Contains reports on three research projects

Buchsbaum, S. J.

Gilardini, A. L.

Gordon, E. I.

Contains research objectives and reports on two research projects

Brown, S. C.

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II. MICROWAVE GASEOUS DISCHARGESProf. S. C. Brown S. J. Buchsbaum Helen R. LandProf. W. P. Allis A. L. Gilardini J. J. McCarthyE. GordonRESEARCH OBJECTIVESOur general aim is to study the fundamentals of gas discharges by microwavetechniques. Since 1946 we have been studying the microwave breakdown of gas dis-charges - an investigation that involves both measurements of the phenomena them-selves and measurements of the electron collision and loss parameters. Through theyears we have studied a number of these phenomena. At the present time measure-ments of high-pressure breakdown in hydrogen and the study of electron collision crosssections in neon fall into this general line of research.The other main emphasis of this group has been on the study of the plasma resonanceand plasma oscillation phenomena which fall in a convenient microwave frequency range.This is also a continuing interest. Several experiments are in progress to further ourprevious studies of the mechanism of plasma oscillations and the details of the inter-action of microwaves with the ionized plasma.S. C. BrownA. HIGH-DENSITY MICROWAVE GASEOUS DISCHARGESExperimental work is being continued on the effect of plasma resonance on the trans-mission of microwaves through plasma(l). Preliminary experiments have shown thatsuch an effect exists and that it is quite pronounced. A transmitting probe in the formof a coaxial line terminated by a disk was inserted in the plasma, 2. 5 cm from a sim-ilar receiving probe. At resonance, transmission was minimum. A value for the elec-2 2 2tron density, n, could thus be obtained (1) from the formula, c = ne /mE o , where wis the frequency of the probing signal and E is the permittivity of free space. A directmeasure of n was also obtained by means of a double probe. There is general agree-ment between the two determinations.With the type of apparatus described, we cannot hope to obtain more than qualitativeresults. It is impossible to match the probes to the line. It is also impossible to con-fine the waves to a small region of the plasma. It may be that this is the reason thatthe curves that show a minimum of resonance also exhibit unexplainable maxima and attimes secondary minima.To avoid these difficulties, we are now working on a different type of probe. It isplanned to utilize the plasma itself as the outer conductor in a section of a coaxial lineand to test the properties of such a line as a function of the density of electrons in theplasma. With this probe, maximum transmission would be expected at and above reso-nance, since in this region the plasma behaves essentially as a metal. This was, infact, observed with the first probe built. The troublesome maxima and secondary min-ima of the disk type of probe were absent. However, the probe, because of its size,disturbed the plasma. Work is now being done on a coaxial probe 0. 125 inch in(II. MICROWAVE GASEOUS DISCHARGES)diameter. It is hoped that with the much thinner probe the disturbance of the plasmawill be negligible.S. J. BuchsbaumReferences1. K. S. W. Champion, Quarterly Progress Report, Research Laboratory of Elec-tronics, M.I.T., July 15, 1954, pp. 8-11.B. MICROWAVE DETERMINATION OF THE PROBABILITY OF COLLISION OFSLOW ELECTRONS IN NEONThe purpose of these measurements was to determine the collision probability formomentum transfer of slow electrons in neon by the microwave method of Gould andBrown (1). The parameter p = (1/Po)(G-r/0-i) (p is the pressure normalized to 0oC;T = - + j -i' the complex conductivity of the plasma) has therefore been measured inthe afterglow of a neon discharge. All measurements were made at room temperature.The value of p will be independent of the post-discharge time and of the pressureif the same is true for the distribution function of the electrons. The distribution func-tion in a decaying neon plasma can change with time if one or more of the following con-ditions are present:a. The electrons have not yet reached thermal equilibrium with the gas;b. The fraction of the electrons leaving the plasma either because of diffusion orrecombination with neon ions is a sufficiently fast varying function of the electronenergy;c. The fraction of the electrons leaving the plasma either because of attachment orrecombination with impurities (probably mostly 02) is a sufficiently fast varying func-tion of the electron energy;d. New fast electrons are entering the plasma from the ionization of neon meta-stables either because of metastable-metastable collisions or the Penning effect(probably with argon atoms).In order to prevent case d, all measurements have been made at post-dischargetimes of more than 1 msec. To prevent case c, activated uranium has been used toreduce the content of impurities (except rare gases). The only way to prevent case dis to have enough argon atoms so that practically all neon metastables are ionized inthe first millisecond of the afterglow. Case b is not present in helium (2), and wehope that it will not be in neon. (Biondi (3) found that the recombination coefficient inneon is independent of temperature in the range from 77 0 K to 410 0 K.)Measurements were made at pressures of 12-14 mm Hg at post-discharge timesvarying from 1 msec to 3 msec; measurements of p cannot be made later in the-9-(II. MICROWAVE GASEOUS DISCHARGES)afterglow, the inaccuracy being too large (more than 10 per cent). The value of pwas independent of the post-discharge time for the bottled neon (spectroscopically pureAirco), and dependent on the time when the argon impurity content was reduced byusing a discharge tube in which the cataphoresis effect was present (4). Values of pat the earliest post-discharge times increased with decreasing argon content. Thisincrease is consistent with the expected behavior in case d and an expected increase ofp with electron temperature. A preliminary value of p at room temperature is1. 7 x 10 - 3 (mm Hg) - l when impurities and metastables are not present in an appreciableamount. Some measurements of p with mercury used as an impurity showed the samegeneral behavior as that of argon but with a greater effect resulting from the largerdifference between neon metastable level energy and impurity ionization potential.Some doubts still remain, however, concerning the previous explanation because nochange was observed in the parameters of the electron density decay curve when theargon content was reduced. This result suggests that the number of fast electronscoming from metastable ionization is relatively small, and approximate calculationsbased on the average electron picture show that in such a case the observed changes inp cannot be easily explained. More investigation on this point is therefore necessary,and we need a better understanding of the phenomena which control the electron densitydecay.The density decay curves obtained during the measurements show (a) no change afterneon has been in the presence of activated uranium (this suggests that attachment toimpurities is not an important factor here); (b) a change with breakdown pulsewidth,which cannot be understood if recombination is the only controlling factor; and (c) timedecay constants that cannot be explained if only diffusion (also of higher modes) andmetastable ionization are the controlling factors. Therefore, three processes are prob-ably important: recombination, diffusion, and metastable ionization. To distinguishbetween the first two processes and the last one we propose to apply a pulsed sweepingfield at a variable time in the afterglow, in order to sweep out most of the electrons ofthe plasma in a very short time; the pulse will not alter the metastable concentration,and the electron decay curve after the pulse will give information about the metastabledecay. To distinguish between recombination and diffusion, criteria have been given byPersson (5).A different criterion will now be discussed; it is based on using as a probing field theresonant modes of the microwave cavity higher than the fundamental one. We have acubic quartz bottle of side d in the center of a microwave cavity of sides L l , L 2 , L 3.We assume a set of corresponding orthogonal coordinates x l , x 2 , x 3 with the origin inthe center of the cavity, and we suppose that the electron density at the post-dischargetime t can be written as-10-(II. MICROWAVE GASEOUS DISCHARGES)n(x , x 2 , x 3 , t) = nl(xl,t) . n 2 (x 2 , t) . n 3 (x 3 , t) (1)If we measure at the same t the frequency shift Af for two different modes TMkimand TMkk"im (I or m being equal to zero) we can show that(Af) glhk' nlh(t)(af)' h=1,3,5 ... (2)(af)k" glhk" nlh(t)h=1,3,5,...where nlh(t) are the coefficients of a Fourier series of the symmetric part (index s) ofnl(xl, t)nl(x , t) ns(x , t) + nd(xl , t) (3)ns(x 1 , t)= nlh(t) cos xh (4)h=1, 3,5, ....and glhk are constants given by the formulah-l(-1) 2glhk- +h(5)If Af is measured as a function of time for a complete set of modes TMki m with varyingk, from Eq. 2 we can determine all the ratios nlh' (t)/nlh,,(t). Practically, if the seriesof Eq. 2 is rapidly converging, the measurements can be limited to just a few modes,and only the ratios of the important terms will be determined; this is particularlyimportant because, for the higher modes, the errors caused by the finite thickness ofthe walls of the quartz bottle and by an off-center discharge will be a limiting factor inthe use of the method. Using modes with different I and m we could determine all ofthe functions nih(t), where i = 1, 2, 3, ..... From the differential decay equation whendiffusion and any linear removing process (like attachment) are the only phenomenapresentan = D Vn - an (6)8twe havean-h D a (7)at ih [D() 2 + n (7)at L"d I i-11-(II. MICROWAVE GASEOUS DISCHARGES)2-D (h'2-h" 2 tnih'(t) nih,(O) d 2 (8)nih(t) nih(o) e (8)Therefore, in this case, the measured ratios plotted in a logarithmic scale vs. timemust be straight lines, and from all of them we must obtain the same D value. If thisis not verified, some other process beside diffusion must be present, and we can com-pute from the measured values the symmetric parts of the functions ni(x i , t). They canhelp in understanding the other processes that are involved in the decay.A. L. GilardiniReferences1. L. Gould and S. C. Brown, Phys. Rev. 95, 897 (1954).2. L. Gould, Ph. D. Thesis, Department of Physics, M. I. T., January 1954.3. M. A. Biondi and S. C. Brown, Phys. Rev. 76, 1697 (1949).4. R. Riesz and G. H. Dicke, J. Appl. Phys. 25, 196 (1954).5. K.-B. Persson, Ph.D. Thesis, Department of Physics, M.I.T., January 1954.-12-

Microwave Gaseous Discharges

II. MICROWAVE GASEOUS DISCHARGESProf. S. C. Brown S. J. Buchsbaum E. GordonProf. W. P. Allis A. L. Gilardini J. J. McCarthyA. HIGH-DENSITY MICROWAVE GASEOUS DISCHARGEThe program of studying the high-density plasma by means of microwaves is beingcontinued. The gap in the thin coaxial line used as a probing element was reduced toonly 1. 5 cm to minimize the effect of the walls of the bottle containing the plasma on thewave transmitted through the line. The power transmitted through the line was meas-ured as a function of the electron density in the plasma (determined by a double probe)for various pressures and different frequencies of the probing signal. A typical curveof power transmitted vs. density exhibits a maximum that is assumed to occur atplasma resonance. A log log plot of the plasma density at maximum transmission vs.frequency of the probing signal at a constant pressure results in a straight line whoseslope seems to depend on pressure. The relation between the two is not yet clear. Forthe range of pressures used (0. 5-1.3 mm Hg), the slope varied from about 3 to 6,increasing with increasing pressure. This is to be compared with the theoretically pre-dicted value of about 1.3.Another way of analyzing the experimental data is to plot plasma density at the maximum transmission vs. pressure for a given frequency of the probing signal. This pro-cedure requires correcting the current reading of the double probe for the changingpressure. The assumption made in the last report that the current collected by thedouble probe is related to the electron density at the probing line by a multiplicativeconstant which is independent of pressure is not a good one. Other workers (1) haveobtained a crude theoretical expression for the pressure dependence of this constant,but there is some doubt in the mind of this writer as to the experimental verification ofthis expression.The theoretical solution to the problem of transmitting an electromagnetic wavethrough a coaxial line in which a part of the outer conductor is a medium of complexconductivity is progressing satisfactorily. The transmission coefficient is beingexpressed in terms of a variational principle. The integrals involved are complicatedand may require machine computation.S. J. BuchsbaumReferences1. G. J. Schulz, Ph. D. Thesis, Department of Physics, M.I.T.(1954), p. 101.B. PLASMA OSCILLATIONSUntil now, the mechanism of plasma oscillations produced by the interaction of abeam of electrons with a plasma in the tube built by Looney (1) and an improved one (2)12-(II. MICROWAVE GASEOUS DISCHARGES)presently in use has been described in the following way. The beam of electrons,entering a uniform region of the plasma of an arc discharge in mercury vapor throughan accelerating positive ion sheath, is modulated in velocity because the plasma oscilla-tions cause the plasma potential at the sheath to vary. After an appropriate drift length,the velocity modulation causes a bunching of the beam electrons which drives the plasmaelectron oscillations.The mechanism by which the energy of the oscillations was fed back to the electronsin the sheath region was never understood. It was thought that the plasma could propa-gate a space charge wave and that it was the returning wave which supplied the energyfor the oscillation, and, interacting with the forward wave, set up the observed standing-wave patterns along the beam. The boundaries off which the waves were reflected couldbe either the sheath or the bounding electrode over which the sheaths were formed.This picture is weak in the following details: It cannot predict the phase velocitiesof the waves; in fact, experimentally, the phase velocities depend on the boundary con-ditions and the bunching points in no well-defined way. The required bunching distancesare much less than simple bunching theory predicts.It is now clear that actually there are two beams to consider. A second beam of com-parable electron density moves within the first beam in the opposite direction. It is pro-duced by secondary electrons, coming off the nickel reflector, which are accelerated bythe fields within the sheath. The velocity spread is small and the beam usually termi-nates in the other sheath.The second beam can provide the feedback mechanism if it is assumed that the beamspropagate space charge waves which interact with one another to produce the standing-wave pattern. The sheaths provide the modulation for the two beams, and the spacecharge waves are coupled to the plasma along the entire length of the beam.This assumption is checked experimentally by varying the sheath voltages in such away as to maintain a particular mode of oscillation. This varies the position of thesheath edges and the velocity of the beams. Calculation of the transit time of a wavefront from one sheath to the other along one beam and back again on the return beamshows that the transit time is the same for the various combinations of sheath voltagesand is compatible with the period of the oscillation. An exact check is not yet possiblebecause the phase velocities are not known.The problem of determining the phase velocity for such a propagation is not too diffi-cult to solve approximately; this is being done.E. GordonReferences1. D. H. Looney, Ph. D. Thesis, Department of Physics, M.I.T. (1953).2. Quarterly Progress Report, Research Laboratory of Electronics, M.I.T., April 15,1955, pp. 11-12.-13-(II. MICROWAVE GASEOUS DISCHARGES)C. MICROWAVE DETERMINATION OF THE PROBABILITY OF COLLISION OFSLOW ELECTRONS IN NEONThe microwave complex conductivity of a neon plasma -c = 0-r + ju-i has been meas-ured as a function of electron temperature in the range from room temperature to about30, 000 K. The method is the same as that used by Gould and Brown (1) for helium. Aplot of the measured parameter p = (1/Po)(-r/ i) (Po is the pressure normalized to O0C)as a function of the electron temperature at the center of the cavity Teo is shownin Fig. II-1. No appreciable change was observed between the p values measured inpure neon and in neon contaminated with argon (approximately 0. 1 per cent), in the rangefrom room temperature to 5000 K. In the last case, the decay is controlled by ambipolardiffusion (2) and in experimental conditions the electron density distribution in the quartzbottle is expected to be cosinusoidal. Therefore, the probability of collision as a func-tion of energy will be determined from the measured p curve by using this hypothesis.Integrals to be used in these calculations are programed to be computed by Whirlwind.Without applying any correction for the disuniformity of electron temperature insidethe cavity, a preliminary value of the probability of collision in neon at room tempera-ture is 1.6 cm2/cm 3 per mm Hg.Small changes in the average electron energy resulting from conduction and convec-tion of energy from regions of high energy to regions of low energy have been observediO -10- O 2 103 Te0o(K)ConductivityFig. II-1ratio p as a function of thethe center of the quarelectron temperature T attz bottle. eo-14-(II. MICROWAVE GASEOUS DISCHARGES)as a function of pressure. The curve shown in Fig. II-I has been measured at high2 2enough pressure, compatible with the condition yc << w , so that energy gradient effectsare unimportant.It has been impossible until now to perform measurements in neon contaminated withargon at temperatures over 5000°K because of instabilities in the afterglow decay. Wehope to overcome this difficulty and use the same apparatus to study the diffusioncoefficient as a function of electron temperature.A. L. GilardiniReferences1. L. Gould and S. C. Brown, Phys. Rev. 95, 897 (1954).2. M. A. Biondi, Phys. Rev. 83, 1078 (1951).-15-

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Microwave Gaseous Discharges

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