Contains research objectives and reports on three research projects.U. S. Atomic Energy Commission under Contract AT(30-1)-1842National Science Foundation (Grant G-9330)U.S. Air Force (Electronic Systems Division) under Contract AF19(604)-599

Allis, W. P.

Bekefi, George

Brown, S. C.

Coccoli, J. D.

Ingraham, J. C.

McCarthy, J. J.

Rose, D. J.

Shapiro, A. H.

Smullin, Louis D.

Terlouw, J. C.

Zimmermann, Henry J.

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PLASMA DYNAMICS*Prof. W. P. Allis Prof. D. J. Rose Prof. L. D. SmullinProf. S. C. Brown Prof. A. H. Shapiro Prof. H. J. ZimmermannRESEARCH OBJECTIVESThis 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 Committee ofthe Massachusetts Institute of Technology. The general objective is to combine the tech-nical 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.XIV. PLASMA PHYSICStProf. S. C. Brown J. F. Clarke J. C. IngrahamProf. W. P. Allis J. D. Coccoli J. J. McCarthyProf. G. Bekefi F. X. Crist W. J. MulliganProf. S. Gruber E. W. Fitzgerald, Jr. J. J. Nolan, Jr.Prof. D. R. Whitehouse P. J. Freyheit G. L. RogoffV. Arunasalam W. H. Glenn, Jr. J. C. TerlouwC. D. Buntschuh R. E. WhitneyRESEARCH 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 production ofplasmas 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 have achieved plasmas of high-percentage ionization by meansof cesium discharges and a hollow-cathode, low-pressure arc discharge.We are also studying ways of determining the characteristics of plasmas by meansof microwaves, infrared optics, and the diamagnetic effect of electrons. Along withthese production and diagnostic studies, we are continuing measurements on the funda-mental physics of loss and gain mechanisms of electrons in plasmas in magnetic fields.Emphasis is also being placed on the study of microwave radiation from plasmas, withand without magnetic fields, both as a tool for measuring the plasma temperature andthermal properties and as a means of understanding more about the motion of electronsand ions in magnetic fields.Theoretical work has been concentrated on the study of waves in plasmas and ofstatistical theories of the nature of a plasma.S. C. Brown*This work is supported in part by the National Science Foundation (Grant G-9330).tThis work was supported in part by the U. S. Atomic Energy Commission underContract AT(30-1)-1842; and in part by the U.S. Air Force (Electronic SystemsDivision) under Contract AF19(604)-5992.(XIV. PLASMA PHYSICS)A. HARMONICS OF ELECTRON-CYCLOTRON EMISSIONFROM A MERCURY-VAPOR DISCHARGEAn increase in the radiation at the electron-cyclotron harmonic frequencies wasobserved in the microwave emission from the positive column of a low-pressure, high-current, mercury-vapor discharge immersed in a magnetic field. Previous measure-ments, 1,2 which were made with low currents and at higher pressures in mercury vaporand other gases, showed increased emission only at the first (that is, fundamental)harmonic.The radiation was received from a section of the positive column, 50 cm long,immersed in a uniform magnetic field oriented parallel to the axis of the column. Theplasma column with a 1-inch diameter was enclosed in a rectangular S-band waveguideby inserting the discharge tube through the broad sides of the waveguide at an angle of80 to the waveguide axis. Thus the propagation vector of the waveguide mode and theapplied magnetic field were roughly parallel.The radiation from the plasma was observed at a fixed frequency o equal to3100 mc, within a bandwidth of 2 mc. The magnetic field was varied from 2000 gaussto zero. As the magnetic field was decreased, an increase in the microwave emissionwas observed whenever the fixed frequency w was equal to a multiple integer, n, ofthe electron's orbital frequency w b = eB/m. Figure XIV-1 shows the power radiated2.3 I6192.2S2.1U)LU 9J1.8-a 1.7wo1.60 0.25 05 075 .0MAGNETIC FIELD (wb/w)Fig. XIV-1. Power radiated from the positive column as a functionof the axial magnetic field. Discharge current, I amp;-1axial dc field, approximately 0.7 volts cm ; vaporpressure in discharge, 0. 0054 mm Hg.(XIV. PLASMA PHYSICS)MAGNETIC FIELD (wb/U)Fig. XIV-2. Radiation temperature of the positive column asa function of the axial magnetic field. Dischargecurrent, I amp; axial voltage, approximately0.7 volts cm--; vapor pressure, 0.003 mm Hg.0.7 volts cm ; vapor pressure, 0. 003 mm Hg.as a function of wb/w. The first harmonic n = 1 was not observed, probably because oflarge internal reflections of the radiation in the vicinity of W b/w = 1. As B decreases,the separation between harmonics decreases and harmonics beyond the eighth are noteasily distinguishable. The peaks of the harmonics are located at the harmonic num-bers n = w/wub = 2, 3, 4, 5 . .. , within an accuracy of ±1 gauss.In Fig. XIV-2 we have plotted the radiation temperature Tr as a function of the mag-netic field, ob/wU. If the free plasma electrons had a Maxwellian distribution of veloci-ties, the radiation temperature T r would equal2 the electron temperature T . Thepronounced harmonics superimposed on a monotonically decreasing background, asshown in Fig. XIV-2, give strong evidence of the non-Maxwellian distribution of elec-tron velocities. The monotonic decrease of the radiation temperature with increasingmagnetic field is indicative of the decrease of the mean electron energy with increasingB; this is in agreement with theory and experiment. 3The mechanism of the generation of the observed higher harmonics is not understood.Harmonics produced by the relativistic motion of electrons with energies of severalelectron volts in the positive column are much too small to account for the observed2.2 I04212.01.9wLU1.8wwUZU0z Iorr(XIV. PLASMA PHYSICS)intensities. Two possibilities are:(a) The helical electron orbits are distorted by the strong space-charge fields inthe plasma sheath.(b) Higher harmonics resulting from the propagation of a wave through a "temperateplasma" in which the finite size of the Larmor orbit must be considered in the compu-tation of the complex conductivity of the plasma. 4G. Bekefi, J. D. CoccoliReferences1. J. L. Hirshfield, Line profiles of cyclotron radiation, Quarterly ProgressReport No. 58, Research Laboratory of Electronics, M.I.T., July 15, 1960,pp. 17-27.2. H. Fields and G. Bekefi, Microwave measurements of the radiation tempera-ture of a plasma in a magnetic field, Quarterly Progress Report No. 62, ResearchLaboratory of Electronics, M.I.T., July 15, 1961, pp. 7-14.3. R. J. Bickerton and A. von Engel, Proc. Phys. Soc. (London) 69B, 468 (1956).4. W. P. Allis and S. J. Buchsbaum, Notes on Plasma Dynamics, Summer Ses-sion Lecture Notes, Department of Physics, M. I. T., 1959.B. BREMSSTRAHLUNG FROM AND RESISTIVITY OF A HIGHLYIONIZED PLASMAPercentages of ionization in an arc discharge in cesium vapor as high as 20 per centwere reported previously.1 The pressures at which the arc operated varied from 3 to29 microns.The experiment has been continued and we have obtained a discharge in cesium-4vapor at pressures as low as 2 X 10-4 mm Hg in a tube with a radius of 1.7 cm, with aconstant magnetic field applied along the axis of the tube in order to make the break-down conditions easier to fulfill. Once the discharge is started it can be maintainedwithout the magnetic field.At these low pressures we could obtain electron densities that closely approacheda fully ionized plasma. However, as soon as the frequency for electron-ion collisionsis large compared with the frequency for electron-atom collisions, the electricaltransport coefficients of the plasma do not change much with an increasing percentageof ionization. The low pressures thus enabled us to decrease the electron density tovalues at which the plasma frequency is less than or equal to the frequency of electro-magnetic waves that can propagate in X-band waveguides, and still maintain approxi-mately 20 per cent ionization. Since the diameter of the tube was just small enoughfor the tube to fit into an X-band waveguide, the electron temperature could be deter-mined with the use of an X-band radiometer.(XIV. PLASMA PHYSICS)1. Bremsstrahlung from Weakly and Highly Ionized PlasmasIf the electrons have a Maxwellian velocity distribution function, the power thatresults from free-free transitions and that is emitted in a frequency interval dw in alldirections and in both polarizations and in the absence of self-absorption, is for a fullyionized plasma: 2dP(w) = 1.09 x 10 -51N N.Z2T- /z G d wm - 3e lwhereN = electron density/m 3N. = ion density/m 3T = electron temperature in 'KZ = ionic chargeG is a slowly varying function of T, w and Ne ; in our case it is approximatelyequal to 7.For discharge currents at which the plasma radiation is well below that of a plasmaradiating as black body the attenuation coefficient is small; thus, since N. ~ Ne , the2 1detected power varies as N if the temperature is a constant.eFor a weakly ionized plasma the bremsstrahlung that results from electron-atominteractions is significant. The temperature dependence of the radiated power is deter-mined by the temperature dependence of electron-atom interactions. As far as theparticle densities are concerned, however, we can expect the emitted power to be pro-portional to N X N , when N is the number of atoms/m 3e a aComparing the emitted power from a fully ionized plasma with that from a weaklyionized plasma, we find a proportionality with Ne and Ne , respectively. If we plotlog P as a function of log Ne or as a function of the log of the current density, thedifference in slope for the curves should be a factor of approximately 2, provided thatthe temperature does not change much with the current. In Fig. XIV-3, P is plottedas a function of the current density on a double logarithmic scale for pressures of0.2 X 10-3 and 14. 5 x 10-3 mm Hg. The angle changes in the anticipated direction.The fact that the difference is less than a factor of 2 means, probably, that at thehigher pressure electron-ion interactions are not negligible. Furthermore, the neglectof the temperature effect makes it unlikely that the results will be very close to thetheoretical prediction.2. Resistivity of a Fully Ionized PlasmaSpitzer and Hiirm 3 find for the resistivity of a fully ionized plasma3GS= 6 .5 3 X 10 3/2 ohm-cm.T3/2(XIV. PLASMA PHYSICS)50P 14.5 X 10- 3 MM Hgz>05-P 0.2X b0 - 3 MMHgN0.2 0.5 10CURRENT (AMPS)Fig. XIV-3. Intensity of the bremsstrahlung from the positivecolumn of an are discharge in cesium vapor as afunction of the discharge current.This equation is based on the assumption that the electric field is so small that thepotential energy gained across one mean-free path of the electrons is negligible ascompared with kT. Here, G is a slowly varying function of the electron density andthe electron temperature. In the region of values for N and T that we have measurede ewe introduce only a small error if we set G = constant, equal to 7. Then we haveI ~ 45.7 X 103 X T - 3/2 ohm-cm (1)a relation in which the electron density does not appear.In Fig. XIV-4, 71 is plotted as a function of the measured temperature. The brokenline represents the resistivity obtained from measurements of arc current and voltage.A total voltage drop of 4 volts resulting from cathode and anode fall was assumed. 4The solid line represents 71 as obtained from (1). Temperature measurements could(XIV. PLASMA PHYSICS)0550 45o>-> 0.350.250.152700 3000 3500 4000 4500TEMPERATURE (OK)Fig. XIV-4. Electrical resistivity of a highly ionized cesium plasma as a functionof the electron temperature.be made only in a limited range of arc currents. A minimum current is determined bythe condition that the plasma must radiate as a black body; that is, the electron densitymust be > 8.5 x 1017/m3 for the frequency at which the radiometer was operating. Anupper limit was introduced by the reflection coefficient on the plasma boundary, whichbecame high at high currents. The measured temperature is higher by a factor ofapproximately 1. 7 than the temperature predicted by Spitzer and Hirm.In order to reduce the diffusion losses (tube diameter was 1. 7 cm) we applied amagnetic field of approximately 600 gauss along the tube axis. The presence of thismagnetic field increased the electron temperature, probably a result of the Lehnerteffect. This rise in temperature may explain the discrepancy between the two curvesin Fig. XIV-4. The influence of a magnetic field on the discharge will be furtherinvestigated.The question may be asked whether or not at the low pressures at which the meas-urements were made, impurities play an important role in the discharge. The tube was-8sealed off at a pressure of approximately 8 X 10-8 mm Hg; the oxide-coated cathodeand also the tube walls must be expected to release gases in considerable amounts. Wethink, however, that the influence of these impurities is small. First of all, cesium isa good getter; second, the ionization potential of cesium (3.87 volts) is much lower than0'O-0""Q MEASUREMENTSSPITZER AND HRMSPITZER AND HARM(XIV. PLASMA PHYSICS)that of the foreign gases, and the average electron temperature in the discharge is solow (< 0. 5 ev) that ionization and excitation of the foreign gases can hardly be expected;third, most measurements were made for values of current and pressure at whichelectron-ion collisions were the main interactions between particles in the discharge,and the frequency for these collisions is independent of the chemical nature of the gas;finally, no appreciable changes in the characteristics of the arc were found afterapproximately two months of use.J. C. TerlouwReferences1. J. C. Terlouw, Arc discharge in cesium vapor, Quarterly Progress ReportNo. 63, Research Laboratory of Electronics, M.I.T., October 15, 1961, pp. 5-8.2. G. Bekefi and S. C. Brown, Am. J. Phys. 29, 404-428 (July 1961).3. L. Spitzer, Jr. and R. Hirm, Phys. Rev. 89, 977 (1953).4. R. K. Steinberg, A Probe Study of Arcs in Cesium Vapor, Ph.D. Thesis,Department of Physics, M.I.T., 1949.C. A TRANSIENT MICROWAVE RADIATION PYROMETERA microwave radiation pyrometer has been described for measuring the radiationtemperature 2 of a steady-state discharge placed in a waveguide. The system describedbelow extends this technique to the measurement of the radiation temperature of awaveguide-contained plasma undergoing some transient process.This technique is being applied, at present, to the measurement of the radiation-temperature decay of a pulsed direct-current discharge in the afterglow. The radiation-temperature decay can be related to the decay of the average electron energy.2 If thedistribution function is Maxwellian, then the radiation temperature equals the electrontemperature. When this condition prevails and when elastic recoil of the hot electronswith the cool gas atoms is the dominant cooling process, the energy dependence ofgvc, the fractional energy loss per second caused by elastic electron-atom collisions,can be determined. This energy loss is determined through the combined use of theexpression for the cooling of electrons caused by elastic collisions with gas atoms 3and a computer program that determines the best form of gv c to fit the temperature-decay curve.The present system is capable of making radiation-temperature measurements at1-4sec intervals over a time interval of 300 psec after the discharge is terminated.The accuracy is approximately ±100 0K over the range of 300°K to 20, 000 0 K, if it isassumed that the standard noise source is exactly known. The discharge is pulsed atthe rate of 1000 times per second and is on for one-fifth of the cycle. The microwave(XIV. PLASMA PHYSICS)MICROWAVE CIRCUIT - 5500MC~1Fig. XIV-5. Transient microwave radiation pyrometer.system operates at 5500 mc.During the first half-cycle, the ferrite switch (Figs. XIV-5 and XIV-6(a)) sends thenoise-standard radiation through the discharge (arm 1) as the discharge is being estab-lished and as it cools down. The discharge has reached room temperature at thebeginning of the second half-cycle, during which the noise-standard radiation is sentthrough arm 2. The resultant signal received by the i-f amplifier is shown inFig. XIV-6(f): in the first half-cycle the amplifier receives the discharge radiationplus that part of the noise-standard radiation that was not absorbed in traversing theplasma, and in the second half-cycle it receives the unattenuated noise-standard radi-ation. A l-4sec variable-delay gate signal (Figs. XIV-5 and XIV-6(j)) then samplesfrom each half-cycle (Fig. XIV-6(k)) of the i-f amplifier signal. These sample pulsesare then integrated, stretched, and filtered until finally the waveform (Fig. XIV-6(o))is identical with the waveform input to the synchronous amplifier for the steady-statepyrometer circuit.The null measurement is now made by adjusting the calibrated attenuator until thereis no signal at the synchronous amplifier. This adjustment results in the effective noise-standard temperature equaling the radiation temperature of the decaying plasma at thegiven time in the afterglow.(XIV. PLASMA PHYSICS)500/SEC 1500SECt=O I 000pSEC IARM I ARM 2 ARM I ARM 2Lt=OVARIABLEDELAYuT hH200-I I II K(a) (b)S I I(a) DISCHARGE RADIATIONPLUS ATTENUATEDSTANDARD(b) STANDARD UNATTENUATEDBY DISCHARGE500LSEC 1500pSECI000 SECF',I L II__ _D- _ __ _L3Fig. XIV-6. Waveforms for transient microwave radiation pyrometer. (Wave-forms F, K, L, and O are shown for a non-null condition.)Preliminary measurements have been made in helium at pressures of 0. 1-6 mm Hgand with curents of 10-300 ma. Helium was chosen because its momentum-lossfrequency is well known and could thus provide a check for the temperature-decaymeasurements. The temperature decay at higher pressures (0. 3-6 mm Hg) isslower than that predicted by an elastic-recoil cooling mechanism. This slownesscould be caused by any of a number of processes, the most likely being the colli-sion between an excited helium atom and an unexcited helium atom which formsthe molecule-ion and an electron with energy of approximately 1 ev. Generally, asthe pressure is decreased, the temperature decay approaches the gv c decay curve.Deviations that depend on longitudinal magnetic field and discharge current are alsonoted at the lower pressures (0. 05-1 mm Hg). Measurements of the dischargetemperature before the afterglow period indicate that these deviations may be caused200-F-200-rB1(XIV. PLASMA PHYSICS)by plasma instabilities that are excited as a result of the breakdown transient. Alonger cycle will be used to test this indication.J. C. Ingraham, J. J. McCarthyReferences1. G. Bekefi, A microwave radiation pyrometer, Quarterly Progress ReportNo. 57, Research Laboratory of Electronics, M.I.T., April 15, 1960, pp. 7-11.2. G. Bekefi and J. L. Hirshfield, Radiation from plasmas with non-Maxwelliandistributions, Quarterly Progress Report No. 59, Research Laboratory of Electronics,M.I.T., October 15, 1960, pp. 3-8.3. W. P. Allis, Motions of Ions and Electrons, Technical Report 299, ResearchLaboratory of Electronics, M.I.T., June 13, 1956, p. 44.

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