Anomalous electron ion energy transfer in a relativistic electron beam

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VOLUME 4IO, NUMBER 7 PHYSICAL RKVIKW LETTERS 13 FEBRUARY 1978reflex tetrode. With this device, it might be pos-sible to exceed significantly the 200-kA usableproton current produced with a coaxial reflex tri-ode on the Gamble II generator. 'This work was supported by the U. S. Office ofNaval Research and the U. S. Department of En-ergy. One of us (J.A. P) is a National ResearchCouncil Research Associate at the Naval ResearchLaboratory.

J.Golden, C. A. Kapetanakos, S. J.Marsh, and S. J.Stephanakis, Phys. Bev. Lett. 38, 180 (1977).C. A. Kapetanakos, J. Golden, and %.M. Black,Phys. Rev. Lett. 87, 1286 (1976).S. J. Stephanakis, D. Mosher, G. Cooper stein, J.B.Boiler, J. Golden, and S.A. Goldstein, Phys. Bev. Lett.~V, 154' (1976).

S.Humphries, T. J. Lee, and B.N. Sudan, Appl.Phys. Lett. 25, 20 (1974); M. Greenspan, S. Humphries,Jr. , J.Maenchen, and B N. Sudan, Phys. Rev. Lett.89, 24 (1977).D. S. Prono, J.W. Shearer, and B.J.Briggs, Phys.Bev. Lett. 87, 21 (1976).BS.C. Luckhardt and H. H. Fleischmann, Appl. Phys.Lett. 30, 182 (1977).S.A. Goldstein and B.Lee, Phys. Rev. Lett. 85,1079 (1975).J.M. Creedon, I. D. Smith, and D. S. Prono, Phys.Bev. Lett. 85, 911 (1975).T.M. Antonsen, Jr., and E.Ott, Phys. Fluids 19,52 (1976).J.Golden, C. A. Kapetanakos, S. J.Marsh, and S. J.Stephanakis, Naval Research Laboratory Report No.8422, 1976 (unpublished)."F.C. Young, J. Golden, and C. A. Kapetanakos,Bev. Sci. Instrum. 48, 482 (1977).B.A. Mahaffey, J. A. Pasour, J. Go]den, and C. A ~Kapetanakos, to be published.

Anomalous Electron-Ion Energy Transfer in aRelativistic-Electron-Beam-Heated PlasmaJ. D. Sethian and D. A. Hammer '~

U. S. Naval Research Laboratory, washington, D. C. 20375and

C. B.WhartonLaboratory of I'Azsma Studies, Cornell University, ithaca, zvFork 14853(Received 18 May 1977; revised manuscript received 21 November 1977)Studies at Cornell University show experimental evidence for an anomalous electron-ion energy transfer in a relativistic-electron-beam eated plasma that is 10 times fast-er than can be predicted by classical processes. Electron cooling, ion heating, and aconstant total plasma perpendicular energy on a time scale of - 1 JL(sec after electron-beam injection are consistent with an empirically derived electron-ion energy equipar-tion time in the presence of current-driven instabilities.

In recent years, several experimental programshave been implemented to study the potential ap-plication of intense relativistic-electron beamsto controlled thermonuclear fusion research. 'With the capability of delivering several mega-joules of energy in times of the order of 1 psecor less, one of the more promising applicationsof a relativistic-electron beam is the rapid heat-ing of a magnetically confined linear plasma. ' Ex-perimental results to date indicate the beam-to-plasma energy transfer is far faster than can beexplained by classical processes. While severaltheoretical mechanisms have been suggested, 'that which is believed to be responsible for thebeam-plasma coupling in most experiments is theelectron-electron two-stream instability. ' Un-fortunately, this mechanism has the undesirable

characteristic for application to controlled fusionthat it heats primarily plasma electrons insteadof ions. Ion heating is possible via other mecha-nisms, such as excitation of the ion-acoustic in-stability" or generation of large-amplitude mag-netosonic waves."However, it is probable thatthese mechanisms alone cannot provide the ionheating required by a high-density linear reactorsystem. ' In this Letter, experimental evidenceis presented for an observed anomalous electron-ion energy transfer in a magnetized beam-heatedplasma that is approximately 10 times fasterthan classical (1-2 @sec at an initial electrontemperature and density of T, =300 eV and n~=4.5&&10" cm ', respectively).The Cornell University experimental facilityused in the present study is shown in Fig. 1, and


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VOLUM E 40) NUMBER 7 PHYSICAL REVIEW LETTERS 13 FEBRUARY 1978IONENERGYANALYZER MICROWAVE ETER

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described in detail elsewhere. " The work re-ported here extends the previous work by Ekdahlet al. ' to include Thomson-scattering measure-ments of nF and fe(uL), results in a density re-gime where the magnetosonic oscillations are nolonger observed, and a study of the plasma ener-gy partitioning as a function of time. The fullyionized cylindrical target plasma (150 cm longx7 cm jn diam), of initial peak electron densityof n~=4.5~10"cm ', and temperature T, =25eV, is produced by a modified conical gun and in-jected through a curved hexapole guide field intoa solenoidal 2:1 ma, gnetic mirror trap (Bo a,t themidplane =2.6 kG). The resulting plasma columnis 10(Po ionized, free of impurities, and confinedby hard vacuum (P ( 2 x 10 ' Torr) from the 40-cm-diam stainless-steel vacuum-chamber wall.The relativistic-electron beam is produced by anoil-insulated Marx generator driving a 5.9-Q wa-ter-filled pulse line terminated with a planarfield-emission diode. The latter is composed ofa 2.5-cm-radius carbon cathode and a 50-pm-thick Ti anode foil. The electron beam is injectedinto the peak of the upstream (opposite to plasmainjection) mirror, which results in a beam diam-eter of 7 cm at the midplane. Throughout theseexperiments, typical beam parameters were V= 350 kV, I = 22 kA, t = 60 nsec FWHM (full widthat half-maximum). Plasma diagnostics includea ruby-laser-light Thomson scattering system, 'several diamagnetic loops, a 4-mm microwaveinterferometer, a charge-exchange neutral-par-ticle energy analyzer, ' and has d-x-ray studies. "The Thomson-scattering system, ion-energy ana-lyzer, and one diamagnetic loop probed the plas-ma within 20 cm of the mirror midplane.The partitioning of the plasma perpendicular en-ergy is plotted as a function of time after elec-tron-beam injection in Fig. 2. The upper curve

FIG. 2. Summary of the plasma pe rpendic ular energyas a function of time after electron-beam injection.~~ is the total plasma perpendicular energy, and thecomponents g, g i and g;i are representative ofthe nonthermal plasma electron, thermal plasma elec-tron, and plasma-ion perpendicular energies, respec-tively. A typical diamagnetic-loop trace is shown inthe inset.represents W&, the total plasma perpendicularenergy. The curve was compiled from sixteendiamagnetic-loop traces after compensating eachfor the contribution from trapped beam electrons,as determined by hard-x-ray studies. Each tracewas normalized to give jj'J=17.8 J (the mean) att = 600 nsec. Comparison with a typical diamag-netic-loop trace shown in the upper right-handcorner of Fig. 2 shows the trapped-beam-elec-tron contribution accounted for less than 10Fo ofthe observed diamagnetic signal and was signifi-cant only at times t &1 &sec. The region indicatedas ~& was obtained by multiplying the thermalelectron energy density, nJ, kT, L (from Thomsonscattering), by the volume of the plasma column,my~'l, where x~ and l are the column radius andlength, respectively. The use of the entire col-umn length was justified as diamagnetic loopsplaced at different axial positions showed no vari-ations in the plasma heating or risetime. At ~=200 nsec, typical values were T,i=300 eV, n~=4.5&&10"cm ', and ~=9. J=0.55~&. Theregion in Fig. 2 labeled ~&,~ is the contributionto WJ from a nonthermal (high-energy) plasmaelectron component, as observed by Thomsonscattering. ' Approximately 3(Po of the indicatedW,~ was estimated, since such a high-energy"tail," while constituting an appreciable fractionof the total plasma perpendicular energy, containsan insufficient number of electrons per unit ener-gy interval to enable full analysis by Thomsonscattering. For this reason, scattering signalswere obtained only from those electrons with en-ergies E ( 670 eV; a detector centered at E = 811

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VOLUME 40, NUMBER 7 PHYSICAL REVIEW LETTERS 13 FEBRUARY 1978eV yielded an ambiguous signal. ~I&was esti-mated by constructing a high-energy Maxwelliantail, such that scattering from electrons in thisdistribution would be consistent with the observeddata at E ~ 670 eV and below the plasma back-ground light level at E = 811 eV. The resultinghigh-energy component is found to have a char-acteristic temperature of 900 eV and contain ap-proximately 20Fo of the plasma, electrons at t =200nsec, decreasing to 350 eV and 15% at & = 600nsec. Plasma background light prevented Thom-son-scattering measurements at times 200nsee, whereas the decreasing plasma density af-ter beam injection precluded analysis of the high-energy tail at ~ & 600 nsec and the Maxwelliancomponent at t & 12 @sec. The estimated contri-butions of ~~and ~&,& in these regions are in-dicated by the dotted lines. The observed rapiddecrease in W~ at t 8 psec is believed to be dueto the sudden loss of these nonthermal electrons,whereas the late time decay of ~~ is thought tobe due to either charge-exchange losses or scat-tering into the mirror loss cone. These resultsare discussed in detail elsewhere. 'From Fig. 2, it can be seen that at times closeto electron-beam injection (200 nsec), the plas-ma electrons contain almost all the plasma per-pendicular energy, i.e.,an observation consistent with those theories thatpredict the relativistic-beam energy is coupledprimarily to the plasma electrons. "However,at ~ = 600 nsec after beam injection, the electronscontain only 48%%uo of the plasma perpendicular en-ergy. This result suggests a transfer of energybetween electrons and ions. The region indicatedas ~;~ in Fig. 2 is representative of the plasma-ion perpendicular energy, obtained from the dif-ference ~~~,~. Measurements with a charge-exchange neutral-particle energy analyzer yieldion temperatures of T;~ 350 eV, in support ofthis claim. ' Whether this temperature corre-sponded to a Mazovellian distribution or a compo-nent of a high-energy tail could not be ascer-tained due to experimental limitations. However,assuming this measurement to be representativeof an average ion temperature, it is sufficient toaccount for the remainder of the plasma perpen-dicular energy. Since primarily plasma electronswere heated during the beam pulse, these meas-urements indicated a significant electron-ion en-ergy transfer had taken place.

Three possible mechanisms have been suggest-ed as being responsible for this observed anoma-lous electron-ion energy transfer in a time of -1psec; (1) the excitation and dissipation of large-amplitude magnetosonic waves, ' (2) pla, sma tur-bulence induced by a lower-hybrid drift instabil-ity (excited by a, cross-field plasma-electrondrift, ") or (3) plasma turbulence induced by anion-a, coustic instability (excited by a drift paral-lel to the magnetic field).Ion heating via large-amplitude magnetosonicwaves is not a viable mechanism in this regime.Calculations show P= n~k&~/Bo'/2po ~0.05 1,indicating the plasma pressure was not sufficientto result in significant radial expansion againstthe magnetic field lines. Moreover the fast rise,continuous decay, and lack of any oscillatory be-havior in the diamagnetic-loop signals (see inset

in Fig. 2) which were observed at lower plasmadensities' precludes the importance of this mech-anism.The plasma was expected to be unstable to thelower-hybrid drift mode, as the diamagnetic(cross-field) drift velocity exceeded the thermalvelocity of the unheated ions immediately afterbeam injection. However, the amount of energycontained in the cross-field currents was suffi-cient to account for only 5% of the observed in-crease in ~;&.The transfer mechanism was probably facili-tated by turbulence induced in the plasma. Bprobe measurements indicated the net current,I,was approximately 300 A at the terminationof beam pulse. Assuming this current is carried

by a fraction of the plasma electrons, this valueis sufficient for v&= c, during this phase, wherev& is the electron-drift velocity and c, is theplasma sound speed. Moreover, since primarilyplasma electrons were heated by the electronbeam, T, would exceed T;, and the plasma wouldbe unstable to the growth of ion-acoustic waves.The presence of plasma turbulence was manifest-ed by the observed rapid radial expansion of theplasma column, as depicted in Fig. 3, whichshows the rapid decrease in plasma density ona.xis (determined by Thomson scattering) duringthe first 2 &sec after beam injection. Assumingthe total number of plasma particles remainedconstant over this period (which is short com-pared to the 90 scattering time for a 300-eV elec-tron) this decay corresponds to a radial expan-sion from x~=3.5 cm to x~=7 cm in 7 =2 p,sec.Calculations of the anomalous resistivity, p*,using this data and the expression for the cross-

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VOLUME 40, NUMBER 7 PHYSICAL REVIEW LETTERS 13 FEBRUARY 19786.0 I I I I I I I I ) I I I I I I I I

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charge-exchange neutral-particle energy analyz-er and Dr. Martin Lampe for several discussionsregarding the possible transfer mechanisms.The assistance of P. Brown in preparing theseexperiment is also appreciated. The experimen-tal results and a portion of the analysis in thiswork is taken from a thesis submitted by one ofus (J.D.S.) to Cornell University in partia. l ful-fillment of the requirements for the Degree ofDoctor of Philosophy.

field magnetic diffusion time yield4g(a)~ = 1.2 && 10""sec 103''C

where g, is the classical cross-field Spitzerresistivity at T, =300 eV.The classical electron-ion energy relaxationtime (in hydrogen) is approximately 1836 timesthe classical momentum relaxation time. If it isassumed, without particular justification, thatthis relationship is valid for the anomalous relax-ation times in a turbulent plasma, then express-ing the anomalous momentum-transfer collisionfrequency in terms of the anomalous resistivity,v* =rt*&u~, '/4m, where'* =1.2&&10 "sec, givesan energy relaxation time 7& of

Tz -1836/v* =1.7&&10 ' sec.This value is comparable to the decay time ofW, ~ represented in Fig. 2 (approximately 1 &sec),suggesting that some anomalous electron-ion en-ergy transfer, scaling as the anomalous turbulentcollision frequency, is taking place.The authors would like to thank Dr. Michael A.Greenspan for the results of his work with the

'& Present address: Laboratory of Plasma Studies,Cornell University, Ithaca, N. Y. 14868.See, for exmaple, W. F. Dove, K. A. Gerber, andD. A. Hammer, Appl. Phys. Lett. 28, 178 (1976), andreferences therein.See, for example, J. Benford et al. , in Proceedingsof the International Topical Conference on ElectronBeam Research and Technology, edited by G. Yonas(Sandia Laboratories, Albuquerque, New Mexico,1975), pp. 476508.See, for example, B. N. Breizman and D. D. Byu-tov, Nucl. Fusion 14, 878 (1974), and references there-in.L. E.Thode, Phys. Fluids 19, 805, 881 (1976).B.V. E. Lovelace and B.N. Sudan, Phys. Bev. Lett.27, 1256 (1971).6K. B.Chu, B.W. Clark, M. Lampe, P. C. Liewer,and W. M. Manheimer, Phys. Rev. Lett. 35, 94 (1975).See, for example, C. Ekdahl, M. Greenspan, B.E.Kribel, J. Sethian, and C. B.Wharton, Phys. Rev. Lett.33, M6 (1974).J.D. Sethian, Ph.D. thesis, Cornell University,1976 {unpublished) .9M. A. Greespan, Ph.D. thesis, Cornell University,1976 (unpublished) .B.Seraydarian, private communication.iiB.C. Davidson and N. T. Gladd, Phys. Fluids 18,1S27 {1975).

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Anomalous electron ion energy transfer in a relativistic electron beam