Anomalous Electron Ion Energy Transfer In A Relativistic Electron Beam

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VOLUME 4IO, NUMBER 7 PHYSICAL RKVIKW LETTERS 13 FEBRUARY 1978 reflex tetrode. With this device, it might be possible to exceed significantly the 200-kA usable proton current produced with a coaxial reflex triode on the Gamble II generator. ' This work was supported by the U. S. Office of Naval Research and the U. S. Department of Energy. One of us (J.A. P) is a National Research Council Research Associate at the Naval Research Laboratory. 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. T. M. Antonsen, Jr. , and E. Ott, Phys. Fluids 19, 52 (1976). Golden, C. A. Kapetanakos, S. Marsh, and S. Stephanakis, Naval Research Laboratory Report No. 8422, 1976 (unpublished). C. Young, Golden, and C. A. Kapetanakos, Bev. Lett. 85, 911 (1975). Golden, C. A. Kapetanakos, S. J. Marsh, and S. 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, B. Boiler, J. Golden, and S. A. Goldstein, Phys. Bev. Lett. J. J. J. J. J. J. "F. Bev. Sci. Instrum. 48, 482 (1977). J. ~V, 154' (1976). B. A. Mahaffey, J. A. Pasour, Kapetanakos, to be published. J. Go]den, and C. A ~ Anomalous Electron-Ion Energy Transfer in a Relativistic-Electron-Beam-Heated Plasma U. J. D. Sethian and D. A. Hammer '~ S. Naval Research Laboratory, washington, D. C. 20375 and C. B. Wharton Laboratory of I'Azsma Studies, Cornell University, ithaca, Fork 14853 (Received 18 May 1977; revised manuscript received 21 November 1977) ¹zv Studies at Cornell University show experimental evidence for an anomalous electronion energy transfer in a relativistic-electron-beam — heated plasma that is 10 times faster than can be predicted by classical processes. Electron cooling, ion heating, and a constant total plasma perpendicular energy on a time scale of 1 JL(sec after electronbeam injection are consistent with an empirically derived electron-ion energy equipartion time in the presence of current-driven instabilities. - In recent years, several experimental programs have been implemented to study the potential ap- plication of intense relativistic-electron beams to controlled thermonuclear fusion research. ' With the capability of delivering several megajoules of energy in times of the order of 1 psec or less, one of the more promising applications of a relativistic-electron beam is the rapid heating of a magnetically confined linear plasma. ' Experimental results to date indicate the beam-toplasma energy transfer is far faster than can be explained by classical processes. While several theoretical mechanisms have been suggested, ' that which is believed to be responsible for the beam-plasma coupling in most experiments is the electron-electron two-stream instability. Unfortunately, this mechanism has the undesirable ' characteristic for application to controlled fusion that it heats primarily plasma electrons instead of ions. Ion heating is possible via other mechanisms, such as excitation of the ion-acoustic instability" or generation of large-amplitude magnetosonic waves. However, it is probable that these mechanisms alone cannot provide the ion heating required by a high-density linear reactor system. ' In this Letter, experimental evidence is presented for an observed anomalous electronion energy transfer in a magnetized beam-heated plasma that is approximately 10 times faster than classical (1-2 @sec at an initial electron temperature and density of T, =300 eV and n~ =4. 5&&10" cm ', respectively). The Cornell University experimental facility used in the present study is shown in Fig. 1, and " VOL UM E 40) NUMBER 7 PHYSICAL REVIEW LETTERS ION 13 FEBRUARY 1978 30 MICROWAVE BEAM CURRENT MON I TOR BEAM ENERGY ANALYZER PLASMA GUN INTERFEROM ETER RECEIVER GUIDE I I I I I I I I I I I I I ELECTRODES FIELD MAGNETIC MIRROR 19.5 J/DIV OIL-FILLED MARX VOLTAGE MONITOR ~h KG I 1 COILS 20— (/) LLj I 0 0CI 0' +DD 0DQ ''0 n O n DD I II I on VALVE DD 5.8 DIODE (Mh FiLLED FARADAY I CUP PULSE LINE SLOW D. LO / a ~~By LOOP TITANIUM IO— PROBE GETTER PUMP FARY DIAMAGNETIC MICROWAVE TRANSMITTER THOMSON SCATTERING REGION 0 O. I I.O t (/LSEC ) IO IOO FIG. 1. The Cornell University relativistic-electronbeam — plasma exper imental facility. described in detail elsewhere. The work reported here extends the previous work by Ekdahl et al. ' to include Thomson-scattering measurements of nF and fe(uL), results in a density regime where the magnetosonic oscillations are no longer observed, and a study of the plasma energy partitioning as a function of time. The fully ionized cylindrical target plasma (150 cm long x7 cm jn diam), of initial peak electron density of n~=4. 5~10" cm ', and temperature T, =25 eV, is produced by a modified conical gun and injected through a curved hexapole guide field into a solenoidal 2:1 ma, gnetic mirror trap (Bo a, t the midplane =2. 6 kG). The resulting plasma column is 10(Po ionized, free of impurities, and confined by hard vacuum (P 2 x 10 ' Torr) from the 40cm-diam stainless-steel vacuum-chamber wall. The relativistic-electron beam is produced by an oil-insulated Marx generator driving a 5.9-Q water-filled pulse line terminated with a planar field-emission diode. The latter is composed of a 2. 5-cm-radius carbon cathode and a 50-pmthick Ti anode foil. The electron beam is injected into the peak of the upstream (opposite to plasma injection) mirror, which results in a beam diameter of 7 cm at the midplane. Throughout these experiments, typical beam parameters were V = 350 kV, I = 22 kA, t = 60 nsec FWHM (full width at half-maximum). Plasma diagnostics include a ruby-laser-light Thomson scattering system, ' several diamagnetic loops, a 4-mm microwave interferometer, a charge-exchange neutral-particle energy analyzer, ' and has d-x-ray studies. The Thomson-scattering system, ion-energy analyzer, and one diamagnetic loop probed the plasma within 20 cm of the mirror midplane. The partitioning of the plasma perpendicular energy is plotted as a function of time after electron-beam injection in Fig. 2. The upper curve " FIG. 2. Summary o f the plasma pe rpendic ular energy as a function of time after electron-beam injection. ~~ is the total plasma perpendicular energy, and the components g„,» g «i and g;i are representative of the nonthermal plasma electron, thermal plasma electron, and plasma-ion perpendicular energies, respectively. A typical diamagnetic-loop trace is shown in the inset. W&, the total plasma perpendicular energy. The curve was compiled from sixteen diamagnetic-loop traces after compensating each for the contribution from trapped beam electrons, as determined by hard-x-ray studies. Each trace was normalized to give jj'J=17.8 J (the mean) at t = 600 nsec. Comparison with a typical diamagnetic-loop trace shown in the upper right-hand corner of Fig. 2 shows the trapped-beam-electron contribution accounted for less than 10Fo of the observed diamagnetic signal and was significant only at times t &1 &sec. The region indicated as ~«& was obtained by multiplying the thermal electron energy density, nJ, kT, L (from Thomson scattering), by the volume of the plasma column, my~'l, where x~ and l are the column radius and The use of the entire collength, respectively. umn length was justified as diamagnetic loops placed at different axial positions showed no variations in the plasma heating or risetime. At ~ =200 nsec, typical values were T, i=300 eV, n~ =4. 5&&10" cm ', and 4 J=0.55~&. The region in Fig. 2 labeled ~&,~ is the contribution to WJ from a nonthermal (high-energy) plasma electron component, as observed by Thomson scattering. ' Approximately 3(Po of the indicated W„, ~ was estimated, since such a high-energy "tail, " while constituting an appreciable fraction of the total plasma perpendicular energy, contains an insufficient number of electrons per unit energy interval to enable full analysis by Thomson scattering. For this reason, scattering signals were obtained only from those electrons with energies E 670 eV; a detector centered at E = 811 represents ( ~„=9. " ( 452 VOLUME 40, NUMBER 7 PHYSICAL REVIEW LETTERS 13 FEBRUARY 1978 eV yielded an ambiguous signal. ~I„& was estimated by constructing a high-energy Maxwellian tail, such that scattering from electrons in this distribution would be consistent with the observed data at E ~ 670 eV and below the plasma background light level at E = 811 eV. The resulting high-energy component is found to have a characteristic temperature of 900 eV and contain approximately 20Fo of the plasma, electrons at t =200 nsec, decreasing to 350 eV and 15% at & = 600 nsec. Plasma background light prevented Thomson-scattering measurements at times «200 nsee, whereas the decreasing plasma density after beam injection precluded analysis of the highenergy tail at ~ & 600 nsec and the Maxwellian component at t & 12 @sec. The estimated contributions of ~„~ and ~&,& in these regions are indicated by the dotted lines. The observed rapid decrease in W~ at t 8 psec is believed to be due to the sudden loss of these nonthermal electrons, whereas the late time decay of ~~ is thought to be due to either charge-exchange losses or scattering into the mirror loss cone. These results are discussed in detail elsewhere. ' From Fig. 2, it can be seen that at times close to electron-beam injection («200 nsec), the plasma electrons contain almost all the plasma perpendicular energy, i.e. , Three possible mechanisms have been suggested as being responsible for this observed anomalous electron-ion energy transfer in a time of psec; (1) the excitation and dissipation of largeamplitude magnetosonic waves, ' (2) pla, sma turbulence induced by a lower-hybrid drift instability (excited by a, cross-field plasma-electron drift, ") or (3) plasma turbulence induced by an ion-a, coustic instability (excited by a drift parallel to the magnetic field). Ion heating via large-amplitude magnetosonic waves is not a viable mechanism in this regime. Calculations show P= n~k&— , ~/Bo'/2po ~0.05 the indicating plasma pressure was not sufficient to result in significant radial expansion against the magnetic field lines. Moreover the fast rise, continuous decay, and lack of any oscillatory behavior in the diamagnetic-loop signals (see inset in Fig. 2) which were observed at lower plasma densities' precludes the importance of this mech- -1 «1, anism. The plasma was expected to be unstable to the lower-hybrid drift mode, as the diamagnetic (cross-field) drift velocity exceeded the thermal velocity of the unheated ions immediately after beam injection. However, the amount of energy contained in the cross-field currents was sufficient to account for only 5% of the observed in- crease in ~;&. The transfer mechanism was probably facilitated by turbulence induced in the plasma. B probe measurements indicated the net current, I„„,was approximately 300 A at the termination of beam pulse. Assuming this current is carried by a fraction of the plasma electrons, this value is sufficient for v&= c, during this phase, where v& is the electron-drift velocity and c, is the plasma sound speed. Moreover, since primarily plasma electrons were heated by the electron beam, T, would exceed T;, and the plasma would be unstable to the growth of ion-acoustic waves. The presence of plasma turbulence was manifested by the observed rapid radial expansion of the plasma column, as depicted in Fig. 3, which shows the rapid decrease in plasma density on a.xis (determined by Thomson scattering) during the first 2 &sec after beam injection. Assuming the total number of plasma particles remained constant over this period (which is short compared to the 90 scattering time for a 300-eV electron) this decay corresponds to a radial expansion 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 cross453 an observation consistent with those theories that predict the relativistic-beam energy is coupled However, primarily to the plasma electrons. at ~ = 600 nsec after beam injection, the electrons contain only 48%%uo of the plasma perpendicular energy. This result suggests a transfer of energy between electrons and ions. The region indicated as ~;~ in Fig. 2 is representative of the plasmaion perpendicular energy, obtained from the dif- " ference ~~ —~, ~. Measurements with a chargeexchange neutral-particle energy analyzer yield ion temperatures of T;~ 350 eV, in support of this claim. ' Whether this temperature corresponded to a Mazovellian distribution or a component of a high-energy tail could not be ascertained due to experimental limitations. However, assuming this measurement to be representative of an average ion temperature, it is sufficient to account for the remainder of the plasma perpendicular energy. Since primarily plasma electrons were heated during the beam pulse, these measurements indicated a significant electron-ion energy transfer had taken place. VOLUME 40, NUMBER 7 6.0 I I PHYSICAL REVIEW LETTERS I 13 FEBRUARY 1978 I I I I I ) I I I I I I I I c +0— V Cl Typlcol Uncetointy IO — o 20— C CL .0 .I I.O 5.0 (@SEC) IO.O t FIG. 8. Electron density beam injection. n& vs time after electron- charge-exchange neutral-particle energy analyzer and Dr. Martin Lampe for several discussions regarding the possible transfer mechanisms. The assistance of P. Brown in preparing these experiment is also appreciated. The experimental results and a portion of the analysis in this work is taken from a thesis submitted by one of us (J.D. S.) to Cornell University in partia. l fulfillment of the requirements for the Degree of Doctor of Philosophy. field magnetic diffusion time yield 4g(a„)~ 7'C = 1.2 && 10" " sec 103' „ '& Present address: Laboratory of Plasma Studies, Cornell University, Ithaca, N. Y. 14868. See, for exmaple, W. F. Dove, K. A. Gerber, and D. A. Hammer, Appl. Phys. Lett. 28, 178 (1976), and v* =rt*&u~, '/4m, where'* =1.2&&10 an energy relaxation time 7& of Tz g, is the classical cross-field Spitzer resistivity at T, =300 eV. The classical electron-ion energy relaxation time (in hydrogen) is approximately 1836 times the classical momentum relaxation time. If it is assumed, without particular justification, that this relationship is valid for the anomalous relaxation times in a turbulent plasma, then expresscollision ing the anomalous momentum-transfer frequency in terms of the anomalous resistivity, where "sec, gives -1836/v* =1.7&&10 ' sec. This value is comparable to the decay time of 1 &sec), W, ~ represented in Fig. 2 (approximately suggesting that some anomalous electron-ion energy transfer, scaling as the anomalous turbulent collision frequency, is taking place. The authors would like to thank Dr. Michael A. Greenspan for the results of his work with the references therein. See, for example, J. Benford et al. , in Proceedings of the International Topical Conference on Electron Beam Research and Technology, edited by G. Yonas (Sandia Laboratories, Albuquerque, New Mexico, 1975), pp. 476 — 508. See, for example, B. N. Breizman and D. D. Byutov, Nucl. Fusion 14, 878 (1974), and references therein. 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) . ii B. Seraydarian, B. C. Davidson and N. 1S27 {1975). private communication. T. Gladd, Phys. Fluids 18, 454