient recorder every 10 ns over a adequate for the sector experiments has been very 20 ps period. The software programming picks out unreliable in the hostile noise environment of the the extrema of the -0.5 PS modulation cycle and Scyllac full torus operation. Two major failure plots integrated density vs time. Digital noise is modes are evident: -1/25 of a cycle (AJ’ Q -1015 cm-2). By assuming (a) Catastrophic failure of electrical components uniformity across the tube and using the digitally due to overvoltage on signal cables. monitored tilling pressure, the preionization level as (b) System failures due to induced voltages which a function of time is obtained and plotted. To obtain cause the timing circuits to operate incorrectly. absolute density after compression by the main bank Most of the first class of failures have been discharge, the relative density profile from luminosi- eliminated by improving the components in suscep- ty is required. tible circuits. The second class has required con- siderable time and effort to locate the mechanisms d. Plasma Beta. By combining the luminosity by-which stray elect romagnet ic energy can penetrate relative density profiles with the measurement of the the gap monitor system, and to conceive and test . total magnetic flux excluded from the plasma, it is curative measures. possible to calculate the plasma beta, as described in We now believe the primary fault is the gap the 1972 Annual Report, LA-5250-PR, pp. 37-40. monitor screen rooms, which are a single-wall During most of the Scyllac torus operation, galvanized steel enclosure electrically continuous luminosity was recorded on-line with Biomations, with the outer Scyllac screen room. These enclosures and excluded flux oscilloscope traces were manually have been found to be ineffective shields when the digitized with the Graf-Pen. The analysis required ground arcs which occur during ScyUac discharges considerable interactive computing with qualitative are simulated by discharging a spark gap nearby. We judgments of data required from the operator, and are investigating ways of improving the shielding, thus was very time consuming. By modifying the ex- either by modifying the present enclosures (especial- cluded flux measurement to also be amenable to 1V the doors) or by constructing double-shielded Biomation recording and considerably increasing the enclosures.

108 PLASMA PARAMETERS VS. TIME

POSITION (cm) RADIUS (cm)

EXCLUDED FLUX (kG-err?) AXIS BETA and

MAGNETIC FIELD (kG)

Fig. IX-3 Plasma position and radius from luminosity (top), excluded flux and magnetic field from probes (bvttom, left), and derived axis beta (bottom, right) us time.

109 In conjunction with modifying the gap monitor The principles by which a three-grating instru- screen rooms, considerable effort is being expended ment rejects stray laser light with very high contrast . to develop an EMI/RFI testing capability. This is in- rat io have been described elsewhere. 2 The new tended to produce a permanent capability for polychrometer is shown in Fig. IX-5. The first two periodically checking out various existing and future stages are high quality, but conventional, plane rul- * shielded enclosures. ed gratings with 600 grooves per mm. The collimating optics are telescope objectives. In the F. Development of Spatially Resolved Thomson third stage, a special design holographic grating is Scattering used with several advantages: (a) stray light is minimized, (b) no collimation optics are required, The Thomson scattering measurement used on (c) a demagnified spectrum of large solid angle il- both the Scyllac sector (LA-5656-PR, p. 16, P.46) lumination. well matched to the S.I.T. tube, is and the Scyliac full torus is capable of measuring the created. Construction of the polychrometer is conl - electron temperature in only one small volume ele- plete and the measured efficiency is 8-15ri over the ment centered on the axis. Considerable progress has entire visible spectrum. The rejection ratio for 6943A been made toward a simultaneous measurement at has not yet been measured, but is expected to be several radial locations within one cross-section. better than 10-]O. The incident laser beam used in the Scyllac The Optical Data Digitizer, ODD, was obtained Thomson scattering experiment propagates side-on from EMR Photoelectric of Princeton, New Jt’rsey. through the radial pressure dist ribut ion of the It consists of an RCA 4826 S.I.T. television camera plasma column as shown in Fig. IX-4. By forming an tube and the necessary electronics to operate the image of the scattering volume on the entrance slit of tube and to produce digital data. a stigmat ic polychrometer, one obtains a two- The ODD will be controlled by a minicomputer dimensional dist ribut ion of the scattered light inten- which is presently being procured. It will include a sity at the output focal plane of the polychrometer central processor with 16K words (16 bits), a high- wit h wavelength dispersion along one dimension, speed teletype, and a floppy disk auxiliary storage and radial position along the other dimension. medium. The disk will permit program development Sensitive television camera tubes such as RCA during the checkout and calibration of the detector. S.I.T. (silicon intensifier target) tubes are capable of In actual use on Scyllac, we will probably need only measuring the space resolved intensity of the the ODD and ce~tral processor connected directly to scattered light. The system being developed consists our Sigma 2. of a three-grating polychrometer and an Optical The heart of the system is the RCA camera tube Data Digitizer, a digitally controlled television which is basically the same as the better known 4804 camera. S.I.T. tube, except that it has a special electrode to

DISCHARGE TUBE

\// ,, POLYCHROMETER

IMAGING LENS I OUTPUT FOCAL PLANE —-----.-xr rlt\ . I-A+ \ H ENTRANCE SLIT INTENSITY (r, X) t INCIDENT LASER

Fig. IX-4 Layout for spatially resolved laser scattering measurement of electron temperature on Scyllac.

110 ENTRAN{E SLIT PLANE GRATING 6943 i MASK PLANE GRATING

—

c s

S.I.T. TUBE’

OPTICAL DATADIGITIZER

1- -1 50 cm

Fig. IX-5 Schematic of three-stage polychrometer and digitally controlled television camera for spatial- ly resolved laser scattering experiment. permit on-off gating of the tube response. The S.I.T. (c) Repeat of (a) and (b) for an array of probably tube consists of an S-20 cathode, followed by an elec- 64x64 points. t rest at ic imaging section which relays a high- ‘(4) Computer subtracts background and applies velocity electron image to a silicon diode array. The various correction factors. accelerated electrons from the cathode generate (5) Digital data is available for processing. many carriers in the silicon target due to an impact Operation oft he ODD has been delayed because of ionization process. This electron image is held by the difficulty in obtaining the minicomputer for control. target until read from the back side by a low energy Lacking the computer, a controller with fewer func- electron beam. tions has been designed for initial use, and will soon The system of ODD and control computer will be be operational. used in the following sequence: Special gating of the S.I.T. tube is required for ( 1) S.I.T. tube is prepared by an erase procedure. Thomson scattering applications, and a 500 volt, 100 (2) S.I.T. tube is gated on for 100 ns in synchroniza- ns pulser has been developed for this purpose. tion with the laser pulse. (:{) Control computer begins a cycle (-30 ~s/data G. Plasma Motion Simulator For Feedback point) in which: (a) Computer sends x-y address to ODD. An optical system has been designed to simulate (b) ODD returns an 8-bit intensity word for the the plasma motion for routine testing of the Scyllac location on the silicon target. feedback system. The system is shown schematically

111 in Fig. IX-6, along with position detectors and f3- therefore gat ed on, simulating t he sudden turn-on of pinch coil. The beam from a 4 MW He-Ne laser ( -1 light emitted by the plasma. . mrad divergence, 1 mm diameter) is focused inside The second gate turns on a tone burst generator an acousto-optic deflector (Isomet Model 1206). A (Wavetek M(~del 164). This provides a video signal ten-power microscope objective at the output (useful range up to -2 MHz) which frequency . magnifies both the deflection and the beam modulates the rf driver. With the rf switch closed, a divergence. The beam is split into two separate modulation of the acoustic wavelength in the deflec- beams, which are then incident on semi-diffuse tor results. This. in turn, produces modulation of’the screens mounted at +45° from horizontal at the direction of the diffracted light, which causes the simulated plasma position. System parameters ar spots on the target screen to oscillate. This simulates designed so that the spot size (-2 cm diameter) ap- small amplitude ( -1 plasma diameter) motion of proximates the plasma size, and the deflection (up the plasma column. The timing of the tone burst is t{) -2 cm, depending on frequency) simulates the independent of the rf switch gate. Typically, it starts plasma motion. The semi-diffuse screens are acrylic some microseconds after the soundwave gate in plastic that has been lightly sand blasted; they are order to simulate plasma motion after a quiescent just diffuse enough so that the laser beam at the period. position detector overfills the lens for all deflections. The tone burst generator also has a variable DC The acousto-optic cell is driven by a frequency offset. This remains on continuously. and is used to modulated rf source (Isomet Model D-1OO) through position the rf source carrier frequency in the center an rf switch (AEL Model 500-1392-11). The system of the allowed Bragg diffraction range. functions as follows: A master trigger generates two Figure IX-7 shows a typical position detector gates with independent start times and pulse response to sine wave deflection at 250 kHz. The widths. One gate closes the rf switch, starting the sum signal modulation visible in Fig. IX-7 is due to acoustic wave in the deflector. This, in turn, in- the image of the light spot moving slightly off’ the itiates Bragg diffraction in the crystal, and the dif- position detector on each swing of the beam. Max- fracted light is used as the source for the rest of the imum slew rate obtainable is -1 beam diameter/ps. system. The light seen by the position detector is Further details of the system may be f(mn(i elsewhere.:]

H. Infrared Laser Developments

1. Interferometric Measurement of Pulsed Laser Beam Profiles. In various plasma diagnostic c applications involving lasers, it is useful to he able to determine the laser beam profile. This is particularly true, for example, in the case of pulsed infrared in- terferomet ry. Since direct photography is not possi - ble at these wavelengths, we have developed a new technique using bismuth films. Spatial resolution can easily exceed 100 Qp/mm, and the entire profile is recorded on one laser pulse. Figure IX-8 shows a comparison of a visible (ruby) r laser profile obtained by the new method (left) and by conventional photography (right). Qualitative in- f(~rmation is obtainable merely from visual examina- tion of the fringe width modulation, and precise profiles are obtained by fringe width measurement across the exposed area.

2. C02 TEA Lasers. The great sensitivity of C02 holographic interferometry might well be useful in the study of the linear theta pinches currently un- Fig. IX-6 der construction by the Staged Theta Pinch and Schematic of plasma motion simulator for Implosion Heat ing groups. In addition. Co ~ feedback system checkout.

112 .

*

.

.

113 interferometrv of the linear transfer capacitor Z- pinch of CTR-2 should prove to be an impor(ant . diagnostic. Because all of these experiments have such rapid implosions, invest igati(ms of techniques t () make COZ holograms with short expfwure times . i -5 ns) have been started. Short ( 1-2 ns) COZ pulses have been report ed by various groups using mode locking. This scheme is not too attractive because it is complicated by the need to select one pulse from a t rain of pulses, and apparatus which wumlrl have suf- ficient energy for holography would be rather large. One of the requirements of a successful diagnostic is that it is reasonably easy to take the diagnostic equipment to the experiment. Because of this, an alternate scheme called cavity clumping is being t ried. A schemat ic drawing of such a laser is shown in Fig. IX-9. The method relies on switching out the energy within the ca~’ity during one transit time. This leads to a longer duration pulse than mode locking, but it should he sufficient- ly short for our purposes. By applying an electric field of about 15 kV/cm, the CdTe crystal rotates the plane of polarization of the energy within the cavity. The germanium polarizer, which before rotation was essentially transparent, now appears as a front sur- face 78’; reflecting mirror. Preliminary tests, using our existing C02 TEA laser, indicate that the small aperture of the CdTe crystal within the laser cavilv seriously reduces the tmitput power of the laser. TwrJ approaches are being pursued to correct this situation. A simple off-axis mirror telescope is being constructed to match the crvslal size with the active volume size of the laser, and a laser amplifier is being designed. A second use for a cavity dumped laser is possible. 11’ one considers a homodyne COi scattering experiment to observe collective scattering from the ion feature of a plasma. the laser pulse shape is critical.4 The information from such an experiment is obtained by F(mrier analyzing the pulse obtained from mixing radiation which is scattered by the plasma with unscattered radiation. If the un- scattered pulse itself has a high harmonic content, the signal will be obscured. Since gain switchd COx

r-— ===7

Fig. IX-8 Comparison of ruby laser beam intensity CavalyD.mpd profile from fringe modulation (top) and con- output Pul,, ventional photography (bottom). Fringe method is equally applicable for infrared Fig. IX-9 lasers. Provisional design of cavity-dumped C02 laser.

114 TEA lasers tend to suffer from this, an attempt at References . feedback control of the CdTe voltage will be made in order to eliminate the sharp initial spike of the gain 1. R. Kristal, “Pulsed HF Laser Holographic switched pulse. Such control would be analogous to Interferometry,” Applied Optics, 14,628 (1975). . that achieved with a ruby laser by Lovberg, et al. 5 2. R.E. Siemon, “P(dychrometer with Extreme Re- 3. Ion Temperature Measurement on jection of Stray Light, ” Applied Optics, 13, 697 Scyllac. The use on Scyllac, in separate contexts, ( 1974). of (a) an HF laser, and (b) a three-stage polychrometer that allows scattering experiments 3. R. Kristal, “Acousto-Optic Plasma Position through the discharge tube walls, raises the Simulator,” submitted to Rev. Sci. Inst. possibility that their combination might yield an ion temperature measurement at a modest forward 4. A. Gondhalekar and F. Keilmann, “Proposal of a scattering angle such that the scattering parameter New Scheme Using Extreme Forward Light Scatter- N is about unity for the longer wavelength. A LAMS ing for Ion Temperature Measurement in Stellerator report is in preparation which concludes that such and Tokamak Plasmas, ” Institute of Plasma Physics an experiment is feasible, but experimentaly dif- report IPP 2/202, IPP IV/26, Garching, West Ger- ficult. Signal to noise ratios for available detectors many, Aug. 1971. are very favorable. The problems center on a weak dependence of the spectral width on Ti for a -1, and 5. R. Lovberg, E. Wooding and M.L. Yeoman, a cumbersome calibration when the absence of “P(llse Stretching and Shape Control by Compound vacuum ports prevents the use of Rayleigh scatter- in a Q-Switched Ruby Laser, ” IEEE J. Quantum ing. Electronics QE-I 1 17 (1975).

115 I

.

X. EXPERIMENTAL PLASMA PHYSICS . H. Dreicer, M. E. Banton, J.H. Brownell, R.F. Ellis, * J. C. Ingraham, and B.L. Wright

A. Summary Another area into which we directed renewed attenti(m was the anomalous absorpti(m above During the past year the LASL Plasma Physics threshold. Our goal was to determine the most im- Research program continued to be devoted to the portant factors that enhance the resistivitv an(i study of the plasma ac electrical resistivity and study them under controlled c(mditions. This re- plasma heating produced by the application of high quired extensions of the microwave technology we frequency electromagnetic radiation to fully ionized used in the past, and these were developed by H. plasmas. At the start of 1974 the status of our work Dreicer, ,J.C. Ingraham, and B. Wright. By the end could be summarized as follows: By utilizing a of 1974 plasma experiments began, hut no results are steady state contact ionized quiescent plasma available yet. column and a high Q microwave resonator we had A third study carried out during the past year, determined the threshold for anomalous microwave principally by J.H. Brownell, inwdves an ex- absorption as a function of density. 112’3The density perimental search for the anomahms absorpti[m range was large enough to separate threshold regions threshold on a new magnetized plasma column controlled by Landau damping from those controlled characterized by Te/Ti >> 1. The techniques used by collisional damping. Although the measured successfully by us earlier to make observations on threshold electric field is a strong function of densi- our Te/Ti = 1 (Q-machine) plasma have so far failed ty, good agreement was obtained with the threshold to disclose a clear-cut anomalous absorption and predicted by ac parametric instability theory over a spectral decay threshold, although there is wide density range. preliminary evidence for both. There is presently In very weak microwave fields, far below the onlv one published observation of anomakms ab- anomalous absorption threshold, our measurement sorption near the electron plasma frequency in a of the ac electrical resistivity was also in excellent plasma system other than a Q-machine. This is the agreement with the theoretical Ohm’s law value observation of the Lebedev group7 made ab[we computed in this weak field limit by Dawson and threshold on a spark-plug plasma source for which Oberman.4 Encouraged by these excellent results in the value of Te/Ti was uncertain, but probably larger two widely differing limits of operation we pressed than unity. It is conceivable that systems in which on in several new directions. One of these, a study of ion acoustic waves are not strongly damped (i.e., the influence that intense ac electric fields have on T/I’i>>l ), show a quite different anomalous absorp- the electron-ion collision rate, yields important tion behavior than systems in which ion acoustic deviations from the weak field Ohm’s law resistivity waves are strongly damped. Theory provides lit t le when the driving field becomes strong. We are deal- guidance on this matter, and this emphasizes the ing here with a decreasing resist ivity brought about importance of this experimental study. by the effect of the external driving field on the W(* are using a dispenser-cathode helium dis- Debve-screened electron-ion Rut herford cross sec- charge which unfortunately suffers from a larger tion, and not with Ohmic heating effects. level of density fluctuati(ms than the Q-machine To observe this phenomenon clearly, it was plasma column used previously in our laboratory. necessary to measure absorption in strong driving This may be responsible for the difficulties en- fields without ohmically heating the electrons. countered so far. Steps are being taken to reduce the . Moreover it was necessary to use large electric fields noise level and to continue the search for anomalous without inducing anomalous absorption due to absorption threshold. parametric instabilities. The successful resolution of All of our microwave absorption and electron these problems was largely based upon the ex- heat ing work is carried out with short microwave perience gained in the earlier measurements of ab- pulses in order to limit electron heating and pertur- sorption and threshold. 1’2$3An account of this work bation of other plasma parameters, i.e., plasma was published 5,6 by J.H. Brownell, H. Dreicer, R.F. potential and density, to controlled levels. During Ellis, and ,J.C. Ingraham during 1974 and is describ- the past year ,J.C. Ingraham carried out a theoretical ed in some detail below (Sec. B).

116 investigation of such perturbing effects for the ex- dependent electron-ion momentum-transfer colli- . perimental conditions we encounter in our work. He sion rate which can also be used to estimate the computed plasma potential and plasma density dependence of other transport parameters upon the changes of the magnitude observed in our ex- strength of applied ac fields. On the basis of these . periments. Of particular importance is applicatifm observations we conclude that the application of in- of these methods to our earlier measurements. ab(we tense electromagnetic heating fields to a long threshold, of the hot electron tail distributi[m and magnetized plasma columnl” could significantly the fraction of anomalously absorbed power that it reduce absorption and equilibration rates and could carried. Ingraham’s results indicate that our earlier significantly increase the electron-thermal conduc- interpretations were accurate, except for tion loss to the column ends compared to the experiments carried out at the lowest densities. In generally accepted values that apply only in the this case it appears that we may have un- absence of an electromagnetic field. In the case of derestimated the fraction of anomalously absorbed the laser-illuminated DT pellet experiment. g power that appears in a hot electrcm tail. increased heat flow could occur in the pellet’s low- Our fruitful two-year collaboration with R.F. Ellis densitv plasma ablation cloud, and this would ended in July when he left LASL to join the faculty reduce the requirements for symmetric laser il- of Dartmouth College. M. Banton, who joined the lumination imposed by the need for a high- group during the past year, assumed responsibility compression spherical implosion. 15 for our on-line data acquisition and data analysis Our experiment measures microwave absorpt i(m and is presently studying anomalous absorpt ion bv a “magnetized 110-150 cm long potassium plasma above threshold. column contact-ionized on a single hot plate at 2250 The Q-machine isotope separation proposal made K. The plasmaz is fully ionized, has a nearly several years ago by Hashmi and Van (l]rdt~ was trapezoidal density profile n(r)/n(0) with a mean subjected to a critical appraisal during the past year diameter of 2.5 cm, and electron cyclotron-to elec- by H. Dreicer. This work will be published during tron plasma-frequency ratio U,,/COP,, = 6-10. 1975. Microwaves are stored in an 8.6 cm long cylindrical TNll10 cavity that is coaxial with the plasma B. Influence of Intense ac Electric Fields on the column, resonates near u/2x = 2 GHz, and has a Electron-Ion Collision Rate in a Plasma loaded Q of 21,000 wit bout plasma. The measured change in Q due to plasma, expressed as .l( I/Q), is Current interest in the heating of several plasma independent of applied magnetic field B and is given configurationsg, ]o to thermonuclear temperatures by16 centers on efficient absorpt ion of electromagnetic energy by plasma particles. In these cases the time- dependent absorption goes hand in hand with other important transport processes, such as heat flow and electron-ion energy equilibration. Although such A(l/Q)=J!?:p[v’;(’:::r’’’dv] ,,, particle heating is well known to influence other E2dV J classical transport processes indirectly through their temperature dependence, it is generally not recognized that the application of intense elec- Here U+,, is the electron plasma frequency at r = 0, E tromagnetic heating fields may also directly modify is the microwave electric field, and veiE,T)isthe classical transport parameters on a time scale that is electric-field- and temperature-dependent electron- much shorter than the heating time, without ion~momentum-transfer collision rate at r = O. . generating plasma instabilities. This effect arises Equation (1) applies when Vei<

117 Electric field. E displaces the plasma electrons to limitations cause the apparent threshold to increase the oscillation amplitude 6=eE/(mu2 ) = VFJU which as ~p is shortened, the threshold for Tp x 5 #s serves may also be expressed in terms of the Debye length as the most conservative boundary for a clear h and the electron thermal speed [VT = ~m] separation of effects. The foregoing considerations as h = @ AD (VE/VT) (Up/U). Considaation of Debye - led us to study the range 0.55< (tip~u) 2S0.65 where shielded binary-encounter dynamics suggests that the density is still large enough to give measurable modifications in Uei will be produced if 6 exceeds classical absorption below threshold, and yet the -0.1 AD during the typical electron-ion encounter density is not so large as to preclude a reasonable duration U+– 1 . These requirements are satisfied by search range in VE/VT without exceeding the (VE/VT) (W/CO) z 0.1 and Lozup, or upon combining threshold at VE/VTC=O.75. these, by VE/VT>O.l. Figure X-2 shows the values of <~ei> (dots clustered about dashed 1ine) deduced from A( I/Q) Pulse length. The need to separate the effect of measurements as a function of 7P at VF~VT = 0.37. Ohmic heating (i.e., temperature changes) on ~ei The brackets on I)ei indicate that it is the average (E,T) from the orbit-modification effect dictates the value measured during ~Q. The normalization ~ei(TU) use of short pulse lengths. In weak electric fields, is the value Of tiei deduced from A( l/Q) with heat conduction ignored, Ohmic heating raises measurements at VE/VT = 0.0035. [In such a weak the electron temperature T at the rate field Ohmic heating is absent for the pulse lengths used and, as shown in Fig. X-3, the theoretical value (2) l% ~ ( l/T) (dT/dt) = (2/3) (ve/vT)2Vei(0,T) of 3( l/Q) (solid line), based upon the local applica- titm of ~ei(0,T)4 to our trapezoidal density profile, is where Uei(O,T) is a function of Ulwp.4 Near U=wp we in excellent agreement with our observed A( I/Q) have ljei(O,T) = ~%Ze41n.i/[3 (2m) li2(kT)3i2]. Use (dots) for a wide range of (copo/ti)2 at the measured of microwave measuring pulses, whose duration r p hot -plate temperature To =2250 K ]. might therefore produce temporal exceeds Vh–~, The strong-field data in Fig. X-2 clearly indicate ~ei that could mask the more changes in that /~ei(TO) approaches -0.55 rather fundamental-orbit modification effect. In our ex- than unity as ~P tends to zero. This limiting behavior periment L( l/Q) is measured with microwave pulses cannot be ex ]Iained by a temperature increase and in the range 0.2 < Tp <30 KS, which, depending upon the usual T–+’2\ temperature dependence of ~ei(O,T), E, gives rp < tih-l as well as ~Pz Ph-l. A typical because the amount of Ohmic heating for small 7P is pulse shape is shown in Fig. X-1. The duration r Q insufficient. According to Eq. (2) the initial heating required for measurement of Q is approximately 0.1 rate for Fig. X-2 conditions is VI)= ( 1.5gs–l. A more PS. During rQ, E varies at most by 570. Orbit careful calculation of electron heating without orbit modification may also be masked by anomalous ab- modification was obtained by computer solution of sorption, which causes a marked decrease in the energy equation resonator Q when E is large enough to excite ac parametric instabilities during the time ~p. The 2 Wv e~(O,T) threshold for these instabilities measured by us on _na#3 ~ KO(T) ~ = + (~) ~~~e;;~ ~lasma with a 7P x 5 ps is described 2 at - ~X 2 (O,T) W2 + Vei Even though instability growth-rate ( )’

~ Switch I Opened which is valid during the relatively long period ( >[1. lgs) after application of the microwave pulse before ion-response mot ions manifest themselves in

our experiment. The classical thermal “ conductivity y17 Ko(T) = 0.96k(kT)5’2/(e4 in.ifi ) wit bout orbit modification was used in this calcula- tion. Orbit modification of Ko(T) would have . increased the heat flow only over the 5-7°; plasma length occupied by the microwave resonator, and would have resulted in an even smaller computed 1- switch closed temperature increase. From T(x, t) evaluated for the interval ~Q at the

Fig. X-1 resonator location we have computed ~ei(O,T)/~ei(’T(]) Pouler transmitted through a resonator as a = (To/T) 3/2 , the theoretical comparison (top solid function of time for a typical short pulse. line) shown in Fig. X-2. This result shows that

118 Lo~ I 1 I I : I 1 These conclusions were subjected to an indepen- TT dent experimental check by measuring T with ‘ongmu’r ‘robe H Langmuir probes. The measurement was made out- 0.9 Microwaves -!-S- side of the resonator to avoid interference with the ● 9 microwave fields. Equation (3) was then used to ex- 0.8- trapolate T to the resonator location at the time of the J( l/Q) measurement. The resulting values of (T/17312, represented by crosses (with error bars) in 0.7- Fig.X-2, approach unity for small 7P. This again supports the view that /Uei(To) approaches 0.55 as TP tends to zero, because is a function 0.6- 8; -:-w of E and not because of heating. 8: The further decrease in < Vei>/~ei(To) shown in 0.5- Fig. X-2 for TP >1 ~s is complicated, because Ohmic heating and orbit modification are occurring 0.4- simultaneously. To minimize Ohmic heating our I 8 I study of the electric field dependence of ~ei(E,T) has ● therefore been carried out with the shortest practical 0.3 I , I I 1 I I , , 1 0,I 0.2 0.5 I 2 5 10 20 50 pulses, i.e., ~P= 0.2-0.4 As. The result for 0.55 < Tp(psoc) (~/0)2 50.65 is shown in Fig. X-4 (black dots). For the smallest field shown, E = 10 V/cm (vtivT = Fig. X-2 0.06), we find /~.i (To) ~ 1.0 as expected. Normalized collizion rate as a funct ion of pulse As E increa6es to E = 150 V/cm (vE/vT= 0.74), lengthfor (uP/w)2=0.6and V~/VTT=0.37. <~,ei(E, T)>/~ei (T. ) falls to about 0.4. In such strong fields there is a small increase in T/’T’o due to Ohmic heating even for the short pulses used by us. We compute this increase by substituting ~ei(E,T) for ●m 0.8- 8 #

0.6 - ●O

‘& ● -- Q4 - ● ●. /

0.2- ●

(q@d

Fig. X-3 J(l/Q) as a function of (wP/u)4 for 0.2 l)[jl)T= 0.0035. (Vei(E,T))/~ei(To)-%o<$~– t i . Ohmic heating cannot account for the appreciable decrease in <~ei >/uei (To) measured for TP < 1.0 KS. oo~ Even with heat flow neglected in Eq. (3) (i.e., KO = 50 100 150 O) we come to the same conclusion for small ~P (see L , , E (V-CM-’) # , 1 lower solid line), and this is because the time cons- 0 0.2 0.4 0.6 0.8 tant for thermal diffusion is considerably larger than ‘E/vT 1 PS. A more consistent calculation which utilizes f~ei(E,T) in place of Uei(O,T) in Eq. (3) results in even Fig. X-4 less Ohmic heating as discussed below. Normalized collision rate as a function of E and VE/VT for short pulses and (uP/u)2 = 0.6.

119 ~lei(O,T) in Eq. (3) and by assuming tiei(E,T) = References (K(E)t~ei(O,T). To compute T and a (E) from our . observed value of (tiei) we utilize Eq. (3) in an 1. H. Dreicer, D.B. Henderson, and J.C. Ingraham, iterative computational procedure based on a(n) (E) “Anomalous Microwave Absorption Near the (T(n) flo)3/2. = ~ci(E, T)/~ei (To ) This scheme Plasma Frequency, ” Phys. Rev. Lett. 26, 1616 . converges adequately for n = 3 or 4 and results in the (1971). (v(E) curve shown in Fig. X-4. The dashed line in this figure provided the starting values for the itera- 2. H. Dreicer, R.F. Ellis, and J.C. Ingraham, “Hot tion. In agreement with our Langmuir-pmbe Electron Production and Anomalous Microwave Ab- measurements we find the temperature correction to sorption Near the Plasma Frequency, ” Phys. R(w. be small and this supports the evidence that the or- Letters 31,426 (1973). bit modification effect has been observed with a(E) < l. Intherange OSE< 150 Vcm– 1, the empirical 3. H. Dreicer, R.F. Ellis, and tJ.C. Ingraham, relation a (E) = (1 + 2VE2/VT2) ‘:)’2, which is “Anomalous Microwave Absorption Near the obtained by substituting kT + mv~2 for kT in Plasma Frequency, ” Proceedings of the Fifth Eur(j- ~ei(O,T), is in good agreement with the a(E) values pean Conference on Cont. Fusion and Plasma deduced from the measurements. The a (E) values Physics, Grenoble 1971, 1, 120& 2, 242. computed by Salat and Kawl 1 in the absence of magnetic field are shown in Fig. X-4 for comparison. 4. J.M. Dawson and C.R. Oberman, “High- Their predicted 1 - a values are only 10-30°; of our Frequency Conductivity and the Emission and Al)- observed 1 - a. A recent numerical re-evaluation of sorption Coefficients of a Fully-Ionized Plasma,” the Salat and Kaw result by Wright 11 reduces this Phys. Fluids 5,517 (1961). difference somewhat, but still leaves a very signifi- cant discrepancy between theory and experiment. 5. J.H. Brownell, H. Dreicer, R.F. Ellis, and J.C. Alt bough we have observed no dependence of on magnetic field we have not yet ex- on the Electron-Ion Collision Rate in a Plasma, ” perimentally ruled out the possibility that a Phys. Rev. Letters, 33, 1210 (1974). dependence of a on B can explain this discrepancy. Our measurements are supported by the 6. J.H. Brownell, H. Dreicer, R.F. Ellis, and J.C. following: (a) We check the time dependence of elec- Ingraham, “Hot Electron Production, Anomalous tron density n and the possibility of E field enhance- Absorption and Effect of Intense Electromagnetic ment in the plasma by monitoring the cavity reso- Fields on Inverse Bremsstrahlung Absorption Near nant frequency during 7P as a function of E. No the Electron Plasma Frequency, ” Paper CN-33/H -4- appreciable frequency shift is observed, and this 2, Proceedings of the Fifth International Conference rules out the possibility that the ~ei reduction on Plasma Physics and Controlled Nuclear Fusion observed as E increases is actually because of a Research, (Tokyo, Japan November 11-15, 1974). sudden reduction in n or an enhancement of E inside of the plasma. (b) Magnitudes of E are deduced from 7. I.R. Gekker and O.V. Sizukhin, “Anomalous Ab- separate measurements of Q and the microwave sorption of a Powerful Electromagnetic Wave in a cavity power absorbed, and by using the microwave Collisionless Plasma, ” Pisma Zh. Eksp. Teor. Fis. 9, electric field distributions predicted by a computer 408 (1969). [JETP Lett. 9,243 ( 1969)]. solution for the actual resonator filled with a plasma column. 8. M. Hashmi and A.J. Van Der Houven Van Oordt We have observed an electric field-dependent, “production and Application of a Uranium Plasma electron-ion collision rate for V~/VT S 0.74 by in a Q-Device, ” Proceedings of 3rd International carefully avoiding masking effects due to Ohmic Conference on Quiescent Plasmas, p. 27, Elsinore, heating and ac parametric instabilities (for v~vT > Denmark 1971. 0.74 this effect is expected to become even stronger). Our observations have application to all classical 9. J.S. Clark, H.N. Fisher, and R.J. Mason, “Laser- transport processes produced by electron-ion en- Driven Implosion of Spherical DT Targets to Ther- counters in the presence of intense electromagnetic monuclear Burn Conditions,” Phys. Rev. Letters 30, fields. 89 (1973).

*Present address: Department of Physics, Dart- 10. J.M. Dawson, A. Hertzberg, R.E. Kidder, G.C. mouth C(dlege. Vlases, H.G. Ahlstrom, and L.C. Steinhauer, “Long- Wavelength, High-Powered Lasers for Controlled

120 Thermonuclear Fusion,” in Proceedings of the 14. H.A. Bethe, “Note on Inverse Bremsstralung in . Fourth International Conference on Plasma Physics a Strong Electromagnetic Field, ” Los Alamos Scien- and Controlled Nuclear Fusion Research, Madison, tific Laboratory Report LA-5031-MS (1972). Wisconsin, 1971 (International Atomic Energy . Agency, Vienna, Austria, 1972), Vol. 1, p. 673. 15. D.B. Henderson and R.L. Morse, “Symmetry of Laser-Driven Implosions,” Phys. Rev. Lett., 32, 355 11. A. Salat and P.K. Kaw, “Nonlinear High- (1974). Frequency Plasma Conductivity, ” Phys. Fluids 12 , 342 (1969); T.P. Wright, “Nonlinear High- 16. S.J. Buchsbaum, L. Mower, and S.C. Brown, Frequency Conductivity of a Fully-Ionized Plasma, ” “Interaction Between Cold Plasmas and Guilded Bull. Amer. Phys. Sot. 18 , 1303 (1973), and private Electromagnetic Waves, ” Phys. Fluids 3, 355 communication. (1974).

12. V.P. Silin, “Nonlinear High Frequency Plasma 17. L. Spitzer, Physics of Fully Ionized Gases Conductivity,” Zh. Eksp. Teor. Fiz. 47,2254 (1965) (Interscience, New York, 1962), Chap. V. [SOV. Phys. JETP 20,1510 (1965)].

13. S. Rand, “Inverse Bremsstrahlung with High- Intensity Radiation Fields,” Phys. Rev. 136, B231 ( 1964); G.J. Pert, “Inverse Bremsstrahlung Absorp- tion in Large Radiation Fields During Binary Ccdlisions-Classical Theory,” J. Phys. A: Gen. Phys. 5, 506 (1972), and “Inverse Bremsstrahlung Absorp- tion in Large Radiation Fields During Binary Collisions - Born Approximation,” Op. Cit.5, 1221 (1972).

121 I

XI. THEORETICAL PHYSICS PROGRAM .

W.B. Riesenfeld, D.A. Baker, D. Barnes, G. Berge, J. Brackbill, B.L. Bu.zbee, R. C. Davidson, D.A. D ‘Ippo[ito, J,P. Freidberg, R. Gerwin, IV.T. Gladd, J. P. G[wdbloed, D. W. Hewett, H.R. Lewis, L. W. Mann, M. Menze[, C. W. Nielson, J.M. ogden, A. Sgro, M. Stein, K. R. Symon, L. Turner, D. Winske

A. General Summary has yielded remarkably detailed correlation with ex- perimental results, so that tests of the assumptions underlying the model could be carried out, and per- During the reporting year the LASL CTR theory mitting quantitative predictions of the results of group has continued to increase its efforts in the field future Z-pinch discharge. A computer modeling of magnetohydrodynamics (MHD) theory as applied program has also been written for the so-called Injec- to the equilibrium and stability of complex toroidal tion Experiment, in which a highly heated and com- confinement systems such as Scyllac and high-beta pressed theta pinch plasma is transferred into an tokamaks. The analyses have become more !2 = 1 confinement sector designed to test the con- sophisticated as they have been extended to treat cept of wall stabilization. diffuse plasma and field profiles and the detailed Finally, considerable effort has been expended on radial mode structure for such systems. The Com- scaling studies of the feedback, wall stabilization, puter Applications program has had a major impact and staging requirements of Scyllac-like confine- in this area, with the development of a useful three- ment systems. This work not only has immediate dimensional MHD numerical code which follows t he application to present experiments, but also has time evolution of magnetically confined plasma direct relevance to the planning for, and design of, columns in realistic and interesting geometries. To future high-beta confinement devices up to and in- complement these efforts, fundamental studies have cluding a possible Fusion Test Reactor. been undertaken of the general mode spectrum of As was the case in the past, the present report on toroidal ideal MHD systems. the theoretical program covers work done during the The second field which has seen concentrated ef- entire reporting year, but emphasizes results ob- forts is the area of Vlasov analysis and numerical tained during the final quarter. computation. Much work was done to map out and analyze high-beta electromagnetic microinstabilities B. Summary of Scyllac MHD Theory acting in theta and Z-pinch implosion sheaths, and to refine several formulations of the so-called hybrid During the past year the MHD Scyllac theory has plasma model, in which the ions are treated been concentrated in four areas. The first concerns kinetically through the Vlasov equations while the studies of the m= 1 stability in a diffuse = 1 electrons are considered to form a charge neutraliz- system. This problem has obvious importance, ing MHD or drift fluid. This work is needed for gain- because the m= 1 mode is the most dangerous mode . ing a better quantitative understanding of the experimentally. Secondly, a large effort was in- stahilitv properties of high-beta confinement itiated to study nonlinear 3-D diffuse equilibria in a systems, as well as for a better understanding of the toroidal Scyllac configuration. Essentially all dynamics of implosion heating. Much progress has equilibrium calculations to date have been been made in the Vlasov analysis and computation calculated from sharp boundary models, and it is our of spatially inhomogeneous equilibria. goal to obtain more realistic answers for diffuse In a third area of work, the numerical Computer profiles. A third area of investigation was a study of Applications program has made significant con- the m = 1 stability in a modified Scyllac configura- t ribut ions to the experimental programs by model- tion. In this system equal amplitude f? = + 1 and ing the dynamics of Z-pinches and theta pinches us- !l = – 1 fields are superimposed providing a closed ing various physical models for the plasma. The one- line geometry. It was hoped that this configuration dimensional hybrid Z-pinch model, in particular, would have more favorable stability properties than

122 the pure f!= 1 system. Finally, we have continued Finally, a helical section of the full torus will be . our studies of scaling laws as applied to the design of studied to examine Scyllac equilibria. We hope to Scyllac experiments. By taking into account the get realistic answers for diffuse profiles as well as ad- proper constraints, it has been possible to find the dressing the more fundamental question of the ex- . optimum design of feedback experiments and stag- istence of 3-D MHD equilibria. ing experiments, using the existing Scyllac facility. Listed below is a brief status report on each of these 3. Closed Line Scyllac Configuration. We have investigations. considered the stability of a sharp b

123 ab[mt 12.5 m. The largest possible 61 is by and large go=fN3-2@)(l-$)/( 2-19) a matter of faith and courage. In our calculations we . take AI = 1. For the feedback experiment, which is far from be- fi = (3-2/3)/2 ing wall stabilized, we fix R and fil and minimize the . m= 1 growth rate, subject to the constraint of One goal of our diffuse equilibrium and stability toroidal equilibrium by varying 6., h and a. The calculations will be to obtain more accurate values of results indicate that a should be as large as possible. go, i+, and fa to be used in the scaling calculations. In the staging experiment, we again fix R and 6 I as above. We then minimize the ratio of plasma to wall C. Diffuse 1 = 1 and Stability (MHD) rat io a/b, required to make m= 1 neutrally stable subject to the constraint of toroidal equilibrium. In The diffuse J? = 1 calculation started last year this case we varv 6., ha, and b. It turns out that the has essentially been completed. The main results optimum design has b as small as possible. This is were present ed at the IAEA Tokyo meeting (Nov. set from shock heating requirements at about b=l 1 1974), and a more complete paper to be published is cm. on the way. The results for the optimum design are given The calculation is based on an expansion in 6 below for each case. (measure of the helical shift), and with arbitrary ha; h = helical pitch number, a = plasma radius. The Fredback Design computational part of the problem was made dif- ficult because of the presence of an accumulation point for the spectrum of u at w = O. Associated with this there was the existence of local m = 1 modes, +=(a-i’’(~r’ localized on both the outside and at the axis of the plasma column. Also in some parameter regions it was very difficult to separate the local m = 1 modes from the global m = 1 mode. However, this problem ““(3)1”kj” has now been solved in sufficient detail to provide an overall understanding. In this connection a study was made of the possible effects on the local modes from changing the zero order pressure profile. .2=:%a (*r32(#4’3 The effect of finite k. (wave number in the axial o 1 direction) was studied and it has been demonstrated .Staging Dc.sign by numerical examples that for finite, but small k, there exist a critical wall-radius beyond which the plasma column is stable. This is because the ac- cumulation point u = O for k, = O is shifted toward the stable side by taking k, # O. Thus a reasonably small but finite kz can effectively remove the local unstable m = 1 modes, without having any noticeable effect on the gross m = 1 mode, which is wall stabilized in good agreement with sharp boun- dary theory. The numerical computation of this problem was done by having a finite density (of a few percent of densitv on axis) extending to the wall. Another ap- proach would be to solve the same problem with a vacuum region outside the plasma and this way one would also expect to eliminate the external local modes. Work on this problem was started, and first Here the f’s and g’s are function of~ given by the proper boundary conditions had to be derived. It turned out that this was more difficult than an- ~1 =b(4-3@)(2-P/8(1-@ ) ticipated. This derivation is completed, but the result is quite complicated to apply and the problem

124 has not yet been pursued further. Instead some effort magnetic axis away from the center of the tube is has been made to look into the possibility of analyz- then of order unity so that the equilibrium is essen- ing a combined !?= O, g = 1 diffuse system by expan- tially two-dimensional. (In the usual 1ow-8 tokamak sion in 8 and for arbitrary ha. Some progress has order where @ - c2, the shift 6 - c so that one- . been made on this problem and it is currently being dimensional approximations are possible). After studied, because of its great significance to the Fourier decomposing modes in the ignorable angle@ Scyllac program. the stability analysis also becomes two-dimensional, so that the basic problem consists of calculating D. The Continuous Spectrum of Ideal equilibria accurately enough that it makes sense to Magnetohydrodynamics in Toroidal Geometry do a spectral analysis of the stability. This problem is solved in the following manner. The continuous spectrum of ideal MHD arises as The nonlinear equilibrium equation for the flux a result of spatial inhomogeneities, in much the function IJ is solved for exponential pressure profiles, same way as the continuous spectrum in the Vlasov exploiting a conformal mapping to a polar coor- description results from inhomogeneities in velocity dinate system f, 0 in which the magnetic axis is at place. Thus, in ideal MHD two continua of b- the center i = O and the plasma boundary at the cir- functions are found analogous to the van Kampen cle i = 1. Both equilibrium and stability are then modes in the Vlasov picture. These continua are solved in this coordinate system so that no accuracy relatively independent of geometry effects like cur- is lost in converting from one coordinate system to vature (which affects the discrete spectrum) and, another. This transformation makes the low-p therefore, play a central role in the understanding of equilibrium trivially concentric circles to leading the structure of the spectrum. In the diffuse linear order, whereas high-~ equilibria can be accurately pinch the slow and Alfven continua are sandwiched represented by an extremely rapidly converging between St urmian and anti -Sturmian discrete spec- Fourier-series in the angle O This Fourier represen- tra clustering at the continua. Both continua consist tation of the equilibrium is also a very convenient of modes localized in a particular magnetic surface, one for the stability analysis as part of it can now be but polarized parallel to the magnetic field for the done analytically. slow modes and perpendicular for the Alfven modes. Limits on the equilibrium typically arise from the In axially symmetric toroidal systems it is much appearance of a second magnetic axis and bifurcated harder to distinguish the discrete subspectra, but solutions when 6 becomes too large (this occurs at one can find the continua cluster points analytically. about 6 = 0.4). This limit fixes a critical value of (3 The singular continuum modes are again localized depending on the safety factor q. From the stability on particular magnetic surfaces but the polarization analysis similar limitations on (3arise so that one can is no longer purely parallel or perpendicular. The then optimize parameters so as to obtain the max- reason is that the magnetic field is not constant on a imum possible 6 as far as ideal MHD equilibria and magnetic surface so that the waves propagate stability are concerned. neither along field-lines nor along goedesics. As a result, the Alfven and slow continua are coupled giv- F. Three Dimensional Computational ing rise to oblique propagation for both continuum Magnetohydrodynamics modes. This complicates the spectral problem con- siderably, especially as regards stability because the A numerical algorithm for solving the fully 2–() coupling is strong near the origin u – . nonlinear, time dependent equations of ideal MHD Curvature effects determine whether the tip of a has been developed this year. This algorithm continuum is a cluster point of localized modes. employs an implicit algorithm to obtain time ad- Thus, the Mercier criterion turns out to be just a vanced accelerations. Hence, the usual Courant special case for modes that are localized around stability condition is relaxed and the time step is not rational surfaces. limited by high signal speeds which are not of physical interest. The difference equations are for- E. Equilibrium and Stability of High-Beta Dif- mulated for an arbitrary three dimensional com- fuse Tokamaks putational mesh. Numerical diffusion is minimized by the use of an arbitrary Lagrangian-Eulerian The limitations on f? as regards equilibrium and (ALE) mesh in which almost Lagrangian zoning stability of tokamaks are investigated. The regime of diminishes convection between cells. interest is obtained for@ - c and BPodBtO~ - c, where t is the inverse aspect ratio. The shift 6 of the

125 Because of the arbitrary shape of the com- were not excited by numerical noise. Hence, it is putational zones, boundary conditions appropriate possible to find unstable equilibria with the . to general configurations are easily implemented. A algorithm and focus attention on those modes found subroutine permits the representation of a conduc- experimentally to be most troublesome. ting wall of specified shape by the definition of a Preliminary results from toroidal calculations in- . single function. In toroidal geometries, periodic dicate that if no equilibrium close to the initial state boundary conditions are imposed in the axial direc- exists, the code will provide a clear indication of this tion in such a way that a toroidal sector of specified by following the motion of the plasma tot he conduc- length may be represented. Thus, for example, a ting boundary. By solving the initial value problem single period of a helical Scyllac equilibrium may be in this way, the problems of equilibrium and stabili- studied. ty may be decoupled. A number of computations have been performed All computations to date have indicated that in straight axisymmetric configurations as well as in numerical diffusion is small enough that reasonable toroidal geometry. A truncation error in the com- physical problems may be represented with the putation of acceleration at the boundary has been relatively coarse grids that must be used in three observed in these initial toroidal computations. This dimensions. effect is due to the toroidal curvature and has been Plans for the coming year include computations to understood and corrected for the case of isotropic study the nonlinear evolution of int ernal kink modes stress. The general case of anisotropic stress due to a in noncircular cross section axisymmet ric devices. magnetic field is currently under investigation and it Various two dimensional toroidal configurations will is expected that soon this effect will be understood be studied in which an equilibrium is possible or not analytically and eliminated from the computation. possible and in which the equilibrium, if it exists, is The implicit phase oft he computation includes all stable or not. These comput at ions will demonstrate coupling terms in the equations determining the the separation of equilibrium and stability time advanced magnetic field and the time ad- questions. Finally, the toroidal code will be used to vanced pressure for each cell. This eliminates cases examine the three dimensional Scyllac configura- in which the relative magnitudes of the various t ion. propagation speeds of Alfv6n and magneto-acoustic waves would otherwise cause convergence dif- G. A One Dimensional Hybrid Simulation of the ficulties in the iteration. The present scheme con- Biased Z Pinch Implosion verges efficiently for the entire range of signal speeds of interest. We have commenced a program to calculate The computation mesh is rezoned by the applica- pinch implosions in which non-thermal effects (such tion of a smoothing algorithm. The algorithm gives as reflected ion streams) are important. Ideally, one the minimal adjustments to the grid which are often would wish to treat both electrons and ions by the sufficient to prevent negative volume cells without Vlasov formalism; however, the speed and storage introducing appreciable relative motion of the grid capabilities of the current generation of computing and fluid. When minimal adjustment is not suf- machines does not allow this. A workable alternative ficient, as in turbulent flow, the algorithm allows the is the hybrid approach, which consists of treating the smooth transition to an Eulerian mode. This gives ions by the Vlasov formalism and the electrons as a the ALE code the full range of applicability of an fluid while assuming charge neutrality and neglec- Eulerian computation with a reduction in com- ting variations on the electron time scale. This may putational diffusion when the flow is resolved by a be rationalized, in the case of the Fuse mode of the Lagrangian mesh. The smoothing algorithm may ZT- 1 experiment, by noting that a typical Fokker- also be used to generate an initial computation mesh Plank relaxation time for the ions is -301.Ls, for the for a problem with an arbitrarily shaped boundary. electrons is - O.Ol~s, while the implosion time is . When the position of boundary vertices is specified, - lgs; and that the Debye length is -10-4 cm while the algorithm will give a distribution of vertices in- a cell is - 10–2 cm. We have written such a hybrid terior to the boundary with the desired properties. code in one spatial dimension (r) and we present a Calculations have indicated a number of key description of the code along with some illustrative features of the algorithm. For the rotating theta results. pinch in an axisymmetric geometry, good agreement The ions reside in a four dimensional phase space wit h linearly predicted growth rates has been observ- (V,, VoV.,r). The Vlasov equation for ions in such a ed. More importantly, even very unstable modes space is solved by the particle simulation

126 technique. 1 Knowing the ion distribution function in the code. The formalism requires CTiI and al, and . we may find the average density and average radial to get these we substitute Vdl I and Vdl into the above

velocity of the ions as a function of position, which equation. Furthermore C I I and Cl, as well as f II and by charge neutrality determine the electron density fl, may differ. . and radial velocity. In Fig. XI-1 is shown experimental field profiles The momentum equation for the fluid electrons for the ZT- 1 derated shot 10115 and calculated

may be written as profiles assuming CII =Cl= 1.0, fll =fl=3.0. As can be seen, the agreement is acceptable. In particular the code reproduces the principal features of the field evolution, namely considerable diffusion in the Bti profile together with a BZ profile which shows considerable compression and which does not diffuse Cfmsistent with our neglect of variations on the elec- away. During the implosion, v = VSnear the center tron- time scale we set the left hand side to zero. while in the sheath region (where Ho is large) v/v S DivB(r) =0 implied B,(r) =0, and in the ~ and 2 may be as high as 105 and vll/vl may be as high as 5. directions gradp~(r) =0, so that the 8 and 2 Evidently turbulence enhances the collision frequen- components of the momentum equation reduce to cy in the sheath region. This conclusion is reinforced field diffusion equations which we solve by in- by Fig. XI-2, which gives field profiles for 10115

troducing the vector potential .2 The conductivity calculated assuming CII =CL = O (v = VS along the field is allowed to differ from that perpen- everywhere). dicular to the field, so that we construct a conduc- In Fig. XI-3 are shown experimental field profiles tivity tensor a.2 The boundary magnetic field may for the ZT- 1 shot 11678 and calculated profiles be specified as a function of time. assuming the same collsion frequency as before Finally, the electron heat equation, which in- (CII =C1 =1.0, fll ‘fl -3.0). Again, the agreement is cludes compressive heating, Joule heating and heat acceptable. That the data from both shots can be conduction may be used to solve for pe while the r matched by using the same conductivity may be component of the electron momentum equation may significant. If this turns out to be a general feature of be used to solve for E,. the hybrid calculations, this approach will be useful This approach requires an electrical conductivity in predicting the results of future shots. and a thermal conductivity to be specified. It is here that the non-Maxwellian aspects of the electrons, H. A Code for Modeling the 0-Pinch Implosion their interaction with the ions, and turbulence enter Including the External Circuit the formalism. One may use coefficients derived from the theory of plasma turbulence or from the As a guide both for designing implosion heating nonlinear evolution of a given instability or one may circuitry and for interpreting the data from the ex- find by trial and error coefficients that allow the periments, we have written a code IMPLOD which is results of a given experiment to be reproduced, and now in active use. then inquire into which processes give rise to such a The plasma model is a one-dimensional hybrid coefficient. model similar to that described by Sgro in the In the results presented below, we have set the previous section (G). Some simplification in the thermal conductivity to O and have chosen a colli- treatment of electron pressure is made to guarantee sion frequency v (where u=e2n/mev) similar to the numerical stability. The circuit is defined in the loop . one suggested by Chodura. In principle, we take v to current formulation by specifying the nonzero be U,, the value given by Spitzer, 3 if Vdf c~. However, in algorithm makes this circuit code considerably order to avoid numerical problems resulting from a faster than library network codes. However, the sim- sudden switch v, we use ple code is somewhat more cumbersome to use for very complicated circuits. The interaction of the circuit and the plasma in- volves a special feature which deserves further dis- cussion. Because of the complex electrical properties ‘s1 ‘==[cu+:vd’fcs)sof a coil containing dynamic plasma, no simple

127 6.0 T Bz(k G) 2.8 .

r 1.6

2.0 -

0.0 0 I I 1

-1.o- R (cm) R (cm) Experiment

2.0 “

0.0 “

-2.00 I 1 I 5.7

R (cm) R (cm)

Theory

Fig. XI- 1 (’[,mprrri,son of theoretical and experimental magnetic field profile for ZT-I shot 10115. decoupling of the circuit and plasma is possible. The the circuit equations one can reduce the set of circuit . boundary condition on the plasma is related to the equations to NIP +dBP =-y even though the numerical circuit through Ampere’s law for lP, values of the current and voltage through the plasma coil are not yet known. However, since a mixed boundary condition on Au produces a well-posed . aAe ~ =LL boundary value problem for Ao, the field diffusion r ar ‘K P ( )1r= SMAX equation can be solved before numerically knowing either the current or voltage in the coil. This having and through Faraday’s law for VP,VP a i3(rAo)/dt Ir. been done, back substitution leads to values for all RMAX. At any time step of the computation one has circuit currents and voltages. Thus a completely N loop equations for the circuit plus the boundary self-consistent solution is obtained without itera- value problem for the magnetic field in the plasma. t ion. Bv proceeding as far as possible with elimination on

128 +6[03 B8(kG) . 4.0, I I . I I

.

2.0 “ 1

0.0 – .~o~. 0.0 1.4 2.8 4.3 5.7 R(cm) R (cm)

Fig. XI-.2 Fi~ld profiles for the same shot as Fig. 1, a.ssurning no turbulent enhancement of the ctmductiuity in the sheath region.

This code is being used by R. Linford to study instant aneous-action-at -a-distance model. Any proposed implosion heating circuitry and by T. Jar- attempt to implement this with a numerical model boe to correlate data in the implosion heating experi- having only local interactions is bound to be ment. numerically unstable. By formulating the Maxwell- L{)rentz equations in a somewhat complicated but 1. The Darwin Model for Plasma Simulation totally elliptic form we have obtained a completely stable numerical model. Two-dimensional particle simulation is one of the This two-dimensional code is now being used to few techniques available for studying the properties study the nonlinear properties of electromagnetic of microscopic plasma turbulence. In high-~ pinches streaming instabilities in highly inhomogeneous magnetic fields and steep gradients complicate this plasmas. turbulence beyond the capability of simple elec- trostatic models. Fully electromagnetic simulation J. Numerical Simulation of the Proposed Injec- codes, while fairly simple to write, must follow all tion Experiment processes on the lightwave time scale. Not only is this inefficient for nonrelativistic plasmas, but the A two-dimensional MHD code for the bremsstrahlung is artificially enhanced due to the axisymmetric geometries is being used to simulate . relatively small number of simulation particles. the proposed plasma injection experiment. 5 Several The correct nonrel?tivistic treatment consists of numerical algorithms have been developed to make neglecting the transverse displacement current in the existing code applicable to this experiment, in- . Maxwell’s equations while keeping the time cluding developing a method for applying time- derivative of the electrostatic field. This was first dependent boundary conditions, and a method for demonstrated by C.G. Darwin4 and is called the the construction of a suitable mesh for a domain Darwin model. One-dimensional simulation codes with sharp corners and an unfavorable ratio of for this model have existed for some time, but two- length to diameter. The first method was described dimensional forms, essential for studying most in a previous quarterly progress report. The second is significant problems, have presented difficulties. an adaptation of an algorithm for generating body- The source of these difficulties is the fact that the fitted coordinates developed by Thompson, et al. 6 reduced model has no retardation, that is, it is an

129 5.0 ~ . 4.0 B8 (kG)

4.0 – r . 3.0 – 2.8 2.4 3.0 –

2.0 – 2.0 -

I.0 – 1.2 1.0’F 0.4,0.8

0.OO ; I 1 ----rrT\\5

R (cm) R(cm)

Experiment

*103 *103 4.0~ 7“0 Be(kG) 2.8 3.0 – 5.0 2.0

2.0 – 3.0 2.4

I.0 – I.0

0.0 -1.o1 I I I J 0.0 1.4 2.8 4,3 5.7 0.0 1.4 2.8 4.3 5,7 . R (cm) R (cm)

Theory .

Fig. XI-3 ( ‘tjmpm-ison of theoretical and experimental profiles for ZT- 1 shot 11678. The curt’es arc labvl~d in m icrosceonds.

130 With this algorithm, only the location of points on A generalized version of the equilibria generating . the boundary need be specified. The solution of a procedure allowing arbitrary T, profiles is presently quasi-linear differential equation then gives a dis- being pursued. Preliminary results indicate that tribution of vertices interior to the boundary which simulation runs initialized with the new equilibria . is suitable for an MHD calculation. That is, the cells exhibit electromagnetic instabilities, which may be are convex and smoothly varying in size as can be related to the Weibel instability.7 Figure XI-5 shows seen in the mesh for the injection experiment shown (a) the initial densities, (b) the magnetic field (BJ, in Fig. XI-4. This algorithm is general in its applica- and (c) the electron temperature profiles as a func- tion, and will be useful in the future in shortening tion of x. The ion temperature is ten times the elec- the set up time for new problems with new tron temperature at x=O; they are equal at large x. geometries. The contour plot (d) of B, in the x-y plane, taken from a PIC simulation run at time t =80 COP,–1 , K. Inhomogeneous Vlasov Equilibria shows definite wave structure, indicative of an elec- tromagnetic instability. Inhomogeneous magnetized Vlasov equilibria which correspond to the situation found in the sheath region of theta pinches have been constructed L. Vlasov-Fluid Research numerically using a hermite transformed Vlasov equation. The primary aim of this work is to find in- 1. Sharp Boundary Pinches. During the first itial states for 2-D PIC simulations of the quarter, extensive analytical investigations were microinstabilities which occur in the sheath region performed in an attempt to apply the Freidberg and are responsible for the observed anomalous Vlasov-fluid model of hot pinches to sharp- resistivity. It is advantageous to initialize these boundary-pinch stability. A significant result of this simulations with inhomogeneous equilibria so that work can be stated as follows. In the uniform region the detailed structure of the instabilities will not be of a near-theta pinch, to leading order in ion gyro- masked by larger dynamical effects resulting from a radius to radial scale length, (rL/a), the ideal-MHD nonequilibrium initial state. equations are valid provided the ratio of specific The basic procedure for generating equilibria by heats, ~, is replaced by ~,ff. ~ –2 (w/kzvi) Z(ukzvi), this new method is to choose a density profile for the where the perturbation has complex frequency w, ions, which are assumed to be Maxwellian and, real wave-vector k with magnetic field projection kZ therefore, electrostatically confined. Electron and ion = k.B/l B 1. where v is the ion thermal speed and Z is temperature profiles in x (which corresponds to the the plasma dispersion function. Moreover, the cor- radial direction in a theta pinch) are assumed cons- rections to this result, of order (r~a)”, have been tant. The electric field required to confine the ions shown to be of order (rL/a)2 in the uniform magneto- may now be calculated from the ion Vlasov equation. plasma region. Thus, -yeffcontains the kinetic effects The electron density is then computed from of free particle motion along field lines. It was then Poisson’s equation, the magnetic field from the elec- decided that further analytical effort on hot pinch tron pressure balance equation, the current from stability would be better spent on the more realistic Ampere’s law, and higher y (i. e., 0) velocity diffuse pinches. moments may then be calculated recursively from the Hermite transformed Vlasov equation. 2. Diffuse Pinches. During the second quarter, Several new features oft his type of equilibria have a near-theta diffuse pinch of Gaussian density been discovered. The first is that if the ion density profile with self-consistent equilibrium electric and outside of the sheath region is toQ small, electrostatic magnetic fields was considered. The deviations from confinement oft he ions by a charge neutral sheath is a straight theta-pinch were assumed small, but not possible. The second feature is that the otherwise arbitrary. The stability of this pinch in- . temperature of the electrons in they direction (TY) is cluding the full effects of the gradient-B particle not equal to that in the x directicn (T.). In the region drifts. A trial-function dispersion relation was deriv- just inside of the current sheath TY is significantly ed and solved numerically. The growth rate of the less than TX, and the effect becomes more m = 1 mode was found to be given by its ideal-MHD pronounced the narrower the sheath. Since one re- expression (the 6W expression) to within l/2’%0, over quires TY to “be greater than zero always, one obtains the large parameter range that was investigated. a restriction on the minimum sheath width and the Because of the finite-Larmor-radius ordering that maximum current allowable. was used in this work, it became necessary to know

131 60

.

. I

\F

E 6

Fig. XI-4 (;roph showing part of the computation mesh in the vicinity of the reentrant corner. that there were no order (rL/a) 2 contributions to the 3. Model Generalization. During the third usual particle drift velocity expressions of order quarter, the Freidberg Vlasov-fluid m~del of hot-ion (rL/a) 1. This can be inferred from a particle-orbit pinches was extended to include finite electron review article by Ira Bernstein, for the case of low- temperature. A lengthy analysis produced a rather beta plasmas (i.e., gradient-B drifts small compared simple final result. Leaf Turner then performed a to ExB drifts). It remains to be demonstrated in small (rL/a) expansion on these new equations, for a general for high-beta plasmas. However, R. Gerwin uniform magnetoplasma, and found that the MHD- has made some progress in this direction by examin- type behavior of pinch stability is again characteriz- ing the orbit equations within the context of a ed by a certain -y~rr,which is a generalization of that gradient-B slab geometry. It was indeed found that described above. The new Vlasov-fluid equation now the leading correction to the usual gradient-B drift encompasses a much more complicated mode struc- was of order (qJa) 3. ture that includes ion-acoustic waves.

132 0.6

Ion ~ a) .- L1. mN

I 1 ! 1 06 8 10 i2 i4 06 8 io i2 x (CAUPJ x(c/COpJ - (0) (b)

i4 x(c/aJpJ x (cAJpe) (c) (d

Fig. XI-5 Profiles of the initial densities, z-component of the magnetic field and electron temperature. anda contour plot of B, at t=80a–\c.

. M. Equilibrium and Microinstabilities in ZT- 1 profiles for application to current-driven microinstabilities that may be a source of anomalous During the third and fourth quarters, R. Gerwin resist ivity and concomitant undesirable diffusion and Leaf Turner constructed a ncmresistive model of of the ZT-1 profiles. A code has been written that the ZT-1 equilibrium that allows for a reversal in the quickly furnishes these velocity profiles in a straight toroidal magnetic field, and a pressure profile that geometry. can be either full or depressed on axis. The purpose The model equilibrium predicts a total toroidal of this model is to furnish electron-drift drift velocity current that is in reasonably good agreement with

133 observation, both for the fuse- and intermediate- where up and w are species plasma- and gyro- modes of ZT-1 operation. It further predicts that the frequencies respectively. In the periphery of ZT-1 . component of drift velocity parallel to the total this amounts to veff -tipi in order of magnitude, and magnetic field is of the order of the ion-thermal is thus similar to an effective collison frequency speed, vi, whereas the component of drift velocity employed by Sgro in his computer studies. However, . perpendicular to the field is small against vi in the it scales differently than wpi. core of the pinch, but rises to the order of vi in the The broad-brushstroke picture that suggests itself periphery of the pinch (densities - 10ri to 30$i of the for ZT-1 now seems to run as follows. In the pinch density on axis). These drift velocities appear to be periphery, microinstabilities probably of the in qualitative agreement with the code of Baker and electron-acoustic type are driven by UL < vi. It is Mann that includes the exact toroidal geometry. important to note that in this part of the profile, The consequences of these properties for toroidal field reversal occurs. Hence U1 is largely in microinstahilities will now be discussed. the toroidal direction in this region, and the R. Gerwin spent most of the fourth quarter exten- microinstabilities it drives will be associated ding the review of microinstabilities to include in- primarily with toroidal resistivity and concomit- homogeneous equilibria with self-consistent drifts, ant diffusion of the poloidal magnetic field. In this thus enlarging the work of the previous quarter on connection, it is also important to note that the unif’orm magnet u-plasmas with relative electron-ion wave-vector k corresponding to maximum growth drifts when Te vi.) R.C. Davidson and N.T. Gladd staging conceptg as a means of achieving wall have examined a k! I=0 drift-wave instability (the stabilization of the Los Alamos high-beta toroidal hot -ion version of the lower hybrid-drift instability) confinement device, Scyllac, has provided strong that has a growth rate which scales exactly like the motivation for understanding the microprocesses standard electron acoustic instability but is a factor which occur in various high-density pinch im- of two larger. Thus, the particular mode appears to plosions. In particular, the turbulence associated . be very relevant to ZT-1. with the existence of microinstabilities in implosion The anomalous resistivity associated with the hot- sheath manifests itself, microscopically, as an ion lower-hybrid drift instability has been calculated anomalous resist ivity which strongly affects the way . and is characterized by an effective electron- in which magnetic fields interpenetrate the plasma. momentum-transfer collision frequency of the form Since to scale up staging from current experiments 9 to reactor-like devices will probably require lj2 knowledge about the scaling of anomalous transport Vef~ u m (Ul/vi)2 (1 + L@:e) (1) ‘Jpi coefficients, it is desirable to understand the microinstability picture as well as possible. This

134 report relates some of the theoretical steps taken in magnetic field (kl!/kl#()). It was found that for . the past year to understand the microinstabilities almost all situations typical of high-density pinch characteristic of high density (uP~/~e>>l ), hot ion implosions that it is the lower-hybrid-drift instabili- (Te/Ti S1) theta-pinch and Z-pinch implosions. ty which has the largest growth rate. Furthermore it . was found that the effects of finite (3 on this domi- 1. Linear Theory. The anomalous resistivity nant instability manifest themselves primarily and other anomalous transport coefficients which through the magnetic field gradients necessarily im- are required as input to macroscopic fluid-numerical plied by finite 8 rather than through coupling of the codes and other theoretical devices used to model electrostatic lower-hybrid-drift mode to various elec- the macroscopic behavior of high-density pinches tromagnetic modes. In this context it was also found are the consequence of nonlinear plasma theories. A that the effect of finite @ is generally destabilizing general characteristic of nonlinear plasma theories is but not strongly so. The statements above constitute that their predictions depend quite strongly on the only a brief summary of the work performed. For linear properties of the instabilities which are most details the reader is directed to Ref. 15. important in the plasma under consideration. An interesting aspect of the dispersion relation Therefore, to have confidence in calculated derived in Ref. 8 is that it is sufficiently general to anomalous transport coefficients it is necessary to allow application to real experimental profiles of have a firm base of knowledge about the linear density, temperature, and magnetic field. In par- stability theory of high-density pinch implosion ticular, the well diagnosed collisionless shock experi- sheaths. To this end a dispersion relation was deriv- ment of Keilhacker, Kornherr, and Steuer 16 was ed from the Vlasov-Maxwell equations which has chosen and the instability characteristics provisions for both finite-beta effects and the effects [frequency (tir), maximum growth rate (-y), and of gradients in density, temperature, and magnetic growth maximizing wave number (kY ~~.PJ 1 were field. calculated as a function of position within the implo- The dispersion relation was applied to study the sion sheath (see Fig. XI-6). In the figure the density instabilities thought to be most important in typical profile is superimposed for reference. Again, for high-density pinch implosions, namely the lower- details the reader is referred to Ref. 8. From this type hvbrid-drift instabilityl” and the modified-two- of analysis some conclusions about the spatial struc- stream instability. 11 Although these instabilities ture of microturbulence within implosion sheaths, to have been previously examined in the literature, the the extent that it can be so described by a local published analyses were deficient in one way or linear Vlasov theory, may be drawn. Possible points another as they related to application in high density of observational interest for this experiment are the pinch experiments. For example the detailed study differences in the microturbulence characteristics in of the modified-two-stream instability 12 showed the shock region [I-2] and the piston region [3-4]. that the maximum growth rate for the instability oc- The general dispersion relation was not expressi- curred in a regime where the electrons required a ble in closed form when all detailed effects were in- kinetic description, but restricted itself to a cluded and so a significant portion of the analysis homogeneous $=0 plasma model. Subsequent required numerical solution of the dispersion rela- analysis of the effects of finite beta 13 on this mode tion. Furthermore, comparison of the general disper- was again restricted to a homogeneous plasma with sion relation with previously published results re- the electrons described by fluid theory and thus the quired, in general, numerical computation. For these most rapidly growing modes were not treated. reasons a numerical code (ANLYZ ) was developed Similar gaps exist in the published analyses of the which allows for the numerical solution of general . lower-hybrid-drift instability. 10’14 dispersion relations and the processing of solution An important question which was initially ad- related information by a number of techniques. The dressed with the more general dispersion relation code is interactive and is designed to run on the . was the question of the relative importance of the LTSS (CDC 7600) system available at Los Alamos. lower-hybrid-drift instability and the modified-two- Intentions are to extend the capability of the code to stream instability. The lower-hybrid-drift instabili- include interactive graphics as soon as the hardware ty is characteristically a flute mode &.~=0) with becomes available. The code itself is independent of maximum growth occurring fork~~- I. The modified the particular dispersion relation which is to be two-stream instability experiences maximum analyzed and thus has general plasma physics growth at somewhat longer wavelength (kM,<

135 0.03 I I I I I i . Model 2 -CL+ .— +-. % - — _. -”- 3 . 0.02 Y– 0.0 I ‘--x’’’””k &o

0.02

0.01 . ------? I Y 0 I I I I I I I 1 I I I I 0 ~ 1.4 1.8 2.2@ 2.4 2.8@ 3.2 @3.6 4.0 r (cm)

Fig. XI-6 1~(’pendcncr of instability properties (frequency, growth rate, and growth maximizing u~al’cnum bet-) on position within an experimental implosion sheath.

2. Nonlinear Theory. The discovery of the understanding the experimental observation that in general dominance of the lower-hybrid drift in- the late stages of theta-pinch implosions the plasma stability over the modified-two-stream instability is hotter than is predicted by existing theoretical es- strongly suggests that the calculation of anomalous timates and fluid-numerical studies. Furthermore transport coefficients associated with microtur- the quasilinear analysis indicates substantial bulence due to the lower-hybrid-drift instability is of anomalous resistivity when VE. Whi,a result which is paramount importance in understanding the in keeping with the observation of enhanced macroscopic characteristics of high-density pinch broadening of profiles during the late stages of im- implosions. Quasilinear theory was applied to study plosion. Details of the results summarized above the nonlinear development of the lower-hybrid-drift may be found in Ref. 19. instability and the anomalous heating rates and In addition to its relevance to the late stages of resistivity due to this mode were calculated in a theta-pinch implosions, the theory appears to have . regime (VE <3V~hi) heretofore not explored application to ZT-1. ZT-1.20 A recent survey by theoretically. Also, upper bounds for the effective Gerwin21 of the instabilities which could contribute collision frequencies for the various anomalous to anomalous resistivity in Z-pinches reaches the . processes were obtained using the thermodynamic conclusion that the hot ion (UfkVthi< 1) version of the met hod of Fowler17 to obtain an upper bound on the lower-hybrid-drift instability is probably the most unstable fluctuation energy. It was found that in- important instability. In the limiting case VESV thi tense plasma heating can occur when the cross-field analytic expressions for the anomalous resistivity electron EX B velocity (VE) is comparable with the have been obtained and preliminary comparisons of ion thermal velocity (Vthi ) = Well as in the large drift the theoretically predicted resistivity with measured velocity regime (VE>>Vthi ) previously discussed by resistivity in ZT- 122 are very encouraging. a Liewer and Krall. 18 This result is imortant in

136 /

O. Electromagnetic Ion Cyclotron Instability The hybrid-kinetic model is an important exten- . Driven by Ion Energy Anisotropy in High-Beta sion of and supplement to existing theories. 24’25-26 Plasmas The particle distribution functions and the elec- tromagnetic fields are calculated self-consistently to ● LOW frequency (w ~tici = eBO/mic) transverse first order in c. To lowest order the electron drift- electromagnetic perturbations propagating parallel kinetic description is identical to the guiding-center to a confining magnetic field B06p07-z are shown to formalism of Grad. 24 However the inclusion of first- exhibit instability in the presence of ion energy order electron inertial effects, E together with the anisotropy with TiL>Till . The characteristic fully kinetic treatment of the ions, allows the

maximum growth rate for Til>>Til I is ~~ application of the present work to experiments ‘(&/2) 112@~i, where ~il= 8~niT~ /B20, and the (high-beta, implosion and post-implosion time wavelengths corresponding to instability are of order scales) and instabilities ( .e.g, lower-hybrid drift) cl~i, where tipi is the ion plasma frequency. Within where the earlier theory24 is invalid. The hybrid- the context of a quasilinear model, it was shown that kinetic description is closely related to the Vlasov- the characteristic time scale for energy isotropiza- fluid model of Freidberg. 26 However, the treatment tion through nonlinear response of the ions to the in- of the electrons in the present work includes physical stability is several ~ ‘h. Since y–h <<~ii (the ion-ion effects (.e.g, finite electron temperature and parallel binary collision time) in typical high-density pinch kinetic behavior) that are absent in the Vlasov-fluid experiments, this instability appears to provide a model, 26as well as physical effects (e.g., electron in- viable collective mechanism for ion energy ertia) that are important on the relatively fast time isotropization during the implosion or post- scale tici >ltiCi1, k~r~l>>l) and strongly magnetized equilibria of collisionless plasmas is important for electrons ( lw+i~ [<<1 wC,1, k%~ <<1) provided the understanding the stability properties of hot ex- local $jL>>l. perimental plasmas produced in 0- and Z-pinch devices; these experimental plasmas are, of course, P. A Hybrid-Kinetic Model for High-Beta always inhomogeneous and of finite extent. Because Plasmas most of the theory for high-e plasmas is based on linearized treatments of the ideal MHD model, a A hybrid-kinetic model for describing major objective of studies based on collisionless or collisionless, high-/3 plasmas has been developed and hybrid models is to assess the modifications of preliminary applications made to the equilibrium linearized MHD predictions by finite gyroradius and stability properties of linear pinches. The model effects. is applicable to high-(? plasmas in which the For several years a program has been underway to characteristic ion Larmor radius is comparable to develop effective means for studying the linearized the macroscopic -c<

137 were due to imperfect understanding of how the 2. Small Ion-Gyroradius Limit of the Vlasov- Vlasov-fluid model itself is to be expressed when Fluid Model Applied to a Sharp-Boundary Screw applying it to a plasma with a sharp boundaw; no Pinch. The numerical computations for sharp- problem has been found with the general method of boundary screw pinches that were discussed in the studying linearized behavior about inhomogeneous previous Annual Progress Reportsl indicated a need equilibria. The question of how a sharp boundary to understand the small ion-gyroradius limit of the should be treated within the framework of the Vlasov-fluid model as applied to a sharp-boundary Vlasov-fluid model has been resolved, and the screw pinch, and an intense effort was made to ob- numerical studies will recommence. tain an analytical understanding of the small ion Work on the sharp-boundary screw pinch has led gyroradius limit with the help of the MACSYMA to involvement with the MACSYMA symbolic symbolic computation system at the Massachusetts manipulation computing system, to calculation of Institute of Technology. A different but parallel ef- compressible MHD growth rates for a sharp- fort was undertaken by R.A. Gerwin. The original boundary screw pinch, and to the formulation of a motivation for the analytical work was to provide a two-fluid model for this problem. The method for firm basis for checking the computer code and to studying the properties of inhomogeneous equilibria determine optimal boundary conditions on the ex- that is being used with the Vlasov-fluid model has pansion functions for the perturbed vector potential been extended to cover rather general situations, at the sharp boundary. In fact, conditions that were and is being applied to one-dimensional, elec- used for the numerical computations were incorrect trostatic equilibria. In addition, a similar formula- and that the basic equations must be modified tion has been made for the two-dimensional guiding- somewhat because of the presence of a sharp boun- center model. dary. The correct boundary conditions and form of Some of the basic numerical methods being used the equations are now known, and thus much of the were introduced as part of a different, but closely original motivation for the analytical small related, computational scheme for studying the gyroradius work is no longer applicable. linear properties of a homogeneous, one- Nevertheless, it is still of interest to obtain dimensional, single-species equilibrium where the analytical results on the nature of the eigenfrequen - equilibrium velocity distribution was arbitrary. 27 cy spectrum for small gyroradius, and so the small However, attempts to generalize that scheme to in- gyroradius approximation will be carried to a con- clude inhomogeneous electrostatic equilibria were clusion. unsuccessful. It appeared to be impossible to The approach being followed with the small preserve certain quite useful formal aspects of the gyroradius calculation parallels the formulation scheme. Despite this failure, it turned out to be used for the numerical computations and makes no possible to develop a similar scheme which could be approximation other than small ion gyroradius. The used to implement the Vlasov-fluid model, which calculation focuses on the elements of the matrix treats collisionless ions and massless electrons in a that determine the natural eigenfrequencies of the low frequency approximation.%-30 system by the condition that its determinant vanish. The scheme for applying the Vlasov-fluid model For the analytical evaluation of the matrix elements, required a realization that expansion of functions of an infinite series was summed in closed form and the position and velocity in terms of eigenfunctions of matrix elements were thereby reduced to five-fold the unperturbed Liouville operator is very useful; it integrals. In order to perform the integrations, the required development of effective numerical integrands must be simplified considerably. This . methods for solving a type of very large eigenvalue can be done by means of an approximation valid for problem; 30’31 and it required an extension to more small ion gyroradii. This approximation is being than one dimension of a previously developed carried out and the integrals are being performed . method of choosing and evaluating matrix elements. with the aid of the MACSYMA symbolic computa- The method of evaluating matrix elements in more tion system at the Massachusetts Institute of than one dimension amounts to a general method of Technology. The matrix elements are being approximating multiple integrals over arbitrary evaluated to zeroth, first, and second order in the ion domains. These developments allowed extension of gyroradius for arbitrary w/wC , k, r~, and m, where WC the scheme to include inhomogeneous electrostatic is the cyclotron frequency, rO is the equilibrium equilibria and other, more general, situations. plasma radius, and the Oand z dependence of pertur- bations is given by exp[i(mtl+ kz) ].

138 This calculation has turned out to be quite am- state that includes the equilibrium but also takes . bitious, even with the aid of MACSYMA. When it is some effects of the moving perturbed boundary into finished, the results should be useful in understan- account to first order. By the introduction of ding the Vlasov-fluid model better, in providing suitably defined new dependent variables to replace e analytic expressions for the eigenfrequency spec- the perturbed vector potential and distribution func- trum from zeroth through second order in the ion tion, the basic equations of the Vlasov-fluid model gyroradius, and in providing direction for future for a sharp-boundary equilibrium can be brought analytical work and improvements in methods for into a form that is very similar to the equations for a numerical evaluation of the Vlasov-fluid model. diffuse equilibrium.

3. Vlasov-Fluid Model for a Sharp-Boundary 4. Compressible MHD Growth Rates. The Equilibrium. When the Vlasov-fluid model is ideal MHD equations with an arbitrary com- applied to an equilibrium with a sharp boundary, at pressibility -y were used for determining the eigen- which individual ions reflect specularly in the rest frequency spectrum for a sharp-boundary screw frame of the boundary, it is necessary to impose ap- pinch. Growth rates for various values of -y will be propriate boundary conditions on the perturbed vec- compared with growth rates determined from the tor potential. The basic Vlasov-fluid equations do Vlasov-fluid model. not provide the boundary conditions because the delta-function electric field at the boundary couples 5. Two-Fluid Model. A two-fluid model has to the discontinuity in the pertufbed magnetic field. been formulated for a sharp-boundary screw pinch The origin of the electric field is as follows. The elec- as a possible phenomenological alternative to the trons are massless, and are therefore tied to Vlasov-fluid model for providing finite gyroradius magnetic field lines. The ions, because of their finite corrections to MHD. gyroradii, try to expand beyond the region to which the electrons are confined, thereby generating a 6. BGK Equilibria. A formulation of the sheath whose thickness is on the order of an ion linearized problem of electrostatic perturbations Debye length. In the sharp-boundary idealization about an inhomogeneous equilibrium is being in- the sheath thickness is assumed to be zero and so the vestigated which is analogous to the method being sheath electric field must be taken as a delta func- used with the Vlasov-fluid model. Specific problems tion. It can be demonstrated that the correct are being studied from an analytical viewpoint. As magnetic boundary conditions at such a sharp boun- with the Vlasov-fluid model, important features are dary are that the normal component of the per- that functions of position and velocity are expanded turbed current density vanish and that the normal in eigenfunctions of the unperturbed Liouville component of the magnetic field be continuous. Two operator, and that the expansion functions for the consequences of the vanishing of the normal compo- perturbed scalar potential are determined by the nent of the current density appear to be significant nature of the equilibrium inhomogeneity. A in determining the physics contained in this sharp- preliminary report on this work has been written boundary problem: (a) one of the expansion func- (University of Wisconsin Plasma Studies Report tions for the vector potential corresponds exactly to a PLP 573 by K.R. Symon). state of the system in which all perturbed current flow only on the surface. (b) The dispersion function 7. General Vlasov Equilibria. A general that determines the eigenfrequencies now has a form approach has been developed for studying the characteristic of a second-order differential equation linearized behavior of inhomogeneous equilibria in in time such as a fluid equation of motion. which one or more particle species are treated In addition to the question of magnetic boundary collisionlessly. The formulation is a generalization of conditions there is the separate question of the ap- the work underway on the Vlasov-fluid model and . propriate form of the Vlasov equation when the BGK equilibria. A previous restriction to system is enclosed by a moving, specularly reflecting equilibrium distribution functions that are functions boundary. This is related to the problem of the only of the total energy has been removed, and we description of a gas by the Boltzmann equation when can now treat equilibrium distribution functions the gas is in a cylinder with a moving piston. We that are functions of all of the global constants of have found an elegant way of deriving the correct motion. Also, it is now possible to include a wide form of the Vlasov equation through making a time- class of possible field operators whose eigenfunctions dependent transformation of the phase space and can be used as expansion functions for the perturbed perturbing about a time-dependent zeroth-order potentials. This allows a desirably wide latitude for

139 choosing the operator on physical grounds. In all it seems unlikely that the exact equations may be cases the final equations to be solved are of a type simplified by imposing the measure-preserving con- . that can be effectively treated numerically with straint a priori. techniques developed by Buzbee, Golub, and Lewis A second approach is to derive approximate for the Vlasov-fluid model. It has been demonstrated equations which reflect the measure preservation ● that the eigenfunctions of the unperturbed Liouville either exactly or to some order. An effort was made operator that are used can be found analytically if to find useful mappings which preserve measure. A there is at most one non-ignorable coordinate in the number of references to this question were found in equilibrium. In that case the eigenvalues are always the literature, but none of these is appropriate to the of the same form and an infinite sum over the eigen- Vlasov problem. If a sufficient number of degrees of values can be performed in closed form. A freedom is retained, the algebraic relations between preliminary report of this work has been written the variables become unmanageable. (University of Wisconsin Plasma Studies Report The work to date will be summarized in a PLP 577 by K.R. Symon). forthcoming paper which will tie together these results and indicate directions for further invest iga- 8. Guiding-Center Model. In an effort to t ion. elucidate further the numerical approach that is be- ing applied to study the linear stability of Vlasov- S. Magnetic Field Diffusion Studies fluid equilibria, we have applied an analogous ap- proach to the simpler dynamics of single-species, in- Recent studies on the LASL toroidal Z-pinch have hornogeneous, two-dimensional guiding-center shown that the dominant effect limiting the contain- equilibria. Some particularly simple special cases ment time is the loss of initially favorable field have been found, and the initial-value problems for profiles as a result of field diffusion. This has spark- two of them have been solved in closed form. An in- ed interest in the properties of nonlinear anisotropic teresting feature is that local density perturbations field diffusion. may grow and lead to spatial “clumping” even as a A group of three 1-D codes solving for the field dif- result of this linear analysis. Also, degenerate real fusion into a hollow cylinder were developed this eigenfrequencies can lead to growth of a perturbation. year to study a classical ZT-I type plasma. The first code solves for the diffusion of longitudinal and R. Nonlinear Evolution of Vlasov Plasmas azimuthal fields for the case of constant conductivi- ty and permeability. This code is a generalized ver- The physically simplest Vlasov problem is the sion of our previous diffusion codes. The second code one-dimensional electrostatic problem. This has allows one to vary conductivity and permeability as been considered as a model problem with the goal of functions of fields, (nonlinear case), radius and t ime. finding more effective means of integrating the The geometry for the I-D anisotrouic diffusion is equations of motion. A significant feature of the mo- illustra~ed by the drawing below. tion is that the mapping from the phase plane at the initial time to the phase plane at any later time is measure preserving, i.e., the phase fluid is incom- pressible. It was conjectured that this property might be used to simplify the integration of the equations of motion. Two aspects of this question have been con- sidered. First, an attempt was made to simplify the . exact equations of motion by the introduction of new variables which a priori reflect the measure- preserving property. A formalism for such a transfor- . mation is provided by the Hamiltonian formulation of the Vlasov equations. After a lengthy investiga- tion it has been shown that it is not possible to canonically transform the exact equations in such a way that the new momenta are related to the measure preservation in any obvious way. This argu- ment is based on a certain integrability condition which canonical transformations must satisfy. Thus,

140 The equations that must be solved are: higher conductivity along the field lines than normal to them. Theoretically the resulting peaked aB aB longitudinal field distribution for this anisotropic z la z a case persists to the steadv state. z-- -F% %er ~ - %Z ~ ‘*6 [ (] T. Mercier Localized Stability Criterion Dependence on Aspect Ratio aBe ~ a aB —.—— J+n ——1a rBe at p ar - ‘z13 ar zz r ar [ ()1 Our tests of stability for the toroidal Z-pinch use a discretization of 8W. As a result the stability test is inherently subject to a finite resolution. To test highly localized modes we have included a separate calculation of the Mercier Q value33 on each flux “,,-4’+(Y’W$Isurface of the computed toroidal equilibrium. Ax- 2 isymmetric toroidal equilibrium can be checked for ‘[[-al Be localized, unstable ideal MHD modes by deter- ~1 + mining if Q < 0 on any flux surface. This test is n=Zz ’11 ( “1 ‘()1 T analogous to the Suydam criterion for a cylindrical [ equilibrium. In fact the Mercier and Suydam criteria become equivalent as the toroidal aspect ratio approaches infinity. n“ %z * Ze Figure XI- shows how the Mercier Q value varies as a function of the aspect ratio of the device. (Aspect ratio is defined as mean radius of the where rl and fill are the conduct ivities toruslradius of the cross section of the conducting perpendicular and parallel to the field lines and p is outer boundary. ) This curve was calculated for the the total permeability. ZT-1 device for fixed pressure and poloidal current These equat ions were solved by transforming our flux functions which are chosen to give a flat-topped equation into a form that could use the linear mul - reversed field profile. The peak value of plasma tistep methods for solving ordinary differential pressure was held fixed at a value where the straight equations. ‘{zOnce the magnetic fields are obtained machine is at the threshold of going Suydam un- the current density ,J=~,J~J + z~JZis computed from stable. The curve shows that as the aspect ratio is l,IxB =P,J (we neglect displacement current 1. The decreased the Mercier Q increases until the aspect electric fields then follow from ratio is about three; it then rapidly drops and the device is Mercier unstable for aspect ratios below E=v., J about 2.4. While the Mercier Q value is not related quantitatively to growth rates, this curve indicates where the resist ivitv diadic is that there is an optimum aspect ratio where a device will hold the highest peak pressure wit bout going un- stable to the local modes. At the peak of the curve shown in Fig. XI-7 the device will hold 10% more The soluti(ms have been tested by ilux and energy plasma peak pressure before it reaches the Mercier checks and verified with an analytical solution for a stability threshold. large radius case. Comparing results from these sim- ple models with ZT-1 experiments showed t hat it’the U. Automatic Experimental Data Processing conductivity model is valid an anisotropic conduc- . tivity tensor must be used in the diffusi(m equation Our ultimate goal is to take experimental data to explain the observed behavior of the pol(]idal and from the Z-pinch experiments, digitize it and ship it toroidal fields. to the CCF, fit the data so that it can be interpolated In particular if a scalar conductivity is used which both in time and space, calculate quantities of in- is consistent with the observed rapid poloidal field terest, plot results, and display critical plots on a diffusion to that of a uniform current in the pinch graphical terminal in time to help determine how column, one calculates that the toroidal field will ap- the next shot should be fired. At the present time we proach the vacuum field on the same time scale. The have the codes running that fit the data with a spline toroidal field is observed to remain peaked for the and develop a plot of the data that is suitable for length of the experiment. This is explained bv a

141 (c) The localized instability ies subroutine calculates the Mercier stability criterion which is a . generalization to a torus of the Suydam criterion. The Mercier criterion for a large radius torus was compared with an independently coded Suydam ● criterion and good agreement was obtained. The ZT- 1 geometry was found to be Mercier stable. I A resistive stability criterion developed at -200 - Princeton has been expressed in variables compati- ble with our code. We plan to have this test of 0-400 - localized resistive instabilities incorporated into the .-: 0 code soon. i -60” - W. ZT-S Design Calculations

-800 - A series of computer runs were made with our equilibrium code to aid in the design of the feed plates of ZT-S, the larger bore version of the ZT-1 -1000 - experiment. The two parameters varied in this study were the half width of the plasma distribution and -1200- the poloidal beta $P for the 4.8 aspect ratio of ZT-S. We found that the ratio of poloidal field at the out- .—-. .— . ..—. —.—. — — -1400- ermost major radius of the primary conductor to that I.0 5.0 10.0 at the innermost radius increased almost linearly Aspect Rotio with @P. This ratio also increased as the half width decreased. There is a point for wide plasma dis- Fig. XI- 7 tributions and low @Pwhere the outside field is lower Mmcier Q value us aspect ratio. than the inside field, see Fig. XI-8. The ZT-S is ex- pected to run at a ratio ranging between 1.05 to 1.2.

publication. We are planning to use the direct elec- tronic fast scanning methods now under develop- ment to digitize the data. Provided money is I40 - available, a graphics terminal can be used advan- tageously with the experiment. This terminal would provide an interactive graphics capability as well. 1.35-

V. Axisymmetric Toroidal MHD Equilibria and 1.30- Stability Code T.- : 1.25- The following subroutines have been added to the equilibria portion of the present code. s \ (a) Energy subroutine which calculates the : 1,20- 2 plasma energy, toroidal field energy, poloidal field m energy and total field energy. This subroutine has -j 1,15- been used to help design the new larger radius Z- pinch device. . 1.10- (b) Electron velocity subroutine which calculates particle density, current density and electron veloci- ty perpendicular and parallel to the magnetic field 1,05- lines. The electron ion and thermal velocities are calculated based on input values of electron and ion I.00- ~, Plosmo Width At Holf Moximum temperature. This subroutine provides inputs for the Conducting Boundory Diometer toroidal case in the study of microinstabilities in ZT- 0,951 1 1 I ! ! 1 discussed in Section M. 0.2 0.4 0.6 0.8 1.0 8P Fig. XI-8 Poloidal field ratio us f?P. 142 . References 13. J.B. McBride and E. Ott, “Electromagnetic and Finite & Effects on the Modified Two Stream 1. C.W. Nielson and E.L. Lindman, “An Implicit, Instability,” Physics Letters A 39,363 (1972). . Two-Dimensional, Electromagnetic Plasma Simula- tion Code, ” Sixth Conference on Numerical Simula- 14. G.S. Lakhina and A. Sen, “Electromagnetic and tion of Plasmas (1973). VB Effects on the Modified Two Stream Instability, ” Nucl. Fusion 13,913 (1973). 2. A.G. Sgro, CTR-6 Quarterly Progress Report, January 1, 1974 through March 31, 1974. 15. N.T. Gladd, “The Lower Hybrid Drift Instabili- ty and the Modified Two Stream Instability in High 3. L. Spitzer, Jr., Physics of Fully Ionized Gases, Density Theta Pinch Environments,” submitted to 1961 (John Wiley and Sons, New York). Plasma Physics (1975).

4. C .G. Darwin, “The Dynamical Motions of Charg- 16. M. Keilhacker, M. Kornherr and K.H. Steuer, ed Particles, ” Phil. Magn. 39, 537 (1920). “Observation of Collisionless Plasma Heating by Strong Shock Waves,” Z. Phys. 223,385 (1969). 5. B.M. Marder and R.E. Siemon, “A Long Confine- ment Experiment (LCE) Proposal, ” Los Alamos 17. T.K. Fowler, “Thermodynamics of Unstable Scientific Laboratory Report LA-5399-P (1973). Plasmas,” Advances in Plasma Physics (cd. A. Simon and W.B. Thompson) Vol. 1, p. 201 6. J.E. Thompson, F.C. Thames, C.W. Mastin, Interscience (1968). “Automatic Numerical Generation of Body-Fitted Curvilinear Coordinate System for Field Containing 18. P.C. Liewer and N.A. Krall, “Self-Consistent Any Number of Arbitrary Two-Dimensional Approach to Anomalous Resistivity Applied to Bodies,” J. of Computation Physics 15, 1974, pp. Theta Pinch Experiments,” Physics Fluids 16, 1953 299-319. (1973).

7. R.L. Morse and C.E. Nielson, “Numerical 19. R.C. Davidson and N.T. Gladd, “Anomalous Simulation of the Weibel Instability in One and Two Transport Properties Associated with the Lower- Dimensions,” Phys. Fluids 14,830 (1971). Hybrid-Drift Instability,” (to be submitted to Physics of Fluids). 8. F.L. Ribe, “Proposed Experiments on Heating, Staging, and Stabilization of Theta Pinches, ” Los 20. D.A. Baker, L.C. _Burkhardt, J.N. DiMarco, Alamos Scientific Laboratory Report LA-5026-P P.R. Forman, A. Haberstitch, R.B. Howell, H.J. (1973). Karr, J.A. Phillips, and A.E. Schofield, “Plasma Parameters and Stability of the ZT-1 Pinch Ex- 9. K.S. Thomas, J.N. Downing, R.F. Gribble and periment,” IAEA-CN-33fE3, Tokyo (1974). R.K. Linford, “Experiments in the Staged Theta Pinch Experiment,” Bull. Am. Phys. Sot. 19, 904 21. R.A. Gerwin (to be published as Los Alamos (1974). Scientific Laboratory report).

10. N.A. Krall and P.C. Liewer, “Low-Frequency 22. D.A. Baker and R.B. Howell (private com- Instabilities in Magnetic Pulses,” Phys. Rev. A 4, munication). 2094 (1971). 23. R.C. Davidson, R.A. Gerwin and N.T. Gladd (to . 11. K.N. Stepanov, “Stability of Ionic Cyclotron be submitted to Phys. Rev. Lett.). Wave in a Plasma,” Soviet Phys. Tech. Phys. 9, 1653 (1965). 24. H. Grad, “Microscopic and Macroscopic Models in Plasma Physics,” Proceedings of the Symposium on Electromagnetic and Fluid Dynamics of Gaseous 12. J.B. McBride, E. Ott, J.P. Boris and J.H. Orens, Plasma Polytechnic Press, Brooklyn, New York, “Theory and Simulation of Turbulent Heating by 1962. the Modified Two-Stream Instability,” Physics Fluids 15, 2367 (1972).

143 25. E. Frieman, R. Davidson and B. Langdon, 30. H.R. Lewis and J.P. Freidberg, “Application of . “Higher-Order Corrections to the Chew-Goldberger- the Vlasov-Fluid Model to High-Beta Stability,” Low Theory,” Phys. Fluids 9,1475 (1966). paper 41 in Proceedings of the Fifth Conference on Controlled Fusion and Plasma Physics (Grenoble, . 26. J.P. Freidberg, “Vlasov-Fluid Model for Study- France, August 21-25, 1972). ing Gross Stability of High-/3 Plasmas. 31. Progress Report, “LASL Controlled Ther- 27. H.R. Lewis, “Linearized Variational Analysis of monuclear Research Program for a 12-Month Period Single-Species, One-Dimensional Vlasov Plasmas, ” Ending December 1973,” Los Alamos Scientific Phys. Fluids 15, 103 (1972). Laboratory Report LA-5656-PR (July 1974), pp. 93- 4. 2$. J.P. Freidberg, “Vlasov-Fluid Model for Study- ing Gross Stability of High+? Plasmas, ” Phys. Fluids 32. C.W. Gear, Numerical Initial Value Problems in 15, 1102 (1972). Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, New Jersey 1971). 29. H.R. Lewis and J.P. Freidberg, “Application of the Vlasov-Fluid Model to High-Beta Stability,” A.C. Hindmarsh, “Linear Multistep Methods for Bull. Am. Phys. Sot. 17, 1013 (1972). Ordinary Differential Equations: Method Formula- tion, Stability, and the Methods of Nordsieck and 33. C. Mercier, “Critere Necessaire de Stabilite Gear,” UCRL-51186. Hydromagnetique Un Plasma En Symetrie De Revolution,” Nuclear Fusion 1, 47-53 (1960).

.

144 XII. CTR ENGINEERING

E.L. Kemp, J.J. Banta, G.A. Barnes, K.J. Bickford, G. Boicourt, W. H. Borkenhagen, D.L. Call, R.S. Dike, W.D. Gutscher, R.A. Haarman, C.F. Hammer, K. W. Hanks, H. W. Harris, R. W. K(’wL~h, K.J. Kutac, R.K. Linford, H.L. Maxwell, T. E. McDonald, J. G. Melton, G. Miller, W. C. Nun- nal[y, L. S. Schrank, M.D. Wickham

A. System Design Construction and Operation To correct this problem the master clock, sub- master delay chassis, slave delay units, and booster 1. Scyllac Operation chassis were moved into the screen room leaving only the 8-kV pulsers in the high noise environment. In a. Full-Torus Operation. Construction of the full addition, a backup system was installed for the four Scyllac capacitor bank was completed by the end of crowbar pulse-charge circuits and the ten crowbar 1973 and the three new racks of capacitors, which start circuits. For the normal shot this backup were constructed during full-torus conversion, were system had no effect; however, in the event the clock successfully fired in January 1974. Assembly of the should stop or be reset after the main bank was fired compression coil and discharge tube was carried out the backup system fired the crowbar system 1.3 PS during the day with system checkout being con- late. ducted in the evenings. The first full-torus plasma Reliability of the crowbar system was improved by shot was achieved in April 1974. An overall view of modifying the crowbar pulse-charge circuit. The the Scyllac full torus is shown in Fig. II-3. original circuit used a single pulse-charge capacitor Two-shift operation was begun in order to increase and a common inductor to fire as many as three the total machine operating time. Bank voltage was master gaps; RG 17 DS cable was used to connect normally 40 kV with a few shots taken at higher the inductor with the master gaps. High-voltage voltages. The full-torus experiments were operated transients which occurred after the firing of the gaps for nearly eight months during which time a total of caused frequent cable failures and resulted in 822 shots were made with 543 oft hese being plasma master-gap failures. The circuit was modified by shots. The full-torus experiment was completed in placing inductors between each master gap and the November 1974. RG 17 DS cables. This change reduced the cable In the final weeks of the experiment a reverse B,, failures to an insignificant level. field was applied to the full-torus plasma. The B. bank in each rack contains four 10-kV capacitors c. Capacitor-Gap Failures. During full-torus which were selected to total 721 YF. The B“ field rose operation (822 shots) 22 primary bank 1.85-PF, 60- to a peak in 60 ps and was fired prior to the primary kV capacitors failed. Fourteen of these capacitors bank so the peak B,, would coincide with the peak . shorted in service, a fifteenth unit was removed theta-pinch field. The Bo bank voltage was varied to because it had a bulged can which indicates near produce fields between 250 G and 1000 G. end-of-life, and seven capacitors failed because their headers were broken due to gap malfunctions. . b. System Modifications. When the full-torus There were also five failures of the 0.7-pF, 75-kV Scvllac Experiment was put into operation the elec- capacitors which are used in the crowbar bank. Four trical noise level generated was larger than that ex- of these were shorted and one had a broken header perienced with earlier sector and linear experiments. due to a gap failure. This increased noise at primary bank time was suf- A total of 176 spark gap units failed during the ficient to reset the master digital clock. This full-torus operation. Seven of the failures occurred in prevented the crowbar system from triggering. the P.I. bank, 14 in the crowbar bank, and 155 in the

145 primary bank. The primary bank has 3150 cableand inside thecrowbargap havebeenresponsi- capacitors with a start gap and crowbar gap blefor more than 45°Aofthe gap malfunctions. Two assembled on the top of each capacitor. The losses improved cables have been desig-ned. The first would caused by gap malfunctions made it necessary to fit theexistinggap hardwarewhile the second,which remove 5% of the primary bank capacitor-gap units has a much higher reliability than the first, would during the full-torus experiment. Table XII-1 gives require modifying the gap hardware at both ends. the major causes of gap failure in the primary bank. Both ofthese cables are being considered assuitable replacements forthe RG 14/59. TABLE XII-1 The second Scyllac component having a high failure rate is a 300-fl liquid-isolation resistor. These SUMMARYOF THE CAUSES OF resistors are connected in series with the charge lead CAPACITOR GAP FAILURES of each gap and are immersed in a mineral oil bath to prevent arcing around the resistor case. The liquid Cause QkwLLY resistor is sealed with a neoprene seal at the top and RG 14/59 trigger cable, 71 bottom of the case. After approximately t~vo years failed inside gap, the neoprene seals deteriorate and permit oil to leak destroying crowbar into the resistor itself. When sufficient oil has trigger jack entered to surround the upper electrode the resistor becomes an open circuit. During the capacitor bank RG 17 DS trigger cable and 26 RG 17/14 load cable failures charge the difference in potential becomes great and~or poor electrical enough at 30-35 kV to produce an arc in the liquid connections of these cablea resistor. The resulting voltage pulse causes the inside the gap associated primary gap to prefire; the energy from the other 209 capacitors in the rack then discharges Air line failures caused by 21 through the one gap. The result ing forces are often low oil level inside the gap large enough to break the gap nylon insulators and Defective isolation 18 even crack the capacitor header. Degraded liquid resistor caustng bank resistors that can be detected by visual inspection prefire and gap rnalfunctlon are replaced as part of a preventive maintenance program; however, even with these checks liquid Internal gap malfunction 12 resistor failures were the direct cause of 12$i of the (Insulator failures, primary bank gap malfunctions during the Scyllac tracking) full-torus operation. Defective units are being Loose charge leads 4 replaced with a modified version which is expected to have increased life. Crowbar chimney current - 3 joint arcf.ng The third troublesome component is the spark plug in the primary-bank crowbar gap which has a 155 limited life of about 2000 shots. At the time this component was developed it was believed that the d. other Component Failures. The majority of Scyllac experiment would not see this many shots. Half of the gaps in racks 11 through 15 have 3620 componentsin the Scvllac machine are verv. reliable and-have failure rates too low to be statistically shots. When crowbar trigger shots are included, the significant. However, there are three components total is over 4000. Figure XII-2 shows the comparison . having failure rates sufficiently high towarrantcom- of new spark plugs with spark plugs used more than ment. 2000 shots. These worn spark plugs may be adversely The most unreliable component in Scyllac is the affecting the quality of the crowbar in racks 11 . RG 14/59 trigger cable that transmits the trigger through 15 and may need to be replaced before these pulse from the crowbar trigger capacitor to the racks are used again in a full-torus feedback experi- primary-bank crowbar gap.It is underrated for this ment. Tests are being planned to determine the service and fails inthe bodyof thecable aswell asat effect of worn spark plugs. the terminated ends as shown in Fig. XII-1. During the eight-month full-torus experiment over 225have e. Modifications for the Feedback Sector failed which is more than 7%of the total installed. Experiment. After the completion of the full-torus Even worse, failures near the terminated end of the experiment on November 22, modifications were

146 ..- .— ——--- .— ~--=+ --

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i 1’1 121 131 141 lsl l? 1? 181 191 /01 1“1 ?21 1131 74

Fig. XII-2 T>pical Faiiurcs of the RG 14/59 Scyllac Trigger Cable

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148 begun for the feedback sector experiment. This ex- stantially different. One machine will be utilized to . periment will use racks 6 through 10 which were form the three-diameter tubes, all with different selected for ease of feedback module installation as wavelengths and helix radii. Initial operation of this well as to avoid putting additional shots on racks 11 machine should begin June 1975. . through 15. Preventive maintenance activities were performed on the portion of racks 6 through 10 used 3. Feedback Stabilization System. The original in the feedback sector experiment. Maintenance in- system design of the Scyllac feedback experiment cluded (a) replacement of 300-0 liquid-isolation called for 60 power amplifiers to be installed on the resistors with the modified units, which were Scyllac machine with five spares. The overall system described above, (b) restoration of liquid charge was expected to have a delay -risetime of ap- resistors to 20 kfl, (c) installation of poly tubing over proximately 0.9 ys. crowbar gap poly-flo nuts to prevent arcing between Construction of 65 power amplifiers was com- the metal nuts and the gap top plate, (d) restoration pleted and 60 of the. amplifiers were installed on the of oil level in all gaps. Scyllac machine by mid-1974. Three intermediate amplifiers with the associated position detectors 2. Mechanical Engineering on !%yllac. The were also installed and the complete system was Scyllac load-coil parameters for the full torus experi- operational by August 1974, driving dummy load ment are given in Table II-1. The rather complex coils. Noise tests were run on the feedback system Q’= 1,0 helical flux surfaces were machined using a under full operating conditions of the Scyllac bank. D’Andrea boring head with the cross sections of the After solving some relatively minor cabling problems coil being circular and each wavelength being made the noise levels at the output of the intermediate up of 330, 1.27-mm-wide machined steps. This amplifiers were reduced to less than 100 mV which is procedure left the surfaces very rough. less than 1“6 of the maximum intermediate amplifier The five-rack sector Scyllac Feedback Experiment output . requires a load coil having an average bore diameter Measurements were made of amplifier risetime of 24.0 cm and an !?=0,1 wavelength of 62.38 cm. and frequency response. These measurements The 4-m major radius is retained. Three of the ex- revealed some major unexpected problems with the isting coil sections make up a wavelength, thus, feedback system. The problems are: (a) The delay- yielding 13 wavelengths for the sector with the end risetime of the system was found to be 2.1 ps instead set of coils having an !2= O feedback coil installed. of the expected 0.9 PS. (b) The saturation time oft he The Q=0 feedback coils will be fabricated using RG intermediate transformer driving the output stage of 223 wire and terminated into a redesigned the power amplifier was found to be approximately transformer unit with a plug-in cable geometry. 15 ps instead of the expected 25 ps to 30 vs. (c) At The load coils for the feedback experiment were less than full input to the power amplifier the 8618 machined with a new hydraulic tracing machine output tube tended to arc. which was designed to bore coils with non-circular The most serious of these problems is the in- cross sections. The machine, which is shown in Fig. creased delay -risetime of the overall system. In order XII-3, has taken approximately one year to design to help relieve this difficulty the number of load coils fabricate, and make operational. The basic system being driven by a power amplifier was halved. consists of a male tracing template which was made Although this modification reduced the delay- on a digitally controlled milling machine, a risetime to 1.5 KS it also required that the number of’ hydraulic tracing unit which was modified exten- modules be doubled. Further significant reducti(ms . sively for the application, and a high-pressure, high- will require more substantial design changes. capacity oil pump. The elliptical cross section of the In order to solve the arcing problem and to reduce pattern requires a 2.5- to 5.O-cm side travel for 90° the delay -risetime a development bay is being con- . rotation of the pattern. Figure III-3 shows the helical structed which will allow the necessary test ing and Q = 1,0 coil bore geometry for one rack of the coil redesign of the amplifiers to be made. system. Because the required number of amplifiers has Design has also started on a quartz-forming doubled, there is now an insufficient number of machine which will form 5-, 10-, and 20-cm- amplifiers to run the feedback experiment in the diameter fused quartz tubes into helical f = 1 full-torus configuration. In addition, the increased toroidal and linear configurations. The basic concept delay -risetime means that the plasma cannot be as is adapted from a machine at the Garching energetic as originally planned. As a result it has laboratory in Germany, but this new design is sub- been decided to run the experiment on an ap- proximate 120° sector of the torus with a lower

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Fig. XII-4 li.vriraulic Tracing Machine Used in Making ,Scyllac Load Coils

150 plasma temperature. The bore size of the machine 5. Toroidal Z Pinch. The encouraging results . load coils was also increased to reduce the load in- obtained from the ZT-1 experiment during the past ductance of the feedback coils as much as possible. few years have prompted studies to be made to Twenty-six amplifiers will be used on the sector determine if a larger bore size could be installed , experiment which required substantial modification within the limits of the present machine. These of the water system, high-voltage cabling and fila- studies showed that an increase in bore size from ment wiring. As of the end of this reporting period 10.31 cm to 15.24 cm was possible while still using the necessary modifications had been scheduled and the existing iron cores and main drum headers. were approximately 50% complete. Figure XII-4 shows a comparison of the present ZT-1 bore and the increased bore size. New feed plates, 4. Scylla IV-P Design and Installation. Scylla primary castings and larger ceramic torus sections IV-P is a 5-m linear theta pinch using 600, 1.85-KF, were designed and fabricated and are now being 60-kV capacitors in the crowbarred mode. It is readied for the transitional installation. This larger designed primarily as a pulsed power supply which geometry, known as the ZT-S, will provide the ex- can be adapted to various experiments as required. perimenter with many advantages which were not Scyllac technology is being used for charging and possible on the ZT- 1 experiment. triggering; however, rather than rack mounting the The larger torus size, necessitating higher capacitors, modular mounting is being designed currents, has required new feed points designed for a with 10 load capacitors and a crowbar trigger double fuse capability and will use a special high- capacitor in each module. energy fuse package specifically developed for this Steel structure has been erected to divide the ex- purpose. *This package is a self-contained assembly perimental area into three levels with the central or and will provide for an inverted mounting arrange- “B” level accommodating 200 capacitors and the ment with assurance that no sand or debris will be collector-plate discharge tube assembly. The expelled into the collector plate region. Higher utilities tear-down required for the modifications has currents and larger bore size will also produce an im- been completed and the new compressed air system proved magnetic field diffusion in the plasma which is installed. The modified electrical system is design- is expected to increase the plasma confinement ed. time. Procurement of the capacitors, cables, collector Peaking capacitor studies and experimentation plates, and gap parts is 90ci complete. Available are continuing using the existing header design and manpower is being used to assemble load gaps, shor- the Maxwell 0.08-pF, 100-kV capacitor. ] While this t ing balls and the trigger system components while particular arrangement is not considered ideal for outside vendors are being employed to assemble load future system designs of this type, it is nonetheless cables, master trigger cables, and crowbar trigger valuable to test the peaking capacitor concept while cables. The cables and load capacitors are being also testing various transfer switch geometries. Two tested by LASL to eliminate the early failure modes. types of switches are currently being tested. One is Designs of the charging and triggering systems are an enlarged version of the transfer switch used on the 90”; complete. Both systems are compatible with ZT- 1 experiment. This switch is of the t rigatron computer control using 5-V logic and solid-state variety but has a specially contoured electrode and switching where applicable. Computer control will insulator designed in such a manner that prefire give a degree of flexibility not previously available possibilities are reduced by assuring a comparability and will be employed at all levels of the operation. of electric field gradients within the gap. The second . However, personnel safety is being assured by a con- type switch is of the field distortion variety where its ventional backup system which can override the center electrode passes through the top electrode in computer, if required. This computer control is the an insulating fashion and is conveniently energized . major innovation in the Scylla IV-P experiment and from the top of the gap geometry. Further tests on the experience and knowledge gained in this system both switches are anticipated and actual plasma is expected to be valuable in future machines. The generation using this device will be performed. computer and most of the necessary interfacing are Plans are being formulated for a new Z-pinch on hand and the 8 ft X 40 ft screen room which is machine and some conceptual design and planning required for the control system will be in place early is now underway. This new concept, tentatively in 1975. dubbed ZT-SP, again will have an increased bore

151 .

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152 size with a minor diameter which is in the range of 25 application is required. The standard 1.85-I.LF, 60-kV . to 30 cm. The major diameter will also increase but capacitor was developed for an oscillatory discharge will be a function of feed point design, volume of iron with 85% reversal, while in a crowbarred circuit, required, and consideration of an appropriate aspect such a high-voltage reversal capacitor is not re- . ratio. Improved peaking capacitor techniques will be quired. The high-density capacitor under develop- included and other capacitors more suited to the ment will store 5 kJ in the same size can as the pre- constraints of this particular design will be sent 3-kJ Scyllac capacitor. The ultimate goal of the employed. program is to produce a 60-kV capacitor that is more economical than the 15 cents per joule, standard 60- B. Advanced Development kV capacitor. A high-voltage test bay has been built to test four 1. Scyllac Fusion Test Reactor (SFTR) 60-kV capacitors simultaneously. The capacitors are Components charged to 60-kV and discharged into a crowbarred RG 17 cable load every 10 s. The first series of test a. Crowbar Ignitron and 10-k V Capacitor capacitors were made with 0.9 gm/cm3 paper which Development. The Magnetic Energy Transfer is somewhat less expensive than the 1.0 gin/cm 3 Storage (METS) System of the proposed SFTR re- paper. Six capacitors were ordered from each of the quires a large capacitor bank of approximately 200- manufacturers, Aerovox, Maxwell and Sangamo. MtJ stored energy. The system also requires a crow- These capacitors were made to the 1.85-PF, 60-kV bar that is capable of circulating 1000 C of charge specification so that the 0.9 gm/cm3 paper could be and 60-kV pulsed operation. Prototype components evaluated against the well known 1.85 -I.LF, 60-kV for the crowbar and capacitors have been tested dur- capacitor characteristics. Twelve capacitors (six ing the past year with a total of 85,000 full voltage each from Maxwell and Aerovox) have been tested to shots being fired in the component test bay. The end-of-life with promising results but the capacitors testing process involves discharging 10 parallel, 170- from Sangamo have not yet been received. KF, 10-kV capacitors into a dummy load at full 10- A second series of six capacitors were ordered from kV charge and crowbarring the resultant 100 kA with the same companies for a 2.85-pF, 60-kV non- an L/R decay of 4 ms. reversing capacitor. The order from Aerovox has The test capacitors have performed exceptionally been received and awaits testing. well with eight of the original ten capacitors still in service after 200,000 shots. Variations of the basic 2. Gap Development. In order to carry out 10-kV, 170-pF capacitor have been ordered from staging in the Staged Theta Pinch (STP) Experi- Aerovox Industries, Inc., General Electric Co., Max- ment a low-inductance, high-capacity spark gap is well Laboratories, Inc., and Sangamo Electric Co. needed between the 50-kV high-energy capacitor for test and evaluation to develop a lower cost, more bank and the PFN collector plates. To achieve the reliable capacitor for eventual use in SFTR. necessary low inductance a multichannel rail gap The presently available size-D ig-nitron is being configuration was selected for the design. The basic evaluated for use as the SFTR crowbar. The in- requirements of the gap are: dustry rating of the size D ignitron is 200 C; however, a total of 10 size-D ignitrons have been tested and 6 Voltage Holdoff = 50 kV dc; 125 kV pulsed of the 10 have gone over 10,000 shots each at 400 C. The greatest single problem is the anode current Peak Current = 380 kA . joint which, it is felt, can be corrected quite easily. A new dummy load is now being installed to increase L/R Decay Time = 30 ps the L/R decay time of the circuit which will allow the ignitrons to be tested beyond the 400-C level now at- Total Charge = 11.5 C tainable. The size-D ignitron has demonstrated the capability of maintaining an 800-C charge for a few Four prototype designs have been constructed and shots in the CTR-9, 300-kJ facility which indicates evaluated. All four designs used rails 15-cm long; the potential for their use as the SFTR crowbar. however, different rail diameters and spacings were employed in the designs. b. 60-k V High-Density Capacitor Development. The first design uses rails which are approximate- A development program was started this past year ly 2.5 cm in diameter with a 2-cm separation. It was to develop a high-density, 60-kV capacitor for use in found that the charge carrying capability of this Scyllac and future systems where a crowbarred design was inadequate due to the small volume of

153 the gap chamber and a second design was made us- These conditions are acceptable for initial operation ing the same rails but having a larger gap chamber of the STP experiment. When the experiment has . volume with spring loaded end plates to relieve the progressed to just the point that higher voltage overpressure. This design was able to carry 14 C; operation is required, the gaps will be retrofitted however, the chamber walls still cracked due to the with the new chamber. Figure XII-5 is a photograph . shock wave of the discharge. In the third design rails of the final gap design mounted on a test stand. having a 5-cm radius of curvature with a l-cm separation were used and a stronger gap chamber C. Engineering Analysis was designed. The larger rails were chosen to dis- tribute the shock from the discharge over a larger 1. Cable Development area of the chamber walls; however, tests showed that spring loaded end plates were still necessary a. Semi- Empirical Design of Optimal Coaxial due to the chamber over-pressure. Cable. Coaxial cables are used extensively in CTR The third design was selected as being basically at voltages much higher than manufacturers’ satisfactory. The parameters of the design are as ratings. One reason is that the large number of follows: cables needed to handle the current requires a minimum cable diameter so the cable bulk can be Fill Pressure = 400 to 700 kPa of air fitted into the space available. Heretofore, a number of cables have been designed, mainly by educated Peak Current = 380 kA guess, and these cables have operated more or less successfully. It appeared that it might be possible to dc Voltage Holdoff = 50 kV use the data obtained from testing and operating previous cable designs to design new cables am-l !() Pulse Voltage Holdoff = 125 kV (with + design them in such a way that the cable diameter 50 kV dc) would be a minimum for a given operating voltage and inductance. Such an analysis has been carried L/R Decay Time = 30 ps out . Three parameters were taken to be critical for Total Charge = 11.5 C CTR cable: the inductance, the peak operating It has also been found that the gap has the ability to voltage, and the maximum electric field. The induc- wit hst and occasional prefire conditions (single tance, L, is more critical in CTR than the cable im- current channel operation). Successful operation of pedance; moreover, in some cases it is vital that it be this gap, however, depends on a fast rising trigger held below a given value. The peak voltage, V, is the pulse of approximately 15 kV/ns. maximum transient voltage that will be seen by the The design which will be used in the staged theta- cable at any time during a normal operation in the pinch machine is basically the third gap design with projects application. Usually V will have to be com- some relatively minor modifications in the header puted using a circuit analysis code. The maximum and collector plate connections which provide a electric field, Em, is the most sensitive parameter in more convenient integration into the staged theta- that it probably determines the life and failure rate pinch machine and also eliminates some of the cable. Suitable values of Em can be est imatcd troublesome oil splattering. As a result of the from the operations data on existing cables. Given modifications a voltage holdoff problem now exists. these parameters and the additional condition that This difficulty is expected to be solved by installing the cable diameter is to be a minimum, it can he . a solid epoxy-cast chamber in place of the present shown that the inside radius of the cable dielectric chain her. The present design has the following satisfies the following transcendental equation: voltage ratings: . V/& =r, Qn(exp(2~L/pO) –K/ri) Maxiumm where PFN Voltage dc Bank Voltage

90 40 kV K = (Si + hi/2) exp(2rL/y”) + (s.+ b,,/2).

110 25 kv Here si and so are the thicknesses of the inner and outer conducting screens and bi and bu are the 125 0 thicknesses of the inner and outer conductors. This

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155 equation can be solved iteratively using the Newton- greater accuracy in fitting boundaries. Testing has . Raphson method. Once rl is found, it is a shown that the code is quite accurate when checked straightforward matter to find all other necessary against configuration for which an analytical solu- cable design values. Example curves of cable tion is available. . diameter versus inductance for constant V are given Automatic data input and solution contour plot- in Fig. XII-6 for a set of Em values. It will be noted ting routines are still required to make the code easy that these curves have a minimum. These minima to use. represent the most economical designs for cable to operate at a given V and Em provided the inductance b. Inductance Calculations for dc Coils. is not important. A complete account of this work Frequently it is necessary to design dc load coils for can be found in Los Alamos Scientific Laboratory use in testing CTR components. The induct ante of report LA-5691, December 1974. these coils must be fairly precise so that the com- ponents under test will operate at, but not over, b. Cable Development Program. The pressing specified ratings. Such coils must operate at high need for better high-voltage pulse cables has led to volt ages and currents necessitate ing conductors hav- an extensive literature search to find methods for ing large intert urn spacing and large cross sectional producing such cable. A number of promising ap- areas. Both these conditions cause the usual easy proaches have been found and a report is being design formulas to break down. When this happens written detailing some results important for cable it is riecessary to turn to a much more complex for- design and outlining a cable development program. mula and, because it is not possiblle to solve backwards given the inductance required, one must 2. Computer Code Development iterate these formulas several times. Formulas such as given by Grover2 are based on treating the a. Electric Field Mapping. When designing currents in the conductor as being made up of multi- components for high-voltage operation it is ple filamentary current. A computer program has necessary to minimize, as much as possible, regions been writ ten which calculates the inductance of such of high-electric field. In most instances this is done dc coils for either square or round conductor cross by guess or occasionally a proposed design is set up section, with or without axial cooling channels in the cm a resistor board or in an electrolytic tank. Work conductor, and for any desired interconductor spac- with resistor boards and electrolytic tanks is tedious ing. The program sets up a large number of current and time consuming. loops to simulate the conductors in the coil and then Another method, which can be applied but is rare- calculates the inductance contributions of each loop. ly used because it is difficult and also time con-- The program was checked against Grover’s formula suming, is the numerical solution of LaPlace’s equa- for a Brooks coil and agreement to 0.0016$/ was tion with suitable boundary conditions using a achieved. digital computer. Numerical solutions by finite A second check was made of a Brooks coil and a difference methods must usually be programmed in- round conductor. Here the solution attained was dividually for each problem and thus can be even within 0.68$% of that given by Grover’s formula. more tedious and time consuming than resistor Because there is no reason to believe that Grover’s boards or electrolytic tanks. The introduction of formula is any more accurate than the computer multiple dielectrics only makes the situation worse. program for this geometry, it is felt that the com A relatively new numerical method is available puter program can be used when such coi which can make the solutions of these problems easy calculations are required. . and quick. This is the Finite Element Method. Finite element codes, while more complex to write References initially, do not have to be altered to fit each new . physical configuration and the inclusion of multiple 1. “LASL Controlled Thermonuclear Researck dielectrics occurs naturally and easily. This means Program for a 12-Month Period Ending December that a series of potential designs can be studied easi- 1973,” Los Alamos Scientific Laboratory report LA- ly, quickly and cheaply. 5656-PR (July 1974). The nucleus of a code to solve electric field problems has been written and tested. The finite 2. Frederick W. Grover, Inductance Calculations elements used are eight-node isoperimetric (Dover Publications, Inc., New york 1946). quadrilaterals. These elements give considerably

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3 . 44 MV/Meter 52 MV/Meter 60 MV/Meter 2 .

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. 100 200 300 400 L(nH/Meter)

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XIII. MAGNETIC ENERGY TRANSFER AND . STORAGE (METS)

K.D. Williamson, A. Bailey, D.J. Blevins, E.G. Enderbrock, R.A. Haarman, C.R. Harder*, C. G. Hoffman, J. Johnson, C. R. King, J. Lindsay, L.B. Lundberg, G.A. Miranda, R. Mjol-sness, J.D. Rogers, W.F. Stewart, C.E. Swannack, W. C. Turner, D.M. We/don, J.J. Wol/an

A. Summary ● Two new hardware items are under development: a cryogenic disconnect (Section H) and a flying disk During the past year significant progress has been interrupter (Section B). Both of these items are a made toward the goal of providing superconducting result of the decision to use superconducting magnetic energy storage for plasma compression in switches (Section E) as backup and not primary the next generation of 0-pinch experiments. The components of the METS transfer system. METS energy storage system will provide the ● An order was placed for a 700 W, 4K QHe primary ener~v for the compression coils in Scyllac refrigerator for the prototype METS/Sl?I’R system. Fusion Test Reactor (SFTR) and the staging energy Design of other major subsystems is in progress (Sec- requirements for the Experimental Power Reactor tion H). (EPR) torus and DEMO plant. In addition, this ● A program has been initiated to measure dielectic work will have application to other CTR programs strength, voltage tracking and arc-discharge shock- such as ohmic heating in tokamak experiments and wave formation in cryogenic fluids (Section J). possible power supplies for laser flash lamps in the laser fusion program. The current program is B. HVDC Interrupter Facility developing the necessary components to accomplish this and will culminate in a demonstration METS- 1. Facility. For the METS/SFTR application it SF’TR coupled superconducting prototype system. was decided that an alternative was needed to Highlights of the year include: replace the superconducting switch in order to ● A Ross Engineering Corporation interrupter was reduce the load on the liquid helium refrigeration successfully operated at 12.7 kA and 41 kV. This per- system. The most promising idea was a low formance exceeds the METS/SFTR requirement for resistance cryogenic disconnect to handle the charg- a single interrupter (Section B). ing current within the storage coil dewar, transferr- ● A superconducting industrial wire and coil ing the actual interruption operation to room program was initiated to provide low loss 300 kJ temperature breakers through small cross section, coils. Though progress has been slower than ex- pulsed current leads. The purpose of the facility is to pected, significant information has been obtained on provide experimental verification of successful fabrication techniques for Nb-Ti wire (Section F). current interruption using room temperature ● Two new facilities have become operable: The breakers and to test various components of the in- High Voltage Direct Current (HVDC) interrupter terrupter circuit. . facility is being used to test interrupter components The facility became operational in early (Section B) and the high current test facility has November 1974. The first test breaker, a commercial been upgraded to permit testing of wire and cable up Ross Engineering Corporation unit was operated at ● I to currents of 50 kA (Section F). 12.7 kA and 41 kV without a single fault. No arc ● The LASL 300 kJ coil, interrupter facility and 300 restrikes occurred. This performance exceeds the k.J facility were combined for prototype METS METS/SFTR requirement of 12.5 kA and 30 kV for a transfer tests. Energy storage reached 250 kJ at 10 single interrupter. Other breakers made by Maxwell kA with 35 kV achieved during the transfer (Section Laboratories and Avco Corp. have not yet been B). tested. The system has experienced several high voltage arcing problems which have been eliminated, high *Present address, General Atomics, San Diego, CA.

158 60.1,1 .,-rem,return voltage noise triggering problems which have been ~, -.—- —. — —.—— . el!bl. $Inw suppressed, and multiple ground loop problems which are presently being isolated. h,h got.*.,1”* “ - ___ I h ‘;;;;+- The dummy load coils used as the inductive * current source for interruption have good voltage standoff but are mechanically marginal under the high current, high internal magnetic field stresses. Improved coils are planned. The interruption facility was combined with the LASL 300 kJ coil and 300 kJ test facility to run ex- periments on the superconducting coil in a prototype

METS/SFTR system. A knife switch paralleled the ----- ,.. .U. Ross Engineering breaker to allow a slow buildup of dc current in the storage coil without excessive Fig. XIII-1 heating of the breaker contacts. Two runs were con- Flying Disk Breaker ducted, each terminated by high voltage breakdown of the load-coil crowbar ignitrons. Before ignitron failure, energy storage reached 250 kJ at 10 kA with slow closure rate to remove all mechanical shock 34 kV achieved during the transfer. degradation of the contacts and pulse coil. The magnetic coupling between the pulse coil and disks 2. Flying Disk Breaker. A LASL development will be improved following initial tests of current in- program is in progress to make a fast breaker which terruption using the mechanical test prototype at opens under “no arc” conditions, with a gap opening low current and voltage levels. velocity which exceeds the voltage rise waveform of the METS/SFTR circuit. C. 300 kJ Test Facility Hardware was devised and built to work out some of the mechanical problems associated with rapid The 300 kJ Test Facility became fully opening and latching of the disks. This interrupter operationalin 1974 and has been used for testing the unit is shown schematically in Fig. XIII-1. The pulse LASL 300 kJ storage coil (Section G) and supercon- coil is rapidly energized by capacitor discharge in- ducting switches (Section E). It will be used for ducing several hundred kA of circulating eddy testing the industrial 300 kJ coils as they become currents on the inside faces of the flying disks. The available. In addition, it will be combined with the field rises to about 80 kG and the resultant magnetic interrupter facility for transfer tests involving the in- pressure on the faces blows each Hisk away at dustrial coils. A discussion of major facility com- -5X 104 g acceleration. ponents follows. As the disk piston unit moves to the travel limit of the cylinder, the highly compressed gas moves the 1. Vapor Cooled High Current Leads. Vapor valve, opening the relief port. As the gas cushion es- cooled leads for the 300 k,J coils supplied by capes, the piston head bottoms out on the valve and American Magnetics Incorporated did not meet the both move to and rebound off of the rubber bumper design specifications of 12.5 kA dc current and 40 kV returning to the cylinder seal. All excess energy is hold-off voltage. Two leads failed at 7 kA and 12 kA dissipated in the valve wall and O-ring friction. The as a result of insufficient cooling, and a third failed gas relief and heavy valve act as the dash pot. at 10 kV. These have been replaced by leads of LASL . The disk piston is vacuum latched to the valve design which have operated successfully at 12.5 kA face after the valve reseats on the cylinder. As the and 35 kV. gas flows through the bleed-back channel to . repressurize the cylinder, the disk piston slowly 2. Superconducting Switch Components. The returns to the initial state. The pressure rises until high voltage trigger system used to drive supercon- the proper closed contact force is reached. ducting switches normal is operating satisfactorily. The opening time for the gap to reach one cm was A sensor to monitor the coil and switch voltage in 350 PS, with less than 5% jitter between test shots. order to detect accidental switch transitions to the Contact separation time is such that only a 10 ps normal resistance state was installed and is current zero time need be applied to assure no-arc operational. This monitor drives the switch trigger separation. A dash pot mechanism latches the on and forces the switch completely normal before breaker open for 25 milliseconds and allows a very localized damage can occur in the switch conductor.

159 3. 10 kA Homopolar dc Generator. This D. 30 kJ Energy Transfer System . generator is used as the power supply for the 300 kJ facility. It was acoustically shielded with fire retar- The 30 kJ apparatus originally built to test dant material reducing the noise level from 85 dB to superconducting switches and other com]xments on . 67 dB. A severe brush problem exists above 6 kA de a small scale was reactivated to study the energy current. Metallurgical analysis by CMB-6 followed required to completely switch superconducting by consultation with the electrical brush industry in- switches to the normal state and to hold them nor- dicated that the brush composition was wrong for mal long enough to begin the energy transfer. In ad- operation at the high altitude (0.78 atm ambient dition the apparatus will be used to int’estigate pressure) and in the dry environment of Los Alamos. energy transfer into resist ive loads using different A new set of brushes has been ordered. values of transfer capacitance and load resistance. Improved reproducibility and measurement ac- 4. Control Electronics, Data Acquisition curacy were obtained from the apparatus by replac- Hardware, Screen Room. Several ground loops ing the external electrolytic resistors with stainless from the 300 k.J facility controller to the high current steel units. system, the switch trigger system and the screen The relative merits of spark gaps and silicon con- room were removed to eliminate false noise trigger- trol rectifiers (SCR) as high-current, high voltage, ing and to remove voltage baseline shifts in the os- fast turn-on devices were investigated. It was con- cilloscopes. In addition all data acquisition os- cluded that the additional costs of an SCR system cilloscopes have been isolated from each other and could not be justified. from ac power grounds. Each oscilloscope has one Theoretical calculations of the current/tinle reference ground to the high current system. profiles for 30 k.J energy transfer were made for Baseline shifts of the current measuring scopes have various capacitance values from 10 pF to 3.4 mF. been reduced to less than 570. The experimentally determined waveforms con- firmed the calculations. 5. 12 kA Rectifier Power Supply. A 12 kA, 20 V dc rectifier power supply was installed as a backup E. Superconducting Switch Development to the homopolar generator, and later will be used in parallel with the homopolar to develop the total 25 During the year more than 20 different switches kA needed for testing prototype METS/SFTR were designed, built, and tested. These switches storage coils. Several internal faults were found and generally fall into four basic types: (a) counterwound repaired. The unit was reworked to improve the cir- spiral or Ayrton-Perry, (b) bifilar wound pancakes or cuit. It now turns on at one volt open circuit, or at 50 hairpin pancakes, (c) circular braid over an in- mV and 250 A when the output bus is shorted. sulating tube or sleeve braided switch, and (d) stack- ed hairpins or accordion type switch. The essential 6. Bolted Current Connectors. An extensive characteristics of each type are as follows: Ayrton- analysis has been carried out on the energy loss Perry— low inductance, easily cooled, good voltage problems associated with the bolted current connec- standoff, poor packaging density; hairpin pan- tors to be used with the 300 kJ test coils. A code cake— low inductance, poor cooling, poor voltage which evaluates the propagation problems standoff, excellent packaging density; sleeve braided associated with the transition to the normal state switch— low inductance, good cooling, good voltage was written based on a model by Stekly. 1“It appears standoff, reasonable packaging density; hairpin ac- that for a discharge time equal to or faster than 10 cordion switch— low inductance, reasonable cool- . msec the 12R losses are less than 25 J. The heat ing, good voltage standoff, good packaging density. conducted along the superconductor into the shroud- Major emphasis has been placed upon the sleeve ed area is of the same magnitude. braided and accordion switches. Several of each of . these types have been built and tested. Low voltage 7. Coil Shroud. A shroud for the 300 kJ coils was quenching currents of 1700 A and 2600 A have been designed and is being procured. This shroud encloses achieved for sleeve braided and accordion switches a coil being tested in QHe and collects gas evolved respectively. by the coil thus giving a measure of the energy dis- Five of the accordion switches were connected in sipated during discharge. parallel and operated at a current of 8000 amps in

160 the300kJ test facility. Ahighvoltage arc occurred (Cu-Ni, Cu, Nb-Ti) wire was not technically at a void in the epoxy casting in one of the five straightforward at the inception of these programs modules which damaged the module. The parallel nor is it now although much progress has been made. combination switch will be rebuilt and tested again During the past nine months these orders have on the 300 kJ storage coil. The superconducting generated significant information for determining switch development will be brought to a conclusion the correct characterization and processing of Nb-Ti with the completion and testing of this switch and a and for determining the process parameters for con- parallel combination of circular braided switches. ventional extrusion. Unfortunately this progress has Experiments were also performed to measure the come as a result of Supercon’s inability to produce switching speed of the superconducting wire used in satisfactory wire consistently, and at the expense of the switches. The wire was switched from the super- wire delivery delays. conducting to normal state by slowly increasing the Because of Supercon’s inability to meet the current through the wire until it started to go nor- original specifications on the Westinghouse wire, a mal. The resistance was measured as a function of design change was made in the coil. Consequently, time thus giving a propagation rate for the normal the originally specified values of jc and wire diameter superconducting interface. Results of these were relaxed from 3X105 A/cm2 and 0.020-in. to measurements gave velocities of the order of 5000 2X 105 A/cm2 and 0.032-in. As a result of this change cm/s at a time 1 ms after driving a point normal and the coil will go normal during discharge; however, velocities of the order of 50 nds 25 ms later. the l~sses are still expected to be less than 0.3%. Even at this lower specification only wire from one billet of the three processed so far has met the short F. Superconducting Wire Development sample requirement. The IGC j~ specification is 2X105 A/cm2 at 30 kG for a 0.0165-in. diameter wire. 1. Industrial Status. The performance All eight billets have been extruded and are in specifications for the industrially fabricated 300 kJ various stages of processing. Preliminary results in- energy storage coils require that the coils operate at dicate that only half of this wire meets 10 kA, be charged in 10 s, be discharged in 0.001 s specifications. without going normal and with a maximum energy A backup program for the IGC wire was initiated loss per cycle of 0.3% or less of the stored energy. at IGC in November 1974. Phase I of this program is These specifications impose unusual requirements to procure the necessary materials for the total wire on the superconductor. Such a conductor must be needed (260 pounds) and to processapproximately multistrand cable or braid and possibly made of 20!; into wire as a qualification program. In Phase H multifilament strands. To meet the large rate of of the program the remaining material will be change of field required without coupling between processed if needed. the individual Nb-Ti superconducting filaments, the superconducting filaments must be small, effective- 2. Wire Evaluation Program. Evaluation of ly isolated electrically and twisted or braided to wire samples produced from the MCA and Supercon yield low energy losses. orders as well as other samples, is being done in Wire production contracts were let to Magnetic three major areas: short sample critical current ( <1 Corporation of America (MCA) and Supercon, Inc. kA) measurements, ac loss measurements, and in April: MCA to produce wire for their 300 k.J coil metallurgical evaluation of ext rusion crops and star- and Supercon to produce wire for the Intermagnetics ting, materials as well as wire. General Corporation (IGC) and Westinghouse coils The critical current measurements are done on (Section G). Each order is for eight four-inch billets. bifilar wound coil samples approximately I meter in The electrical coupling between filaments is length. They provide data up to 500 A and 70 kG at minimized in the MCA coil wire by using 0.005-in. wire resistivity values as low as 10 – *2 ohm-cm. The monofilament, Cu matrix wire that is cabled and loss measurement apparatus is capable of measuring braided into a 1215 strand conductor. The wire static hysteresis losses up to 30 kG and dynamic manufacturing by MCA was technically straight- losses up to B’s of 3X107 G/see. The apparatus is forward and has been completed. The braiding and presently being calibrated using a high purity Nb cabling operations are now underway. sample. When the calibration is completed, quan- The electrical coupling between filaments is titative hysteresis measurements can be made minimized for the IGC and Westinghouse wire by routinely. Spurious imbalances and pick-up have putting Cu-Ni resistance barriers between the now been reduced to the point that semi- filaments in each wire as well as by braiding and quantitative pulsed losses can also be made. cabling. The manufacturing of such triple matrix

161 The metallurgical evaluation includes the in- low loss coils. Best estimates for completion of the vest igation of Cu-Ti interdiffusion, second phase MCA, IGC and Westinghouse coils are now June, . precipitates in Nb-Ti, and hardness. These data are July, and September of 1975, respectively. being correlated to process parameters and wire per- formance. 2. LASL 300 kJ Coil. In order to get experience . in energy-storage coil construction and to have a coil 3. High Critical Current Testing Facility. The available for facility checkout and transfer studies, a high current test facility has been upgraded from 25 300 k.J unit was constructed in house. This coil goes kA to 50 kA with the addition of a new flux pump. A normal upon discharge and does not meet the low new dipole magnet is currently being designed which loss requirements of the industrial coils currently be- will accommodate large braided conductors and ing fabricated. provide a field of up to 50 kG. This will be used to The Los Alamos 300 kJ energy storage coil was evaluate braided and cabled conductor manufac- successfully operated in the 300 kJ test facility. Field tured as a result of our industrial wire and coil measurements along the axis of the coil were within program. 2% of the calculated value, peaking at 1.65 GIA at the center. At 12.5 kA the center field reached 20.6 4. LASL Wire Braiding. LASL capabilities for kG, with a calculated maximum field of 22.7 kG on assembly of wire into conductor geometries in- the conductor. The maximum current run in the coil creased during the year. A larger braider was was 12.5 kA with a corresponding stored energy of purchased, has been set up, and is being checked 386 M. Uniform magnet field tests on Kryo 210 wire out. A small braider was rebuilt and upgraded. A from which this coil is fabricated indicate that the small cabling machine was purchased and is being coil would go normal between 10.6 and 12.7 kA. The rebuilt. A rig for insulating wire was built and is coil has not gone normal at currents as large as 12.5 currently operational. kA. The coil has been used to test superconducting G. Coil Development Program switches up to 8 kA with no problems and has been operated in a prototype METS/SFTR circuit. The 1. Industrial 300 kJ Coils. Three 300 kJ circuit was operated up to 10 kA corresponding to superconducting energy storage coils are being 250 kJ of stored energy, with a peak transfer voltage designed and fabricated by three industrial contrac- of 35 kV. No problems associated with the coil were tors: Intermagnetics General Corporation (IGC), noted. During transfer runs at 5 kA storage current Magnetic Corporation of America (MCA) and the coil did not go normal when ~ reached 6.5x 106 Westinghouse. These coils are the basis of an in- G/s at the coil conductor. At 8 kA current, when 5 dustrial qualification program to establish the ex- reached 107 Gls, the coil went normal, and pert ise within industry for the production of some dissipated less energy than the calculated maximum 800 coils for the SFTR facility. This work is also the value of 3 kJ. foundation for the production of coils to be used in the EPR torus and DEMO plant. Each coil is unique H. SFTR Prototype METS System in its basic wire design, the manner in which the wire is cabled and braided to form the conductor, and the Work is in progress on an experiment to study the manner in which the conductor is supported struc- behavior of energy storage and transfer from coupled turally in the coil. Wire for the MCA coil is being superconducting coils into8-pinch compression coils. made by MCA and wire for the IGC and This system will be based upon a three storage coil . Westinghouse coils is being made by Supercon on section of the SFTR and is to establish completeness separate contracts (Section F). All three of component development as well as engineering organizations have produced, o-n schedule, satisfac- feasibility. Detailed progress on the various sub- tory designs with novel features furthering the state- systems follows. of-the-art. Predicted performance for the coils is well within LASL requirements. 1. Cryogenic Disconnect. A mechanically All three manufacturers have encountered coil actuated high current, very low resistance switch to assembly delays as a result of wire fabrication, cabl- replace the superconducting switches is being ing and braiding difficulties. It is probably fair to say designed to operate in He. The apparatus for that everyone underestimated the magnitude of the testing contact materials for the disconnect has been conductor development work required to produce designed, procured and assembled.

162 If the disconnect is not staged, arcing would occur lubricated two-stage, balanced, opposed-piston unit . as the unit opens which in principle could generate a with a throughput of 680 kglh. During times when shock wave within the dewar. Theoretically such a the primary experiment is not operating, the shock wave would produce a pressure wave on the refrigeration system will operate as a liquefier to . order of 50 to 100 psi. While not expected to be a provide an inhouse source of liquid helium for in- major problem, since the disconnect can be staged, dividual coil testing and other cryogenic ex- this will be investigated experimentally (Section H). periments. Two vacuum-jacketed fiberglass reinforced, epoxy 2. Cryogenic Refrigerator and Experimental dewars are to be custom-built since large dewars of Dewar. The refrigeration system for the prototype this type are not standard commerical items. Design was ordered in June 1974 with delivery scheduled for details have been completed for the first dewar ,January 1976. This is a major component of the which will be used to test single 490 kJ superconduc- prototype test facility and consists of a helium ting coils. refrigerator, compressors, transfer lines, cold gas li- A LASL computer program called RASH was used quid helium storage dewar and a gas recovery to evaluate the mechanical and thermal stresses in system. A schematic drawing of this system is shown both shells of this dewar. With overall dimensions of in Fig. XIII-2. The helium refrigerator will produce 1016 mm id. by 2590 mm high, this unit will be in- 290 literslh of liquid helium when operated as a li- stalled and evaluated in the existing 300 kJ facility. quefier (no cold gas return). In actual practice it will The second dewar, an SFTR prototype dewar, will operate as a hybrid refrigeratorllique fier providing be taller than the first dewar and will incorporate the 700 W at 4.5 K to the experimental dewar. The best design features of the single module dewar. It machine will utilize two gas bearing turbine ex- will be used to test three prototype coils in the SFTR panders in series and will utilize a full flow purifica- configuration. tion system. The 375 kW compressor will be a non-

Fig. XIII-2 Schematic Drawing of the Refrigeration System

163 3. 60 kV, 25 kA Electrical Leads. Work is in progress to develop a pulsed electrical lead for use in . the METS/SFTR applications. The ultimate goal of -I CUh TfRpUL:C 7 RIGGi R & emRKTirAdb, / , CLI%RCNT SWITCH (LOW KILTAGCJ the development program is to design a pulsed lead J that will carry the required 25 kA current pulse and ,- COMb.4UTAl10N [NCRGY AND . TRANSf CR CAPAClrOR (C, ] “1 allow a minimum of heat input to the cryogenic -. = W_-- system. a ,;~ The proposed lead is coaxial which offers the par- r ticular advantages of a single dewar penetration, ~ > HKK WUWU INTCRRUPTCR (13L] limiting lead inductance and lessening of 5A TuR413.11 RIACrOR JOR dI/41 ,,

164 coil and magnetic energy storage system would . necessarily be quite large (approximately 18 meters) and the effect of stray fields from separate solenoidal storage systems would be much reduced. In addition the benefits of modularizing the storage system were thought to be sufficient to consider a METS system made of 80 cylindrical dewars positioned vertically. With the modularized dewar concept, refrigeration requirements are not increased because the ad- ditional coil charging electrical lead heat load is offset by the lower heat leak from the cylindrical dewars. As envisioned, each of the vacuum jacketed, fiberglass reinforced, epoxy dewars will be a right circular cylinder approximately six meters in height and will accommodate ten storage coils each. The refrigerator will provide approximately 1700 kg/h of liquid helium and will have a total compressor input I I I power of approximately 10 MW. k----4------’ 5u13-M4STf R 3. Interrupter Module. The interrupter module CON7 ROL LOG lC UUS design was finalized early in the SFTR conceptual k= design study. Vacuum interrupter tests based upon this design proved that the approach was conser- vat ive. Further testing of commerical and LASL built breakers may lead to simplified designs which Fig. XIII-4 will only make the resulting module cheaper and HVDC Interrupter Module smaller. The mechanical layout minimizes the structural strength needed and the internal geometry to store 100 kJ of energy using six disks in electrical minimizes the module inductance with a conser- series, capable of a rev-up and rev-down in one vat ive spacing between low and high voltage com - millisecond. The design of the homopolar capacitor ponents. The sub-master control electronics are is considerably different than for an energy storage located outside the shielded cabinet to alleviate arc homopolar. The steady state condition would be zero and high voltage noise infiltration. Each of the ten or near-zero rotation, which would imply use of a modules within a cabinet can be removed and simple nonretractable electrical brush system. replaced rapidly. The electrical design of the module Energy storage and electrical circuit transfer losses is shown in Fig. XIII-4. make competing demands on material and geometry Provision is made to assure equal current and design parameters. voltage sharing in each interrupter unit. The The big advantages of a homopolar transfer saturable reactor lowers the dI/dt to a small value capacitor within a METS system or other similar bracketing I = O to ass~re arc deionization during LCL type systems would be several, and may be commutation, and the V capacitor holds the im- probed in detail by further work. This inertial energy pressed voltage near zero during the 50 ws required storage system would have much higher energy den- for vacuum recovery. The damping resistor quenches sity than conventional inductive storage systems all parasitic stray circuit oscillations which may be and be an order of magnitude better than a . large enough to cause an arc hold-on voltage. capacitive storage system, thereby leading to more Voltage and current monitoring within the module compact power systems. The cost per joule for even will be used to detect malfunctions, and, if megajoule size packages should be less thanl cent/ necessary, blow the triggerable fuse to isolate the in- joule. terrupter. 5. Cryogenic Consultants, Inc. (CCI) Design 4. 100 kJ Homopolar Transfer Capacitor. A Study. The CCI cryogenic system design study2 for computer study is in progress to analyze a small a toroidal, theta-pinch system was completed. This scale homopolar transfer capacitor. The capacitor is study utilized a single toroidal dewar as opposed to

165 the current modular dewar concept consisting of 80 various electrode configurations within the dewar dewars. Many of the CCI design features and con- was built and installed in the CTR-4 high voltage . cepts have been carried over into the current research laboratory. An external high voltage circuit modular dewar system. capable of providing a 60 kV pulse with 500 PS rise . time is connected to the electrodes. The discharge J. Dielectric Strength, Voltage Tracking and current is limited by a resistor so that electrode Arc Discharge Studies damage is minimized. Electrode gap separation is adjusted external to the dewar with a micrometer A program is in progress to study the dielectric and the breakdown characteristics are measured by strength of helium and nitrogen in both the liquid oscilloscope with a high voltage probe and a Pearson and gaseous state, voltage tracking along insulator current transformer. surfaces in helium and nitrogen, and shock wave for- Data are completed for air and nitrogen as the mat ion during arc discharges in liquid helium. The dielectric medium using sphere-sphere, plane-plane purpose of this work is to obtain engineering data to and point-point configurations. The data are permit proper design of high voltage components presently being analyzed. Testing in helium is un- (leads, cryogenic disconnect, etc.) for the SFTR derway. system. Some literature is available regarding low References temperature helium and nitrogen dielectric proper- ties, but the majority of the articles written are con- 1. Stekly, Z. J. J., Advances in Cryogenic Engineer- cerned with ac or dc application. It is difficult to ex- ing, 8, 585, Plenum Press (1963). trapolate such data to the SFTR pulse voltage applications since dielectric breakdown is a function 2. Vander Arend, P.C. West, J. E., Krishna, G. V., of many parameters including electrode size and “Cryogenic System Design for a Toroidal, Separated shapes, dielectric pressure and temperatures, and Shock Theta-Pinch System,” Reports of May 1, applied voltage waveforms. August 9 and November 14, 1974, Cryogenic Con- A test set-up consisting of a nitrogen shielded, sultants, Inc., Allentown, PA. stainless steel dewar with the capability of installing

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166 XIV. FUSION TECHNOLOGY

R.A. Krakowski, L. Booth, G.E. Bosler, J.M. Bunch, F. W. Clinard, Jr., D.J. Dudziak, T. Frank, A. W. Gerstl, W. V. Green, G. M. Hale, D. R. Harris, J. G. Hoffman, D. W. Muir, T.A. Oliphant, D.M. Parkin, M. L. Simmons, P. D. Soran

A. Introduction I , I 18 The Fusion Technology task assesses the long- 1.0,,020- n vs Al? - 1.0110 range technological requirements of fusion power derived from high-o confinement concepts. The ef- ni fort includes theoretical analyses and plasma engineering, neutronic studies, nuclear data assess- ni ‘n ment, electrical insulator and structural alloy research, and general engineering; progress within each of these areas is summarized herein. On the /“ basis of a conceptual engineering design of a ‘n Reference Theta Pinch Reactor (RTPR) 1‘2 an environmental impact study has been completed 3 and a technological assessment is near completion. 4’5 The Fusion Technology task has also supported engineering design activities for the I Scyllac Fusion Test Reactor (SFTR, Sec. XV) in the 0.0~ areas of tritium handling, radiation shielding, 0.0 0.01 0.02 materials, vacuum technology and environmen- AR(m) tal/safety analyses. Preliminary design studies of a Linear Theta-Pinch Hybrid Reactor (LTPI-IR) have commenced,6 and more detailed design studies of Fig. XIV- 1 this fission/fusion concept are proceeding. The ion density nl and neutral gas density n n are plotted us the distance ATaR from the B. Theoretical Analysis center of the diffuse plasma sheath at a time 200 ps after introduction of the neutral gas. Theoretical analysis and computational modeling efforts support many of the systems studies. Impor- the nature of the incoming neutral atoms in more tant highlights are reviewed below. detail. The neutral gas is modeled with “simulation . slabs”, each of which has a well defined position and 1. Neutral Gas Cooling Layers. The velocity component in the direction-of gas flow. The effectiveness of the neutral-gas layer in controlled density and temperature dependence of both charge cooling of the hot post-burn plasma has been exchange and collisional rates are consistently and . analytically demonstrated in the steady state accurately taken into account by these new com- approximation.7 The question of charge exchange putational methods. occurring during the transient phase of the neutral gas blanket/plasma interaction and the ensuing wall 2. Thermonuclear Burn Calculations for damage has been addressed. The results of LTPHR. A thermonuclear burn computer code has preliminary computations8’9 are shown in Figs. been written in which the dynamics of plasma com- XIV- 1 and XIV-2 as radial density and temperature pression is coupled to an external circuit analysis. profiles at 200 KS after introduction of the neutral These burn calculations provide input for the gas. A new and superior calculation is being systems analysis of the LTPHR,6 discussed in Sec. developed, which treats the plasma dynamics and VIII.C,2,Thecircuitanditsequationsareillustrated

167 I

5.0

‘EXT “ Lp=#ovb2(l-X2) T“

(o) Implosion/Compression Phase S1 = Closed, S2= Open

(b) Crowbar Phase SI = Open, S2- Closed RI-(LExT+L~*Lp)~. I$P

Fig. XIV-3 0.0 I Circuit diagram used to model the ther- -0.0 0.01 0.02 monuclear burn for the LTPHR. AR(m)

2J I p Fig. XIV-2 C=0,18F/m The ion temperature Ti and neutral gas temperature T. are plotted vs the distance JR /–\ ;;[;;” - , from the center of the diffuse plasma sheath at / \ a time 200 PS after the introduction of the /- Compressmn F!eld (T) x20 neutral gas. 1, - 6 / \

in Fig. XIV-3; Fig. XIV-4 illustrates the calculated time dependence of ion temperature, plasma radius, and neutron yield. The simple bounce modulel” was IJ used for the results of Fig. 4, but more sophisticated, mixed-bounce, snow-plow calculations 11 were also made. A comparison of these two models with Scylla IV experimental data12 indicates that the simple bounce model adequately describes the implosion process. Hybrid calculations (i.e. a combination of o analytical calculations with simulation calculations) are being formulated to model the implosion process, / Neutron Fluence \ \’: I which may be computationally complicated by t\. / simultaneous compression. T~- / Plasma.To.Well _ \/ ! I B~ ~ 1 , ,\ \ 3. Calculation of SF’I’R Operating Point. The ( I 50 100 150 200 250 30% thermonuclear burn code DTBURN 13 has been Time (Ps) modified to monitor the plasma stability conditions and plasma Q (neutron energy/plasma energy) for a variety of input parameters. Figures XIV-5 through XIV-7 give computation results generated for Fig. XIV-4 theSFTR design. DTBURN has yielded a range of Typical results for the LTPHR thermonuclear operating points for SFTR based on parameters burn for a simple, LC-ringing circuit. determined by implosion-heating and stability- theory.

168 {25 . R=40m E8= 3hV/cm )i=3.2m 81= 1.5 . o= 7m Torr 80 ~0.18

I Q

twx 10-’4

0.5

0 0 10 20 30 40 t(ms)

Fig. XIV-5 Time dependence of feasibility number Q, confining field B, and nr during the burn.

4. Systems Analysis Code Development. The 6. End-Loss Calculations. The effects of alpha- increased detail used to describe a given system has particle heating and adiabatic compression on end made it imperative to develop a generalized systems loss from a straight theta-pinch have been es- code. The development of the LASL fusion reactor timated. These calculations at present serve mainly systems code began with an ergodic analysis of the to identify the direction to be taken by code develop- RTPR14 (See XIV. C.l.a). Ultimately the system ment and will be pursued in collaboration with analysis code will provide a continuous update of the CTR-6. End-loss phenomena will eventually be in- reactor concepts for RTPR, LTPHR, SFTR, as well corporated into the thermonuclear burn com- as other (Z-pinch, high-~ stellarator) fusion reactor putations for LTPHR. concepts. 7. Advanced Thermonuclear Burn . 5. Theta-Pinch Coil Design Calculations. Calculations. Calculations were made on the Work has progressed on general 3-D, distorted- alteration to the shape of the reacting plasma sur- mesh calculations of static magnetic fields. These face as a result of the presence of alpha-particle reac- calculations will impinge on almost every ex- tion products. This analysis is continuing, and plans . perimental project now being considered in CTR. exist to develop more sophisticated transport theory The major steps taken over the past year are the for describing general spatial variation. development of a 3-D spline interpolator and the successful solution of 3-D magnetic scalar potential C. Reactor Design Studies problems. The next steps are to develop a useful for- mat for present applications and to extend the The systems analysis task at LASL assesses method to vector potential problems. present technology, analytically identifies re- quirements, and forecasts research and development

169 Stabilitv . Factors—- vs t 7 1 I I 1 R =40m E~= 3hV/cm . A = 3.2m 81= 1.5 po= 7m Torr 80 S0.18 . -. 5 [

4

3

2

i # c o Iu Cu au -u t(ms)

Fig. XIV-6 Stability criterion numbers form= landm=2 . ... stablllt.y us burn time. needed for fusion Dower systems. All reactor con- Equilibrium/Stability: Freidberg and Ribe 15 have cepts being conside~ecl are ‘based on high+?, pulsed- summarized the implications of toroidal equilibrium magnetic confinement schemes. Past efforts (1972- and MHD stability on the design of the SFTR. The 74) have focused on the engineering design of the final compression ratio selected for the RTPR is too RTPR. ”2 shown in Fig. XIV-8. The focus of the CY large for effective wall stabilization of m= 1 modes 1974 effort in this area has been the en~~nmental during a major portion of the burn cycle, and feed- study, 3 the technological assessment, t and the back stabilization will be required. resolution of problems revealed by these latter studies. Designs of fusionlfission reactors based on Thermonuclear Burn/Energy Balance: The original the linear theta-pinch concept are also underway. RTPR design 1’2 did not consider the effects of Progress in each of t hese areas is summarized below. impurities on the thermonuclear burn, the influence on the overall energy balance of the staging re- 1. RTPR Studies quirements, or the optimization of burn parameters . (particularly under-compression vs over- a. Technology Assessment. In an assessment of compression). Subsequent analyses 14 have partially the RTPR design, technological problems and uncer- resolved these uncertainties. tainties were categorized into nine major areas:4’5 . Neutral Gas Cooling: Central to the operation of ● Plasma Physics. The major areas of uncertainty the RTPR is the need to cool the hot, (5-10 KeV), associated with the plasma physics are stability/e- post-burn plasma by means of a neutral-gas blanket. quilibrium, thermonuclear burnfenergy balance, Past analyses 1’7 assumed a quasi steady state, and neutral gas cooling. continuum model, which has subsequently been

170 W Plasma Energy vs t 0.07 R =40m Eo= 3hV/cm

0.06

0.05

~ MJ ‘“04 ()-iii 0.03

0.02 .

0.01

0 1 0 10 20 30 40 50

t (ins)

Fig. XIV- 7 Plasma interval energy W(hJlm) as a funct ion of burn time for no alpha heating (q =0.0) and u~ith alpha heating (rl=O.5).

refined by Monte Carlo techniques. “a Although the ● Materials and Radiation Damage: A materials wall fluxes of charge-exchanged neutrals have been assessment of the RTPR first wall and blanket l’17!18 estimated,8 more realistic, transient computations shows that the insulator/metal composite first wall must be made and are now in progress. presents the most crucial materials problem, from both a radiation-damage and a thermal stress view- ● Implosion and Compression Energy and point. New first-wall concepts, which include Storage: The RTPR design uses capacitive storage sacrificial “bumpers”, purely ceramic first walls, for implosion and staging, and reversible inductive and new geometric configurations, are being con- storage (METS) for adiabatic compression. Energy- sidered to reduce the radiation damage and thermal balance considerations demand METS transfer ef- stress problems. Materials-related uncertainties ficiencies of -95%, and staging energies equal to and associated with magnetic coils, molten lithium, . not much more than the implosion energy 14 are tritium diffusion barriers, superconductors, molten- needed for an acceptable energy balance. The cost salt containment (in the tritium extractor), and and efficiency of the compression energy storage was blanket materials have been investigated. . subsequently elucidated by an independent systems analysis. 16 On the basis of this study and the ● Tritium Handling: An RTPR operating at a 12 problems inherent to a purely capacitivefMETS GWt power level must actively circulate 28.8 kg/d of driven RTPR, on-going designs are considering tritium, most of which is transferred unburned capacitive implosion, METS staging, and a com- through the vacuum and fuel injection/ recovery pression field driven by homopolar motor generator systems. Effective handling and containment of (HETS) sets. tritium is both an environmental and economic

171 .– \ ‘n .

.

.

.

u .) ,’

172 necessity. The fuel supply/removal system and the b. Environmental Assessment. The . isotope separation system do not appear to present environmental assessment of the RTPR has been severe design or economic demands. The molten-salt completed. 3 This study indicates that the un- extraction system for tritium recovery from lithium vironmental impact of theta-pinch fusion reactors . is more uncertain from a physical-chemical view- would be minimal. In terms of radioactivity, point, althou h recent experimental results look material needs, and land despoilation, the an- encouraging. 1f Similarly, containment of tritium ticipated advantages associated with the abundant from the environment does not appear to present in- fuel supply and less harmful reaction products surmountable problems. 3~20 appear to be without seriously offsetting disadvan- tages.

● Blanket Neutronics: Neutronic computations Several environmental aspects appear identical based on the results of the thermonuclear burn with other large energy sources (fossil, fissile). The calculations yield neutron and gamma-heating waste heat from a fusion power plant, like all other rates, radioactivation, tritium breeding, radiation power plants, is dependent on the maximum ther- damage rates (dpa, He and H production, mal conversion temperature. If advanced (high- transmutations, etc.), radiation shielding re- temperature) energy conversion cycles are used, the waste heat is reduced regardless of the specific heat quirements, and other important design parameters. source. The waste heat problem could, in principle, These neutronic computations have been based on be worse for fusion reactors than for fissile or fossil one-dimensional, time-independent models; fuer power plants because of the larger circulating although adequate for the purpose of conceptual power required by the former. This problem is reduc- reactor designs, neutronic techniques must be refin- ed in the RTPR power plant by the direct conversion ed for more detailed studies. Although the of -9ri of the total fusion energy. 1 neutronics is well in hand, areas where improvement Land despoilment by fusion reactors appears to appears desirable21 are: (a) application of differ little from other heat sources. Presently, the perturbation techniques to facilitate more rapid and likelihood of siting a fusion power plant in an urban far-ranging parametric systems studies; (b) op- setting and close to the load point appears to differ timization of blanket thickness vs tritium breeding little from a fission or fossil power plant. The mining rates and Be inventory; (c) detailed studies of the requirements for fuel and structural materials, sensitivity of displaced atoms (dpa), breeding ratio, although differing significantly in kind, do not etc. to neutron cross sections; (d) time-dependent appear to differ significantly between fusion, fission, calculations (e.g. 6Li burn-out); (e) two- or fossil power plants. dimensional, Monte Carlo computations to model The major environmental effects of a fusion reac- critical regions of the segmented (axially and radial- tor that employs D-T fuel and magnetic confinement ly) RTPR blanket; and (f) more accurate modeling are associated with (a) the need to breed t ritium of the “deep-penetration” problem. (tritium inventories, lithium burnout), (b) the need to store large quantities of magnetic energy and the ● Construction, Operation and Maintenance: In associated resource requirements on niobium, this category are the many engineering problems helium, copper, and steel, (c) the need to operate which are highly design-dependent and which deter- radioactive components as well as to transport and mine the technological and economic viability of the to store radioactive waste, and (d) the need to RTPR. For instance, the interaction between duty replace on a regular basis substantial quantities of cycle, first-wall loading (e.g. lifetime), and the radiation-damaged metals for a given amount of feasibility of rapid module change-out will have a energy generated. . significant influence on the RTPR economics. The RTPR power plant actively circulates 28.8 Although the modular approach adopted by the kg/d of tritium, passively stores 1.43 kg of trit ium, RTPR design will facilitate rapid (i.e. short down- and consumes 1.38 kg/d of tritium. Table XIV-II . times) replacement of the first-wall/blanket regions, summarizes the RTPR tritium inventory. If a much more engineering of the proposed remote- t ritium part ial pressure of 10 – 10 torr in the lithium handling, maintenance, and repair schemes must be coolant is assumed, and a copper diffusion barrier is evolved before these ideas truly become credible. placed in the primary heat exchanger, the leak rate Details of construction, operation and maintenance of tritium to the environment (condenser water for problems are given in References 1 and 4. the case of the present RTPR power plant design) Table XIV-I gives a synopsis of the above- amounts to 6 Ci/d. Table XIV-III gives the resulting radiation doses for three cooling water options. described technology assessment. More detail is given in Vol. III of the RTPR design study.5 Since 81% of the tritium breeding occurs in 6Li, a total of 14,600 kg/y of natural lithium is consumed

173 TABLE XIV-I

SYMFOSIS OF THE RTPR TECHNOLOGY ASSESSMENT

Area Problems, Uncertain ies, and Needed Research/Development PLASNA PHYSIcs

●Plasma Stability ●Achieve toroidal equilibrium with acceptably 10V m-l, k-O (“fat” plasma) and m ~ 1, k-O (“skinny” plasma) grovth rates for reasonable aspect ratios

●Incorporation of 9.-1,0perturbation onto blanket and coil flux surfaces 4Thermonuclear Burn/Energy Balance *Optimize risetime, burntime, and compression field with respect to RTPR Q-value *Influence of impurities on energy balance

●Neutral Gas Cooling *Cooling effectiveness and influence on maximum allowable burn intensity

-ransient phase of gas cooling and influence of charge exchange *Effect of neutral gas cooling on energy balance (increased heating requirement)

IMPLOSION HEATING *End-fed coil and electrical feedthrough design (1OV inductance) *IJR time constant of implosionfstaging circuit and influence on Q-value *Large first-wall radius and fluting of ion sheath +Interactfon of :1..:..Oneutral D-T gas with imploding plaama

*FIux return path and related heating efficiency *Effects of 6 < 1 and impurities on implosion efficiency *Effects of desorbed gases (D,T)~, 02) on Implosion heating

ADIABATIC COMPRESSION (METS) *Staging of implosion field into compression field *Storage and transfer efficiencies ~ 95% and acceptable Cost *Development of storageltransfer system with high peak-power requirement. (Nested coils/transformer, homopolar generator, short-circuit ac generator-inverter system) *Ceneratlon of quench-and-hold fIeld ●Distribution of.direct-conversion energy *Coil, leads, disconnect, circuit design

MATERIALS ●Fir6c-wall composite (neutron swelling, transmutations, fie/R generation, sputr.ering,blfsrering, thermal shock and fatigue, chemical stability, dielectric strength and resistivity of insulators in a radiation field) ●Radiation, chemical and thermal stability of blanket materials (Be, C, Li) . *tfagnaticcoils fabrication, radiation damage, stress, fatigue *Development of fast-pulsed superconducting matricea ●Materiala transport in liquid-metal systems (Li and Na) *Tritium interactions and containment

174 . TRITIUM HANDLING

● Fuel Supply/Reznoval *Development of high-capacity vacuum system (pumps and . ducts) ●Dynsmics of a pulsed vacuum system which must supply bnth initial fuel charge and neutral gas blanket as well as remove spent fuel ●Isotope Separation *Develop cryodistillation system which separates II,D, T, and He and has small hold-up time (inventory) ●l!ritiumRecovery from Lithium *Better physical-chemical understanding of molten-salt extraction systsm

●Ffnd other extractants with higher partition coeffi.cients *Understand effects of sxtractant soluhility in lithium coolant on corrosion ●Tritium Containment *Develop tritium barriers for high-temperature (heat exchanger, steam generator) containment *Develnp low-temperature tritium barriers (glasses, He purge, rotating seals)

NEUTRONICS ●Perturbation techniques required for parametric systems analyses

*TwO-dimensiOnd. irIUtLLe Carlo) calculations of neutron stresming and local heating ●Sensitivity studies on tritium breeding, neutron heating, etc. to determine effects of cross section uncertainties *Enlarge and improve cross section data base

RADIOACTIVIIl AND AFTERHEAT ●Influence of impurity activation on radwaste problem must be resolved *Mre detailed heat transfer calculation needed for loss+ f-roolant accident ●Use of low activation msterials in blanket and magnetic coils

CONSTRUCTION, OPERATION, MAINTENANCE ●Develop a detailed eystems analysis to determine interaction between duty cycle, materials, and economic constraints *Mnre detailed design of module replacement scheme to aseure a viable means to rapidly remove and replace first wall ●Elucidate more the influence of pulsed operation of plant output, coolant pumping requirements (flow surges) and fieldlcoolant interactions *A wide range of fabrication techniques (electron beam welding, plasma spraying, metal forming, etc.) must be extended to and developed for the RTPR .

*The complexity of “routine” operation of this power plant will require advancements in plant control. . feedback, & situ system interrogation. and remote procedures to protect the large capital and energy investment as well as to assure an acceptable (80-85%) operating factor

RESOURCES *If niobium is used, resource limitations will demand recycling of structural material. Remote reprocessing techniques must be developed *Unless a substitute for a neutron breeder is found, a substantial fraction (-50%) of the world Be resource will be used. The world resource of Be is not well known

*LI usage IS large

175 TABLE XIV-II blanket design details. Hence, consumption of blanket materials is nearly proportional to the in- . SUMMARY OF TRITIUN INVENTORY tegrated thermal output of the fusion power plant. A preliminary safety analysis for RTPR has been Location Inventory (g) made. In the unlikely event that the total circulating . Reactor Blanket 53 tritium inventory were released to the atmosphere, the external radiation dose to the surrounding pop- Lithium Circuit (not including ulace would amount to 7.6 rem at 600 m and 1.8 rem Tritium in Blanket) 404 at 3 km from the release point. A liquid-metal fire could produce this kind of release, althuugh the Fuel-Ash Processing and likelihood of an instantaneous and total release of all Fuel Injection 1913 actively circulating tritium appears highly im- probable. The losof-cooling accident (LOCA) Sodiuma 0.3 appears more probable. However, if the LOCA is steam 7 detected in time for the reactor to be shut down, the damage to the reactor should not be serious. None of Storage 1426 the possible consequences of the LOCA should propagate outside the reactur containment. Total 3804 Although other accident situations have been dis- ‘Baaed on 0.1 ppb concentration and cussed in Ref. 3, more must be known about the 3.026 x 106 kg Na. details of plasma physics and the engineering design before conclusive remarks can be made. However, based on the tentative evidence accumulated thus forabreeding ratio of l.ll. Approximately 1.0x106 far, the RTPR power plant appears to have an ex- kgofniobium and 1.3)(106 kg ofhelium is required tremely low potential for a publicly hazardous acci- for inductive energy storage, and approximately 76,- dent. 700 kgly of radioactive niobium from the blanket must be handled (transported, stored, and c. RTPR Systems Code. The RTPR design reprocessed). An additional 1800 kg/y of low-level effort has entered a “problem solving” phase radioactive niobium must reprocessed asa resultof whereby the aforementioned key uncertainties lithium corrosion. The anticipated resource require- (energy storage, neutral gas blanket, insulating first mentfortheRTPR issummarized onTableXIV-lV. wall, feedback stabilization, staging, etc. ) are being The quoted values of tritium losses, resource more completely resolved by either more detailed depletion, and radwastes are for the 12 GWt (4.0 analysis or design change. The focus of this effort is GWe) RTPR power plant design described in Ref. 1. an integrated systems code, which analytically These effects are highly design-dependent. For in- models all physics aspects of the RTPR burn cycle; stance, depending on the emphasis placed upon other aspects of the RTPR (blanket neutronics, minimizing the tritium release rate and inventory, tritium handling, power conversion, etc.) are not in- different coolant and breeding schemes can be corporated into the LASL systems code. Evaluations adopted which, in principle, could reduce the 6 Ci/d will be made primarily on the basis of overall energy tritium release rate to a level determined hy the leak balances. integrity of the helium purge system (0.01 to 0.1 This code in a preliminary version was used in op- Ci/d). The level of radwaste handled by the RTPR timization studies of the RTPR burn cycle. 14 Figure power plant could be reduced by the replacement of XIV-9 illustrates the dependence of the overall Q- niobium in the blanket by metals which activate to a value (thermal energy deposited into blanket/recir- . lesser extent. These examples serve to illustrate the culating energy) on the excess compression field AB variability of important environmental effects above the minimum compression field B,, required result ing from engineering design changes. for plasma ignition. Four burn times TB are . Structural and blanket material requirements, illustrated as is the propensity for plasma re-ignition however, show little sensitivity to design change. For after quench, as measured by the time rate of a given total energy output the neutron flux will plasma temperature increase without neutral gas produce a given number of displaced atoms in the cooling. For the particular conditions shown on Fig. surrounding structural material. The radiation- XIV-9, a minimum field &+AB is required to damaged material must be replaced at a rate (19.1 obtain an economic Q-value for a given TB, whereas a kg/M We-y), which is roughly independent of the maximum fieldis established by the desire to quench and cool the plasma after the burn is complete.

176 TABLE XIV-111A

SUMMARY OF ANNUAL INTEGRATED POPUI.ATION (AIP) DOSE (MAN REM/YR) AT 6 Ci/DAY RELEASE RATE Site 1 Site 2 Baily (Lake, Oconee (River, 5.8x106 People/ 7.3x10= People/ Cooling Case 50-Mile Radius) 50-Mile Radius)

Case (1) (Once-through cooling) 46 (Water) 1.7 (Water)

Case (2) (Wet cooling tower) 12.7 (Water) 0.4 (Water)

Caae (3) (Dry cooling tower) 0.6 (Air) 0.5 (Air) Bkg/50-mile radius 13.3 (Total) 0.9 (Total) (125 mrem/yr) 9. 9X105 9.1X1(34

Fission plant (Prorated) 248 15.4

TABLE XIV-IIIB

MAXIMUM ANNUAL AVERAGE INDIVIDUAL DOSES FROM THE RELEASE OF 6 Ci/DAY OF TRITIUM (MREM/YR)

Site 1 (Baily) Site 2 (Oconee) a —IcL-a ——KGKb ICY: —M&Kb Case (1) (Once-through cooling) 0.064 (water) O.O64 (water)

Case (2) (Wet cooling tower) 0.80 (water) 0.80 (water)

0.0059 (air) 0.12 0.027 (air) 0.18 0.81 (total) 0.92 0.83 (total) 0.98

Case (3) (Dry cooling tower) 0.18 (air) 0.77 0.17 (air) 0.14

(21) aMethod of International Commission on Radiological Protection b (22) Method of Morley and Kennedy

. Shown on Fig. XIV-10 is adiagram of the LASL curately the response ofthe implosion (IMPL), stag- systems code as it is presently being developed. In ing (STG) and compression (COMP) phases of the addition to a more refined energy balance that incor- RTPRcycle aswell as the dynamic behavior of the . porates energy requirements of feedback stabiliza- plasma (DTBURN), gas blanket (GASBLK) and tion, the thermonuclear burn subroutine DTBURN first wall (WALL). is coupled by means of a gas blanket model, GASBLK to the impurity emission rates from the 1. Linear Theta-Pinch Hybrid Reactor first wall bythesubroutine WALLandHTRANS .In (LTPHR) Studies. The overall energy balance for addition to output in the form of energy balance a linear theta pinch reactor can be improved by use quantities, the LASL systems code monitors the ofa fission-enhanced, energy-multiplying blanket. A plasma stability/equilibrium condition, the plasma study has been made6 of constraints established by radius and temperature, and the conditions of the plasma physics, neutronics, energy balance, and firstwall. Thetask ofeachsubroutine istomodelac- economics on the design of a LTPHR; although

177 .

. i

I 1

“z 0“ 0 .-l

6=

z

m

u-03 u. 0

u : Vm N.-l 0 .-4 00 00 & 0“ I

m .s -4 .

.

: .tJ 3

178 40[ I I I 1/ I I I 1 rR=30 ms loo\ rB.llom~ & 7.83T \ Oxygen.O% / \ 1 90\ “\ \\ / \ ‘Bm k5x%ii9@

Fig. XIV-10 LASL systems analysis code for physicsltechnology studies. I O--AL , storage inductor; the homopolar motor/generator behaves electrically as a capacitive circuit element. The mix between fission and fusion energy produc- tion is not specified. Preliminary cost estimates of Fractional“Kick” Field (A B/ ~) major portions of the “nuclear island” (power supplies, switches, blanket, prorated fission burner) indicate costs in the range of 6001KWe. A major Fig. XIV-9 portion of the cost (400 -500fKWe) is associated with Dependence of the RTPR Q-value on AB/Bo for the capacitive power supply; alternative magnetic various burnt imes. energy storage schemes will be explored. A 1000 m long LTPHR which has a 18 kg/m 233U preliminary, this study integrates these four impor- loading gives an intrinsic doubling time of 14 y (0.72 tant requirements in a consistent way. The tonnes/y 233U production) for a first-wall, fusion 23%%/233U fuel cycle has been selected for this neutron current equivalent to 1.0 M W/m2. Table study on the basis of potential environmental advan- XIV-V summarizes the neutronic characteristics of a tages. Only well-understood technology is used for reference fission/fusion blanket, and Fig. XIV-12 both the fission (HTGR) and fusion (Scylla) portions gives a conceptual illustration of a “typical” LTPHR of the LTPHR. On the basis of a generalized energy module. This system has a net tritium breeding balance developed for the fusion-fission symbiosis, gain, generates - 10 times its internal circulating as shown in Fig. XIV-11, favorable energy mul- power needs (for reversible transfer efficiency of tiplication (QE = total electrical power/recirculated 95’%), and provides 7.38 M We/m of electrical energy power -5- 10) results for theta-pinch systems which (12.8 MWe/m3 of enriched seed or 2.44 kg ‘3U/ . are below 1000 m in length and self-sufficient for MWe) for a thermal conversion efficiency of 0.40. Approximately 10 GJ of stored energy will be re- tritium. Although some ‘3 U-enrichment of the blanket is shown to be necessary, the optimum quired, which must be switched at a frequency of 2-4 . blanket configuration has not been determined. Hz to maintain 1.0 MW/m2 fusion-neutron wall An electro-technology based on LC-resonant circuits loading. The design presented here in many ways is is proposed, and reversible transfer of magnetic conservative, but these preliminary, favorable energy with efficiencies >90Y0 (including joule losses results warrant further exploration of the LTPHR in the theta-pinch coil) will be required. Although a concept. capacitive energy store will be required for the im- plosion heating phase, the energy for the compres- D. Theta-Pinch Nucleonic Studies sion field will be derived from a homopolar 1. Radioactivity and Afterheat. As part of the motorlgenerator set, which discharges slowly into a assessment of the RTPR, a comprehensive

179 [cV-j PC’PB(l‘@ E ’23

~ 123/[DT] * + ?f+ PE E* Burner P;H P: (H(P; +PE) 1;3 m

*All Power Expressed as MW/m

Fig. XIV-II Schematic diagram of the LTPHR energy balance. parameter study 33’34 was performed on induced Target expense and radioactivity have structural radioactivity and afterheat. This limited94Nb cross section measurements, but parameter study varied the first-wall 14.1-MeV several determinations of the thermal neutron cap- neutron current (0.2 to 6.7 MW/m2), the reactor ture cross section have been made, as well as two operating time (1 to 20 y), the time after shutdown (O measurements of the capture resonance integral. to 1012s), and the blanket structural material The recommended values for these parameters are (Nbl’%Zr, V20’%Ti). The variation of blanket 13.6+ 1.5 b and 125+8 b, respectively; radioact ivit (Ci/Wt or Ci/Wt y), relative biological measurements of the energy dependence of the cap- hazard (km { /Wt ), and nuclear afterheat (fraction of ture cross section are not available. Fortunately, operating power) was investigated. A radioactivity reasonable estimates of the energy dependence can burn-out effect shown in Fig. XIV-13 was be made if the total cross section measurements are demonstrated for the Nbl%Zr RTPR, whereby taken into account. This measurement, from which higher wall loadings lead to higher short-term the capture cross section up to 50 eV can be inferred, radioactivity and lower long-term radioactivity. A revealed a large resonance at 11.6 eV and a much comparison was made with other fusion reactor smaller one at 22.6 eV, The recommended resonance designs as well as with a typical fast fission reactor. parameters account for 90+9 b of the 125 b capture Figure XIV-14 presents a summary of the relative resonance integral. The plausible assumption can biological hazard for several fusion reactor designs, therefore be made that the remaining 35+12 b as a function of shutdown time. Also shown are the results from resonances above 50 eV. fission product and actinide (plutonium) curves for a To determine the effect of the unknown distribu- typical fast breeder fission reactor. Figure XIV-15 tion of resonances (above 50 eV) on the 94Nb capture shows analogous curves for total afterheat power as a rate, the neutron energy spectrum has been examin- fraction of operating power. ed. In the region (below 100 keV), where most cap- Although calculations showed that 95Nb (tl/z=35 tures occur, the spectrum in the RTPR (and most d) is a major source of afterheat in the RTPR, uncer- other fusion reactor blankets) follows a l/E shape tainties in the cross section for the reaction glNb down to rather low energies (typically 1-100 eV). At (n,~) 5Nb may introduce large errors in the lower energies, absorption becomes increasingly im- calculated afterheat. This source of uncertainty has portant and the spectrum becomes increasingly been examined in further detail.35 depleted relative to the pure l/E spectrum used to

180 TABLE XIV-V

REFERENCE BLANKET CONFIGURATION AND PERFORMANCE

Inner Radius Outer Radius &23&2!l (m) (m) Material Plasma Chamber 0.0 0.100 Vacuum

coil 0.100 0.115 No, 30 vjo He

Tritium Breeding 0.115 0.415 7Li (99 a/o), 25 v/o He

233~, Clm = 21.$, 25 V/o He Inner Enriched Seed 0.415 0.665 10 aio

233~, Clm = 214, 25 v~o ‘e Outer Enriched Seed 0.665 0.865 4 alo

Fertile Seed 0.865 1.215 cl 232Th = 214, 25 v/o He

PERFORMANCE CHARACTERISTICS

[BR] = 1.35

[CV] = 0.233 (including leakage)

E = 413.5 MeV/n

E + E* = 454.4 MeV/n 232Tn (n,Nn) = 0.0087jDT neutrOn

12~ = 18.2 kglm _18 E/Iz, = 3.64 x 10 MJ/kg per nfm

(E+ E*)/Iz3 = 4.00 X 10-18 FfJ/kg per nfm

233U production at 1 MW/m2 wall loadingl’f R = 0.72 (kg/my) [

i- 1 MN/m2 of 14.1-MeV neucsc=c

form resonance integrals. Hence, itisclear that the previously. 34 A wall 10a&ng of 2.0 MW/m2 was 94Nb capture rate will be minimized ifthe available assumed, and the reactor operating time was either resonance integral is concentrated in low energy 5,200r50y. The longer operating times arerelevant resonances. On the other hand it is entirely possible to Nb recycle studies. The results of these that the major resonances are concentrated above calculations for the three operating times are given 200eV, where the spectrum isnot severely depleted. in Tables XIV-VI through XIV-VIII, respectively. From these considerations, hypothetical cross sec- All data are calculated at time of shutdown, and tion shapes were constructed, which tend to results are shown for each of the three cross section minimize or maximize the capture rate, while main- shapes discussed above. Shown for comparison are taining a35bresonance integral above50 eV. the.results of a calculation using the 94Nbca ture cross section assumed inRef. 34 (15 times the &Nb . Low Capture: at(E) is assumed to be dominated capture cross section at all neutron energies). From above 50eVby a single resonance at 55 eV. the results shown in Tables XIV-W through XlV- VIII, the distribution effect should produce errorsno . Medium Capture: CT=(E) is assumed to have a I/v greaterthan about 25% in RTPRafterheat and long- shape from 50 eV to several MeV. term radioactivity calculations.

High Capture: a,(E) is assumed to bezerofrom50 2. RTPR Blanket Nucleonic Studies. Studies eV to 200 eV, with a lIv shape above that region. have continued on alternative materials and blanket thicknesses for the RTPR. Table XIV-IX illustrates To illustrate the sensitivity ofRTPR afterheat and a typical parameter study performed for the post- activity results to this effect, the total afterheat at design assessment. Because of the large energy time ofshutdown was calculated, as well asthe total storage and transfer requirements of the RTPR a 94Nb activity, using the method described

181 .

.

CMwm!- x-l I

Fig. XIV-12 Cfmceptual illustration of a LTPHR blanket module.

strong incentive exists for minimizing blanket mm and 1.2% per mm of reduction in blanket thickness. To a first approximation, as the blanket is thickness, which does not impose serious limitations thinned, the increased (radiation induced) waste on reduction in blanket thickness. Rather, the ul- heat in the coils is equal to the decreased recoverable timate reversal of tritium breeding ratio with heat in the blanket. Tritium breeding has been decreasing blanket thickness limits the minimum shown previously to be easily maintained at a value blanket volume and hence the amount of stored >1.0 by adjusting the beryllium region thickness. magnetic energy. The recoverable and waste energies will both in- Other neutronics studies concentrated primarily crease with increased beryllium thickness; e.g., a 10 on a review and revision of source data used for the mm increase in beryllium thickness provides a 1.1- calculation of appropriate response functions. Table MeV increase in recoverable energy per D-T neutron XIV-X summarizes the dpa values using two alter- and a 0.07 increase in tritium breeding ratio. Radia- native displacement functions. Included are results tion heating in the coil varies linearly with small (20 for two neutron spectra, based on niobium or mm) changes in graphite thickness for a niobium molybdenum structures. In each case dpa values structure. However, for molybdenum structures were determined for three candidate structural large changes of the graphite region were considered, materials (Nb, Mo, and V); i.e., it is implicitly and the effects were nonlinear (cf. Table XIV-IX). assumed that the response is weakly dependent on . In general, application of perturbation theory by the spectrum variation, an assumption which has Gerst 136 to moderate (10 to 20 mm) changes in been verified. beryllium and lithium regions of the RTPR, and to Analysis of transmutation and dpa in beryllium, . substitution of structural materials, has proven graphite, and copper also reveals differences successful. between molybdenum and niobium structures. A In further analysis it has been found that the out- slight increase in transmutation rates generally board graphite region in a molybdenum RTPR results from using molybdenum because of the in- blanket can be reduced in thickness by at least 60 creased (n,2n) neutron production. Tritium mm, while maintaining an adequate breeding ratio. breeding, however, is lower for a molybdenum struc- Over the range of O to 50 mm reduction in graphite, ture because of increased low energy neutron capture the parasitic absorption and (n,2n) reaction rates in (0.530 for Mo vs 0.378 for Nb), especially in the the coils increase approximately linearly at 1.070 per graphite regions. Sensitivity studies have shown that

182 I ,rcmobu “b.,,..(0,,,..0 ,,”WI.4 \\--\ !00=””””2-=-m

\

+-’—-===>,.ly ,. my Coay 8 100 102 104 106 1( do 10” [myTime After Shutdown, t. [s) i

Fig. XIV-14 [ntercomparison of BHP for various fusion and fission reactor concepts: (a) Ref. 26. (b) Ref. 27, (c) Refs. 28 and 29, and (d) Ref. 30.

and of Behrisch.41 The Kaminsky and Das 14 MeV sputtering coefficient of 0.25 atomslneutron would lead to rapid ( -0.27 mm/y) destruction of 1 mm niobium walls, while the alternative coefficient

TotalThermal Energy Generated, PnT [GWt-y) presents acceptably small ( - 10%) erosion over an estimated 5-y maximum wall lifetime. Hence, no definitive conclusions can be drawn regarding the effect of 14 MeV neutron sputtering until further ex- Fig. XIV- 13 perimental evidence establishes confirmed and .Dc’pendence of a{Ci[ W(th) yr] } on PTHT repeatable sputtering coefficient values* [(7 W(th) yr)] for various values of t,.

3. Resonance Self-Shielding in 93Nb. A decreasing the outboard graphite thickness, and formalism to account for resonance self-shielding hence total blanket thickness, by up to 60 mm effects, the f-factor method, has been applied to the increases tritium breeding ratio in a molybdenum RTPR.42143 For a given material, the group self- structure RTPR by -0.1% per mm of reduction. shielding factor, f, is defined as the ratio of the Similar studies for niobium show the opposite effect, resonance-shielded cross section to that for infinite because of the more predominant epithermal cap- dilution. Formally, f is a function of all the . ture in niobium resonances. parameters (temperature, atom density, and Prediction of first-wall surface effects is com- resonance parameters), which define the total plicated by two factors. First, the inner niobium sur- macroscopic cross section of the mixture. However, face is really the interface of a composite alumina- in practice the f-factors are specified as a function of niobium structure, so the neutron sputtering or temperature, T, and a single parameter, Uo, which chunk injection effect is uncertain at this surface. represents a conglomerate effect of the remaining Secondly, and perhaps more important, is the large parameters of the mixture. In essence the f-factors range of uncertainty in 14 NleV neutron sputtering are used to account for flux depression in the vicinity coefficients. To illustrate the range of values and of large resonances. their effect on erosion rates of. the 1 mm niobium portion of the first wall, sputtering rates were com- *The uncertainty in neutron sputtering coefficients puted using the coefficients of Kaminsky and Das40 is discussed further in Sec. VfII.F.2.c.

183 101 1 I 1 .

8 RTPR (Nb-lZr, T=5y, Iw=2.0MW/m2 ) Tokomak(b)[ Nb- I Zr, T=lOy, Iw=LOMW/m7 I - ~ 0. Tokamok(’)(Nb-l Zr, T=IO y, IWS1.1MW/m2 )- c .- Tokomok(d)lNb-l Zr, T=IO y, IW=I.25 MW/m2) I : —-—- —-—. -—- —-— --- . $

—-_ ___ 8 ~ x

1! 10-4 z a“o & RTPR (C. coils, T=5y, Iw= 2.0 MWhn2]

10-5 1 1 100 ,0( 102 103 ,04 @ 106 107 Ioa 109 1010 . Time After Shutdown, ts (s)

Fig. XIV- 15

Comparison of nuclear afterheat, P/PO,for the RTPR (Nb-1 TO Zr and V-20Y0 Ti, 1,,~2. O and 6.7 M Wlm2, T=5 yr) with other fusion reactors and fission reactors: (a) Ref. 31, (b) Ref. 32, (c) Ref. 30, and (d) Ref, 29.

One material of special interest in the RTPR 4. TR3A and Other Code blanket is 93Nb, for which the capture cross section Development. Continuing studies of afterheat and exhibits a large number of resonances. Although N b radioactivity have led to modifications to the constitutes a small volume fraction of the blanket, transport code post-processor TR3A. The princ~pal its presence significantly affects the breeding poten- modification was to the equations for 94Nb, 95’90Nb tial, energy deposition, and radioactivity of the radioactivity. Whereas previously the assumed cross blanket. sect ion behavior for 94Nb(n,~) reactions was Gerstl and Henryson44 performed a detailed implicit in the equations, the code now accepts input calculation of the resonance self-shielding in multigroup cross-section data. Modifications to niobium using the MC2-2 code, and ISo values compute biological hazard potentials (BHP) from averaged over the resolved energy region of Nb. input maximum permissible concentrations have Work at LASL employs f-factor tables which have also been made. been generated by the MINX code using ENDFfB- As part of the data assessment program the 111 data. After determining the proper a. in each perturbation-theory code SENSIT has been energy group and the corresponding temperature, modified to accept DTF-IV output and to improve self-shielded multigroup data sets were obtained and several features of the code. For example, both applied in RTPR blanket nucleonic calculations. design sensitivies and cross-section sensitivity The results of the nucleonic calculations are profiles can be computed for simultaneous pertur- . presented in Table XIV-XI. All analyses were per- bations in all spatial regions, and automatic plotting formed using the LASL CTR Nuclear Analysis Com- options have been incorporated. putation System. 21 Table XIV-XI verifies the assumption that resonance self-shielding will in- 5. Fusion/Fission Hybrid Studies with crease tritium breeding ratios by -7°A in the RTPR Z38U/Z39Puo First scoping stUdies45 of a linear bianket. Additionally, niobium self-shielding will theta pinch hybrid considered an LMF13R-blanket decrease blanket radioactivity, as well as total design as a fertile seed within the fusion reactor recoverable energy and magnet-coil heating. The net blanket. The fertile seed region was cooled by liquid recoverable energy decreases by 0.37 MeV and the lithium, which also served to breed tritium. Several coil heating by 0.23 MeV (per D-T neutron) in going studies were made for the ‘8U blanket system. The from the infinite dilution tot he 1100 K, self-shielded requirement of placing the (copper) magnet coil as cross sections. Temperature effects change these close as possible to the plasma seriously degrades the parameters by less than 2%. a024 energy spectrum of the 14.1 -MeV neutrons released

184 “!MSLEXIV-VI

RTPR ACTIVITYANDAFTERHEATAT 5 YEARS

A96/Po A95/Po PIP~ Case (Cilw) (WV) (Percent)

Times fifteen 4.10 x 10-4 1.31 x 10+0 1.18

High capture 4.84 X 10-4 5.67 X 10-1 0.81 -4 Medium capture 4.98 x 10 4.09 x 10-1 0.73 -1 Low Capture 5.12 X 10-4 2.52 x 10 0.65

TAELE XIV-VII

RTPR ACTIVITYANDAFTERREATAT 20 YEARS OUXYCLEl

A9+fP0 A9~/P0 P/P. Case (ci/w) (Cilw) (Percent)

Times fifteen 8.44 X 10-4 2.52 1.80

High capture 1.40 x 10-3 1.61 1.34

Medium capture 1.56 X 10-3 1.26 1.17

Low capture 1.74 x 10-3 0.84 0.95

TAHLE XIV-VIII

RTPR ACTIVITY AND AFTERHEAT AT 50 YEARS (RECYCLE)

A94/P0 A95/P0 P/P~ Caee (Cilw) (ci/w) (P ercent)

Times fifteen 9.53 x 10-4 2.56 1.82

High capture 2.04 x 10-3 2.23 1.66

Medium capture 2.50 x 10-3 1.96 1.52

Low capture 3.13 x 10-3 1.47 1.27

. in the D-T reactions. Forcoils ofapproximately 5cm Renewed studies of a LTPHR, employing the thickness, the neutron energy spectrum emerging 238U/x~uc clehave evolved from experience with x from the coil has been softened considerably, reduc- the232Th/23 Ucycledesign (Sec. XIV.c.2). Blanket . ing the probability of fast fissioning in 238U and of designs now consider much thinner coils made of 7~i(n,n,a)T reaCtiOn; the both reactions are molybdenum alloys, followed by a depleted 238U important for neutron economy in that the 238U multiplier (fast-fission) region. The fertile seed is fission reaction multiplies neutrons and the 7 Li also lithium cooled, but now uses carbide fuel reaction produces tritons without the loss of a technology being developed in the fission program, neutron. Alternatives of increasing 239Pu and 6Li in the form of 238UC or 232ThC. No fissile (e.g., enrichments are possible, but not as desirable. 23~u) loading of either multiplier or breeding por- Tritium breeding ratios greater than unity arepossi- tions of the seed is contemplated, except for the nor- blefor this system, but only for blankets which use mal equilibrium fissile content caused by breeding 239pu . fertile seedsenriched in during the fuel element lifetime.

185 TABLEXIV-IX .

EFFECTOF GRAPHITETHICXNESSON TIUTIUMBREEDING,COIL HEATING, ANDCOIL TRANSMUTATIONIN THE RTPR . coil(c) Graphit% Heating cll(tl,211) ‘c) Cu(n,y) T(a) ‘c) Structure ~. (% change) (% change) (% change) ~(b) 0.1474 1.108 — —- —-

0.1374 1.106 9 10 9

0.1274 1.105 18 20 18

Mo 0.1474 0.924 — -— —-

0.1274 0.943 20 22 19

0.1074 0.961 42 50 40

0.0874 0.979 69 83 66

(a) Including an estimated correction of 0.07 for resonance self-shieldinz. (b) RTPR reference design case, for which waste heat (>99% in the coild and insulation) is 0.80 MN/m and recoverable heat is 9.6 MW/m. (c) Relative to 0.1474-m thickness.

TA8LE XIV-X

MAXIMUM ATOM DISPLACEMENTRATES AT FIRST WALL METAL AND IN GRAPHITE

(lW = 2.0 MW/m2)

Structural 0 TOT I$(E> lMeV) Material” Response Rsdtus Original(a) Revised(a) -2s-1 -2s-1 (Spectrum) Material Location L (dpa/y) (dpafy) Nb Nb First Wall 0.500 36.2 18.2 9.:2 x 10’8 3:5 x 10’8 Nb Mo First Wall 0.500 36.7 17.5 9.02 x 1018 3.95 x 1018 Nb v First Wall 0.500 54.7 26.0 9.02 x 1018 3.95 x 1018 Nb c Inner Graphite 0.605 -. 11.7 6.13 x 1018 1.72 x 1018 . Mo Nb First Wall 0.500 36.9 18.6 9.40 x 1018 4.06 x 1018 MO Ffo First Wall 0.500 37.5 17.8 9.40 x 1018 4.06 x 1018 Mo v Firat Wall 0.500 56.0 26.6 9.40 x 1018 4.06 x 1018 MO c Inner Graphite 0.605 6.39 12.0 6.35 x 1018 1.76 x 1018

(a) The original calculations were performed with response functions for V, Nb, and Mo as given by Ref. 37, and for C as given by Ref. 38. Revised valuea are from Refs. 39 and 40, respectively, and are currently considered to be the best available values for the reference design.

186 .

?-( .

C-4 l-i . r-l 2 2 0 G

w u ?-l l-i r-(

0

. -t C-4 0 14 .

I I

187 E. Nuclear Data and Sensitivity Analysis In Eq. (1) Xi is the cross section for a particular nuclear reaction at a particular neutron energy. . The effort to provide reliable nuclear data for the Cov(x,Xj) are the covariance matrix elements for CTR program concentrated on the assessment of cross sections Xi and XJ and contain the estimated

near-term nuclear data needs and expansion of the errors, together with correlations, of existing cross- ● LASL/CTR multigroup data library. section sets. The quantities ilR/tlXi in Eq. (1) are sensitivity coefficients which result from a sensitivi- 1. Assessment of CTR Cross Section ty analysis of the particular transport problem of Needs. To coordinate with other laboratory int crest. 48-50 programs, active participation has been maintained To illustrate results expected from this data in the CTR Subcommittee of the U.S. Nuclear Data assessment program, the methods outlined above Committee, in the ASTM Neutron Dosimetry Stan- were applied to the neutronics evaluation of the dards Committee, and in the Cross Section Evalua- proposed TFTR. 46 As a critical design parameter we t ion Working Group. Critical reviews of CTR-related selected the production of the 5.3-y half-life cobalt- nuclear data have been made, including cross sec- 60 isotope from the GsCu(n,a)60Co reactions in the tions for the D-T and T-T fusion reactions. Also, in- copper coils was selected. The TFTR coils are shield- put was provided to the national nuclear data re- ed by a magnet shield consisting of commercial lead- quest list for new cross section measurements and loaded berated polyethylene. The effectiveness of evaluations required for CTR applications. this shield against high energy neutrons is derived Work has begun on a program to determine quan- largely from its hydrogen (2 wfo) and carbon con- titatively the cross-section requirements and highest tents (17 w/o). Therefore, it seemed appropriate for priority areas for near-term nuclear data research the sample case to evaluate the sensitivity of the and development for the national CTR program. ~o production in the coils to the carbon cross sec- This assessment takes into account the quality of tions of the magnet shield. currently available data, the sensitivity of important The estimated uncertainties in the carbon cross nuclear design parameters to these nuclear data, and sections for the TFTR shield, 47 together with the accuracy required in CTR design applications. calculated sensitivity coefficients, gave rise to the & The computational system used to perform these uncertainty of the Co production calculation as analyses employs forward and adjoint transport shown in Table XIV-XIII. The overall uncertainty of calculations to calculate sensitivities, and constructs 2.1% indicates that for this specific application the covariance matrices from ENDF/B error files or accuracy of the carbon cross sections is adequate. other sources. A perturbation theory code combines To calculate sensitivity coefficients for secondary the sensitivity information with the covariance energy distributions, an extension of the usual per- matrices to obtain the uncertainties of calculated turbation approach has been developed. The main nuclear design parameters, which are then the quan- feature of this method is the introduction of a “sub- titative basis for a judgment on the adequacy of partial” reaction cross section 6, which corresponds cross sections. The capabilities of this approach were only to those events yielding high-energy secondary demonstrated with a sample calculation for the neutrons. The sensitivity coefficient for 6 is TFTR* design. 46 Subsequently, in close cooperation calculated by an algorithm which allows the effect of wit h Princeton Plasma Physics Laboratory and uncertainty in the spectrum to be separated from Westinghouse Research Laboratory, a more detailed uncertainty in the magnitude of the energy- assessment of nuclear data requirements for the integrated cross section. One important application TFTR design has been initiated. of this method is to provide a quantitative basis for the assignment of priorities to measurements of An appropriate tool for studies of this type is per- . turbation theory. In this approximation, the stan- neutron emission spectra. dard deviation AR in a design parameter R can be written as follows:47 2. The LASL/CTR Multigroup Library. One- . hundred group neutron interact ion cross sect ions have been prepared for vanadium and the results placed in the LASL/CTR processed nuclear data (1) library described in Ref. 51. These cross sections were obtained by processing the ENDF/B-lV evalua- tion using the processing code MIINX.51 A multigroup data set for the analysis of fusion-fission hybrid reactors based on the 238U cycle has been *Tokamak Fusion Test Reactor, formerly Two Com- ponent Tokamak (TCT).

188 TABLE XIV-XII

* 12 ESTIMATED UNCERTAINTIES 6E/.Z FOR C CROSS SECTIONS IN TFTR MAGNET SHIELD . Cross Section Neutron Energy Type 5t09MeV 9 to 15 MeV

ZT 0.03 0.04

E 0.15 0.15 Abs .

z 0.05 0.15 Scat.

TAELE XIV-XIII

PRRDICTED UNCERTAINTY OF 6oCo-PRODUCTION IN TFTR COILS DUE TO CROSS SECTION UNCERTAINTIES SHOWN IN TAELE XIV-XIII

m 6R x x E R x

Total 0.0059 overall uncertainty [ Abs . 9.0022 !2.9211assuming ..- .-. relations Scat. 0.020 (between individual cross sections.

prepared. A25-group structure was formed asasub- 4. Cross-Section Library Utility Codes. set of both the LASL/CTR and LASL/TD mul- Because of storage and running time requirements tigroup structures. A second group-collapsed data of various codes used in CTR nucleonic studies, con- set was produced for the analysis of fusion-fission ventional P3, 100-neutron group, 21-photon group (hybrid) reactors based onthe 232Th.’233U cycle in a libraries used in previous studies are not always graphite lattice (thermal hybrids) .This library con- practical. To reduce the number of neutron energy sists of data in a 19-group format, including 3 up- groups, an existing LASL collapsing code was scatter groups. The previously reported portion of modified to additionally collapse neutron portions of the multigroup library containing activation and photon-production matrices. At the option of the transmutation cross sections has been revised and us.e~, the 100-groups can be collapsed into subsets of . expanded. Resulting multigroup data (for 687 dis- any number (< 100) and coupled neutron-gamma tinct nuclearreactions) areavailableona BCD card- cross-section sets formed. image tape for external distribution. F. Insulator Studies . 3. Cross Sections for Insulator Research. Spectrum-averaged transmutation cross sections Emphasis was placed on problems associated with have been calculated for Be, N,O,Al, and Siusing the first-wall liner of the RTPR; however, informa- thedata in the multigroup library described above. tion from these studies is also applicable to other in- These data allow predictions of the build-up ofgas- sulator uses in fusion reactors. eous and metallic impurities in electrical insulators Experimental work was directed toward evalua- such as BeO, Si3Nl, SiOz, AIN, andAl~03. tion of electrical and structural behavior of in- sulators at elevated temperatures and under irradia -

189 tion. Damage simulation experiments for 14 MeV neutron were also conducted. Calculations on . sputtering, transmutation product generation rates, and ionization effects on resistivity were carried out. Dielectric strength of insulator-coated . metal segments for possible use as an SFTR first wall was evaluated, and calculations made of an- ticipated water resorption from the SFTR first wall. Finally, a stockpile of ceramic materials for use by LASL and other CTR insulator laboratories was begun. 1. Electrical Properties Experiments

a. DC and Pulsed Voltage Dielectric Strength of Insulators at Elevated Temperatures. The Pdxrmtoku A120, N:’”’ 0’ 100 COOISAD 995 % insulating liner of the RTPR must withstand a puls- 1 \ / . S**al wow ekfrode \.\ ed voltage of 3 KV over a thickness of 0.3 mm (i.e., 0 Mamfachrer% dol. , I I , I 100 kV/cm) at 800-1100 K. Measurements of the 300 Sm 700 900 1100 dielectric strength of a high-density polycrystalline Temp (K) A120,1 as a function of temperature show that pulsed-voltage dielectric strength was much greater Fig. XIV- 16 than that measured with dc voltage at elevated Pulsed dielectric strength of alumina as a func- temperatures. The effect of electrode geometry has tion of temperature. since been studied using diffuse-edge electrodes. This technique gives greater field uniformity than did measurements with point-contract electrodes used previously, and should more closely simulate breakdown conditions in fusion devices. Results ob- Polycrystolline A1203 tained are shown in Fig. XIV-16; a significant in- Coors AD 995 crease in dielectric strength is realized with a Temp=973K diffuse-edge electrode. Sample thickness =0.3m An important variable in pulsed-voltage dielectric-strength measurements is the time re- quired for electrical breakdown. This variable has been investigated experimentally for a vitreous o enamel glass at 873 K and compared with theoretical 0 breakdown models. Results obtained agree qualitatively with theory, in that the voltage vs time-to-breakdown curve shows the predicted shape in Fig. XIV-17. The results shown in this figure for AIzO:I at 973 K are explainable by assuming that Vitreous Enomel Glass CIsicogo Vitrmua Enombl Co. characteristic breakdown times for this insulator are ~ #SL- 13290 B much longer than those for the enamel. Since the T.smp= 873K voltage induced during the implosion heating in a Sompla thickness= 0.9mm . theta pinch will appear across the first wall insulator for less than one psec, the higher dielectric strengths of Fig. XIV-17 should be applicable to the RTPR. . Earlier results on the dielectric strengths at 300 K + and 873 K have been reported, for a number of in- I I I II I sulators known to contain some porosity. The porosi- 4 8 12 16 ty is an important parameter, since high porosity Applied Voltage (kV) can reduce breakdown strength. Work in this area has continued and more recent results are shown in Fig. XIV- 17 Table XIV-XIV. Although the data are too sparse to Time to breakdou!n us applied voltage for permit detailed conclusions, the following in- alumina and vitreous enamel. dicat ions seem evident: for porous materials little or

190 TASLS XIV-XIV . DIELECTRICSTRSNGTSOF INSULATOR/NSTAL AND INSULATOR SAMPLES

Temperature, Dielectric Strength, kVlmmb Density, Z s Insulator” R dc Pulsed of Theoretical Remarks InsulatorlHetaF Samples 300 28 30 85 IU203 plasma sprayed (LASL) 873 11 9

A2~o, 300 .- 32 82 plasma sprayed 873 20 (Plasmadyne)

300 25 32 — plasma sprayed (LASL) 873 -7 21

Ensmeld 300 27 -- 0.8 mn thick LASL 300 23 23 (lAL) 873 6 17 -- 0.9 m thick(LASL)

Insulator Samples

AIN 200 5 5 77 hot-pressed (NRC) 873 12 13

300 20 25 54 hot-pressed (FfRC) 873 12 16

Si20N2 873 -2 10 96 hot-pressed (Norton)

22 25 92 x~os-loz Tho~ 300 hot-pressed (LASL) 873 13 15

Y*O, 300 24 29 94 slip cast and sintered 873 -5 10 (LASL)

~Insulator thickne:: ‘.? n.5 mm, unless -*&--.-~s- spccif fed. c Spherical upper electrode. Metal aubstratss were austenitic stainless steel, Inconel, or Nb-1% Zr, -1 mm thick; no effect of substrate composition on dielectric strength was observed. d Chicago Vitreous Enamel Co. #SL-13290 B, applied by coating and firing.

no enhancement of dielectric strength with pulsed In these proton irradiation tests, SCB* glass voltages is apparent, perhaps because breakdown is (modified frit No. 1, of barium-aluminum-silicate initiated in the pore gas on a time scale short com- composition) was irradiated. The incident protons pared with that for bulk thermal breakdown. Hence passed through the 6X 10’3 cm thick glass, losing 1 the dielectric stremgth for a porous material is lower MeV to the specimen; the transmitted proton beam than that for the same material near theoretical den- subsequently embedded in the bonding metal sub- sity. st rate. The 1.5 MA/cm2 proton beam current gave a damage rate equivalent to that from an RTPR first- b. Resistivity of Proton-Irradiated Glass. The wall neutron flux of -1014 n/crn2 s. Ionizing RTPR first-wall insulator must exhibit a resistivity radiation was absorbed at a rate of -107 rad/s. By >1oG \]-cm at 1073 K within 3-10 s, after irradiation comparison the ionizing radiation at the RTPR first by neutrons, charged particles, and photons (i.e., at wall during a pulse is estimated to be -4x 108 rad/s. 1 . the start of the next burn pulse). Preliminary Typical results obtained are shown in Fig. XIV-18. measurements have been made of the effect of 6 During the first minute of irradiation, the glass ex- MeV proton irradiation on electrical resistivity of a hibited a resistivity decrease of a factor of three; lit- . glass insulator at this temperature; for protons (6 tle additional change was noted during the MeV), both displacement damage and ionization remainder of the 5-m bombardment. After irradia- damage resulted. Irradiation-produced defects are tion the SCB glass recovered its initial resistivity in expected to decrease electronic conductivity, since roughly 1-m. they can serve as charge traps. However, enhanced If the degradation of resistivity is assumed to have ionic conductivity can result from displacements. an electronic nature and to be a linear function of Ionizing damage should increase conductivity by creating electron or hole charge carriers. *SCB is a designation of special glass originally developed as a hydrogen permeation barrier.

191 were aligned, as shown in Fig. XIV-19 (Coors All I I 1 1 1 1 1 .—. .—— —... .--. — . 999). Analysis of this photomicrograph shows the .Beam on average pore diameter to be -35A and pore density to be -5x1017/cm3 (assuming the foil thickness to be 1000~). From these rough values a swelling of E 1.1”6 can be calculated, which is in reasonable agree- x ment with the macroscopic value of 2.0~1 measured :108 .- SCB gloss, frlt No.I for the sample as a whole. No pores were seen in .-> T = 1073 K AIzO,J irradiated at 723 K (0.31 T~). % 6 + 5 MeV protons, .G The AlzO:j pore orientation was determined in al 107 n<1.5 x 10-GA/cmz u another foil by comparison of the photomicrograph -1 with a corresponding electron diffraction pattern. 106////////////////RTPR desian resistivity/////// Pore alignment was found to be parallel to the c-axis [0001] of the hexagonal structure, with the [ 1010] I I I t t t 1 1 I o I 2 34 5 6 direction in the plane of the foil. Time (rein) Irradiation-induced pores were occasionally seen in Yz03 (Fig. XIV-20) as were “black spot” defects (unresolved damage) and dislocation loops (Fig. Fig. XIV- 18 XIV-21). However, structural damage in the Y“fls Effect of 5 A4eV proton irradiation on the elec- samples is not so severe as that in A1Y03, consistent trical resistil~ity of SCB glass insulators. with the low macroscopic swelling values observed for Yz Os. The good stability of YY03 under irradiation may result from its defect structure. This ionizing flux, the resist ivity of this glass during ceramic has a stable array of vacancies in the oxygen irradiation at the RTPR first wall would be -107 fl - sublattice which may reduce pore formation by cm. The resist ivity, therefore, would never be enhancing the recombination of irradiation-induced degraded to the minimum acceptable value of 10%2- vacancies and interstitials. cm. The subsequent 10-s anneal would of course im- prove the resistivity before the next power cycle. b. Fission Neutron Irradiation Studies of 2. Structural Properties Experiments Ceramics and Glasses. A new EBR-11 irradiation experiment is planned and will encompass a large a. Fission Neutron Damage to A 1203 and Y203 number of CTR candidate ceramics, glasses, and in- A major problem for fusion reactor insulators will sulator/metal composites. Samples will be irradiated be radiation-induced swelling. Transmission elec- at 923 K and 1073 K at a flux roughly equivalent in tron microscopy was used to evaluate the damage calculated dpa to that expected at the RTPR first structures of some potential first wall insulators wall. Fluence will be comparable to a one year ex- after fission reactor irradiation at elevated posure at the RTPR first wall. After irradiation, temperatures. AlzOrj in three forms, Y2.Os, and YzOs, samples will be evaluated for defect content, dimen- and Yz Os - 10% ZrO~ were irradiation at 723K, 873K, sional changes, dielectric strength, thermal conduc- and 1023K in EBR-11 to fluences of 3 to 6X1021 tivity, and interdiffusion effects with metal sub- n/cm2 (E”>O.1 MeV. )* strates. The experiment has received “Approval in Principle” from the Division of Reactor Research Macroscopic measurements showed that all three and Development, (ERA), and samples and irradia- forms of A1203 (polycrystalline Lucalox, tion capsules are being fabricated. polycrystalline Coors AD 999, and monocrystalline . TECO) swelled significantly (1 to 2%) after irradia- t ion at 1023 K, while Y203 and YzOS-1OTO Zro 2 c. Evaluation of Chunk Sputtering from 14 McV actually densified slightly. This densification may Neutron-Irradiated A 1203. After it became known” . have resulted from sintering during the reactor ex- from the work of Kaminsky41’58 that some materials posure. Examination by transmission electron suffer gross sputtering (removal of -10 ~m chunks) microscopy revealed a high density of irradiation- under 14 MeV neutron bombardment, a single- induced pores in all Alz03 specimens irradiated at crystal Alz 03 sample used in optical absorption 873 K (0.38T~) and 1023 K (0.44T~). These pores studies was examined for such effects. This sample had been irradiated to -1017 n/cm2 with 14 MeV *Irradiations were conducted as part of another neutrons in room-temperature air. If chunk-type LASL project.52 sputtering had occurred, the resultant holes left in

192 .’ .,-. .~ + ‘1.-*: Fig. XIV- 19 #

A It():{

%)o,omx.

Fig. XIV-20

Y~():{-lO’ f Zr(lj 1.20,000X.

. # Fig. XIV-21 . Yj (1:$

1(-)0.000X.

193 either front or rear surfaces should have been readily I I I I I . identified by the replica electron microscopy ,VF!sslon neutrons ( Levy] ~ technique used (resolution x 150~). No evidence of , , I-5 X1017 nkmz. EII>OIMeV) 0 II - 120 ; any surface damage was found, even though the (i & . f 1 M Mev e.lfons % neutron fluence was -20 times that utilized by (- IxK311 n/cm2) ~ 1’1 Kaminsky. 42@ Kaminsky has shown that the II ‘E amount of chunk sputtering can be greatly reduced ~ by polishing and annealing samples before bombard- z eo: ment and has postulated that internal strain is I“c,ocnl tI MeV pfo?om .- released by 14 MeV neutron bombardment, (AE . lMeV) 5 resulting in chunk emission. Since single-crystal v c A120J should have a low internal strain content, the .-0 Inc ,dcnt 5 MeV pro!LuM z negative results for sapphire may be explainable by A- ‘ the same model. Generally, the nature of chunk sputtering is still in doubt; recent work by Thomas and Harling 54 failed to repeat the results of Kaminsky.

; ~+.” ~ 3. 14 MeV Neutron Damage Simulation I O( ? 5 4 Experiments Photon Energy (eV]

a. 14 Me V Neutron and High-Energy Proton Fig. XIV-22 Damage in Single-Crystal A1203. Insulators in Optical absorption spectra for neutron and fusion reactors will be irradiated with neutrons at proton irradiated sapphire (alumina). energies up to 14 MeV. However, intense sources of 14 MeV neutrons are not available, so that fusion irradiation studies must be conducted with other damaging particles. Low-level damage from 14 MeV neutrons in single-crystal A1z03 have been compared b. Simulation of 14 MeV Neutron Damage with with that from 5 MeV protons, 15 MeV protons, and Heavy Ions. Although -15 MeV protons appear to fission neutrons, to determine whether damage from produce damage which closely simulates that protons and fission neutrons can simulate that from produced by 14 MeV neutrons, it is difficult to fusion neutrons. The fission neutron results were ob- achieve proton fluences from available electrostatic tained by Levy. 55 accelerators high enough to produce in a short time Damage was evaluated by measurement of structural damage equivalent to that from -1 y ex- irradiation-induced optical absorption. This posure of the RTPR first wall. Irradiation with high technique is sensitive to low levels of damage, energy heavy ions (He, Li, B, O, N, etc. ) in theory differentiates bet ween different kinds of defects, and would produce 100 to 1000 times more damage per gives information primarily on isolated point defects incident particle; this approach is being explored for which are expected to contribute to electrical effects. generating higher levels of damage. Two difficulties Results obtained are given in Figs. XIV-22 and with this technique are: XIV-23. Figure XIV-22 shows the room temperature

as-damaged optical absorption spectra, while Fig. (a) possible differences from neutrons (or high- XIV-23 presents the isochronal annealing curves for energy protons) in details of the damage produced; the three principle absorption peaks. The shapes of and (b) the small penetration depths of heavy ions, the damage spectra show that fission neutrons and leading to inhomogeneous damage and difficulties in 15 MeV protons can simulate 14 MeV neutron interpret ing experimental results in the case of elec- damage accurately, whereas incident 5 MeV protons trical effects. are not simulated as successfully. The same con- elusions can be drawn from evaluation of the anneal- Calculations of heavy ion penetration depths and ing curves. These findings are consistent with the damage production have been carried out, and theoretical prediction by Logan56 that for a niobium development of the necessary experimental techni- target 16 MeV protons should simulate 14 MeV ques has begun. neutrons. Calculations are being made for low-Z targets, such as A1203 to support experimental studies.

194 The calculational results are shown in Table XIV- 6.02 eV peak XV. Wall thinning by ion sputtering is very much 80 - dependent on particle energy, with serious erosion \ \ predicted if ion temperatures are near those of the \ 60 – \ plasma. However, if the neutral gas blanket reduces \ \ \ these energies significantly, wall thinning will not be 40 - ~. -.. a problem. Sputtering by neutrons will be low, un- <. less chunk sputtering by highest-energy neutrons oc- 20 – curs. For the latter case thinning will be a serious problem. It should be noted that these calculations address only physical sputtering, and do not include ----14 MeV neutrons the effect of a distribution of ion energies. — F@on neutrons (Levy) 80 - “” “ “ Incident 15 MeV protons b. Transmutation Rates of Insulator Elements. ‘~, –.-Incident 5 MeV protons - Knowledge of the rate at which insulator elements 60 - transmute under neutron bombardment to other elements is important to an understanding of in- 40 – peak sulator behavior in fusion reactors. Gaseous transmutation products can enhance swelling and 20 - ‘-. degrade electrical properties, while metallic o I I I products can alter both structural and electrical I I I I I I I I behavior. The generation rates of neutron-induced 4.85 eV peak transmutation products in typical insulators at the first wall of the RTPR were computed (Sec. VIII. E). Calculated results are given in Table XVI, and for 6 o– most isotopes both gaseous and metallic transmuta- tion products are generated at the rate of about 500 4 o– to 2000 appm/y. Exceptions are ‘Be, which shows a high helium generation rate, and 15N, which 2 o– transmutes at a low rate. These results indicate that --- I I I -1 low-Z elements transmute relatively rapidly, and 0 1 L 400 600 1o:o- point to the importance of experimental studies to Temperature (K) determine the effect of these impurities on insulator performance.

Fig. XIV-23 c. Effect of Ionizing Radiation on the RTPR First- Isochronal annealing curves for proton and Wall Insulator. During a thermonuclear bum the neutron irradiated sapphire (alumina). first wall insulator will absorb bulk ionizing radia- tion (bremsstrahlung), neutron-induced gamma 4. Calculations on Radiation Effects rays), and the electrical conductivity will be in- creased. Concurrent displacement damage will . a. Physical Sputtering of the RTPR First Wall probably reduce the conductivity, since defects can Insulator. A potential problem for the RTPR first- serve as traps for these charge carriers. Preliminary wall insulator is physical sputtering by D, T, He, calculations have been made57 of conductivity and neutrons. Preliminary calculations on wall thin- during irradiation at first-wall dose rate of -4x 108 ning by sputtering have been made, assuming rad/s. Displacement damage effects were neglected. different particle energies for monoenergetic im- The resulting resistivity of -107 fl-cm, is above the pinging ions (i.e., different efficiencies of the gas minimum acceptable value of 106 Q-cm at the start blanket in degrading particle energies). Ion sputter- of a burn. Furthermore, the 10 s annealing time ing yields were taken from the literature and are not between one pulse and the start of the next should greatly dependent on target material. Yields for result in significant recovery of the resistivity. neutron sputtering are not well known, and so three calculations were made, each using different values whichhavebeenreported.

195 TABLE XIV-XV

Sputtering Yield Thinninga Particle !Z!SE8Y (atoms/ion) (mmlyr) -2 D,T 3 keV 10 0.5 -4 0.2 keV 10 5 x 10-3

He 4 keV 10:: 0.1 0.3 keV 10 10-2

b Neutrons 1st wall spectrum 5 x 10-2 0.3 1st wall spectrum 10-2 6 X 10:: 1st wall spectrum IO-4 6x10

ainitial insulator thickness = 0.3 mm b assuming that 20% of the neutrons cause chunk sputtering with x = 0.2, and 80% cause atom-by-atom sputtering with x = 10-2

TA8LE XIV-XVI

TRANSMUTATION RATES (IN APPM/YR) OF SOME INSULATOR ISOTOPES AT THE FIRST WALL OF THE RTPR

Transmutation Products c 14C Isotope He H — — total . —.Al Li __ B N _Si x 2]U 852 1881 57 2078 160 2240 373 2240 111

Si (natural) 1599 2254 541 1271 14N 1322 1183 1220 638 1322 15N 162 359 308 108 34 9 Be 10,328 400 442

5. SFTRFirst-Wall Insulator Studies enamel glasses and plasma-spray edA120:l. Detailed . results have been reported elsewhere. 58 The tindings a. Dielectric Strength of Composite can be summarized as follows: Insulator/i14etaiDischargeTubes. Onedesignofthe . SFTR first wall envisages an assembly ofinsulator- (1) Dielectric strength of theinsulators when free of coated metal trapezoids stacked into a cylindrical flaws is high. discharge tube. These trapezoids should be ableto withstand high voltage across the thin insulator, (2) All as-fabricated insulators suffered degradation and, therefore, high dielectric strength ofa number of dielectric strength due to the presence of flaws. of insulator-on-metal test disks, tubes, and trapezoids at room temperature have been (3) Flaws in enamels were primarily isolated measured. Insulators evaluated include anumberof bubbles formed during the firing process.

196 (4) Flaws in plasma-sprayed Alq03 were primarily reactors. The intense neutron irradiation will dis- . interconnected pores formed during the spraying place atoms, produce hydrogen and helium and process. metal impurity atoms by nuclear reactions, and cyclic thermal stresses. Void formation induced by . (5) A judgment as to the effect of flaws on insulator neutrons will cause_ high-temperature embrittle- performance in a discharge tube configuration ment. Facilities to simulate the combination of should be based on tests in an existing fusion device, cyclic stress, elevated temperature, and neutron since conditions there will be different from those irradiation do not exist so effort has been focused on used in these dielectric strength measurements. developing the appropriate facilities.

b. Evolution of Water From a Glass First 1. Cyclic Stress. The first wall of a theta-pinch Wall. Plasma contamination by impurities from reactor is a layered composite with an insulator fac- the first wall is a potential problem for all fusion ing the plasma and a metal backing facing the Li devices, including the SFTR. It is anticipated that blanket structure. Cyclic tensile stresses will occur the SFTR first-wall insulator will be a glassy in the metal backing of the first wall. The life of material, and water will be the principal outgassing metals under conditions of temperature (about 0.4 of constituent. Calculations of water outgassing have, the absolute melting temperature, T~, of the therefore, been carried out for such a material in the candidate metals), neutrons irradiation (about unirradiated condition. The glass was assumed to 101%/m2s) and cyclic stress will be limited by have outgassing characteristics similar to those of a fatigue damage or the accumulation of pulses of soft lime glass for these calculations. This glass is thermal creep or by pulses of irradiation creep. The well characterized and shows significantly greater first step in establishing the metal life is to deter- outgassing than does a typical hard glass such as mine high-temperature strengths of candidate Pyrex or fused quartz. Calculations show that the metals under cyclic stressing. quantity of loosely-bound surface moisture can be Initial results obtained on molybdenum were up to three times that of the D-T fuel and must be reported. 59 Deformation appeared to be dominated removed prior to system operation. A 673 K, 1 hr by pulses of thermal creep for all stresses at 1200 K vacuum bakeout was then assumed, and this was with a 1 Hz stressing rate. Figure XIV-24 presents found to remove the surface water and sufficiently the cyclic stress results and compares them to the dehydrate the material so that first-wall heating life under constant stress creep. Both published and during a burn (assumed conservatively to be new creep data are included, the creep data of equivalent to 673 K for 1 m) would produce a PughGo being obtained at a lower temperature. The negligibly small additional quantity of water from new constant stress creep data fall along the same within the glass (mole fraction of water in the DT line as the cyclic stress data, whereas the data of plasma would be 1.5x 10–4). Proper baking Pugh at a different temperature fall along a parallel techniques should control the problem of plasma line. The displacement between these data reflects contamination by water resorption in SFTR. the strong temperature dependence of rupture life on temperature. 6. CTR Insulator Materials Figure XIV-25 shows the surface of a cyclicly Stockpile Insulator samples used in studies by stressed sample as revealed by scanning electron different laboratories should be produced from a microscopy relative to interior microstructure of a single source when possible, so that results obtained constant stress tested molybdenum sample as can be directly compared. Accordingly, a stockpile of revealed by light microscopy. Both show many inter- . insulators for use by the CTR insulator laboratories crystalline cracks aligned transverse to their tensile is being assembled. Materials obtained to date in- axes. This failure mode is characteristic of high- clude monocrystalline and polycrystalline Al 20 a, temperature creep; transgranular cracking (few in . AIz Q1. MgO, and Alz03; and polycrystalline BeO, number) is characteristic of fatigue. SiINQ, and AIN. Samples have been supplied to The cycle stress testing reported to date utilized CTR insulator groups at Brookhaven National saw-tooth tensile stressing. The RTPR will generate Laboratory, Argonne National Laboratory, and square wave stressing of the metal structural com- Pacific Northwest Laboratory. ponents, and a creep machine was modified to more nearly simulate this waveform. Debugging was G. Alloy Research started and the first few cyclic stress tests com- pleted. The objective of the alloy research task is to determine the limits of metals in future fusion power

197 measured by the number of displacements per 500 I t I I1I t 1 1 1 I 1 Ill 1 I I neutron in the given spectra are similar for Cu, Nb . and Au, whereas Al has quite a different behavior. In Stol,c creep rupture(P.9~1 ( 1140 K) ‘E using damage energy or displacement cross sections 2 ■ -0+ z in evaluating neutron spectra, such as those in Table . ■ ● ● XIV-XVII as fusion simulation spectra, it is : 100:- necessary to consider the materials to be studied. G ● Cychccreep:upfure1200 K usinqmaximum stress ■ static crew wpl.re 1200 K In the lower portion of Table XIV-XVII the 50 I 1 damage energy cross sections have been divided by t——uuLL~ the corresponding (n,a) cross sections and nor- 104 105 malized to that in a fusion reactor first wall spec- Time (s) trum (denoted Bench in Table XIV-XVII). Although the (n,a) cross section does not represent total Fig. XIV-24 helium production in all cases, such a ratio does give Cyclic stress curve for molybdenum. an indication of the number of defects produced per helium nucleus produced. This ratio can be thought of as a “CTR damage parameter”. The results sum- Mechanical testing was initiated on molybdenum marized in Table XIV-XVII show that only neutron- because it is an important candidate metal to the fu- spec.tra with significant high-energy components sion reactor program; additionally, molybdenum have CTR damage parameters similar to that in a requires less expensive vacuum systems for high- fusion reactor first wall. temperature testing than niobium or vanadium. The comparison of radiation effects for neutron Stainless steels are very radiation resistant and so spectra is not only dependent upon the material would be less attractive for initial Los Alamos Meson studied but also is a function of the model used and Physics Facility (LAMPF) experiments than the type of radiation effect described. Normalized molybdenum. parameter cross sections for Nb using four models In summary, saw-tooth cyclic stressing of are given in Table XIV-XVIII. Each model describes molybdenum at 0.4 T~ leads to rupture life and a different aspect of radiation damage: number of fracture mechanisms that are equal to those produc- displacements, total recoil energy, a hardening ed by constant stress creep at the same stress as the parameter which described the initial radiation maximum stress. The extensive creep data available hardening rate, and the number of free vacancies in the literature can be used to predict life and duc- produced at about 500 K .62 The free vacancy model tility when neutron radiation is insufficient to was used by Doran et al. W to describe swelling. For produce voids. example, approximately a factor of two difference between displacement and free vacancies at “ 14 2. Radiation Damage Analysis. The damage MeV’* is observed. analysis program is directed toward the develop- Table XIV-XIX shows the effect of using three ment of techniques for analyzing neutron spectral models that describe the number of displacements. dependent radiation damage and applying these Model D is the damage energy Kinchin-Pease model techniques to the design and analysis of ex- used above; RT-B and RT-3 are based on the com - periments. This effort utilizes computer calculated puter calculations of Robinson and Torrens. 63 In the radiation damage parameters based on damage first, model (D) the damage energy per defect is cons- models in the analysis. The first project for this year tant, in RT-B the damage energy per defect is a was to modify the computer program DON, which is weakly increasing function of recoil energy and in used in the calculations, to run on the LASL com- RT-3 it is a strong function of recoil energy. The puting system.61 results are essentially independent of the model for In Table XIV-XVII damage energy cross sections the two fission spectra, whereas, for the four spectra . normalized to the respective values in EBR-11 row 7 with high energy components as much as a factor of are given for Al, Cu, Nb and Au in several neutron three variation is noted. spectra. Since in the simple Kinchin-Pease type The data in Tables XIV-XVII, XIV-XVIII and model currently used in radiation effects studies, the XIV-XIX are average values integrated over the fast number of displacements is proportional to the neutron flux above 0.5 eV, and show some of the damage energy, the normalized damage energy cross characteristic properties of the radiation effects in sections are equivalent to normalized displacement these spectra. The spatial characteristics of defect cross sections. The data in the upper part of Table production, however, are not adequately given by XIV-XVII show that the relative radiation effects as these integral data. Recoil energy and damage

198 The surface microstructure of molybdenum after cyclic stressing at a rate of 1 Hz and a temperature of 0.4 T~. Note grain boundary cracks and slip bands both common to constant stress creep.

The interior microstructure of molybdenum after high temperature creep. Again note grain boundary cracks. (Slip bands are not observed on polished planes without special etching.)

Fig. XIV-25 Scanning electron micrograph of failed specimen.

199 TABLEXIV-XVII . NORMALIZEDDAMAGEENERGYCROSSSECTION

.

Spectrum —Al —Cu .Nb —Au HFIR 0.6 0.7 0.8 0.8

EBRII-7 1.0 (51bkeV)a 1.0 (32 bkeV) 1.0 (28 bkeV) 1.0 (18 bkeV)

M-LAMPF 1.2 1.9 2.0 2.2

BENCH 1.7 3.1 3.4 3.7

19 MeV Li 2.8 6.1 6.1 6.8

“14 MeV” 3.4 8.5 9.8 10.8

NORMALIZED DAMAGE ENERGY CROSS SECTION/O n,a HPIR 61 28 35 141

EBRII-7 239 94 116

M-LAMPF 7 3 3 0.4

BENCH 1.0 1.0 1.0 1.0

19 MeVLi 1:1 1.1 1.5 2.7

“14 MeV” 0.5 “...-! o-., 0.06

%it. of damage . ..ss .sectim in barn-keV

TABLEXIV-XVIII

NORMALIZED PARAMETER CROSS SECTIONS FOR Nb(1164)a

Recoil Free . Spectrum .Displacements z!!!?xw Hardening Vacancies EFIR 0.76 0.79 0.85 0.61 EBRII-7 1.0 1.0 1.0 1.0 . M-LAMPF 2.01 2.28 2.51 1.5 LLL 2.40 2.69 3.00 1.6 BENCH 3.38 3.86 4.36 2.16 24 MeV Be 7.02 8.15 9.39 3.9 “14 MeV” 9.67 11.5 13.4 5.24

200 TABLE XIV-XIX Kaminsky. 41’W If cracks do grow by the proposed . mechanism, they may seriously limit the life of the NORMALIZED PARAMETER CROSS SECTIONS FOR CU(1087)= first-wall material of fusion reactors. Weertman also made an analysis of LCTR first- ● Spectrum D RT-B RT-3 — wall fatigue. Thermo-elastic stress pulses will start HFIR 0.7 0.7 0.6 at the inner wall and move into the interior. The EBRII-7 1.0 1.0 1.0 stress pulse magnitude is large enough to cause rapid crack growth. However, these short wavelength M-LAMPF 1.9 1.3 1.2 stress pulses may attenuate rapidly with distance. BENCH 3.1 2.8 1.6 High-stress internal-friction measurements with and 19 MeV Li 6.1 5.5 2.9 without radiation are necessary to establish suitable high damping materials. “14 MeV” 8.5 7.5 3.0 3. LAMPF Neutron Irradiation Facility. Al (1193) LAMPF is being developed as a neutron radiation HFIR 0.6 0.6 0.5 effects facility with provision to heat and stress EBRXI-7 1.0 1.0 1.0 samples during irradiation. Both cyclic and constant stress testing will be possible. The neutron radiation M-LAMPF 1.2 1.2 1.0 damage cavity at LAMPF should be useful to the BENCH 1.7 1.6 1.1 national fusion reactor radiation damage program. 19 MeV Li 2.8 2.6 1.4 a. Neutron Flux and Spectrum Calculations. “14 MeV” 3.4 3.1 1.4 Three Dimensional Monte Carlo neutron transport calculation and radiochemical dosimetry were utiliz- ed as independent evaluations of flux intensity. A ‘ENDF)B material number detailed Monte Carlo calculation of the “as built” radiation effects facility at LAMPF was made with a energy spectra forNb and Cuinthree fission reactor minimum of geometric simplification so that spectra and two fusion spectra are given in Table neutron flux intensities and spectra could be directly XIV-XX. These data give a measure of the spatial related to a concurrent foil activation dosimetry and defect density distribution of radiation damage. program. The Nuclear Meson Transport Code Significant differences in the defects produced (NMTC)65 was used to transport all particles with between these neutron spectra are shown, especially energies greater than 20 MeV. Neutrons with for the fast reactor (EBR-11), and the water- energies less than 20 MeV were transported with the moderated reactor (HFIR) irradiations. neutron Monte Carlo Code (MCN).66 A delta- function proton pulse in time and energy (800 MeV) -J. Weertman* made an analysis to resolve whether uniformly spread over a 50 mm-diameter spot irradiation-induced fatigue crack growth could ex- located at the lower half of the copper beam stop60 plain chunk formation observed by Kaminsky.64 was used in the calculations to produce neutrons. Growth of pre-existing cracks was considered as a This position will be that of the proton beam during possible cause of chunk formation. Bombardment by LAMPF operation. energetic neutrons would cause localized stresses Figure XIV-26 gives a plot of neutron fluence per that fluctuate both in time and position. It is not cer- unit lethargy in a representative irradiation cavity, tain whether cracks will grow; the growth rate is at . for a proton beam current of 1 mA. This will be the the threshold level measured in conventional fatigue full beam current of LAMPF. In this case the total experiments. The crack growth mechanism cannot neutron flux is 2.38x 1017/m2s and the neutron flux explain chunk formation at the fluences used by . above 1 keV is 2.19 X1017 /m2s. Neutron fluxes were also computed for other locations, using track length and surface estimates. The representative position is not the location of highest flux intensity; the flux in- *Summer staff member, Los Alamos Scientific tensity expected to exist at the furnace location of Laboratory, permanent position, Walter P. Muikly highest flux intensity will be at least twice as high. Professor of Materials Science and Professor of Foil activation used (n,-y), (n,2n), (n,3n) and 235u Geophysics, Departments of Materials Science and (n,4n) reactions in 197Au, and (n, f) reactions in Geological Sciences, Northwestern University, and ‘8U. Radiochemical analysis ~ielded a full Evanston, Illinois. beam total neutron flux of 1.47x 101 /m2s with the

201 TABLE XIV-XX . RECOIL ENERGYAND DAMAGEENERGYSPECTRA

Nb(1164)a .

Recoil Energy EBRII-2 — EBRII-7 HFIR BENCH “14t4eV” keV %P(T) %En %P(T) AL‘- %P(T) %ED %P(T) %ED %P(T) ZED =— — D — — —— —— o -0.1 2.2 0 3.8 o 57.2 0 4.4 0 0.3 0 0.1 - 1.0 15.8 1.0 22.8 2.1 11.4 1.1 20.6 0.5 2.9 0 1.0- 5.0 36.9 12.4 40.3 18.8 12.1 7.7 30.3 3.9 11.0 0.4 5.0- 10 19.1 17.0 16.4 20.8 6.4 10.9 13.2 4.6 10.1 0.9 10 - 50 24.0 53.3 15.9 48.5 11.0 50.7 19.8 18.1 21.4 4.8 50 - 100 1.7 12.1 0.7 7.3 1.6 21.2 2.9 8.9 6.2 4.9 100- Tmx 0.3 4.2 0.1 2.5 0.3 8.4 8.8 64.0 48.1 89.0

CU(1087)= o- 0.1 1.9 0 3.8 o 63.4 0.1 5.5 0 0.2 0 0.1 - 1.0 14.2 0.6 23.2 1.7 15.0 1.3 25.2 0.5 1.5 0 1.0- 5.0 29.8 6.6 35.0 12.1 7.7 4.5 26.5 2.7 6.1 0.2 5.0- 10 17.6 10.6 15.3 14.7 3.4 6.0 10.3 3.1 6.3 0.4 10- 50 31.2 48.7 20.5 50.6 7.6 37.3 19.5 16.7 24.3 4.7 wl - 100 3.9 21.5 :.: 14.0 2.” 28.4 3.0 9.7 6.9 3.4 100- T_ 1.4 12.0 0.5 6.9 0.9 22.4 9.4 67.3 54.7 91.3

aENDF/B materialnumber

proton beam centered about 10 cm above the loca- tion considered in the Monte Carlo calculation. This beam position will be changed to the more desirable lower position during present accelerator modifications. The 6 foil reactions considered were analyzed us- ing spectrum unfolding techniques with good agree- ment to the Monte Carlo calculation results shown in Fig. XIV-26. The high energy data (E >20 MeV) are now available and show decreasing intensity with increasing energy.

b. Radiation Damage Calculation and Evaluation. The evaluation of LAMPF as a radia- tion effects facility and the relationship to other on 11 , I I I I I In.1 neutron irradiation facilities is being evaluated by ~-s ~ 3 !0-s 2 593-*2 50-12 5 Id 2. 30-’ 2312302 , ~a

mew Iud both calculations and experiments. Results of these calculations are given in Tables XIV-XVII, XIV- XVIII and XIV-XIX. A review of these data in- Fig. XIV-26 dicates that the radiation effects expected in Neutron fluence per unit lethargy at the LAMPF will be intermediate between those in fis- LAMPF Irradiation Facility for a 1 ma proton sion reactors and those expected in fusion reactors. beam.

202 LAMPF has a “CTR damage parameter” similar to technology trade-off and comparison studies, and b that for a fusion reactor first wall and hence has a the identification of problems requiring long-term significant advantage over fission spectra for fusion development efforts. Studies of such potential com- simulation. Experiments are being prepared for mercial applications of laser fusion as the production ● LAMPF that will enable direct comparisons of of fuel for fission reactors and providing high- several forms of radiation damage in LAMPF to that temperature process heat are also included. observed in other neutron spectra. Some of these ex- periments are being prepared in cooperation with 2. Pellet Microexplosions. Laser-fusion reactor other laboratories including Brookhaven National concepts are based on the energy release Laboratory, Argonne National Laboratory, characteristics of bare-DT fuel pellet microex- Lawrence Livermore Laboratory and Hollifield plosions. The nominal pellet yield used as the basis National Laboratory. for design considerations is 100 MJ. Theoretical calculations indicate that -1 MJ of laser light will c. LAMPF Irradiation Facility Development. be required to heat and compress reference fuel Development of the LAMPF radiation damage pellets to conditions that result in a thermonuclear facility is preceding by two routes. The first route in- energy gain of 100. The characteristics of the energy- volves a system for attaching experiments on release mechanisms from a typical calculation for a stringers which penetrate through the radiation 100 M-J fusion-pellet energy release are summarized shielding surrounding the beam stop. The second in- in Table XIV-XXI. volves the development of an experimental tester The released energy must pass through or interact which will heat and stress tensile bars in vacuum with the pellet material that was ablated during the during neutron radiation. The stringers must pellet implosion-and-compression stage, must pass provide cooling water, electric power, thermocouple through or interact with any ambient gas in the cavi- control signals, and high- andlow-pressure gas to the ty, and, finally, interact with the cavity wall and tester. Neutron leakage past the stringer in its hous- structure. The expansion dynamics are important ing must be at an acceptable level. The testers are because the temporal profiles determine the impulse remote and miniaturized. Their design is based on on the cavity wall. proven “in reactor” test devices used in Canada. 67 LAMPF is presently undergoing modification for 3. Laser-Fusion Reactor Concepts. Several high-level beam operation, which involves the addi- reactor concepts are being considered for possible tion of more radiation shielding. The radiation use in central-station power plants. Preliminary damage stringers have been used to insert several engineering analyses have been done for .WO con- dosimetry experiments. Improvements of the inser- cepts, the wetted-wall and the magnetically- tion and removal system and blockage of neutron protected designs, that may be attractive for this leakage pathways are being made. application. The first LAMPF furnace power supply and The spherical cavity wall in the wetted-wall reac- temperature controller system has been assembled tor concept, shown schematically in Fig. XIV-27, is and evaluation has been started. Miniaturized protected against energy deposition by energetic radiation resistant heaters are being evaluated. particles from the pellet microexplosion by a film of liquid lithium on its interior surface. The energy of the alpha particles and the pellet debris and part of the x-ray energy is deposited in the lithium layer H. Feasibility and Systems Studies of w~lch is evaporated and ablated from the surface of Applications of Laser Fusion the cavity wall. The lithium vapor is exhausted b through a nozzle prior to the next pellet microexplo- 1. Introduction. Feasibility and systems studies sion. are being done to assess the technical feasibility and Minimum cavity diameters for the wetted-wall the economic incentives of various commercial and < reactor concept are determined by surface military applications of laser fusion. Emphasis is temperature increases due to x-ray energy deposi- placed on systems studies of the direct production of tion; the minimum niobium cavity diameter cor- electricity in central-station power plants. The responding to 100 MJ pellet microexplosions is -3.4 general objectives of these studies are: the concep- m. Conceptual blanket designs provide for the cir- tualization and preliminary engineering analyses of culation of liquid lithium for the removal (If heat and laser-fusion reactor and power-plant concepts, the the breeding of tritium. Initial estimates indicate development of parametric computer mooels of that acceptable tritium breeding ratios (1 .07 to 1.40) power-plant subsystems for economic and

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performed to determine the temporal and spatial can be obtained from designs ( -1 m thick) con- dependence of energy deposition in the blanket taining natural lithium, whose structural re- region of a spherical laser-fusion reactor with quirements are satisfied by either stainless-steel or niobium structural material. The results of these refractory metal components. calculations were used to calculate pressure profiles The magnetically-protected reactor concept is in liquid lithium regions of the blanket due to ther- shown schematically in Fig. XIV-28. The cavity is mal expansion. The responses of structural shells cylindrical with an impressed steady-state magnetic were then determined from these inputs in time- field produced by a solenoid concentric with and ex- dependent, finite-difference, wave- propagation terior to the cavity wall. Energetic charged particles computer programs. From calculated stresses and resulting from fusion-pellet microexplosions are materials property data, required structural wall diverted by the magnetic field to conical energy thicknesses were determined. The wetted-wall con- sinks in the ends of the cylindrical cavity. Laser- cept with 100-MJ microexplosions and 0.9 m of beam transport tubes are arranged symmetrically natural lithium in the blanket requires two struc- about the axial and radial center of the cavity. The tural walls and an outer envelope. For a 2 m radius energy sinks are readily accessible for replacement cavity, the structural walls are 0.03 m thick and the without disturbing the lithium blanket, the laser- outer envelope is 0.02 m thick. beam optics, or the fuel injection system. The minimum niobium cavity diameter for 100 M*J pellet 5. Lasers and Laser-Beam Transport Systems. microexplosions is -5 m and is determined by sur- A total laser-pulse energy of 1 MJ has been asa.um - face heating due to x-ray energy deposition. ed for reference laser-fusion reactor design studies. It Estimates have been made of magnetic field is anticipated that quasi-symmetrical illumination strengths and field configurations necessary to divert of fusion pellets by laser light will be required; thus, 1- charged particles to the energy sinks for theoretical conceptual reactor designs provide for eight laser fusion-pellet outputs ranging in yield up to 100 MtJ. beams arranged symmetrically about the centers of Maximum field requirements are -0.3 T. Several reactor cavities. .+ solenoid concepts have been modeled for the systems The electron-beam sustained-discharge COZ laser analysis program, including the use of cryogenic system shows promise of achieving the required per- superconducting coils as well as conventional copper formance at reasonable cost and operating efficien- coils. There is no apparent technical or economic ad- cy. Experimental C02 lasers at LASL provide the vantage realized from the use of a particular con- basis for designing larger systems. The reference cept. power- amplifier design hasan output of 0.125 MtJ in a 1-ns-wide pulse and is expected to have an efficien- 4. Stress Analyses. Time-dependent, neutron- cy of 6 to 7%. It is pumped by an electric discharge, and gamma ray-transport calculations have been with ionization provided by an electron beam. Laser

205 pulse repetition rates of from 35 to 50 per second 6. Conceptual Laser-Fusion Power Plant. appear to be desirable for power plant applications. The preliminary design of nominal 1000-MWe For pulse rates in this range, circulation of laser gas laser-fusion power plants have been developed. Im- for convective cooling will be necessary. At 35 pulses portant considerations which led to design choices per second, the reference-design laser amplifier will included component reliability, redundancy of es- require -60 MW of cooling capacity, and because sent ial components, access to components for service amplifier performance is significantly degraded by or replacement, and minimization of hazards from excessive temperatures, the waste heat is assumed radioactive materials. dissipated to the environment. For power plants based on the wetted-wall reactor The C Oz laser systems model includes capacitive concept, twenty-four reactors are included in a 1000 electrical energy storage and pulse-forming networks MWe power plant; whereas, because of the higher for power conditioning. In order to accommodate the pellet -microexplosion repet it ion rate, only three high pulse rates and long lifetimes desired, the magnetically-protected reactors are required for this capacitors must be designed for low stress levels and power level. The overall layout for a power plant that convective cooling. utilizes wetted-wall reactors is shown in Fig. XIV-29. The HF chemical laser is also a viable contender for application in laser-fusion power plants and may 7. Systems Studies. Systems analyses of be advantageous due to its relatively short alternativelaser-fusionpower plantshave been wavelength (2.7 pm compared to 10.5 pm for COd, carriedouttocomparethefollowingoptions:CO 2 or its relatively low capital cost, and its high operating HF laser technology and wetted-wall or temperature (permitting partial recovery of waste magnetically-protected reactor concepts. A serious heat for conversion to electricity). The HF laser attempt has been made to use a consistent set of cost model adopted for systems analysis includes: the data in the comparative economic analyses; laser and associated optics, controls and gas however, because of rapidly changing costs and the supplies, an electric storage and power conditioning difficulty of predicting future trends, the calculated system, an HF electrolysis system, and a turbine- costs of electric power and of plant capital costs were alternator for converting waste heat in the Iasing normalized to costs for a plant based on the wetted- media to electricity. The net efficiency of the laser wall reactor concept and C02 laser technology rather system using nominal component efficiencies is than being given in absolute values. Calculated - If)%. power and capital costs are competitive with similar Because the laser system represents a significant costs for other advanced power plants within the fraction of the capital investment of a laser-fusion context of the cost data used. power plant, it will apparently be economically ad- The results of recent systems calculations with vantageous to centralize components so that each nominal values of systems parameters are given in laser system serves several reactor cavities. A cen- Table XIV-XXII. Important figures of merit are tralized laser system requires rapid beam-switching given for each of several conceptual - 1000-MWe from laser power amplifiers to selected cavity beam power plants. Variations of - 10To in the cost of elec- ports. Conceptual devices for this purpose include tric power and of -25’%. in plant capital costs were the use of rotating mirrors that direct laser beams found among the various concepts considered. sequentially to reactor cavities arranged in a circular Current systems models predict substantial advan- pattern around a central laser system. tages in both net plant efficiency and circulating Beam-transport systems will consist of a large power fraction for plants based on HF laser number of mirrors, windows and possibly lenses. For technology compared to those based on CO z laser C02 laser beams, sodium chloride windows and technology. Lower plant capital costs are associated lenses and bare metallic mirrors are used. Assumed with plant concepts based on the magnetically- laser-light fluence limits are 3 and 10 J per cm2 per protected reactor than with those based on the pulse for windows and mirrors, respectively. wetted wall reactor, but higher microexplosion Sapphire windows and coated metallic mirrors are repetition rates per reactor cavity result in higher used to transport HF laser beams, and fluence limits maintenance and operating costs for the are 10 J per cm2 per pulse for both materials. magnetically-protected design; thus, net power costs Catopt ric beam reflection systems are used to are essentially the same for these two reactor provide indirect beam paths through biological designs. shielding surrounding reactor cavities.

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208 References 4? 10. J.P. Freidberg, R.L. Morse, F.L. Ribe, “Staged 1. R.A. Krakowski, F.L. Rlbe, T.A. Coultas, A.J. Theta Pinches with Implosion Heating, ” Texas

● Hatch, “An Engineering Design Study of a Symp. on Technol. of Controlled Fusion Ex- Reference Theta-Pinch Reactor (RTPR)”, USAEC periments and Egn. Aspects of Fusion Reactors, p. Rept. LA-5336/ANL-8019 (March 1974). 812, NOV. 20-22, 1972.

2. F.L. Rlbe, R.A. Krakowski, K.I. Thomassen, T.A. 11. T.A. Oliphant, “A Mixed Snowplow/Bounce Coultas, “An Engineering Design Study of a Model Shock Heating in a Staged Theta Pinch,” Reference Theta-Pinch Reactor (RTPR),” Nuclear Nucl. FUS. 14, 377 (1974). Fusion, Special Supplement on “Fusion Reactor Design Problems,” 1974. 12. E.M. Little, W.E. Quinn, G.A. Sawyer, “Plasma End Losses and Heating on the Low-Pressure 3. T.A. Coultas, J.E. Draley, V.A. Maroni, R.A. Regime of a Theta Pinch,” Phys. Fluids, 8, 1168 Krakowski, “An Engineering Design Study of a (1965). Reference Theta-Pinch Reactor (RTPR) - An En- vironmental Impact Study,” Vol. II, USAEC Rept. 13. T.A. Oliphant, “Fuel Burn-up and Direct LA-5336/ANL-8019 (April 1975). Conversion of Energy in a D-T Plasma, ” Proc. BNES Conf. on Nucl. Fus. Reactors, UKAEA 4. R.A. Krakowski, K.I. Thomassen, T.A. Coultas, Culham Lab., p.309, Sept. 17-19, 1969. “A Technological Assessment of the Reference Theta-Pinch Reactor (RTPR)”, 8th Symp. on Fus. 14. R.A. Krakowski, “Ergodic Optimization and Tech., p. 623, Noordvijkerhaut, Netherlands, June Parameter Study on the RTPR Burn Cycle, ” First 17-21, 1974. ANS Topical Meeting on the Technology of Nuclear Fusion, p. 112, April 16-18, 1974, San Diego, Califor- 5. R.A. Krakowski, K.I. Thomassen, R.J. Burke, nia. T.A. Coultas, “An Engineering Design Study of a Reference Theta-Pinch Reactor (RTPR) - A 15. J.P. Freidberg, F.L. Ribe, “Scaling of Wall Technological Assessment,” Vol. III, USAEC Rept. Stabilized Scyllac Experiments,” Comments on LA-5336/ANL-8019 (to be published). Plasma Physics and Controlled Fusion, 2, 163 (1974). 6. R.A. Krakowski, D.J. Dudziak, T.A. Oliphant, K.I. Thomassen, G.E. Bosler, F.L. Rlbe, “Prospects 16. R.E. Stillwagon (Principal Investigator), for Converting 232Th to 233U in a Linear Theta- “Design Studies of Reversible Energy Storage and Pinch Hybrid Reactor (LTPHR) ,“United States Transfer Systems for the Reference Theta-Pinch Energy Research and Development Administration Reactor,” Westinghouse Elec. Corp. Rept. EM-4620, Report ERDA-4, pg. 249 (Dec. 1974). Sept. 1974.

7. T.A. Oliphant, “Plasma Cooling of a Pulsed 17. J.M. Bunch, F.W. Clinard, D.J. Dudziak, W.V. Thermonuclear Reactor by Means of a Neutral Gas Green, R.A. Krakowski, “An Evaluation of Major Layer,” Nucl. Fus., 13, 521 (1973). Material Problems Anticipated for the Reference Theta-Pinch Reactor (RTPR) ,“ 5th Symposium on Engineering Problems of Fusion Research, m 8. T.A. Oliphant, “Monte Carlo Treatment of Heat Flow Through a Neutral Gas Layer,” J. Nucl. Princeton, NJ, Nov. 6-9, 1973. Mater., 53, 62, 1974. 18. R.A. Krakowski, F.W. Clinard, F.L. Ribe, T.A. * 9. T.A. Oliphant, “Heat Transfer Through a Coultas, “Surface Effects at the First-Wall of the Reference Theta-Pinch Reactor (RTPR) Cooling Reference Theta-Pinch Reactor (RTPR),” J. Nucl. Layer, ” Proc. of First Topical Meeting on the Mater., 53, 54, (1974). Technology of Controlled Nuclear Fusion, p. 677, April 16-18, 1974, San Diego, California. 19. V.A. Maroni, personal communication, ANL (1974).

209 1

20. J.E. Draley, V.A. Maroni, T.A. Coultas, R.A. 33. Donald J. Dudziak and R.A. Krakowski, “A Krakowski, “An Engineering Impact Study of a Comparative Analysis of D-T Fusion Reactor . Reference Theta-Pinch Reactor (RTPR),” First Radioactivity and Afteheat,” Proc. First Top. Mtg. ANS Topical Meeting on the Technology of Con- Technology of Controlled Nucl. Fusion, San Diego, trolled Nuclear Fusion, p. 564, April 16-18, 1974, San CA, 16-18 April 1974. . Diego, CA. 34. Donald J. Dudziak and R.A. Krakowski, 21. Donald J. Dudziak, “Fusion Reactor Nuclear “Radioactivity Induced in a Theta-Pinch Fusion Analysis Met hods and Applications, ” 8th Sym- Reactor,” Nucl. Technol. 25,32 (1975). posium on Fusion Technol., p. 915, Noorwijkerhaut, Netherlands, June 17-21, 1974. 35. D.W. Muir and Donald J. Dudziak, “Sensitivity of RTPR Afterheat and Radioactivity to Nb-94 Cross 22. ICRP Publ. No. 2, “Recommendations of the Section Uncertainty,” Trans. Am. Nucl. Sot. 19, International Commission on Radiological Protec- 465 (1974). tion,” Pergamon Press, (1959). 36. S.A.W. Gerstl, “Blanket Design Sensitivity 23. F. Morley, J.W. Kennedy, “Fusion Reactors and Calculations Based on Perturbation Methods,” Environmental Safety,” BNES Nuclear Fusion Proc. First Top. Mtg. Technology of Controlled Reactor Conference, p. 54, Culham Laboratory, Nucl. Fusion, San Diego, CA, 16-18 April 1974. (Sept. 1969). (CONF-74-0402).

24. Fusion Power:An Assessment of Ultimate Poten- 37. D.G. Doran and G.L. Lukcinski, U. of Wiscon- tial,” USAEC Rept. WASH-1239 (Feb. 1973). sin, personal communication, July 1972.

25. G.L. Kulcinski, Univ. of Wisconsin, private 38. W.J. Gray and W.C. Morgan, “Projection of communication ( 1973). Graphite Behavior in the LASL Reference Theta- Pinch Reactor,” Pacific Northwest Laboratory 26. “Final Reort, Project Definition Phase, 4th Report BNWL-B-289 (1973). Round Demonstration Plant Program, ” Vol. I, Westinghouse Electric Corp. (Dec. 1970). 39. W.C. Morgan, Battelle Northwest Laboratory, personal communication, 1973. 27. W.B. Cottrell and A.W. Savolainen, “U.S. Reac- tor Containment Technology,” ORNL-NSIC-5, p. 40. M. Kaminsky and S.K. Das, “Particle Release 4.2, U.S. Atomic Energy Commission (1965). from Solids under 14-MeV Neutron Impact,” Conf. Surface Effects in Controlled Thermonuclear Fusion 28. W.F. Vogelsang, G.L. Kulcinski, R.G. Lott, and Devices and Reactors, ANL, 10-12 January 1974. T.Y. Sung, “Transmutation Effects in CTR Blankets,” Trans. Am. Nucl. Sot., 17, 138 (1973). 42. R. Behrisch, R. Gahler, J. Klaus, “Sputtering Yields of Au by 14 MeV Neutrons and Emission of 29. B. Badger,et al., “UWMAK-1, A Wisconsin Recoils from (n,2n) Reactions in Au and Nb,” J. Toroidal Fusion Reactor Design, ” UWFDM-68, Vol. Nucl. Mater., 53,183 (1974). 1, U.S. Atomic Energy Commission (1973). 42. Patrick D. Soran and Donald .J. Dudziak, “Bon- 30. D. Steiner, “The Nuclear Performance of darenko Formalism Applied to Theta-Pinch Reactor Vanadium as a Structural Material in Fusion Reac- Nucleonics,” Trans. Am. Nucl. Sot. 19, 468 (1974). tor Blankets, ” 0RNL-TM-4353, Oak Ridge National Laboratory (1973). 43. Patrick D. Soran and Donald J. Dudziak, “Application of Bondarenko Formalism to Fusion 31. K. Shure and D.J. Dudziak, “Calculating Reactors,” Proc. Conf. on Nucl. Cross Sections and Energy Released by Fission Products, ” Trans. Am. Technology, Washington, DC, 3-7 March 1975. Nucl. Sot., 4, 30 (1961); also, WAPD-T-1309, U.S. Atomic Energy Commission. 44. S.A.W. Gerstl and H. Henryson, “The Effect of Resonance Self-Shielding in Niobium Structures on 32. D. Steiner and A.P. Fraas, “Preliminary Obser- Tritium Breeding in CTR Blankets,” Trans. Am. vations on the Radiological Implications of Fusion Nucl. Sot. 18, 25 (1974). Power,” Nucl. Safety, 13,5, 353 (1972).

210 45. Gerald E. Bosler, Donald J. Dudziak and 54. M.P. Thomas and O. Harling, results presented * William R. Ellis, “A Preliminary Appraisal of a at the 21st National Vacuum Symposium of the Fusion/Fission (HYBRID) Reactor Based on the AVS, Anaheim, CA, October 1974. Linear Theta Pinch, ” Proc. Ninth Intersociety . Energy Conversion Engineering Conference, San 55. P.W. Levy, “Color Centers and Radiation- Francisco, CA, 26-30 August 1974. Induced Defects in A1203,” Phys. Rev. 123. 1226 (1961). 46. “TCT — Two-Component Torus,” joint concep- tual design study, performed by Princeton Plasma 56. C.M. Logan, “Proton Simulation of Displace- Physics Laboratory, Princeton, NJ and ment Effects Induced in Metals, ” USAEC Rept. Westinghouse Electric Corporation, Pittsburgh, Pa., UCRL-51224 (1972). Vol. II, Section 6.1 (1974). 57. V.A.J. van Lint, personal communication, 47. D. Steiner, Coordinator, “The Status LASL, ( 1974). ofNeutron-Induced Nuclear Data for Controlled Thermonuclear Research Applications: Critical 58. Contribution to the LASL CTR Technology and Reviews of Current ‘Evaluations, ” Oak Ridge Development Quarterly Report for the Period April 1 National Laboratory report USNDC CTR-1 (1974). - June 30, 1974.

48. S.A.W. Gerstl, “Second-Order Perturbation 59. R.A. Yeske, W.V. Green and E.G. Zukas, “The Theory and Its Application to Sensitivity Studies in Tensile Fatigue Behavior of Molybdenum at Shield Design Calculations, ” Trans. Am. Nucl. Sot. 1153 K,” Proceedings of the First Topical Meeting on 16, 342 (1973); S.A.W. Gerstl and W.M. Stacey, Jr., the Technology of Controlled Nuclear Fusion, p. 456 “A Class of Second-Order Approximate For- San Diego, CA, April 16-18, 1974, (1974). mulations of Deep Penetration Radiation Transport Problems,” Nucl. Sci. Eng. 51, 339 (1973). 60. J.W. Pugh, “The Tensile Properties of Molybdenum at Elevated Temperatures, ” Trans 49. S.A.W. Gerstl, “The Application of Perturba- ASM 47, 984( 1955). tion Methods to Shield and Blanket Design Sen- sitivity Analyses, ” AP/CTR/TM-28, Applied 61. D.M. Parkin and A.N. Goland, “A Com- Physics Division, Argonne National Laboratory putational Method for the Evaluation of Radiation (1974). Effects Produced by CTR-Related Neutron S pec - tra,” USAEC Rept. BNL 50434, (Sept., 1974.) 50. D.E. Bartine, E.M. Oblow, and F.R. Mynatt, “Radiation-Transport Cross Section Sensitivity 62. D.G. Doran, R.L. Simons, and W.N. McElroy, Analysis - A General Approach Illustrated for a “Spectral Effects in Neutron and Charged Particle Thermonuclear Source in Air,” Nucl. Sci. Eng. 55, Irradiations, ” to be published. 147 ( 1974); M.J. Katz, (cd.), “LASL Controlled Thermonuclear Research Program,” Los Alamos 63. M.T. Robinson and J.M. Torrens, “Computer Scientific Laboratory report LA-5656-PR (1974). Simulation of Atomic-Displacement Cascades in Solids in the Binary -Collission Approximation,” 51. D.R. Harris, R.J. LaBauve, R.E. MacFarlane, Phys. Rev. B9, 5008 (1974). P.D. Soran, C.R. Weisbin, and J.E. White, “MINX, . A Modular Code System for Processing Multigroup 64. M. Kaminsky and S.K. Das, “Particle Emission Cross Sections from Nuclear Data in ENDF/B For- from Solids Under 14 MeV Neutron Impact, mat,” Los Alamos Scientific Laboratory report LA- Proceedings of Surface Effects in Controlled Ther- ● UR-1766 (Jan. 1973). monuclear Fusion Devices and Reactors, ” Argonne National Laboratory, January IO-12, 1974. 52. W.A. Ranken, “Quarterly Report on the Space Electric Power R&D Program,” USAEC Rept. LA- 65. W.A. Coleman and T.W. Armstrong, “The 5113-PR, (Nov. 1972). Nucleon-Meson Transport Code MNTC,” Oak Ridge National Laboratory report ORNL-4606 53. M. Kaminsky, J.H. Peavey, and S.K. Das, “Par- (1970). ticle Release from Niobium Irradiation with 14 MeV Neutrons,” Phys. Rev. Lett. 32, 599 (1974).

211 66. E.D. Cashwell, J.R. Neergarrd, W.M. Taylor 67. B. Fidleris, I.R. Emmerton, R.D. Delaney, “An . and G.D. Turner, “MCN:A Neutron Monte Carlo In-Reactor Creep Machine for High Flux Code,” Los Alamos Scientific Laboratory Report Application,” J. of Phys. E., Sci. Inst., Vol. 5, p. 442, LA-4751 (1972). 1972. .

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212 XV. SCYLLAC FUSION TEST REACTOR DESIGN

D.J. Dudziak, S.A. Gerstl, D.L. Houck, R.A. Jalbert, R.A. Krakowski, R.K. Linford, T.E. Mcllonald. J. D. Rogers, K.1. Thomassen

A. Introduction 4. T.E. McDonald: Electrical systems and con- trols, alternative energy storage and charging In August 1974 the overall conceptual design of a system. large-radius toroidal theta pinch was initiated, The machine, which is designated as the Scyllac Fusion 5. W.A. Bradley: Overall engineering coordina- Test Reactor (SFTR) *,-is designed for D-T operat ion tion, scheduling and cost estimating. to achieve Q= 1, i.e. the total neutron energy (at 20 MeV/n) is equal tot he internal energy of the plasma. Over 30 persons have contributed to the proposal The machine has a major radius of 40 m, a minor in areas of materials development and fabrication, (first-wall) radius of 0.1 m, and an ~ = 1 (helical) electrical design, cryogenic engineering, facilities wavelength of approximately 3.2 m. The SFTR will design and layout, radiation activation studies, be wall stabilized with the possibility of requiring a shielding design, and health and safety studies. modest feedback system for long-term stability. Table XV- 1 is a list of the principal contributors. Figure XV-I is an illustration Of the SJj’TR, showing the plasma chamber and implosion-heating C. General Design capacitors in a concrete cell having 1.5-m thick walls. The dewars for the superconducting coils of The design effort has been divided into the the METS system are placed immediately outside following areas: (a) first wall and implosion-heating the cell with the refrigeration system shown on the system; (b) tritium handling and vacuum system; left of the facility. The tritium handling system is (c) radiation shielding system; (d) magnetic energy shown on the lower right of the facility. The SFTR is storage system [METS I: (e) instrumentation and being designed for 1000 D-T plasma discharges per control; and (f) general facilities design. In addition year and a repetition rate of a discharge every 15 to these design categories, work is also being done on min. the environmental and safety aspects as well as the quality assurance program. B. Project Organization The designs of the majority of the SFTR sub- systems have progressed through at least one The SFTR design project covers a wide range of preliminary conceptual design and for some sub- disciplines and requires extensive interaction among systems through several conceptual designs. The experts throughout the Laboratory. K .1. Thomassen specific design of the first wail and implosion- (CTR-DO) has overall responsibility for the project heating circuit has presented a difficult problem. * with the following assignments made to coordinate Although the basic operation is known, it is an- the effort in specific areas: ticipated that further iterations of the implosion- heating hardware design will be required. b 1. .J.D. Rogers: Cryogenic energy storage and Tables XV-2 and XV-3 give the major parameters transfer. for the SFTR. Table XV-2 lists t he parameters of t he machine while Table XV-3 lists the plasma and field 2. R.A. Krakowski: First wall, vacuum systems, parameters immediately after implosion heating and tritium handling, CMB-liaison, radiation shielding. at peak compression. A typical cross section of the SFTR is shown in 3. T. Oliphant: Theoretical aspects of implosion, Fig. XV-2. The plasma chamber and implosion- compression, burning, stability, and equilibrium. heating system are shown inside a concrete cell which is a secondary neutron shield and also *previously denoted Fusion Test Reactor (FTR) provides a secondary containment for tritium. The primary neutron shield is placed immediately

213 I

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.

214 TABLEKV-1 TABLEXV-2 . CONTRIBUTORS TO FIR DESIGN SFTR MACHINE PAIUKSTERS b Implosion and Burn Calculations PlasmaChamber—— MajorRadius 40 m T. Olfphant, CTR-7 Minor Radius 0.1 m R. Linford, CTR-7 Wavelength 3.2 m L-1 Perturbation 1.5 Marshall Coil and First Wall Module Length 0.2 m

R. Linford, CTR-7 Implosion System K. Hanka, CTR-4 Capacitance/Module c 0.12 !Jf Capacitor Voltage v 270 kV D. Sandstrom, CMB-6 Induced E-Field 3.8 kVfcm J. Dickinson, CMB-6 System Energy Storage ‘e 4.4 MJ

Tritium Handling and Vacuum CompressIon System B-Field Risetime 0.7 ms ‘R R. Krakowski, CTR-7 B-Field Decay Time 250 ms ‘L/R J. Anderson, CMB-3 System Energy StoraSe 488 M.J D. Vier, CMB-3 Plasma Time at Q-1 120-170 ms Diagnostics and Instrumentation ‘B UT >1.5 (10)1” S/cm’ F. Jahoda, CTR-8 Filling Pressure P 4.5 mtorr R. Sienon, CTR-8

TABLS XV-3 Magnetic Energy Storage AFTER INPLOS1ON J. Rogers, CTR-9 SFTR PARAMETERS AND AT PEAX COMPRESSION K. Wi.lliemaon,CTR-9 D. Weldon, CTR-9 Implosion Compression C. Swannack, CTR-9 Normalized Plasma Radius alb 0.S 0.33 H. Vogel, E–DO Ion Temperature 2.5 keV 7 keV R. Bartholomew, ENG-7 ‘i Electron Temperature T 1.2 keV 5 keV e Facilities Design Magnetic Field B 8.3 kG 35-55 kG 1).Houck, ENG-9 R. Turner, ENG-9 arfmnd the plasma chamber. The primary radiation J. Rand, EliG-? shield prevents neutron damage to the implosion- D. Kirby, ENG-7 heating capacitors and limits the personnel radia- V. Starkovich, ENG-7 tion exposure inside the cell. The shielding is suf- ficient to allow unlimited personnel access inside the Capacitor Bank Design cell when the machine is not in operati(m and per- E. Kemp, CTR-4 sonnel access adjacent to the outside ofthe cell dur- R. Hahrman, CTR-4 ing operation. L. Hansborough, CTR-4 Four cryogenic vacuum pump stations are equally spaced around the machine and are located inside Shielding Design and Neutronics the cell. The vacuum is maintained in a toroidal D. Dudziak, T-1 manifold located immediately below the plasma S. Gerstl, T-1 chamber and isconnectedto theplasmachamber by a series of downcommers. In case of an accidental Safety tritium release to the cell, cell air is circulated R. Jalbert, H-1 through manifolds, which are routed through the bottom of the cell, to the main tritium cleanup Quality Assurance facility. The air is then either recirculated back to E. Brazier, ENGDO-QA the cell or, when the tritium concentration is low enough, vented to the atmosphere. Scheduling and Estimating The pulse charging and triggersystems arelocated T. McDonald, CTR-4 on top of the cell with cable feeds through the cell W. Bradley, ENG-7 top. The METS system is locatedon the outsideof D. Orr, ENG-8 the toroidnexl tothe cell with cable feed~ from the

215 I

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Fig. XV-2 Typical Cross Section SFTR crowbar switches to the compression coils through the cell bottom. The diagnostics area is located on I I the inside of the toroid adjacent to the cell with op- tical ports being placed through the cell to provide access for optical diagnostics.

D. Implosion-Heating System Load L(t) The implosion heating system is a high-voltage low-inductance capacitor bank feeding a load coil which provides a fast-rising magnetic field for shock 1 ~Puls:+2;~ing heating the plasma. The energy capacity of the Staging 1 implosion-heating capacitor bank is approximately 5 MJ . Fig. XV-3 One possible implosion-heating circuit is shown in Implosion fieating Network Fig. XV-3. In this concept the pulse-forming network employs voltage levels in the range of 270 compression and burn phase. Work is now under way kV to provide magnetic fields which rise to about 11 to determine the most efficient circuit for producing kc in 100 ns for shock heating. The fields are then the proper implosion-heating field so that a large sustained by the 60-kV staging bank and crowbar radius plasma will be produced. until the compression field can be raised. The ion The implosion-heating load coil is in the form of a temperature after the shock is approximately 2.5 Marshall coil, which is illustrated in Fig. XV-4. This keV. The concept of wall stabilization requires that configuration has low inductance and produces the the radius of the plasma column be at least 35@i of desired Z directed magnetic field while allowing a the radius of the implosion-heating load coil. As a compression load coil to be placed around the result, the radius of the plasma column must be as plasma chamber. The Marshall coils will be placed large as possible after shock heating to avoid over back-to-back to form modules as shown in Fig. XV- compression and loss of wall stabilization during the 5. Weld joints are made between modules to allow

216 Fig. XV-4 Marshall Coil for Implosion Heating

removal for maintenance. The compression coils are closing the interrupter switch and building up a placed around the Marshall coils with a magnetic current flow through the superconducting storage material between the two to reduce the amount of coil and interrupter; the current is transferred into energy required in the implosion system. the compression coil by opening the current in- * terrupter. The current resonates with the transfer E. Compression System (METS) capacitor bank into the compression coil and the crowbar switch is then closed. The transfer capacitor )’ Approximately 488 MJ of energy is required for bank is necessary to prevent losing half the energy in the compression field which is in the range of 50 kG. the interrupter switch and must have half the energy This energy will be stored in the form of current storage capacity of the superconducting coil. flowing in a series of superconducting coils. Upon fir- A typical graph of the build up of the magnetic ing of the machine the current will be switched from field produced by the implosion-heating and com- the superconducting storage coil into the compres- pression systems is shown in Fig. XV-7. The current sion coiland crowbarred. reaches its peak in the compression coil in ap- The basic METS circuit is shown in Fig. XV-6. proximately 750 PS and decays with an L/I? time of The energy is stored in the superconducting coil by 250 ms.

217 ,

HNIJ lMFLualu Ix LUIL ““’2L~- 1

4)-/ VACUUM MATERIAL 5= PUMPING I PORT

L 80CM MODULE

Fig. XV-5 Module of the 80M Diameter FTR Torus

6. I 1 I I

;4 EEEII!;:ionCrowbot -. lrrtrrrPtW Switch coil ~ I .- : t Tronsfer Supor”- .-0 conducting &oykcitor = Storago Coil z 2. - x Fig. XV-6 Compression Circuit

F. Tritium Handling and Vacuum System Time (w) The major funct ions of the trit ium handling system are: (a) to provide precisely measured D-T Fig. XV-7 mixtures to the SFTR discharge tube in preparation Magnetic Field us Time for a D-T discharge; (b) to recover and/or to account fi]r ail unburned tritium after a D-T discharge; (c) to ● Passive Storage Facility (PSF) Vnult provide safe storage of gram quantities of tritium:

[d) to m(mitor and to control the chr(mic release of ● Tritium Injection System (TIS) tritium; and (e) to present safeguards and cleanup capabilities in the event of a significant accidental ● Tritium Recovery System (TRS) release of tritium. The major subsystems that com- prise the tritium handling system are: ● FTR Vacuum System

218 ● Tritium Waste Treatment (TWT) Facility . Off-site !r\tium ● Cell Cleanup Facility (CCF) adelivery . Figure XV-8 depicts schematically the in- terrelationship between components of the tritium handling system. In addition to the functions of Possive storage, injectitm and recovery, the overall system storage Trjtium ;a:y; y also includes the SFTR vacuum system, D-T im- Buriol mjecjion purity control, and post- discharge gas analyses. (PSF) Cell recovery clean-up The interface bet ween the major subsystems ere Tritium facility (Tis,TRsJ waste Stack multifarious and diffuse: for instance, the vacuum systems (CCF) treatment -o system per se plays important roles in both tritium focility (TWT) injection and recovery and to some extent impinges L I I J upon the design of the TWT and CCF. The tritium injection will use standard volumes r and vacuum transfer techniques. A uranium bed will

supply clean tritium to the injection system and 2’ //A ////’ / 1/ / / / / / / / used (D,T)2 gas will be recovered at the cryogenic Exhaust stotian vacuum pump station and then stored on a second ~ uranium bed. In addition to metal hydride storage of +%’%nl, tritium, a vault will be used f’or more permanent and 1 ti Vaccuum manifold secure storage of gaseous tritium. Chronic t rit ium h 9 releases are expected to occur at the vacuum pump + 4’ + stations (four stations are located within the SFTR J Discharge tube cell) and at the locati(ms of major tritium handling 1 /////// FTR cell////// components, e.g., cleanup units, uranium beds, etc. Such components will be located in ventilation hoods, and tritium released during routine Fig. XV-8 maintenance of these components will be carried to a Schematic Diagram of the Tritium Handling small 7 ~/s (I5 cfm) cleanup unit. A larger 4700 J2/s System (10 kcfm) cleanup unit will be provided to rem(we possibly damaging doses of’ 15 Gy/pulse ( 1.5 [ 1013 tritium from the air in the SFTR cell should a rad/pulse) would occur in the capacitors. Also, ac- tritium release occur within the cell. tivation of coils and capacitor structures without a The tritium system described above is designed to primary shield would cause doses in the tunnel of’ provide for 1000 D-T discharges/week, each dis- greater than 1 rem/h for several hours after each charge requiring on the average 15 mg of T?. On the pulse, precluding routine access for maintenance, basis of 20 D-T discharges/week. a total tritium and adjustment. supply of 0.3 g (one week’s supply) will be stored as uranium hydride and 2.(I g (two month’s supply) will A primary shield was, therefore, provided to be in gaseous form. protect the ‘capacitor insulation, minimize air and othep activation throughout the chamber, and shield against activated coils and other magnetic G. Shielding and Activation of the Scyllac Fusion 4 Test Reactor (SFTR) materials. A 0.5-m thick annular shield around the coils consisting of’ laminated aluminum, graphite. Initial analysis of the radiation problems of the and berated-lead polyethylene will reduce the max- & SF”I’R has concentrated on (a) air activation in the imum neutron dose in the capacitors to a negligible cell; (b) doses to organics in the compression load value and cell gamma-ray doses from the coils to -1 coils and in the implosion-heating capacitors [castor mrem/h. Air activity consists primarily of short - oill; (c) activation of the implosion-heating and lived 13N and 16N, 1.83-h 41Ar, 260-y 39Ar, and 5 compression coils; and (d) activation of the 730-y 14C. Calculations, however, show that the air implosion-heating capacitors. Exploratory activities are wit hin allowed occupational levels calculations were made under the assumption of no even before dilutions. primary shield. The results of these calculations are The 1.5-m-thick concrete cell walls provide suf- given in the graph in Fig. XV-9 and show that ficient secondary shielding to reduce the total

219 I

.

.

Neutron Physical Dose (grays)

A In ‘“’” Vessel 0.246 .0 Primary

0 Shield 0.746 E b Air

1.40 ~ Capacitors 1.761-‘L g g “:t- E I ~ ‘ Air I ~b –

~

y _ 0

“$ — 4.16 Concrete * I 11111111 I I 1111111 I 1 II IHII 1 11111111 1 I I 111111 I 1 11!111 1 I IL b

Fig. XV-9 Radiation Levels us Coil Radius

220 biological dose on the outside of the cell to less than design phase. The major effort thus far has been in . the design value of 0.5 rem/yr. the area oft rit ium cent rol, structural and air activa- The neutron transport calculations have been bas- tion by neutrons, radiation shielding, and ed upon a conservatively assumed source of 1.8x1016 chemical/radiation waste. All calculations have been . nlm per D-T discharge and 1000 discharges per year. of’ a preliminary, scoping nature and have served Equivalently, the time-averaged 14.1-MeV neutron primarily a feedback function in the engineering wall loading is 2.0 W/m2. Maximum neutron plus design process. All safety and environmental con- gamma-ray energy densities in the load coils are <1 siderations will be quantified once the SFTR design M.J/mq per pulse, so temperature rises will be <1 K. becomes firm. Transmutation effects in the coils (copper or aluminum) or the Fe-Ni alloy will be minor at the References SFTR fluence levels; namely, <1 ppm/yr. Likewise, maximum dpa value in the Fe, Ni, Al, or Cu is 1. K.I. Thomassen, “A Theta-Pinch Fusion Test -2x 10–8 per pulse, or 2X 10–5 per year which is a Reactor,” Trans. Am. Nucl. Sot. 20 (1975). negligible value. 2. Code of Federal Regulations, Title 10, Part 20, H. Safety and Environmental Aspects “Standards for Protection Against Radiation, ” Appendix B (Jan. 1, 1975). K(IV safety and environmental problems anticipated with the SFTR design have been iden- 3. R. Jalbert, Los Alamos Scientific Laboratory, tified and quantified. H-Division personnel with ex- personal communication, January 1975. (MPC for pertise in the areas of radiology, hydrology, geology, 39Ar is conservative, based upon lens of the eye and meteorology, and industrial hygiene have been iden- skin as critical organs. ) tified for contribution to the safety and environmen- tal aspects of’ the SIWR early in the conceptual

221 JOURNAL ARTICLES

J.P. Adams Internal Coefficient Measurements Phys . Rev. C F.K. Wohn for Transitions i.n 140Xe ~, 1467 (1974) W.L. Talbert, Jr. W.E. Schick, Jr. J.R. McConnell

D.A. Baker Pressure Balance Limitations in Phys . Rev. Lett. J.A. Phillips Z Pinches with Diffusion Heating ~, 202 (1974)

D.1. Brown The Two-Stream Instability Studied J. Computat. Phys. S.J. Gitomer with Four One-Dimensional Plasma Vol. 14, No. 2 H.R. Lewis Simulation Models (1974)

J.H. Brownell Influence of Intense AC Electric Phys . Rev. Lett. H. Dreicer Fields on the Electron–Ion ~, 1210 (1974) R.F. Ellis Collision Rate in a Plasma J.C. Ingraham

J.M. Bunch Damage of Single–Crystal A120~ J. Am. Ceram. Sot. F.W. Clinard, Jr. by 14 MeV Neutrons 57_, 279 (1974)

G.H. Carlson Decays of Mass–Separated 138Xe Phys . Rev. C ~, W.L. Talbert, Jr. and 138CS 283 (1974) J.R. McConnell

D.J. Dudziak Radioactivity Calculations for Nucl. Technol. ~, R.A. Krakowski the Reference Theta-Pinch 32 (1975) Reactor (RTPR)

D.J. Dudziak Neutron Flux Distribution Trans. Am. Nucl. M.L. Simmons Calculations for the WF SOC. 19_, 465 (1974) G.J. Russell Radiation Effects Facility

W.R. Ellis CTR Applications of the High Nucl. Fusion ~, 2 Density Linear Theta Pinch (1975)

W.R. Ellis Plasma Equilibrium and Nucl. Fusion ~, F.C. Jahoda Stability in the Scyllac 841 (1974) R. Kristal Toroidal Sector Experiments W.E. Quinn F.L. Ribe G.A. Sawyer R.E. Siemon

J.P. Freidberg Kink Instabilities in a Phys . Fluids N_, F.H. Haas High-e Tokamak with Elliptic 440 (1974) Cross Section

222 J.P. Freidberg Stability of Diffuse High Beta Nucl. Fusion ~, B.M. Marder Helical Systems 809 (1974) . H. Weitzner

. J.P. Freidberg Endless from a Linear fl Pinch Nucl. Fusion H. Weitzner (To be published)

R.A. Gerwin Energy Loss of a Relativistic, Phys . Fluids Finite Electron Beam in a Plasma (To be published)

W.V. Green Increased Efficiency of a Radiat. Eff. ~, 9 J. Weertman Dislocation Line as a Sink for (1974) Vacancies when it Oscillates

R.F. Gribble Multifringe Electro–Optic Phase Rev. Sci. lnstr. R. Kristal Modulator ~, 520 (1974)

D.W. Hewett Numerical Simulation of a J. Computat. Phys. Radially Inhomogeneous M_, 49 (1974) Cylindrical Plasma

D.W. Hewett Nonlinear Landau Damping in a Phys . Fluids ~, T.P. Armstrong Radially lnhomogeneous Cylindrical 595 (1974) Plasma

R.A. Krakowski Radioactivity Induced in a Theta– Nucl. Technol. D.J. Dudziak Pinch Fusion Reactor (To be published)

R.A. Krakowski Surface Effects at the First–Wall J. Nucl. Mater. F.W. Clinard, Jr. of the Reference Theta–Pinch 53_, 54 (1974) F.L. Ribe Reactor (RTPR) T.A. Coultas

R. Kristal Pulsed HF Laser Holographic Appl. Opt. ~, 628 Interferometry (1975)

H.R. Lewis A Comparison of Three Two- J. Computat. Phys. C.W. Nielson Dimensional Electrostatic Plasma ~, 17 (1975) Simulation Models

B.M. Marder Kink Instabilities in the Phys . Fluids ~, Belt Pinch 447 (1974)

B.M. Marder Kink Instabilities in Arbitrary Phys . Fluids ~, .- Cross–Section Plasmas 634 (1974)

B.M. Marder GAP – A PIC–Type Fluid Code Mathematics of > Computation (To be published)

D. Montgomery Fokker–Planck Equation for a Phys . Fluids ~, L. Turner Plasma in a Magnetic Fieid 954 (1974) G. Joyce

223 D. Montgomery Magnetic Field Dependence of Plasma Phys . Fluids ~, G. Joyce Relaxation Times 2201 (1974) . L. Turner

K.F. McKenna Measurements of Plasma Density Phys . Rev. Lett. . R. Kristal Distribution and Current-Sheath 32_, 409 (1974) K.S. Thomas Structure in the Implosion Phase of a Theta-Pinch Discharge

K.F. McKenna Transient Flow and Expansion of a Plasma Phys. ~, 1 T.M. York Pinch Discharge Plasma i.n Self- (1975) Induced Magnetic Magnetic Fields

G. Miller Motion of a Plasma Column in a Phys . Fluids Perturbing Magnetic Field (To be published)

D.W. Muir Sensitivity of RTPR Afterheat and Trans. Am. Nucl. D.J. Dudziak Radioactivity to Nb-94 Cross Section SOC. @ 465 (1974) Uncertainty

T.A. Oliphant A Mixed Snowplow Bounce Model for Nucl. Fusion ~, Shock Heating in a Staged Theta 377 (1974) Pinch

T.A. Oliphant Monte Carlo Treatment of Heat Flow J. Nucl. Mater. Through a Neutral Gas Layer ~, 62 (1974)

D.M. Parkin Recoil Energy Distributions in Trans. Am. Nucl. A.N. Goland CTR-Related Neutron Spectra SOC. ~, 23 (1974)

W.G. Price D-T Fusion Reactor Activation Trans. Am. Nucl. D.J. Dudziak and Afterheat Sot. ~, 459 (1974)

F.L. Ribe Fusion Reactors as Future Energy Science, 186, 397 R.F. Post Sources (1974)

A.G. Sgro The Collision of a Strong Shock Astrophys. J., Vol. With a Gas Cloud: A Model for 197, May 1975 Cassiopia A (To be published)

R.E. Siemon Polychrometer with Extreme Appl. Opt. ~, 697 Rejection of Stray Light (1974)

P.D. Soran Bonarenko Formalism Applied to Trans. Am. Nucl. D.J. Dudziak Theta-Pinch Reactor Nucleonics SOC. ~, 468 (1974) . K.S. Thomas Plasma Experiments on the Linear Phys . Fluids ~, H.W. Harris Scyllac Theta Pinch 1314 (1974) F.C. Jahoda G.A. Sawyer R.E. Siemon

224 K.I. Thomassen Prospects for Converting Th–232 to Trans. Am. Nucl. . D.J. Dudziak U-233 in a Linear Theta Pinch SOC. ~, 6 (1974) R.A. Krakowski . K.I. Thomassen First Wall Fluxes in a Theta–Pinch J. Nucl. Mater. ~, T.A. Oliphant Feasibility/D–T Experiment 48 (1974)

L. Turner Image Effects in Bounded Plasmas Phys . Fluids ~, 369 (1974)

J. Weertman Theory of Irradiation Growth of J. Nucl. Mater. Fatigue Cracks (To be published)

J.M. Williams Laser-Controlled Thermonuclear Nucl. Technol. ~, T.G. Frank Reactor Materials Requirements 360 (1974)

D. Winske Partial Trapping of a Beam in a Phys . Fluids ~, E.A. Jackson Cold Collisional Plasma 389 (1975)

J.J. Wollan Phase Transition at Hcl for Phys . Rev. B ~, K.W. Haas Superconducting Nb and V 1874 (1974) J.R. Clem D.K. Finnemore

225 FIFTH IAEA CONFERENCE ON PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION RESEARCH . Tokyo, Japan November 1974 .

D.A. Baker Plasma Parameters and Stability Paper IAEA-CN 33/E3 L.C. Burkhardt of the Programmed Pinch J.N. DiMarco Experiment ZT–1 P.R. Forman A. Haberstich R.B. Howell H.J. Karr J.A. Phillips A.E. Schofield

J.H. Brownell Hot Electron Production, Paper CN–33/H–4–2 H. Dreicer Anomalous Absorption and Effect R.F. Ellis of Intense Electromagnetic Fields J.C. Ingraham on Inverse Bremsstrahlung Absorption Near the Electron Plasma Frequency

E.L. Cantrell Plasma Experiments in the Paper CN-33/El–2 W.R. Ellis Scyllac Toroidal Theta Pinch H.W. Harris F.C. Jahoda R. Kristal M.D. Machalek J.R. McConnell W.E. Quinn F.L. Ribe G.A. Sawyer F.T. Seibel R.E. Siemon

J.P. Freidberg Stability of Kink Modes in Paper CN-33/A13–4 J.P. Goedbloed High Beta Tokamaks W. Grossmann F.A. Haas

N.T. Gladd Theoretical and Numerical Paper CN-33/E8–3 D.W. Hewett Studies of High-Beta C.W. Nielson Implosion Heating T.A. Oliphant A.G. Sgro

226 R.A. Krakowski Engineering Deisgn of a Fusion Paper CN-33/G3-3 . R.K. Linford Test Reactor (FTR) and Fusion (A Joint LASL/ANL T.A. Oliphant Engineering Research Facility paper) . F.L. Ribe (FERF) Based on a Toroidal Theta K.I. Thomassen Pinch

K.S. Thomas Implosion Heating Studies in the Paper CN-33/E-8-4 R.F. Gribble Scylla lB, Implosion Heating, and R.K. Linford Staged Theta Pinch Experiments I. Heni-ns J. Marshall A.R. Sherwood J.E. Hammel F.C. Jahoda R. Kristal K.F. McKenna

MEETING OF THE AMERICAN PHYSICAL SOCIETY

Chicago, Illinois February 197.4

F.L. Ribe Physics Problems of Thermonuclear Bull. Am. Phys.

Reactors SOC. @ 85 (1974) K.S. Thomas Scyllac Theta-Pinch Experiments Bull. Am. Phys. Sot. & 99 (1974)

MEETING OF THE AMERICAN PHYSICAL SOCIETY

Salt Lake City, Utah June 1974

D.A. Baker Improved Stability of the ZT-1 Bull. Am. Phys. L.C. Burkhardt Toroidal Pinch by Programming SOC. @ 642 > J.N. DiMarco (1974) P.R. Forman R.B. Howell . H.J. Karr J.A. Phillips A.E. Schofield

D.A. Baker Equilibria and MHD Studies for a Bull. Am. Phys. L.W. Mann High-Beta Tokamak SOC. ~, 642 (1974)

227 EIGHTH SYMPOSIUM ON FUSION TECHNOLOGY

Noordwijkerhout, The Netherlands June 1974

Proceedings Published as Euratom Report EUR 5182e (1974)

D.J. Dudziak Fusion Reactor Nuclear Analysis Methods and Applications

R.A. Krakowski A Technological Assessment of the Reference Theta-Pinch K.I. Thomassen (RTpR) T.A. Coultas

1974 APPLIED SUPERCONDUCTIVITY CONFERENCE

Argonne National Laboratory, Oakbrook, Ill. September 1974

Proceedings Published in IEEE Transactions on Magnetics Msg. 11, No. 2 (1975)

J.D.G. Lindsay Development of A Superconducting Switch p. 594 D.J. Blevins for Magnetic Energy Storage Systems H.L. Laquer G.A. Miranda J.D. Rogers C.E. Swannack D.M. Weldon

G.A. Miranda Adjacent Conductor Field Corrections p. 582 J.D. Rogers to High Critical Current Short Sample Measurements

M.C. Ohmer Improved Superconducting Properties of p. 159 J.J. Wollan Multifilamentary Niobium Carbonitride J.C. Ho Wire

D.M. Parkin Neutron Irradiation of Nb3Sn and NbTi p. 166 A.R. Sweedler Multifilamentary Composites

C.E. Swannack 10 kA 800 kJ Magnetic Energy Transfer p. 504 D.J. Blevins and Storage (METS) Test Facility C.R. Harder J.D.G. Lindsay J.D. Rogers D.M. Weldon

228 CONFERENCE ON ENERGY STORAGE, COMPRESSION AND SWITCHING

Torino, Italy November 1974

Proceedings to be Published

L.C. Burkhardt The Magnetic Energy Storage System Used on ZT-1 R.S. Dike J.N. DiMarco J.A. Phillips R.A. Haarman A.E. Schofield

R.F. Gribble Implosion and Staging Systems for a Theta-Pinch Fusion R.K. Linford Test Reactor K.I. Thomassen

J. Hammel High-Voltage Low-impedance Electrical System for Driving I. Henins a Theta-Pinch Implosion-Heating Experiment J. Marshall A. Sherwood

76TH ANNUAL MEETING OF THE AMERICAN CERAMIC SOCIETY

Chicago, Ill. April 1974

Am. Cer. Sot. Bull., Vol. 53, No. 4

F.W. Clinard, Jr. Ceramics for CTR Systems p. 314

F.W. Clinard, Jr; Electrical Insulator Studied for the p. 364 J.M. Bunch Theta–Pinch Fusion Reactor

229 16TH ANNUAL MEETING, DIVISION OF PLASMA PHYSICS AMERICAN PHYSICAL SOCIETY

Albuquerque, NM ● October 1974

Abstracts published in Bulleting of the American Physical Society ✎ Series II, Vol. 19, No. 9 (October 1974)

N.II.Abt Investigation and Control of Flute-Like MHD Modes in Laser T.R. .Jarboe Plaamas from Pellets W.B. Kunkel A.F. Leitzke G.H. Rankin D.A. Baker Magnetic Field Programming in ZT-1 L.C. Burkhardt J.H. DiMsrco H.J. Karr D.A. Baker Stability of the ZT-1 Toroidal Z Pinch at Reduced L.C. Burkhardt Toroidal Currents J.N. DiMarco A. Haberstich H.J. Karr D.A. Baker Energy and Pressure Balance Consideration in L.C. Burkhardt Z-Pinches J.N. DiMarco A. Haberstich H.J. Karr J.A. Phillips D.C. Barnes Stability of a Toroidal Theta Pinch V.H. Weston G. Berge Equilibrium and Stability of 8=1 Helically Symmetric, J.P. Freidberg Finite 8, Diffuse Plasmas J.U. Brackbill A Numerical Study of the Rotating Theta Pinch

E.L. Cantrell Plasma Column Motion in the Scyllac Torus R. Kristal M.D. Machalek J.R. McConnell W.E. Quinn J.N. DiMsrco Temperature Measurements on ZT–1 P.R. Forman R.B. Howell H.J. Karr W.R. Ellis Beta–Dependence of Axial and Radial Plasma Equilibrium K.B. Freese in the Scyllac Torus R.E. Siemon K.B. Freese Electron Heating and High Energy Tail Formation in a

M.R. fiOSS Turbulent Beam-Plasma System J.E. Walsh J.P. Freidberg Toroidal Kink Mode Stability of a Finite ~, Arbitrary Cross W. Grossman Section, Tokamak Plasma D.A. Freiwald Approximate Spherical Blast Theory with Source Mass R.A. Axford

N.T. Gladd Effects of Finite 6 and Temperature Anisotropy on the Modified Two Stream Instability

230 J.P. Goedbloed The MHD Spectrum of Axially Symmetric Systems R.F. Gribble Shock Heating and Staging Circuit for FTR Test R.K. Linford Module G.P. Boicourt

;.E. Hsmmel The LASL Implosion-Heating Experiment I. Henins T.R. Jarboe J. Marshall A. Sherwood D.W. Hewett Two-Species Vlasov Confinement Equilibria C.W. Nielson .3.Y.Hsu Thermal Relaxation of a Plasma in a Uniform Magnetic G. Joyce Field D. Montgomery L. Turner G. Vahala F.C. Jahoda C.W. Laser Density Measurements on Scyllac R. Krfstal J.W. Lillberg F.T. Seibel

T.R. Jarboe Formation Process of Isolated Laser-Produced Pure W.B. Kunkel Deuterium Plasma Clouds A.F. Lietzke

R. Kristal Holographic Interferometry on Scyllac H.R. Lewis Stability Analysis of Inhomogeneous Plasma Equilibria K.R. Symon A.F. Lietzke Early Stagea of Expansion of Isolated Deuterium Plasma T.R. Jarboe Clouds in a Magnetic Field W.B. Kunkel R.K. Linford Theta Pinch FTR Test Module K.E. Thomassen K.W. Hanks M.D. Mschalek Iz Current Measurements in the Scyllac Torus E.L. Cantrell W.R. Ellis P.C.T. van der Laan

K.F. McKenna Radial Plasma Structure of the Scylla 1-B Theta Pinch R. Kriatal Implosion: Flute Instabilities E. Zimmerman K.F. McKenna Estimation of Laser–Plasma Interactions in the Scylla 1-C T.M. York Theta Pinch G. Miller Scyllac Feedback Stabilization System R. Kristal K.J. Kutac R.F. Gribble C.W. Nielson An Inductive Model for Multidimensional Plasma Simulation H.R. Lewis W.E. Quinn The Scyllac Full Torus Experiment G.H. Rsnkin Plaama-klagneticField Interchange Observed in Laser Plasmas T.R. Jarboe from Pellets W.E. Kunkel A.F. Lietzke

231 F.L. Ribe The Design of the Scyllac Toroidal Theta-Pinch H.W. Harris Experiment E.L. Kemp . W.E. Quinn G.A. Sawyer 4 A.G. Sgro A Hybrid Simulation of Pinch Implosions C.W. Nielson T.A. Oliphant R.E. Siemon Thomson Scattering on Scyllac G.I. Chandler J.W. Lillberg F.T. Seibel K.R. Symon Stability Analysis of BGK Wavea H.R. Lewis K.S. Thomas Experiments in the Staged Theta Pinch Experiment J.N. Downing R.F. Gribble R.K. Linford

232 1. .

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..-( v F. L. Ribe The Theta-Pinch Toroidal Reactor International School of Fusion Reactor Tech- nology, Pulsed Reactor . Course, Erice, Sicily, September 1974

F. L. Ribe Thermonuclear Reactor Systems Conference on Advanced Energy Systems, Denver, Colorado, June 21, 1974

234 OTHER REPORTS

R.A. Krakowski Prospects for Converting Th-232 to U-233 in a USERDA Report D.J. Dudziak Linear Theta-Pinch Hybrid Reactor (LTPHR) ERDA 4 (1975)

D.M. Parkin Computational Method for the Evaluation of Brookhaven A.N. Goland Radiation Effects Produced by CTR-Related National Neutron Spectra Laboratory Report BNL-50434 (1974)

LOS ALAMOS SCIENTIFIC LABORATORY REPORTS

M. Katz, editor Annual Progress Report on LASL Controlled LA-5656-PR Thermonuclear Research Program for a 12- (1974) Month Period Ending December 1974

W.R. Ellis Scaling Laws for the Linear Theta Pinch, LA-5499-MS II: Circulating Power in a High-Field (1974) Reactor

W.R. !?,llis Supplement to Proposal for the Construction LA-5474-P, Suppl. J.P. Freidberg of a Scylla IV-P Confinement Studies Theta (1974) W.E. Quinn Pinch W.R. Ellis Preliminary 1,1,0Feedback Force IA-5788-MS R.F. Gribble Experiments on Scylla IV-3 (1974) C.R. Harder J.P. Freidberg High-Beta Toksmak LA-5476 J. Marshall (1974) A.R. Sherwood D.A. Freiwald Approximate Spherical Blast Theory and LA-5641-MS Laser Initiated Pellet Microexplosions (1974)

D.A. Freiwald Laser Fusion for Laymen LA-5706-MS (1974)

D.A. Freiwald On CTR Breakeven Including Energy Transfer IA-5640-MS R.A. Gerwin and Recovery Efficiencies (1974)

F.C. Jahoda Toroidal Mode Structure in the Scyllac LA-5853-MS R. Kristal Full Torus (1975) W.E. Quinn K.F. McKenna Laser–Plaams Interactions in the IA-5957-MS T.M. York Scylla 1-C Experiment: Preliminary (1975) Analysis

G. Miller Calculation of Magnetic Fields with LA-5779-MS Given, Nearly Cylindrical, Conducting (1974) Walls b J.A. Phillips The Present Status and Future Program 1.A-5530-SR J.N. DiMarco of the ZT-1 Experiment (1974) F.C. Jahoda

J.D. Rogers Magnetic Energy Transfer and Storage I&5748-MS C.E. Swannack (METS) Program Schedules for Fusion (1974) K.T. Thomsssen Test Reactor D.M. Weldon

J. Weertman Potential Fatigue Problems in First-Wall LA-5664-MS Laser-Controlled Fusion Reactors (1974)

235 D.M. Weldon Methods of Energy Transfer from a LA-5631-MS J.D.C. Lindsay Magnetic Energy Storage System Using (1974) a Transfer Capacitor and a Superconducting Switch

J.M. Williams Laser Controlled Thermonuclear Reactor IA-5718-MS T.G. Frank Systems Studies (1974)

* U.S.GOVERNMENTPRINTIN~0F71CE 1975477-343/19

236