Contains reports on three research projects.United States Atomic Energy Commission (Contract AT(30-1) 1842

Buchsbaum, S. J.

Gordon, E. I.

Meyerand, R. G., Jr.

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II. MICROWAVE GASEOUS DISCHARGES*Prof. S. C. Brown Dr. E. I. Gordon J. J. McCarthyProf. W. P. Allis Dr. M. P. Madan R. G. Meyerand, Jr.Dr. D. O. Akhurst H. Fields W. J. MulliganDr. S. J. Buchsbaum W. R. Kittredge D. R. WhitehouseA. MICROWAVE PLASMA CONDUCTIVITYIn microwave studies of gaseous discharges frequent use is made of the expressionfor the plasma conductivity which was first derived by Margenau (1)4rr ne 1 af 3S3 m Vm + jo ) v v dv (1)where vm is the electron collision frequency for momentum transfer, c is the radianfrequency of the microwave field, and f is the electron distribution function. Equation 1was derived for a uniform infinite plasma. Since uniform infinite plasmas are notrealized experimentally, questions arise concerning the limits of validity of Eq. 1 withrespect to pressure, density gradients, space-charge fields, and so on. We havestudied this problem for two cases: (a) the electron mean free path is assumed smallcompared with the extent of the microwave field and with the dimensions of the plasmacontainer, but the effect of density gradients and space-charge fields is considered;(b) the electron mean free path is large compared with the extent of the field, but thedensity is assumed uniform.In case (a) the problem was studied in the usual manner with the aid of the Boltzmanntransport equation - without, however, neglecting the time-varying part of the isotropicdistribution function. We find that in the presence of density gradients and space-charge fields the microwave current is given bye2 e (V21= [nE + nlE ] + + * _ 2 Vn (2)1 m(v m + j) oE 1 lE] (vm + j) 3 (2)with vm assumed independent of energy. The subscripts zero and one denote dc and acquantities, and ( v 2)1/3 is related to the ac diffusion coefficient. The first term on theright-hand side of Eq. 2 is the one commonly used to obtain the plasma conductivity.We find that the other terms are small compared with the first when the followinginequality is satisfiedE Vne o (3)m 2 2 j VW)n 0)p mThis work was supported in part by the Atomic Energy Commission under ContractAT(30-1) 1842.(II. MICROWAVE GASEOUS DISCHARGES)where wo is the plasma frequency. For microwave plasmas under conditions of ambi-polar diffusion Eq. 3 reduces tov2 Vn 23 2 1 (4)3K (0  - + j v W) (n 1where Kv2 /3 is related to the dc diffusion coefficient. When w < o, Eq. 4 yields theconditionVnODn < (5)where f D is the Debye length. The condition given by Eq. 5 is less stringent whenp > w. When w wp , inequality 4 yields a lower limit on pressure below which Eq. 1may be incorrect.For de plasmas, when w = wp the inequality to be satisfied isvd Vn- << 1 (6)W nowhere vd is the electron drift velocity. Inequality 6 states that the distance drifted inone period of the ac field must be small compared with (n /Vno).In case (b), wherein the mean free path is large compared with the extent of the field,the usual method of expanding the distribution function in spherical harmonics in veloc-ity and in Fourier series in time, and terminating each expansion after the first twoterms, is not adequate. A more fruitful approach is to consider the motion of theindividual plasma electrons by using small-signal analysis and averaging over thevelocity distribution function.If a uniform ac field E 1 is maintained between the planes z = 0 and z = d in a uni-form plasma, we find that the average conductivity of the gap is given by4r ne v 3 jf - d 1 dv (7)3 m v vm + jW 4d(j + Vm )In obtaining Eq. 7, terms of the order exp(-3w2d2 /vZ)) 1/ 4 were neglected comparedwith unity. This limits the validity of Eq. 7 to those cases in which the average elec-tron spends more than three cycles of the ac field in the gap. When (vm/) 2 and(v/dw) 2 are small compared with unity, Eq. 7 is analogous to Eq. 1 if an effective col-lision frequency v' is defined asmv' = v + 3 v (8)m m 4d(II. MICROWAVE GASEOUS DISCHARGES)Equation 8 indicates that, when the extent of the ac field is small compared with themean free path, the width of the gap defines, as far as the microwave field is concerned,an effective mean free path. The factor 4/3 comes in because the electrons enter thegap obliquely. We also find that the smallness of the gap does not alter the energy-storing ability of the plasma electrons.S. J. Buchsbaum, E. I. GordonReferences1. H. Margenau, Phys. Rev. 69, 508 (1946).B. HIGHLY IONIZED PLASMASIn a further attempt to produce a highly ionized microwave plasma in hydrogen amicrowave system similar to that described previously (1) but capable of supplying cwpower of 1000 watts was assembled. It was necessary to construct a variable attenua-tor capable of dissipating 1000 watts with negligible insertion loss. It was possible touse a probe for coupling into the microwave cavity by surrounding the probe with aTeflon shield.The cavity was designed to resonate in the TE111 mode at S-band, and in the TE011and TM i l l modes at C-band. The last two modes are utilized to measure the electrondensity. Preliminary attempts have yielded degrees of ionization of approximately 0. 5per cent at a pressure of 10 - 3 mm Hg.E. I. Gordon, S. J. BuchsbaumReferences1. Quarterly Progress Report, Research Laboratory of Electronics, M.I.T., Jan. 15,1957, p. 17.C. HIGH-CURRENT PROTON SOURCEConstruction was completed and initial testing has begun on a high-current protonsource.-3The source employs hydrogen gas at a pressure of 10-3 mm Hg that is ionized bythe action of 100-mec rf power. The protons are extracted from the ionized hydrogenand focused into a beam by electrodes whose shape was determined by considering thespace-charge field of the proton beam. The focusing was satisfactory.A magnetic field which is applied parallel to the axis of the beam serves three pur-poses. First, it helps contain the beam. Second, it reduces electron loss in theionized gas region, which results in a higher plasma density and consequently gives ahigher proton density. Third, as the ionizing electric field is applied perpendicular tothe magnetic field, it provides an efficient means of transferring energy to the electrons(II. MICROWAVE GASEOUS DISCHARGES)by cyclotron resonance.An attempt will be made to correlate the effect of gas pressure, accelerating volt-age, rf power, and magnetic field upon beam current.R. G. Meyerand, Jr.

Microwave Gaseous Discharges

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Microwave Gaseous Discharges

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