Contains research objectives and reports on two research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 36-039-AMC-03200(E

Brown, S. C.

Waletzko, J. A.

Wright, B. L.

DSpace@MIT

XVI. GASEOUS ELECTRONICSAcademic and Research StaffProf. S. C. Brown Prof. G. Bekefi J. J. McCarthyProf. W. P. Allis Prof. J. C. Ingraham W. J. MulliganDr. D. R. WhitehouseGraduate StudentsJ. C. de Almeida Azevedo G. A. Garosi T. T. Wilheit, Jr.A. J. Cohen L. D. Pleasance B. L. WrightJ. A. WaletzkoRESEARCH OBJECTIVESA great deal of effort continues to be spent on the fundamental interaction of theparticles of plasma physics. In this group we have concentrated on measuring diffusioncoefficients, collision probabilities, particularly in partially ionized and fully ionizedgases, and on the mechanism of production of radiation. Within the last few years wehave studied the production of microwave radiation, and we are pushing this towardshorter and shorter wavelengths in the direction of the very long infrared. Our objectivein this area is to study as many of the mechanisms involved in electron-atom andelectron-molecule collisions as are susceptible to our microwave, infrared, and probetechniques.S. C. BrownA. MICROWAVE MEASUREMENTS OF A TIME-DEPENDENT ELECTRONVELOCITY DISTRIBUTION FUNCTIONThe aim of the present work is to extract information about the velocity distributionof electrons in a plasma from measurements of the spectrum of emitted radiation.Microwave emission from plasmas has been a subject of continuing interest in this lab-oratory and the work reported here represents an extension of techniques developed byH. Fields, G. Bekefi, and S. C. Brown for the study of cyclotron radiation from weaklyionized discharges. Basically, the method involves measurement of the power per unitfrequency (intensity), IT( ), of radiation received from a plasma column inserted in awaveguide. For an optically thick plasma in thermal equilibrium, this intensity is givenby IT(w) = kT in the limit hw << kT. In this context , we define an effective radiationtemperature, Tr(w), by the relation IT(w) = kTr(w). Thus, if the emission can beattributed to the motions of individual electrons (the weakly ionized case), the departureof Tr(w) from a constant value reflects the departure of the electron velocity distribution,f(v), from a Maxwellian. These effects are most easily observed in the neighborhood ofthe electron cyclotron frequency of an applied magnetic field. In the present study,Tr(w) and hence f(v) are examined as functions of time by sampling the radiation duringThis work is supported by the Joint Services Electronics Programs (U. S. Army,U. S. Navy, and U. S. Air Force) under Contract DA 36-039-AMC-03200(E).QPR No. 80(XVI. GASEOUS ELECTRONICS)various 1l-isec intervals in the afterglow of an argon discharge pulsed at a rate of-1200 secOff resonance, the plasma column may not be fully opaque with respect to the radia-tion. To overcome this defect, it has been customary to provide an incident noise sig-nal, Io, at one end of the waveguide and to balance this against the emergent signal, II,received at the other. Thus, for a plasma slab of width X and absorption coefficient,a(x), the balance condition gives I = I = EI0 + (I-E)IT, where E = expL- " a dx .L )0NOISESOURCE 4 6VARIABLE FERRITE COMPARISONATTENUATOR SWITCH RADIOMETERNOISE---- 13 I 1SOURCE PULSED 3 5 7DISCHARGE 2Fig. XVI-1. Fig. XVI-2.Diagram of waveguide system. Illustrating power flow.The apparatus previously employed for this measurement was one in which I and I werealternately sampled by a ferrite switching device before amplification and comparison ina synchronous detector. Because the isolation of the two channels in the switch could bemade scarcely better than 20 db, serious errors arose from interference effects. Indeed,if E were not small, that portion of I1 coherent with Io could, by leaking through theswitch and interfering with the Io sample, produce errors as great as 20% in the meas-urement of Tr G)The present form of the waveguide system shown in Fig. XVI-1 is one which elim-inates these effects. Directional couplers are used to feed the signals of two noisesources through the same variable attenuator and into the two branches of the system.Figure XVI-2 illustrates the power flow and the pertinent intensities in each section.Ferrite isolators are used to quench any reflected signals. The intensities 13 and 14 arerelated to the incident signals and the attenuator setting by13 = Y6 1 (11 +-I2 ) 14 = Y6 2(I21 1i'where y is the fraction of incident power transmitted through the variable attenuator,and the 5 represent the 3-db losses in the couplers plus any fixed attenuations.The parameters crl and a2 defined by these equations represent leakage across thecoupler system and are not independent of y. By choosing the sampled microwave fre-quency (3020 Mc) carefully, it was possible to obtain o < 10 - 3 over the range of y used.The intensity 15 is given as indicated above by 15 = EI 3 + (1-E)IT. Finally, 16 and 17 areQPR No. 80 100(XVI. GASEOUS ELECTRONICS)the received intensities when the switch samples the upper and lower branches. Ifwe let p represent the leakage fraction between the two channels in the switch, theseintensities are given by16 = 14 ~ P1I5 17 = 15 2 1 16'where @ indicates that coherent components (originating from the same noise source)in the combined intensities must be added vectorially, not algebaically.In practice, one adjusts I1 with no plasma (E=1) to obtain the balance 16 = 17. Then,with the discharge on (E#1), y is varied to again balance the outputs. Working out thedetails, one finds the balance condition to beI 662 + Pl -Z + terms of order -'Tand 1-_"1Thus IT is proportional to y, providing the terms that depend on a- and E are small.The denominator (1-E) merely reflects the loss of sensitivity off-resonance as theplasma becomes transparent. Indeed, forthe effects of interference to be important,we only require cr, 1-r < T, where AT6 rARGON PRESSURE is the minimum detectable temperature ofS50.718 TORR -2 -3P CURR the radiometer. With AT ~ 10 T , < 10PULSE CURRENT r< 4 12.2 ma and p < 10 , this inequality is satisfied.-~ Y 0* The constant relating T to y is deter-S2 s. mined from a standard discharge of known2 5 temperature situated in the lower branchS- of the system.o12ps A sample of data taken by this method0.7 8 0.9 1.0 1.1 1.2 1.3 is shown in Fig. XVI-3. Here, as is oftenthe case, it is the magnetic field (wB), andFig. XVI-3. not the sampled frequency w, which isData sample. varied. The five curves give averages ofTr(w/wB) over l- ±sec intervals triggeredat the afterglow times indicated. They represent the development of an originallynon-Maxwellian distribution of electron velocities which is allowed to relax after themaintaining electric field is removed. The disappearance of the resonant peaks withtime indicates the relaxation to a Maxwellian (T r() = constant). This is accompaniedby a decrease in the mean electron energy.To proceed beyond these general remarks, the detailed mechanisms of emission andabsorption in the discharge must be considered. For the weakly ionized case, Tr (0)has been shown I to depend on f(v) through the relationQPR No. 80(XVI. GASEOUS ELECTRONICS)o v(v) v40 v(v) 2 f(v) dvo v(v) + (+-2kTr(w) -v)4 _fdvO v (v) + ( WB)2 auwhere v(v) is the collision frequency for momentum transfer between electrons and neu-1 2.tral atoms, and U = -mv is the electron energy. Here the electron velocity distribution,f(v), is assumed to be isotropic - a condition well met by the experiment. If the denom-inator on the right side of this expression is moved over to the left, the result is a lin-ear, homogeneous relation that, in principle, can be solved for f(v) once Tr(W/W B) andv(v) are known. The scatter in the measured values of Tr, however, will not permitdetermination of the details of f(v). One must assume a form for f(v) based on a fewvariable parameters which can then be adjusted to best fit the data. The form nowemployed is2N1f() -(v/w) 2f(v) = e FnH2 n(v/Wo),3/2 3 n=T w n= 0oa Maxwellian term times a correction factor represented here as a finite sum of Her-mite polynomials of even degree with variable coefficients F . If a value of the scalefactor wo is assumed, substitution of this form in the preceding relation yields, for eachdata point, a linear equation in the F . The equations thus generated are solved in theleast-squares sense to obtain the best fit to Tr(w) from the assumed form of f(v). Itshould be noted that w 0 may be chosen at will, but this freedom can be removed byrequiring that the Maxwellian term have the same mean energy as f(v). Furthermore,should f(v) as given be negative beyond some cutoff velocity vc, it is to be taken asstrictly zero for v > vc, and this fact must be incorporated in the evaluation of allrequired integrals.A computer program has been developed to invert the relation between T r() and f(v)in the manner described above. Tests show that if only a few independent coefficientsare required, the results are fairly insensitive to errors of the kind that may beexpected from the experiment. Figure XVI-4 shows the results of applying this treat-ment to the data of Fig. XVI-3. Plots of v f(v) are shown scaled for comparison in eachcase with a Maxwellian of the same mean energy, U. The first two curves are based onfour independent coefficients; the rest, on three. The solid curves of Fig. XVI-3 givethe fitted emission peaks based on these distributions. Roughly speaking, the time scaleof relaxation is ~6 F sec - a figure not inconsistent with the rate expected from electron-electron collisions. Also apparent is a rapid initial decrease in U at a rate comparableQPR No. 80 102(XVI. GASEOUS ELECTRONICS)/ \ .2 5sevc // U 1.6evO Ot5 sec t5 12Lsec/ U: 2.2ev U 1.2evo o0Fig. XVI-4. Results of computer program appliedto data of Fig. XVI-3.to that of the relaxation and far greater than expected from electron-atom collisions. Theelectron density in this case, as determined with a microwave cavity, remained constantat -1. 0 X 1010 cm 3 throughout the interval of interest.Thus far, trials have been made with argon pressures of 0. 2-0. 8 torr and dischargecurrents of 10-35 ma. Further work will be devoted to extending these ranges andstudying the effects of metastable atoms on the relaxation process.B. L. WrightReferences1. H. Fields, G. Bekefi, and S. C. Brown, Phys. Rev. 129, 506 (1963).B. RADIOFREQUENCY DIPOLE RESONANCE PROBEIn Quarterly Progress Report No. 74 (pages 91-98) D. F. Smith and G. Bekefi pre-sented a theory for the spherical dipole resonance probe. They derived an expressionfor the complex admittance of a probe-plasma system in which the sheath region aroundthe conducting dipole sphere was assumed to be a vacuum and the surrounding plasmaextended to infinity. Numerical evaluations of the series solution show that theseries converges very slowly. A large number of terms are required, because of thefringing electric fields in the region near the infinitesimal gap separating the two hemi-spheres of the idealized dipole. In order to minimize the effect of this small region ofQPR No. 80 103(XVI. GASEOUS ELECTRONICS)the probe on the solution for the admittance, the probe hemispheres were constructedas shown in Fig. XVI-5. By rounding the edges of the hemisphere with a known curva-ture, it is possible to use the geometry of the experimental probe in the boundaryR +d4sin e3RFig. XVI-5. Dipole hemisphere.conditions for the potential in the theoretical problem.The potential on the surface of the probe is represented as a series of Legendrepolynomials whose coefficients are determined by a least-squares fitting method. Under1 3 5 7 913579 11 13 15 17Fig. XVI-6. Ratio of calculated admittance forto that of probe with a sharp edge.probe with a round edgeQPR No. 80ZaDI0i104SUSCEPTANCE4TrEopaCONDUCTANCEA 0.22/ f 1.2v = 0.20.565 0.8550.2 0.4 0.6 0.8 1.0 1.2w/ wp0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8w/wpFig. XVI-7. Theoretical admittance vs normalized fre- Fig. XVI-8.quency for probe with rounded edge.Theoretical admittance vs normalized fre-quency for probe with founded edge.5.00-1.0-2.00.9 1.0CONDUCTANCEA9.5 Mc20fR 78 M-2-4-840 50 60 70 80 90 100 110FREQUENCY ( M )9.5 Mc2.fR 71.5Mcr I ix "X .r V-/ *xr30 40 50 60 70 80 90 100 110FREQUENCY ( Mc )Fig. XVI-9. Measured admittance for a probe with1.75-in. diameter.Fig. XVI-10. Measured admittance for a probe with2-in. diameter.(XVI. GASEOUS ELECTRONICS)the assumption that the presence of the plasma has a negligible effect on the potential inthe region near the rounded corner (which is true if fringing fields do not penetrate theplasma), the potential, V, can be determined at r = R as a function of 0. We now havea spherical boundary condition, V = V(@) at r = R, and the derivation proceeds as before.1Figure XVI-6 shows the effect of rounding the hemisphere edge on the solution for theadmittance. Here, f is the summation index in the series solution. Changing the gapsize for the probe with the rounded edge has a negligible effect on its contribution to theadmittance. Higher order terms are greatly reduced in magnitude and the series nowconverges rapidly.Figures XVI-7 and XVI-8 are theoretical plots of the real and imaginary parts of theadmittance of a round-edged probe. The admittance values are normalized to the free-space admittance of an ideal dipole at the plasma frequency. Here, f is the ratio ofsheath radius (measured from center of probe) to the probe radius, and v is the effectivecollision frequency normalized to the plasma frequency. In Fig. XVI-8 the contri-butions of terms in the series for f > 1 cause a kink in the admittance curves. Anincrease in v causes the kink to disappear.The experimental arrangement has been illustrated previously.2 Figures XVI-9and XVI-10 are representative plots of experimentally determined admittance curves.Data for Fig. XVI-9 was taken with a probe of 1. 75-in. diameter, and for Fig. XVI-10with a probe of 2-in. diameter. The plasma parameters for both cases are n 02.4 X 10 8/cm 3 , T_ 5. 1 ev, and pressure =6 X 10 - 4 mm Hg. Argon was the gas that wasused.Figures XVI-11 and XVI-12 are plots of the ratio of resonant frequency to plasmafrequency as a function of probe size for constant plasma parameters. For Fig. XVI-11,0.8-0.7-0.60.5 -0.75 1.00 1.25 1.50 1.75 2.00PROBE DIAMETER (in.)Fig. XVI- 11. Ratio of resonant frequency to plasma frequency vs probe size.QPR No. 80 107(XVI. GASEOUS ELECTRONICS)0.9-0.80.70.60.5 -0.40.75 1.00 1.25 1.50 1.75 2.0PROBE DIAMETER ( in )Fig. XVI-12. Ratio of resonant frequency to plasma frequency vs probe size.n 2 . 4 X10 8 /cm 3 , T_ 5.1 ev, p=6X10-4 mm Hg. For Fig. XVI-12, n = 1.0 X 108/cm ,-4T z 3. O0 ev, p = 6 X 10 - 4 mm Hg. The curve drawn in each figure is the variation onegets, using the present theory, for the dipole term only when one assumes a constantsheath thickness. The curves have been fitted to the value for the 2. O -inch probe. Thesheath thickness for the curve in Fig. XVI-11 is 4. 6 XD = 0. 68 in. , and in Fig. XVI-12it is 5. 2 k D = 0. 51 in.The widths of the observed conductance peaks are wider than the theoretically pre-dicted values (A 1. 1 v) by approximately a factor of 10. More data are being taken todetermine experimentally the variation of peak widths on plasma parameters.J. A. WaletzkoReferences1. D. F. Smith and G Bekefi, "Radiofrequency Probe," Quarterly Progress ReportNo. 74, Research Laboratory of Electronics, M. I. T. , July 15, 1964, pp. 91-98.2. J. A. Waletzko, "Radiofrequency Dipole Resonance Probe," Quarterly ProgressReport No. 79, Research Laboratory of Electronics, M. I. T. , October 15, 1965,pp. 95-98.QPR No. 80 108

Gaseous Electronics

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Gaseous Electronics

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