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

Bekefi, George

Frankenthal, S.

Hirshfield, J. L.

Rose, D. J.

Ward, C. S.

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II. MICROWAVE GASEOUS DISCHARGESProf. S. C. BrownProf. W. P. AllisProf. D. J. RoseProf. D. R. WhitehouseDr. G. BekefiDr. L. MowerD. BuntschuhD. CoccoliFrankenthalB. HallL. HallL. HirshfieldW. R. KittredgeJ. J. McCarthyW. J. MulliganG. B. NicholsJudith L. ShaverC. S. WardA. ACCELERATION OF A NEUTRALIZED ION BEAMA class of velocity distributions exists which permits acceleration of one type ofparticle in a dc electric field, without any space-charge effects. Consider, for example,the diagram of Fig. II-i, and the acceleration of an ion beam. The ions travel to theI ION CURRENT i,dV vVELECTRON V+VCURRENTL= L( ' V dVFig. II-1. Voltages and currents in space-charge-free sheath.right, and have final energy V (electron-volts) in the region at the right of the figure;the potential of that region is conveniently set equal to zero. To the left, there is anuphill region for ions, and its mirror image for electrons. Finally, the ions camefrom a region where they had energy V 1 , and thus they were accelerated through thedifference V - Vo0 1Now let there be an electron current di at an energy V' relative to zero in theenergy interval dV'. At some place where the potential is V, the velocity of such anelectron is[2e(V' +V) 1/2and the contribution dn to the electron density n isThis work was supported in part by the Atomic Energy Commission underContract AT(30-1)-1842.(II. MICROWAVE GASEOUS DISCHARGES)i_(V') dV'dn_ = eI 2e( -V) 1/2 (1)We must now integrate over all contributions, and set the density equal to that of theions of mass m+ in the beam i +. In this example, electrons incident from the left withenergy less than zero are reflected, and their contribution must be counted twice. Thus,after cross-multiplying, we havem 1/2 00 i (V') dV' 0 i (V') dV'i+ m_(V - V) (V + V) 1/2 + 2 (V-+V)1/2 (2)as the defining equation for i_(V).Any reasonable function can be chosen for i (V') in the energy range V' > 0, aslong as neutrality is achieved on the right of Fig. II-1. Suppose again, for example,that a beam i 2 of electrons at final energy V 2 provides this neutralization. The firstintegral of Eq. 2 is trivial. If we setE = -V' (3)for convenience (electron energy measured as positive down from zero), we obtainIV i (E) dE i 1/2 V 1/2(VE) 1/2 2 (V - V) 1/2 V o(VI+V (4)0This is a Volterra equation of the first kind whose solution isi (V)1 1 (5)i_(V) (V - V) 12 Tr m - V W OO - (V V ) /2 (1 + V /V )We can find the total electron current (- i+(m +/m_ )1/2 or greater) by integrating i(V)over all contributions. We can also take other suitable functions for the electron dis-tribution at positive energy.Since no space charge arises, the concept is applicable to a beam of any lateraldimension.D. J. RoseB. MICROWAVE NOISE RADIATION FROM PLASMASPreviously, we reported (1) measurements of the microwave noise from a plasmacolumn radiating into a waveguide. The results were compared with calculationsbased on a geometrical-optics model for the transfer of radiation from within the body(II. MICROWAVE GASEOUS DISCHARGES)of the plasma. In this model, scattering from the boundaries of the plasma was neg-lected. This neglect may lead to a considerable error whenever boundary effectsbecome important, as, for instance, with very dense plasmas (i. e., high electronconcentration).A general formulation of the theory, free from these objections, has been obtainedwith the aid of Nyquist's theorem (2, 3). The low-frequency noise power P per unitfrequency interval received from a body at a temperature T isP = kT - A (1)Here A represents the absorption coefficient of the plasma, defined as that fractionof the total incident power absorbed by the plasma from a test wave launched from theposition of the noise detector. If more than one mode can propagate down the guidewithin the given frequency interval, A represents the sum of the absorption coefficientsof all the modes.Let E. and H. be the field components of the incident test wave, E the field within1 1the absorbing plasma of electric conductivity a-, and J the current density. ThenA = Re E. J * dv Re E X H. da (2)plasma / waveguidewith J = 0-E. The integration in the numerator of Eq. 2 is carried out over the volumeof the plasma; the integration in the denominator is over the waveguide cross-sectionarea. The evaluation of A from Eq. 2 is a boundary-value problem that is amenableto solution in a limited number of cases. One such case is for a low-electron-densityplasma of arbitrary shape and of arbitrary electron-density distribution. When theratio of plasma frequency to radian frequency is small, the incident test wave is per-turbed very slightly, so that E - E i and J a-E.. The results for A thus obtained,and hence the magnitude of the noise power P found from Eq. 1, are identical with thosefound from the geometrical-optics model that was discussed previously (1).Numerical computations of A for other than weakly ionized plasmas are being madefor a uniform-plasma slab that completely fills the cross section of a rectangular wave-guide, and for a uniform-plasma cylinder (4). These computations for variousplasma parameters are being made with the view of establishing the limitations of thegeometrical-optics approach.Despite the difficulties of finding the absorption coefficient corresponding to ourexperimental arrangement (nonuniform-plasma cylinder traversing a rectangularguide), A is amenable to direct measurement. In terms of the reflection and trans-mission coefficients F and T, A is given byA= 1- r2 Z - TI (3)(II. MICROWAVE GASEOUS DISCHARGES)0--16 / .-160 25.8-0/6 * /LU PCALCULATED2 /CL)-40 17* * * MEASURED NOISE*--- MEASURED AeCALCULATED-48* 0.4110 1010  IO 1012 1013ELECTRON DENSITY (CM-3 )Fig. 11-2. Microwave noise power as a function of electron density.The test wave should be bandlimited noise with a bandwidth equal to that of theradiometer (2 mc). However, in our measurements of A, a monochromatic source setat the center of the frequency band (3000 mc) was used.Figure II-2 shows a comparison between measurement and theory for a heliumplasma at gas pressures of 25. 8, 1.7, and 0.41 mm Hg. The solid dots representnoise-power measurements in decibels below the maximum as a function of electrondensity. These noise-power measurements are corrected for reflections from theplasma (1). The solid straight lines are computed from Eqs. I and 2 for the limitingcase of a tenuous plasma and should, therefore, agree with the noise measurements inthe limit of low electron densities. The dashed lines indicate results obtained from dataof the transmission and reflection coefficients of the plasma, as a function of electron(II. MICROWAVE GASEOUS DISCHARGES)density. Specifically, it is a plot of Ae related to A througheAe = A/(1I- I 2 )The effective absorption coefficient, A e , can be defined as the fraction of the availablepower absorbed from the test wave after removal of the gross effects resulting fromreflections from the plasma. When Ae is unity, P = (1 - FI I2 )kT, and the radiatingplasma may then be looked upon as a "black body" mismatched to its surroundings.Measurements for the three gas pressures of Fig. II-2 have shown that the maximumvalue of A lies between 0. 86 and 0.89.eThe measurements of A e agree fairly satisfactorily with the noise measurements.The accuracy in the determination of A e is governed by the precision in finding r andT, which, in turn, is chiefly governed by the accuracy of the available precision atten-uators. These have been calibrated with an accuracy of ±0. 5 per cent. If, for instance,Ae < 0. 1, the error in Ae can exceed ±90 per cent.G. Bekefi, J. L. HirshfieldReferences1. G. Bekefi and J. L. Hirshfield, Microwave noise radiation from plasmas,Quarterly Progress Report No. 52, Research Laboratory of Electronics, M.I.T.,Jan. 15, 1959, pp. 6-12.2. S. M. Rytov, Theory of Electrical Fluctuations and Thermal Radiation (Izd-voAkademiia Nauk S.S.S.R., Moscow, 1953).3. M. L. Levin, J.E.T.P. (Soviet Physics) 4, 225 (1957); Dokl. Akad. Nauk(S.S.S.R.) 102, 53 (1955).4. N. Marcuvitz, Waveguide Handbook, Radiation Laboratory Series, Vol. 10(McGraw-Hill Book Company, New York, 1951).C. ANOMALOUS CONSTRICTION IN LOW-PRESSURE MICROWAVEDISCHARGES IN HYDROGENIn the course of experiments on low-pressure microwave plasmas a discharge con-striction was observed. The experimental apparatus that was used may be describedas follows.A discharge tube, 1 cm in diameter, filled with hydrogen at 1-5 1 Hg pressure, ismounted coaxially inside a cylindrical cavity, 10 cm in diameter, placed between thepole faces of an electromagnet. This magnet furnishes a longitudinal dc magneticfield whose strength can be varied between zero and approximately 1200 gauss. Theempty cavity resonates in the TE111 mode at S-band and is probe-coupled to amicrowave line that is fed by a 50-watt magnetron. A discharge occurs throughcyclotron resonance. The TM020 mode at C-band is also used as a probing mode to(II. MICROWAVE GASEOUS DISCHARGES)_ _ _ __ B 860 GAUSS8-920 GAUSS B 900 GAUSS8 940 GAUSS100 200 300 400 500POWER ABSORBED (N W)600 700 800 900Fig. 11-3. Electron density versus power absorbed.8 = 860 GAUSS8=900 GAUSS8-=920 GAUSSB=940 GAUSSLINES OF SLOPE 1/2 HAVE BEENFITTED TO THE POINTS BY EYE.]I 1 J I 1 i 1 I200 300 400 500 600 700 800 1000POWER ABSORBED (MW)Fig. 11-4. Discharge diameter versus power absorbed.measure average electron densities.For absorbed powers greater than approximately 900 mw the discharge completelyfills the discharge tube. Decreasing the absorbed power below this figure causes thedischarge to pull away from the side walls and to continuously decrease in diameteruntil the absorbed power is so low that the discharge can no longer be maintained. Thesmallest diameters observed in this manner were approximately 1. 5 mm at absorbedpowers between 20 and 50 mw. This lower limit varied somewhat with applied magneticfield.Figures II-3 and II-4 show the electron density and discharge diameter as a functionof absorbed power for different magnetic fields. Note that the electron density remainsessentially constant for any given magnetic field. The values shown were obtained byI i / I I I(II. MICROWAVE GASEOUS DISCHARGES)normalizing the data on frequency shifts of the TM020 mode to the visible diameter ofthe discharge. As would be expected from the observation of constant electron density,Fig. II-4 shows that the absorbed power is directly proportional to the discharge volume.Notice also that average electron density decreases, whereas the discharge volumeincreases with increasing magnetic field. Hence, for any given absorbed power, thedischarge becomes more tenuous as the magnetic field is increased.The search for a mechanism to explain the cause of the constriction continues.C. S. WardD. CONSTRUCTION OF A MAGNETIC MIRRORA theoretical design of a mirror magnetic field was presented in a previousreport (1). The objective of the design was to generate a magnetic mirror having a hillratio of approximately 5:1 and possessing a field of 1000 gauss, with a uniformity of0. 5 per cent, over a central cylindrical region of 6-cm length and 2-cm radius.The design was achieved by selecting the following solution of Laplace's equationin cylindrical coordinates:B = V4 = Ak {Iar[J(kr) sinh (kz) - I (kr) sin (kz)]- 1 [J (kr) cosh (kz) + Io(kr) cos (kz)]}This magnetic field satisfies the uniformity requirements in the central region and risesrapidly along the axis farther away from the center.The shapes of the constant flux contours and of the equipotentials associated withthis solution were calculated. The desired field can be generated by placing an azi-muthal current sheath along a constant-flux contour, with a surface-current density.J= B8o zwhere B is evaluated along the contour, and by terminating the unit with equipotentialboundaries. (See Fig. 11-5.)Aside from the fact that it provides a field with a known, and relatively simple,analytical expression, this unit will be more economical of power than one consistingof a conventional solenoid equipped with more turns at the end than at the center, sincethe increase of magnetic field is partly achieved by a reduction of the diameter of theturns at the end, rather than by an increase in magnetomotive force.The unit is to be operated at a high current (2000 amp) and low voltage (4 volts).This should result in a low inductance, and make the unit easier to operate in a pulsedfashion.(II. MICROWAVE GASEOUS DISCHARGES)CONSTANT - FLUXCONTOURSFig. 11-5. Equipotentials and constant-flux contours in the mirror-- magnetic field.STEEL SHELLINSULATIONINSULATIONCOPPER RINGSCOPPER SHELLEND CAPFig. 11-6. Mechanical structure of the mirror magnet.1. ConstructionThe current sheath was simulated by a series of coaxial cylindrical rings, of dimin-ishing diameters and cross sections, forming a copper shell whose shape resemblesthat of a constant flux contour. To insure the accuracy of the generated field, theH-field outside the copper shell was forced to vanish by enclosing the copper shell in asteel shell. Steel end caps provided equipotential boundaries at the ends. (See Fig. 11-6.)The unit was constructed in two halves, each of which was mounted on a rollingcarriage, to permit the installation of equipment. Four access ports were drilledaround the central rings.Initial attempts to electroform the copper shell were not successful. As a result,each copper ring had to be manufactured and shaped individually. Insulation betweenrings consisted of 2-mil P-18 material, and the joints were soft-soldered. Hydrogenbrazing was impossible because of impurities in the copper. Mechanical joints wereconsidered, but the problems associated with designing and constructing them (espe-cially for the smaller rings) were sufficiently complex to warrant the selection of soft-soldering.The magnetic shells were made of low-carbon steel. The specifications called formachining them to fit the shape of the outside surface of the copper shell, leaving a1-mil gap for a sprayed layer of insulation (Teflon). (The thickness of the gap is(II. MICROWAVE GASEOUS DISCHARGES)critical because it impedes the heat transfer from copper to steel.) This specificationwas not met. Gaps of 20 mils were found and had to be filled with epoxy resin.The end caps were constructed of low-carbon steel; 1-cm access ports were drilledin the center of each. Current was supplied to the copper shell by means of a boltpassing through each end cap.Cooling was achieved by water-carrying copper tubing wound around the outside ofthe steel shell.2. OperationThe magnetic field was tested with a 600-amp current flowing through the unit. Atthis level, the field was 320 gauss at the center and 1350 gauss at the ends.Because of inefficient cooling, the magnet could not be operated at a 2000-amplevel. At that level, the copper temperature rose to 1250 C, and the expansion of therings, although it was partly limited, stressed and broke the joints between them.3. EvaluationThe magnetic field configuration provided by the unit is satisfactory. Its failureresulted from weakness in the structure of the copper shell (soft-solder joints) andinefficient cooling. The mechanical weakness could probably be tolerated if the coolingwere more efficient. It is evident, however, that with 20-mil gaps between the copperand steel shells, the heat dissipated (8 kw) cannot be carried away efficiently.The present unit can be rendered operational if the copper shell is cooled by waterflowing directly on its inside surface. This modification is under construction. Thiswill require the drilling of additional access ports for the copper tubing, and will makedisassembly of the unit difficult. This undesirable feature is, however, a necessaryevil. It may also be advisable to consider strengthening the structure of the coppershell by using mechanical or hard-soldered joints between the rings.S. FrankenthalReferences1. D. C. White, Inhomogeneous magnetic-field design, Quarterly Progress Report,Research Laboratory of Electronics, M.I.T., July 15, 1957, p. 1 6 .

Microwave Gaseous Discharges

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Microwave Gaseous Discharges

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