Contains research objectives and reports on two research projects.U.S. Atomic Energy Commission (Contract AT(30-1)-1842)U.S. Air Force (Electronic Systems Division) under Contract AF19(604)-5992National Science Foundation (Grant G-24073

Bekefi, George

Brown, S. C.

Hirshfield, J. L.

Jameson, P. W.

Whitehouse, D. R.

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PLASMA DYNAMICSThis heading covers all of the work that is supported in part by the National ScienceFoundation and is under the over-all supervision of the Plasma Dynamics Committeeof the Massachusetts Institute of Technology. The general objective is to combine thetechnical knowledge of several departments, in a broad attempt to understand electricalplasmas, to control them, and to apply them to the needs of communication, propulsion,power conversion, and thermonuclear processes.(The members of the Plasma Dynamics Committee are: Prof. S. C. Brown (Chairman),Prof. D. J. Rose, Prof. A. H. Shapiro, Prof. L. D. Smullin, Prof. H. J. Zimmermann.)XIII. PLASMA PHYSICS*Prof. S. C. Brown F. X. Crist D. T. Llewellyn-JonesProf. G. Bekefi H. Fields J. J. McCarthyProf. D. R. Whitehouse E. W. Fitzgerald, Jr. W. J. MulliganM. L. Andrews W. H. Glenn, Jr. J. J. Nolan, Jr.V. Arunasalam E. B. Hooper, Jr. G. L. RogoffJ. F. Clarke J. C. Ingraham F. Y-F. TseJ. D. Coccoli P. W. Jameson R. E. WhitneyR. L. KronquistRESEARCH OBJECTIVESThe aim of this group continues to be the study of the fundamental properties ofplasmas with particular emphasis on plasmas in magnetic fields. In emphasizing ourinterest in high-density plasmas, we have spent a great deal of effort on productionof plasmas of high-percentage ionization at low pressures under steady-state conditions,the achievement of which will allow us to carry on the fundamental studies in which weare most interested.We are also studying ways of determining the characteristics of plasmas by meansof microwaves and infrared optics. Along with these production and diagnostic studies,we are continuing measurements on the fundamental physics of loss and gain mechanismsof electrons in plasmas in magnetic fields. Emphasis is also being placed on the studyof microwave radiation from plasmas, with and without magnetic fields, both as a toolfor measuring the plasma temperature and thermal properties and as a means of under-standing more about the motion of electrons and ions in magnetic fields.Theoretical work has been concentrated on the study of waves in plasmas and of sta-tistical theories of the nature of a plasma.S. C. BrownA. LOW-FREQUENCY PLASMA WAVESA study has been initiated into the response of plasmas at frequencies much belowthe electron plasma frequency. Our object is to establish longitudinal ion plasma wavesThis work was supported in part by the U.S. Atomic Energy Commission(Contract AT(30-1)-1842); in part by the U.S. Air Force (Electronic Systems Division)under Contract AF19(604)-5992; and in part by the National Science Foundation (GrantG-24073).QPR No. 68(XIII. PLASMA PHYSICS)in a plasma column and measure their propagation and attenuation characteristics. Theexperimental arrangement shown in Fig. XIII-1 has been built and is at present undertest.The fundamental idea behind the experiment is to produce a plasma column with cwmicrowave power into the TE 1 1 1 mode of the cavity. The frequency is adjusted to theelectron-cyclotron frequency for resonance heating at low gas pressures. A small mod-ulation is then impressed on the microwave power to vary the electron heating withinMICROWAVE CAVITY p = 0.05 TO 10 ITE1 MODE"-CYLINDER8._9 CM 2.8 CMMOVABLE-RINGTO PICKUPVACUUMTODETECTORv71.6 CMS-BAND POWER- 105.5 CMMODULATED FROM.02 TO 3 MCFig. XIII-1. Experimental apparatus.the cavity. As the electron energy is varied, the ionization frequency should also bemodulated, and hence there will be a local modulation in the electron and ion density.Simple calculations of the ion plasma wave show that for frequencies of approximately1 mc the wavelength of the ion (and electron) density perturbations can be made as smallas a few centimeters, and we should observe a definite wave propagating down the col-umn.The presence of the wave is particularly easy to determine by measuring the poten-tial that is external to the plasma column at the modulation frequency. Typical dataare shown in Fig. XIII-2.The appearance of the ac potential at the modulation frequency seems to be asso-ciated with the flow of charges in the body of the plasma, and because of the extremelylong wavelength, it must be a flow of the hot electrons rather than the cold ions. Sincethe electron plasma wave is attenuated for frequencies below wp, we were encouragedto re-examine these waves with particular reference to the mechanism for transportof energy. The normal Boltzmann formulation for electron waves is solved for the per-turbation of the distribution function away from some equilibrium distribution. CouplingQPR No. 68(XIII. PLASMA PHYSICS)4000 r3000 - p= 0.1p, ARGON GASEND OFCOILSEND OF5 TUBEBEGINNINGJ LOF CAVITYSHIELD 90I I I I I I I I I80 70 60 50CM40 30 20 10 0Fig. XIII-2. A-C amplitude of 1. 1-mc signal on mov-able ring pickup when S-band powerinto cavity is modulated at 1. 1 mc.this result with Poisson' s equation, we get the dispersion relation (assumingc = 0)S 0 f dv1 0 . (1)np  0 )o -oo (w-k v)The difficulties of this integral are associated with the pole at v = o/k and lead to thephenomenon of Landau damping. If we approximate the denominator for small velocities,we get2 2 2 2S= mW + 3k ( v zp(2)This steady-state dispersion, however, cannot be valid for the more complicatedboundary-value problem in which the electron energy is periodically varied atsome plane. The propagation characteristic will, in fact, depend on the partic-ular variation of the distribution function, and also on the unperturbed distri-bution function.QPR No. 68(XIII. PLASMA PHYSICS)At this point, therefore, we switch to a hydrodynamic approach that assuredly willmiss Landau damping but, on the other hand, will show how momentum and energy aretransported in this longitudinal wave. The derivation starts with the first four momentsof the transport equation. For simplicity, we assume that electrons collide with neutralsand that it is possible to define a local temperature T associated with a Maxwellian dis-tribution of velocities. This derivation thus differs from the Boltzmann approach, whichactually tries to solve for the local distribution.an-t-+ V r= o (3)ar (ne T ne-+ "( ) + E = -vc (4)(nT) +7 TI +- F = - ng v -(T T >(5)a H 5 ne T 5 ne T (6)+- + E=- vH, (6)at 2 m 2 m cwheren = particles/M 3  vc = collisions/secF = particles/M2 sec g = energy-loss parameterI = volts/M sec E = volts/MT = voltsOne can derive Eq. 2 from Eqs. 3 and 4 by making an assumption about the temp-erature variation in the longitudinal wave, that is, either assuming it to be isothermalor adiabatic, and linearizing the equations with small perturbations of the variables. Amore complete analysis is made possible by assuming an arbitrary variation in thetemperature, and by linearizing all four equations. For small-signal analysis, weassume thatH = Hej(wt - kx) T = T + Te j ( wt - kx)-= ej(wt-kx) n = n + nej(wt-kx)E = Eej(wt-kx)Now we set the collision frequency equal to zero, even though this is con-trary to our assumption of a maintained local Maxwellian distribution. The char-acter of the resulting waves will thus become evident, and we can add collisionaldamping later. The determinant of the linearized equations, although rather com-plex, results in a dispersion relation that, when written in nondimensional form,isQPR No. 68(XIII. PLASMA PHYSICS)K 4 + (1-2W 2 ) K2 +-(W 4 W) = 0,5(  =0where W 2 = /2, and K2 = k(eT /m) 2 / P . There are two waves associated withEq. 7,both of which are shown in Fig. XIII-3. Wave I islike the normalelectron plasma wave,while wave II propagates down to zero frequency. The ratio of heat flow H to particleflow F for these waves isH 3 W - 1_FT °  2 K2o KFor wave II, the heat flow is zero at w = wp, and the wavelength is finite. At very lowfrequencies, wave II has a large wavelength and phase velocity equal to the adiabaticelectron sound velocity. This result seems to predict closer correlation with our exper-imental results than Eq. 2.The presence of two electron waves is somewhat plausible, since we know that it isphysically possible to excite independent variations in electron density and temperatureat some plane in the plasma, and thus two waves will be needed to satisfy these boundaryFOR WAVE I22p-1 0K2= k 2 eTo/m2pPFig. XIII-3. Waves associated with w.QPR No. 68(XIII. PLASMA PHYSICS)conditions. Experimental and theoretical work is continuing.D. R. Whitehouse, P. W. JamesonB. DECAMETER RADIATION FROM JUPITERThis report is a summary of a paper that has been submitted for publication toNature.The observed correlation between solar-flare activity and intense radio bursts fromJupiter in the 5-38 mc region has prompted several suggestions about the origins of this1-3radiation. With the premise that the radioactivity is brought on by sudden eruptionsof fast solar electrons as they arrive at Jupiter, we have shown that an existing theory 4 - 6for maserlike amplification of synchrotron radiation from electrons with a non-Maxwellianenergy distribution orbiting in the Jovian magnetosphere can provide a quantitative modelfor the emission.The theory predicts a narrow frequency band of amplification near the local electrongyrofrequency, but the intensity predicted for the second and higher harmonics is smallerthan that of the fundamental by more than four orders of magnitude. Thus the appearanceof a single band of radiation should not rule out the synchrotron mechanism, as hasbeen suggested. 2G. Bekefi, J. L. Hirshfield(Dr. J. L. Hirshfield is in the Department of Physics, Yale University.)References1. J. W. Warwick, Science 132, 1250 (1960).2. L. Landovitz and Leona Marshall, Nature 195, 1186 (1962).3. G. B. Field, J. Geophys. Research 65, 1661 (1960); also "Jupiter's RadioEmission, " Princeton University Observatory Report (unpublished).4. R. Q. Twiss, Australian J. Phys. 11, 564 (1958).5. J. Schneider, Phys. Rev. Letters 2, 504(1959); Z. Naturforsch. 15a, 484(1960).6. G. Bekefi, J. L. Hirshfield, and S. C. Brown, Phys. Fluids 4, 173 (1961);Phys. Rev. 1 1037 (1961).QPR No. 68

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