Contains research objectives and reports on one research project.Joint Services Electronics Programs (U. S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E

Wilheit, T. T., Jr.

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XXII. GASEOUS ELECTRONICS*Academic and Research StaffProf. G. Bekefi Prof. J. C. Ingraham Dr. W. M. ManheimerProf. W. P. Allis Prof. B. L. Wright J. J. McCarthyProf. S. C. Brown W. J. MulliganGraduate StudentsW. B. DavisG. A. GarosiT. T. Wilheit, Jr.RESEARCH OBJECTIVESAn ionized gas can provide a unique environment for populating atomic and molecularstates. For this reason the gaseous electronics group continues to study fundamentalatomic and molecular processes including measurements of cross sections and trans-port properties involving metastable states, molecular ions and free radicals. Theexperimental techniques include the use of microwaves, infrared and optical spectros-copy and lasers.Since the distribution of charged particle velocities plays a dominant role in deter-mining transport characteristics, much attention has been paid in the past to methodsof establishing experimentally and theoretically the distribution function in steady-stateand decaying plasmas.In addition to the above, experimental and theoretical studies are carried out on thepropagation of ion acoustic and diffusion waves, and on the effects of neutral gas turbu-lence on the electrical conductivity of partially ionized gases.G. BekefiA. MEASUREMENT OF ELECTRON-NEUTRAL COLLISIONFREQUENCIES IN AN ARGON PLASMAIn two previous reports, Ingrahaml 2 has reported and discussed a measurement ofcesium electron-atom collision frequencies. Because of disagreement with other pub-lished work,3 it is suggested that these data may be anomalous. In order either to gainconfidence in the cesium data or to understand the anomaly a similar experiment is beingbeing performed in argon.1. ExperimentThe experimental arrangement is shown in Figs. XXII-1 and XXII-2. It is both atransient absorption bridge and a transient radiometer. Thus the microwave absorptionand the temperature can both be measured at any point in the discharge afterglow. Tem-peratures and absorptions are measured as a function of magnetic field strengths. PeakThis work was supported by the Joint Services Electronics Programs (U. S. Army,U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E).QPR No. 88 153(XXII. GASEOUS ELECTRONICS)'- ---K KLYSTRON 5500 MHzI I70-dB ATTENUATORL._ __ .NOISE STD18,000 -KCALIBRATED CALIBRATEDMICROWAVE ATTENUATOR ATTENUATORSWITCHING (TEMPERATURE) MAGIC (PLASMA MICROWAVEDIODE E ABSORPTION) SWITCHINGDIO TEE I -- I IODE2' DIODEMATCHEDLOAD30-MHz GATEDIF AMPLIFIERSYNCRONOUSDETECTORFig. XXII-1. Experimental arrangement.absorption occurs at electron-cyclotron resonance, and the value at the peak is typi-cally from 0. 1 dB to 10 dB for the 22-cm absorption length. Typical temperaturesrange from 300°K to 1500 K. If the measured temperature is independent of magneticfield, the electron velocity distributionis assumed to be Maxwellian.sic \/ The operation of the apparatus hasbeen described previously in detail byIngraham. 1 Some changes have beenmade in the microwave circuit since itwas previously described. The isolationC-B AND  of the adjacent channels of the ferriteMICROWAVE WAVEGUIDECHOKES switch is only approximately 20 dB.ARGON Because of the coherence of the two sig-TUBE nals, this results in some sensitivity toFig. XXII-2. Detail of discharge tube and the phase shift introduced by the plasma.waveguide. To correct this, two microwave switchingQPR No. 88 154(XXII. GASEOUS ELECTRONICS)diodes have been added to give approximately 40 dB isolation. Reflections from theswitching diodes made an additional isolator necessary. The phase sensitivity has beenmeasured with the phase shifter in the plasma arm of the microwave bridge. We foundit to be absent, within experimental error.The cesium tube has been replaced with a sealed argon discharge tube. Pressuresare changed by changing tubes.The parametric amplifier was added to give added sensitivity in the temperaturemeasurements. With this parametric amplifier the entire system has a noise figurearound 4 dB.2. Theoretical ConsiderationsIn a previous report, 3 the author has sketched the derivation of the power absorptioncoefficient2(W 2 2 2 3- 2p x +y = p d v ( V fa = 2dxdy sin2  - -kc vTab 0 v c +(w-kv -/c zwhere p is the electron plasma frequency (noe2/E Om) , and vT - (KT/m)1/ 2 . It wasshown in the previous report 3 that the Doppler shift term, (kv ), could be ignored forthe experimental conditions in question. This left us with24p 2 2 2/y\ oo dvv4a Z dxdy sin + co3kc VTab c0 0The basic assumption made here is that the plasma does not significantly alter the wave-2 2guide fields. Clearly, this is true in the limit w - 0. But, in reality, w is not zero,so this expression for a is not exact. An exact calculation to second order in o2 wouldpbe extremely difficult. In this report, several heuristic models are presented in orderto estimate possible second-order effects. These will be called, for lack of moredescriptive names, "finite k. effect," "upper hybrid effect," "phase velocity effect," and1"dielectric rod effect."a. Finite ki EffectWillett4 has shown that if we allow for the fact that the attenuation length is finite,there is then an imaginary part to the propagation constant k, and a term similar toa Doppler shift arisesQPR No. 88 155(XXII. GASEOUS ELECTRONICS)2W 2 2 2 2a Tab  +y =pkc vTab 0T2 (.r) $dxdy sin (- ) d3 v(v) v fd V x co(v -kiv )2 + (0- )C 1Zwhere ki is the imaginary part of k. As in the previous report, 3 we canvelocity directions and define a resonance function2 2o _ _ 2 2+k 2R. F.( ) 2 c 1 log2 2 3 3 logk v 2ki ck. an- c i - tan13 3 t-Q1integrate over(W-) + (Vc+kiv)v - kiv-1 c -¢e-0This has a half-width at half-maximum of approximately[12 7(ki)2 2 ] 1/2or in terms of a collision probability-[2 2 2 7(ki)1/2jA1/2 cPO - 0. 7(k ) V,Owhere Pc is the collision probability at 1-Torr pressure, po is the pressure in Torr,and (ki)o is the peak value of the imaginary part of the collision frequency. This gives2 22a 1% error when 0. 7(ki)o /Po = 0. 02. The minimum value for Pc for argon is approx-imately 0. 5 cm1 Torr . In this experiment, p = 10 Torr. Thus, for 1% error, k. =-1 o 10. 85 cm . In this experiment, the absorbing length is 22 cm, which corresponds to160 dB power attenuation by the plasma. Therefore this effect is not large for 0.1-10 dBrange of the present experiment.b. Upper Hybrid EffectIn the calculation we have ignored the fact that the magnetic and propaga-tion axes differ by 5.7* (see Fig. XXII-2). So, rather than have a resonanceat the electron-cyclotron resonance frequency, we might expect the resonanceto be that of a right-handed wave propagating at an angle of 5. 7 to the mag-netic field.Allis, Buchsbaum, and Bers 5 give for the index of refraction of a right-handedwave in an electron plasma:QPR No. 88 156(XXII. GASEOUS ELECTRONICS)2 (WZ/2)( 1- W/W)n = 1 - -( 2-Z-z sin 0-Dwhere22 a24  4 42 P cD =-sin + - cos .For our case,2sinE 8<< cos 0,so222 pn = 1-(2/W2) sinz1- - cos2 -p p2n- /w 1- 2/W2) sin2 0with sin2 0 = 0. 0100. Thus the resonant frequency for a right-handed wave propagatingat 5.7 with respect to the magnetic field is 0 + 0. 0005 w2/Wp 2If we substitute this value in our expression for a, consider w a function of position,Pand approximate vc by a constant, we get2 ('ry\ 22 dxdy sin (-a -.0 W(x, y) vS- - 0.005p (+ VApproximate the plasma profile byQPR No. 88 157(XXII. GASEOUS ELECTRONICS)2 2W (x, y) = 1p po2 (x, y) = 0pApproximate sin2 (ry/a)22 22k Wp 2o poa =abk (Wzp/WVgp c )2x2 + y y2for x 2 + y < pfor x 2 + y2 > pby 1 for the region in which o2 0.p2. 5 X 10 5 ( /v - 102-c I)+ 2 - itan-1 5 X) tav tcNote that the absorption depends only on the dimensionless ratios (c2 o/wvc) and(w -2/v). Thus for constant peak absorption the broadening is proportional to pressure(vc). This function was calculated numerically on an IBM 360/65 computer for the pres-ent experimental case (5. 5 GHz in C-band waveguide), and for a 1-cm inner diameterof the discharge tube. The result may be scaled to other tube diameters by noting thatthe total peak absorption is proportional to the square of the inner diameter of the dis-charge tube. We found that the resonance is broadened by 1% for -390 dB total absorp-tion. In the data presented here, the discharge tube I. D. was 0. 6 cm, so this is reducedto 1% broadening for ~110 dB absorption. Thus, once again, we have an effect that maybe ignored in the present experiment.c. Phase Velocity EffectNotice that a is proportional to w/k = vp, the phase velocity of the electromagneticwave. The presence of the plasma does alter this phase velocity. If the waveguide werefilled with a uniform isotropic dielectric, the dispersion relation would be k2 + iz/a2 =K w2/c2k = K w/c2 - /a2where K is the dielectric coefficient. Consider the waveguide to be uniformly filledwith plasma at an averaged density<n> = ab dxdy n(x,y) sin2 .QPR No. 88log 121010 - 3  2 _ 3 - tan-1\oy V158(XXII. GASEOUS ELECTRONICS)The weighting factor of sin2(wy/a) occurs because the energy dissipation at any pointis proportional to the square of the magnitude of the electric field strength. For thelowest waveguide mode (TE 0 1), the electric field has the formE = Ejx sin - cos (kz-t).2 ( a )For the dielectric constant K, take the diagonal part of the cold-plasma dielectric ten-5sor.The resulting half-widths have been calculated numerically on an IBM 360/65 com-puter. Again the broadening is dependent only on the peak absorption. We found that1% broadening occurred for a peak absorption of 15 dB. This may again be neglectedin the present case.d. Dielectric Rod EffectIn all of these models we have assumed that the interaction between the plasma andthe electromagnetic wave was essentially that of a plane wave propagating through aninfinite plasma. The actual geometry is quite the opposite, however. The dimensionsFig. XXII-3. Two-dimensional dielectric rodproblem.of the plasma perpendicular to the direction of propagation are much smaller than awavelength. The interaction can be modeled in the quasi-static approximation, in whichwe approximate the electric fields as the gradient of a scalar potential. We also approx-imate the plasma by a uniform rod of gyrotropic dielectric of radius P.The resulting two-dimensional problem is illustrated in Fig. XXII-3. Let 1 be thescalar potential for r > p.QPR No. 88r=p159(XXII. GASEOUS ELECTRONICS)A B= -Er sin 0 + A-sin 0 + -B cos 08,0 r rand for r < p,€2 = Cr sin 0 + Dr cos 0.For r < p, we have a two-dimensional dielectric tensor K such thatD = EoKEo= oD x K -K X EUsing continuity of 1 and the normal component of D at the boundary r = p, we candetermine the electric field inside the plasma.2E[(1 +K )x-Kxy]E.inside (I+K) 2 + (Kx)2A Awhere x and y are unit vectors in the x and y directions, respectively. The rate ofpower absorption is proportional to E* K E. The values of K and Kx , from Allis,5Buchsbaum, and Bers, are21K = 1 -2 +ivcK - iP2K -2 + ivHence the resonance is shifted by an amount w 2/2w. To estimate the magni-ptude of this effect for the present measurements, we make the very crude approxi-mation that this shifted resonance describes the absorption at each point in anQPR No. 88 160(XXII. GASEOUS ELECTRONICS)inhomogeneous plasma. If we approximate the plasma profile by a parabola, we havean expression identical formally to the expression for the "upper hybrid effect." The(Dzw0m lzwUw9-Fig. XXII-4. Broadening attributable to the"dielectric rod effect."2 5 10 20 xdB/cm2only difference is that we now get the same broadening for 1/100 of the density. Thatis, 1% broadening occurs for 3. 9 dB for a 1-cm I. D. discharge tube. Similarly,for the 0.6 cm I.D. tube of the present experiments, 1% broadening occurs at1. 1 dB. This must be considered in evaluating the data. Figure XXII-4 is a plotofpeak power absorption in dB(inner diameter of the discharge tube)2against percentage of broadening.3. Experimental ResultsWe shall consider the second-order effects negligible for peak absorption<2 dB. This gives ~4% error, because of the "dielectric rod effect." The othereffects are smaller. We shall only use the data for which we can ignore theseeffects. A typical data run, showing absorption and temperature measurementsversus magnetic field, is shown in Fig. XXII-5. In Fig. XXII-6, we show mea-sured half-widths versus temperature for 20.0-Torr argon pressure. Ingraham2has calculated half-widths from the data of Frost and Phelps.6 These are shownalso in Fig. XXII-6. The dashed portion is an extrapolation; it was not cal-culated. Figure XXII-7 shows the same for 10.0-Torr pressure. The uncer-tainties in the half-widths are essentially the uncertainties in individual pointsQPR No. 88 161(XXII. GASEOUS ELECTRONICS)near the half-maximum in the raw data.Another way to analyze the data is to note that the ratio of the peak absorption10009008007001.21.00L125I T= 760 + 40 'K135 140MAGNETIC FIELD (ARBITRARY UNITS)Fig. XXII-5. Typical data run.to the area under the absorption curve is equal toirv , ( v )4f dvv4 fo dv = / cIngraham 2 has calculated these averages also. The data for 10.0 Torr and20.0 Torr, respectively are shown and compared with Ingraham's calculationsin Figs. XXII-8 and XXII-9. The large error bars result from approximatingthe contribution to the area under the curve from the unmeasured portions inthe wings. We have assumed an ( - f) -2 dependence. A numerical fit of theform A/(-) 2 + 62, where A and 6 are fitted to the data in the wing, wouldimprove this.QPR No. 88I II I162SI I I I I I400 600TEMPERATURE (OK)Fig. XXII-6. Half-width data for 20. 0-Torr pressure.5 x 107I I I I I I I400 600TEMPERATURE (OK)Fig. XXII-7. Half-width data for 10. 0-Torr pressure.QPR No. 885 x 101000 20001000 2000163I I I I I I I300 400 500 600 800 1000Fig. XXII-8. -1 data for 10. 0-Torr pressure.x 107 r5 x 104 x 103 x 10-2x 10107I20 0I I I I I I I I300 400 500 600 800 1000Fig. XXII-9. - -1v ) data for 20. O-Torr pressure.QPR No. 886x 107 -5 x 1074 x 107 -3 x 102 x 107 kI2020( 20002000164I ~ ~~ ~ I0I i I I I I I I I00(XXII. GASEOUS ELECTRONICS)4. ConclusionThe agreement between calculations and measurements seems reasonably good.Certainly, if there were an anomaly in Ingraham's data, it is not present here. Thisgives added confidence to Ingraham's data, and, incidentally, to the argon data of Frostand Phelps.T. T. Wilheit, Jr.References1. J. C. Ingraham, Quarterly Progress Report No. 77, Research Laboratory of Elec-tronics, M.I.T., April 15, 1965, pp. 113-118.2. J. C. Ingraham, Quarterly Progress Report No. 81, Research Laboratory of Elec-tronics, M.I.T., April 15, 1966, pp. 63-67.3. T. T. Wilheit, Jr., Quarterly Progress Report No. 86, Research Laboratory ofElectronics, M.I.T., July 15, 1967, pp. 138-142.4. J. E. Willett, J. Appl. Phys. 33, 898 (1962).5. W. P. Allis, S. J. Buchsbaum and A. Bers, Waves in Anisotropic Plasmas (TheM.I.T. Press, Cambridge, Mass., 1963).6. L. S. Frost and A. V. Phelps, Phys. Rev. 136, A1538 (1964).QPR No. 88 165

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