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

Buchsbaum, S. J.

Gilardini, A. L.

Gordon, E. I.

Madan, M. P.

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II. MICROWAVE GASEOUS DISCHARGESProf. S. C. Brown S. J. Buchsbaum J. J. McCarthyProf. W. P. Allis A. L. Gilardini R. G. Meyerand, Jr.Dr. M. P. Madan E. Gordon W. J. MulliganA. HIGHLY IONIZED MICROWAVE PLASMA*In an effort to determine the optimum conditions for the production of a highly ion-ized hydrogen plasma, microwave breakdown experiments in hydrogen in the presenceof a magnetic field (1) are being extended to low pressures (10 - 3 to 10 - 5 mm Hg). Aquartz cylindrical tube, 1 cm in diameter and 6 cm in length, filled with hydrogen to adesired pressure, is placed along the axis of a cylindrical cavity that is oscillating inthe TEll l mode at S-band. A variable, axial magnetic field of approximately 1000gauss is provided by an electromagnet. The pole pieces of the magnet are shaped toinsure the uniformity of the magnetic field over the central portion of the quartz tube.The purpose of the magnetic field is twofold. First, by adjusting the cyclotron fre-quency wb so that it is equal to the operating frequency w, a very efficient means isprovided for the transfer of energy from the microwave field to the electron cloud.Second, the strong magnetic field severely limits the loss of electrons by diffusion in theradial direction. Thus far, no effort has been made to limit the loss in the axial direc-tion, but a magnet with a specially shaped magnetic field that will also impede this lossis being designed. The effect of the magnetic field on microwave breakdown is gener-ally exhibited by plotting the breakdown field E b against the magnetic field for a con-stant gas pressure. The plot usually exhibits a resonance minimum at w = wb. Thewidth of the resonance curve is characteristic of the process or processes that impedethe transfer of energy from the microwave field to the electron cloud. At pressures ofthe order of millimeters of mercury, the width is the result of collisions of electronswith neutral atoms or molecules. The relative width of the resonance curve at half-power points is then given by v /w, where v is the collision frequency (for hydrogen,v c = 5 X 109p, where p is the pressure in mm Hg) and o is the operating frequency. Inthe present experiment, neither collisions with neutral atoms nor the much more fre-quent collisions with the end walls of the quartz tube occur sufficiently often to ac-count for the observed widths. The explanation lies partly in the inhomogeneity of themagnetic field in the axial direction. The inhomogeneity, if it exists, limits the volumein which electrons gain energy efficiently to only a fraction of that of the quartz tube.To check this, the inhomogeneity of the magnetic field was varied by extending theshims on the pole pieces of the electromagnet by increments of one-quarter inch. Theresultant breakdown curves for three such increments are plotted in Fig. II-1, whichThis work was supported in part by the Atomic Energy Commission underContract AT (30-1) 1842.(II. MICROWAVE GASEOUS DISCHARGES)Fig. II-1.MAGNETIC FIELD (RELATIVE UNITS)Effect of inhomogeneity of magnetic field on microwave breakdown-4in hydrogen (pressure, 6 x 10 mm Hg).shows distinctly the dependence of the breakdown field on the homogeneity of the mag-netic field. In addition, the widest curve shown in Fig. II-1 is asymmetrical. Theasymmetry is thought to be the result of an inhomogeneity in the radial direction,which must exist if there is a large inhomogeneity in the axial direction, but this is notyet conclusively determined.S. J. Buchsbaum, E. GordonReferences1. B. Lax, W. P. Allis, and S. C. Brown, Technical Reporttory of Electronics, M.I.T., June 30, 1950.165, Research Labora-B. DIFFUSION DECAY IN NEON AFTERGLOWSIn the Quarterly Progress Report of Oct. 15, 1955, page 16, we discussed some ofour experimental results concerning the behavior of the diffusion coefficient in the(II. MICROWAVE GASEOUS DISCHARGES)afterglow of a microwave discharge in the transition region from free to ambipolardiffusion, and our plans for investigating the decay of a discharge in neon contaminatedwith argon (0. 1 per cent) in cavities that have very small diffusion lengths A. In thiscase, we expect an electron density decay that is approximately exponential, with aslowly varying time constant that decreases with increasing postdischarge times,because in going to lower densities, we move from ambipolar to free diffusion condi-tions. The decay was investigated for a cylindrical metal cavity with A = 0. 1 cm, andthe effect was found to be present, as shown in the typical curve of Fig. II-2. Duringthe investigation, we also found that, in our experiment, the value of the ambipolardiffusion coefficient is not linearly related to pressure, as we expected; therefore wedecided to study this effect first.In the afterglow of a discharge, in a Penning mixture like neon contaminated withargon, we expect the diffusion to be controlled by the mobility of argon ions in neon;consequently, from the known values of mobilities of -alkali ions in different gases (1)we expect a Dap value of about 310 cm2 mm Hg/sec. In our experiment, the measuredvalues range from 260 to more than 400 when the pressure varies from 7 to 30 mm Hg.We tentatively explain the values above 310 by assuming the formation of a neon-argonionized molecule, which, if it exists, is supposed to have a higher Dap value than theargon ions in neon, and probably will also have a recombination coefficient of the sameorder as the one for the ionized molecules of the rare gases. It can be shown (2) thatin our case we measure an apparent (DaP)a which is related to the true Dap by therelation(D p)a = Dp + A2p 3  (1)where (C p2) is the frequency of formation of a molecule, according to the reaction,A+ + 2Ne - (ANe) + Ne (2)According to Eq. 1, the measured (DaP)a must be a linear function of p , and the inter-cept at zero pressure gives the true DaP. Figure II-3 shows our experimental dataplotted in this way, and the graph seems to confirm, within the experimental error,the p 3 dependence and the expected true Dap value, except for pressures less than 15mm Hg. We explain the low Dap values in this low-pressure region by the hypothesisthat here the ions are not all argon but partially neon; the Dap value for neon molecularions in neon is, in fact, 250 cm2 mm Hg/sec (see ref. 3). This explanation is consis-tent with breakdown measurements (4), which show that at low pressures a contamin-ation of 0. 1 per cent of argon is not sufficient to produce minimum breakdown.-1From the data of Fig. 11-3, we obtain for the approximate value 0.5 sec(mm Hg) - 2, which is about one-hundredth of the measured value for the conversion ofUi)2-1.8-1.6-1.2-1.0--0.806-0.42.0 2.5 3t(MSEC)Fig. II-2. Frequency shift Af versus postdischarge time t.p3 (MMHg)Fig. II-3. Measured D p values versus p 3. As usual, the pressures are normalizedto 00 C and the diffusion coefficients to 300°K and 1 mm Hg.(II. MICROWAVE GASEOUS DISCHARGES)ionized atoms of helium into molecules (2); therefore the value seems reasonable.In the next experiment, we hope to verify the correct dependence of Eq. 1 on A andto increase the amount of argon contamination in order to show an increase in D avalues in the low-pressure region.A. L. GilardiniReferences1. C. F. Powell and L. Brata, Proc. Roy. Soc. (London) A 138, 117 (1932).2. A. V. Phelps and S. C. Brown, Phys. Rev. 86, 102 (1952).3. R. J. Munson and A. M. Tyndall, Proc. Roy. Soc. (London) A 177, 187 (1941);M. A. Biondi and L. M. Chanin, Phys. Rev. 94, 910 (1954).4. H. J. Oskam, J. Appl. Phys. 27, 848 (1956).C. MICROWAVE DETERMINATIONS OF FREQUENCY OF IONIZATION ANDCOEFFICIENT OF FREE DIFFUSIONA direct method of determining the significant quantities, vi, the coefficient ofionization, and D , the coefficient of free diffusion, was described in the QuarterlyProgress Report of July 15, 1956, page 8. The present report deals with the theory ofthe method, necessary corrections to be applied to experimental data, and the resultsobtained.The equation for the build-up of the electron density, in the absence of space charge,is written asan= v.n + DV2n (1)at 1where v.n is the production of electrons per second by ionization and D V n is the lossof electrons per second by diffusion. For a cylindrical cavity of length L and radius R,when v. and D- are independent of position, the solution of Eq. 1, for the case of a1single electron entering the cavity at t = 0, at the point Z = Z , r = 0, and theboundary condition that n = 0 at the walls of the cavity, isn(F, Z, t) sin Z sin ) exp (ym It)  m = 1, 3, 5...co L j2 (om)mf 1 (2)whereD F 2 ( Py = v. - =v.-D f +rjmi A 2  i - L Rmkand m, I are positive integers, and Bof is the root of the zeroth-order Bessel function.(II. MICROWAVE GASEOUS DISCHARGES)The fundamental mode is represented by k = 1, m = 1. It can be shown that higher modesin the Z-direction are important only at very short times and thus can be neglected. Thecontribution of higher modes in the radial direction is dependent on the radius of thecavity, pressure, and time. By writing the ratio of the first two terms, it can be seenthat at large R and small t (of the order of a few microseconds in the present experi-ment), many higher modes are present, and the electron density distribution that resultsfrom all these modes is concentrated within a narrow central region. For this case, theelectron density does not have time enough to diffuse out of the narrow central region,which can be seen by writing an alternative expression for n, obtained by the use of theBorn approximation.2 rZ 0 tZ exp ( -r2/4Dt) ( (3)n(F, Z, t) = sin sin 4Dt exp - D 2 t (3)Equation 3 satisfies the postulated initial and boundary conditions. In this expression, aterm of the order ofexp (-R2/4Dt)4TrrDtnecessary to satisfy the boundary condition at r = R, is omitted, since R2/4Dt > p > 15mm Hg.Since the quantity obtained experimentally is essentially fv n(Y, Z, t) E 2 dv, let usdefineN = nE dv (4)oVwhere N is the total number of electrons in the cavity averaged over the electric energy.The cavity oscillates in the TM 0 10 mode; therefore, if we write E = EoJ° (Poi r/R), weobtain2 iTZ exp (-r 2/4Dt) 2N = -sin - sin dz 2Tr dr 4TrDtL L L 0 't o oRX exp v i - D( t (5)Small error is made by allowing R to go to oo, since the exponential for r > R is less-20than e . This yields(II. MICROWAVE GASEOUS DISCHARGES)N =sin exp - - i j 0  )exp - DT-L - e R 2 o 2 R 2  i L2 24 0 o 4Dt of4Dts(6)sin L 2 2 4 2 2Experimentally, we seek the minimum time tm in order to achieve a given density N.This corresponds to an initial electron appearing at Z 0  L/2, which makes sin rrZ /Lapproximately unity. Furthermore, since the quantities of interest occur in the expo-nential and2of 4Dt 12 2 10and N is of the order of 10 9 , an error of less than 1 per cent is made by writingNb =exp - D( t m  (7)With the help of the method discussed in the Quarterly Progress Report of April 15,1956, variation of the electric field E with the total electron density N can be computedfor the present case, with v /w as a parameter for the 1/8-inch cavity (see Fig. 11-4).f(Vc/W)This slight variation of N with v /w can be taken care of by writing Nb , takingNb = 5 X 10 8 . Since vi/p and D p are functions of E/p only, Eq. 6 can be written in theformf 1 (v i  Dp(8)tmp - (In Nb)\P (p)(8)where Nb is the total electron density at which the power begins to be reflected fromthe cavity and corresponds to the minimum time tm.Experimental measurements of the effective field Ee and t m , with po, the pres-sure at O0C, as a parameter, are plotted in Fig. 11-5 for the 1/8-inch and 1/16-inch-2cavities. With the help of this plot, we can draw another curve of f/tp against (pA) - 2with Ee/Po as a parameter. But before this can be done, tm should be corrected forthe effective diffusion coefficient D s , which includes the diffusion caused by spacecharge. This is necessary because, until now, we have assumed that the controllingFig. 11-4. Variation of electric field with total electron density N.200 400 600 800 1000 1200 1400 400 600EeVOLTS/CM800 1000E (VOLTS/CM)(b)1200 1400Fig. 11-5. Experimental measurements of effective electric field versusminimum time t m , with p o the pressure at 0OC, as parameter.(a) 1/8-inch cavity. (b) 1/16-inch cavity.I I I I I I I II i I I I I I I Io.o-0.0S06S0.060.05 --0 0.1 0.2 0.3 0.4 0.5 O 0.7 0.8 0.9 1.0 LI 1.2 13 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.31/(poA)* [(MMH9 CM)']"Fig. II-6. f/tmp against (p A)- 2 with Ee/Po as parameter.THEORY0 EXPERIMENT50 -4o-0 0 -IC20-In 1 I I 1111 1 I0.1 0.2 0.3 0.4 as 0.8 Ip,oA(CM-MM Hg)2 3 4 5Steady-state breakdown voltages as a function of pA. The lineis theoretical, the points experimental.IS X 10515 20 25 30 35E,/Po(VOLTS CM"IMM Hg')40 45Fig. 11-8. Comparison of experimentally determined (Dp ) with the theoryof Allis and Brown.Fig. II-7.S 0 --- THEORYEXPERIMENTI I I I I II - _ -- -a(II. MICROWAVE GASEOUS DISCHARGES)to10W-I~10 15 20 25 30 35 40 45 50 60Ee /Po VOLTS (CM-MM Hg) - 'Fig. 1-9. Comparison of experimentally determined vi/Powith the theory of Allis and Brown.factor over the period t is the free diffusion D .mWith the help of Eq. 6, this correction can be written aspAt =(pA) 2 V i Dp 2(pA) /2)dn(D- D ) ds nin order to yield the corrected values of tmP. In this equation, D s can be written in termsof D , by fitting an analytical expression to the curves computed by Allis and Rose (1).Figure II-6 is a plot of f/tm Po against (p A) - 2 , with Ee/Po as a parameter. Each-2E/p-value line intersects the abscissa at different values of (pA) - 2 , giving the pressureto which that particular value of E/p will correspond for the case of steady-state break-down. Steady-state breakdown voltages as a function of (poA) are plotted in Fig. 11-7.The slope gives the value of D p, while the intercept with the ordinate gives vi/p. Thesevalues are plotted in Figs. II-8 and 11-9 (see also ref. 2).These experimentally determined vi/p-values require a correction, on account ofthe radial variation of the applied field, and can be treated by solving the diffusion equa-tion for the electron density distribution for the case of a nonuniform field. This will bereported later.M. P. MadanReferencesW. P. Allis and D. J. Rose, Phys. Rev. 93, 84 (1954).W. P. Allis and S. C. Brown, Phys. Rev. 87, 419 (1952).00- THEORYO EXPERIMENT0IUI

Microwave Gaseous Discharges

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Microwave Gaseous Discharges

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