Contains reports on six research projects.United States Navy, Office of Naval Research (Contract Nonr-1841(78))Lincoln Laboratory (Purchase Order DDL B-00337)United States ArmyUnited States Air Force (Contract AF19(604)-7400)United States NavyNational Science Foundation (Grant G-9330

Bers, Abraham

Cooke, A. R.

Fiocco, G.

Hartmann, G. C.

Hsieh, H. Y.

Morse, D. L.

Smullin, Louis D.

DSpace@MIT

XI. PLASMA ELECTRONICS*Prof. L. D. SmullinProf. H. A. HausProf. A. BersProf. D. J. RoseProf. T. H. DupreeProf. E. P. GyftopoulosDr. G. FioccoDr. K. TakakiW. L. BrassertH. BreindelJ. R. CogdellA. R. CookeL. J. DonadieuW. D. GettyG. C. HartmannW. C. HomeyerH. Y. HsiehA. J. Impink, Jr.P. W. JamesonL. E. LidskyP. A. MandicsD. L. MorseA. PoeltingerS. D. RothlederW. D. RummlerA. J. SchneiderP. E. SerafimP. S. SpanglerG. C. TheodoridisE. ThompsonJ. S. TulenkoS. WilenskyJ. N. WilsonA. LARGE-SIGNAL ELECTRON-STIMULATED PLASMA OSCILLATIONSThe present study has been completed by W. D. Getty and the results have beenpresented to the Department of Electrical Engineering, Massachusetts Institute of Tech-nology, as a thesis in partial fulfillment of the requirements for the degree of Doctorof Science.L. D. SmullinB. PROPERTIES OF WAVES IN TIME- AND SPACE-DISPERSIVE MEDIAConsider Maxwell's equations for the real fields in the form8BVxE=-atV XH= atFor a homogeneous, time-invariant medium the linearized relationship between BH and D and E will, in general, be of the formB(r,t) = S (F- ', t-t ') t(r ', t') dr 'dt'D(r,t) = E(r-r',t-t') -E(F',t') ct-'dt'.(1)(2)and(3)(4)A Fourier analysis in both time and space of Eqs. 1-4 gives*This work was supported in part by the National Science Foundation under GrantG-9330; in part by the U.S. Navy (Office of Naval Research)under Contract Nonr-1841(78);and in part by Purchase Order DDL B-00337 with Lincoln Laboratory, a center forresearch operated by Massachusetts Institute of Technology with the joint support of theU.S. Army, Navy, and Air Force under Air Force Contract AF19(604)-7400.- (_ w) R w)(XI. PLASMA ELECTRONICS)-(Y, W) = (Y, w) • -(y, w) (6)y XE = j - F. (7)y xH = -j -E  (8)In Eqs. 7 and 8 we have not shown the explicit dependence of E, H, ., and E upon yand o. In determining the properties of the waves it is convenient to restrict ourselvesto a lossless medium. ThusS-= (9)E =E. (10)Here, the dagger denotes the complex conjugate transpose operation.Dot-multiplying Eq. 7 by H and the complex conjugate of Eq. 8 by -E, we obtainy.EXH =jwH . H (11)y . -E H -jwE E E. (12)Lety =a + j-A (13)~ XR* =p + J (14)1 - H = u (15)4 m4 E * E = u (16)4 eWe note that Eq. 14 is the complex Poynting vector, and Eqs. 15 and 16 are real butmay be positive or negative. The sum and difference of Eqs. 11 and 12 then givesa • pe = 0 (17)7-"4 e w(u -u e) (18)S- T =W(u +ue ) (19)Sqe = 0. (20)From Eqs. 17-20 we note that three kinds of waves are possible: complex waves (E 0,P* 0), propagating waves (a= 0), and cutoff waves (P = 0). In nondispersive media, umand u e are the energy densities, and the only waves that can exist are the propagating(XI. PLASMA ELECTRONICS)waves (-= 0, uniform plane waves), and the complex waves (a # 0, p 0, nonuniform planewaves).Consider a variation of Eqs. 7 and 8:6y XE = -y X 6E + j6(w ) H + j-" 61H (21)6y XH = -y x fH - j6(wE) E - jw - 6E. (22)Dot-multiplying Eq. 21 by H and adding to it the complex conjugate of Eq. 7 dot-multiplied by 11, and dot-multiplying the complex conjugate of Eq. 22 and adding to itEq. 8 dot-multiplied by -bE , we obtain*R -- H* E -*6y EX H = j  6(ow) H - y 6E XH - E X 8H (23)-- * -• - -- -b -- E XH -jE b(w) " E - "6 xH - • E X 6H . (24)Adding and subtracting Eqs. 23 and 24, and using Eqs. 13 and 14, we establish the fol-lowing relationships:6(a. p ) = 0 (25)e 4 4- . IRe (6E XH -EXH*) (26)6 .p e  ¥ H  • (w L) *H + •6(wE)*a -. Im (6,XT---~X 6H) (27)8 -. e ) = 0. (28)For propagating waves- = 0, y= j, and Eq. 27 gives6- 1 -* 1 (-*2-e i H  6(w) H + E 6(WE) E, (29)where (j-) and (wo) are functions of w and , so that- 6 + - 8 (30)a( ) a (()ap(XI. PLASMA ELECTRONICS)Substituting Eqs. 30 and 31 in Eq. 29, we obtaine 1+ i* a( H) -_ 1 ()(1- * a() 1 -4H H +-4E4 aw 4a (o) .- ) w(32)We can now identify the time-average energy densityw =- H - - H + -E - E4 a8 4and the time-average power density associated with the mediumm 4 H-a p aT(33)(34)Equation 34 provides a new way for identifying the linearized power density in a mediumdirectly from the linearized tensor description of the medium.Equation 32 can now be written6p' - (pe +pm) = w 6c. (35)At a fixed frequency we have6 ' Ce++Pm) = 0. (36)Thus the total time-average power density vector, electromagnetic and medium, isperpendicular to the index surface (see Fig. XI-1). The group velocity vector alsoPe + PmINDEX SURFACEFig. XI-1. Illustration showing the total time-average power densityperpendicular to the index surface.(XI. PLASMA ELECTRONICS)follows from Eq. 35:aw Pe + Pm- m(37)apand hence is also the energy velocity vector. For anisotropic media that are only time-dispersive, p = 0 and Eqs. 35-37 reduce to well-known relations.Work on the application of Eqs. 33-37 to electron-beam and warm plasma media willcontinue.A. BersReferences1. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (PergamonPress, Oxford, N.Y., and Addison-Wesley Publishing Company, Inc., Reading, Mass.,1960); see Section 77.C. ELECTRON BEAM-PLASMA INTERACTIONThe studies of electron-stimulated plasma oscillations by Gettyl are being con-tinued to investigate the possibility of ion heating by means of electron beam-plasmainteractions. A pulser that is capable of delivering 10 kw peak power of pulse lengththat is variable from 1 to 100 jisec has been built by Peter Mandics of the ResearchLaboratory of Electronics. Preliminary investigations in argon at pressures of 10--3to 10-3 mm Hg with magnetic field of 100 to 1000 gauss have shown these two generalcharacteristics:(a) With long pulses the collector current increases to as much as twice the originalbeam current.(b) With low magnetic fields, the light intensity as observed by a 931A photo-multiplier remains nearly constant throughout the length of the pulse after "beam-breakup. "2Further investigations in hydrogen will include tracking of radiofrequency oscillationsas a function of time, as well as detailed studies of light and current.H. Y. HsiehReferences1. W. D. Getty, Large-signal electron-stimulated plasma oscillations, QuarterlyProgress Report No. 64, Research Laboratory of Electronics, M. I. T., January 15,1962, pp. 113-117.2. L. D. Smullin and W. D. Getty, Large-signal electron-stimulated plasma oscil-lations, Quarterly Progress Report No. 61, Research Laboratory of Electronics, M. I. T.,April 15, 1961, pp. 33-36.(XI. PLASMA ELECTRONICS)D. ELECTRON BEAM-PLASMA INTERACTION EXPERIMENTSThe apparatus described previously for the investigation of interactions betweenan electron beam and a plasma has been put into operation. The electron gun isdriven by a 5- psec, 10,000-volt pulse at a repetition frequency of 250 cps. Thebeam passes down the axis of a "waveguide" constructed of copper screen, 6 incheslong and 1. 5 inches in diameter, with a mesh size of approximately 0. 05 inch. Thearc discharge is run outside this screen, and plasma diffuses through the "waveguide. "The system then approximates a plasma-filled waveguide for which the modes of propa-gation are well known. The diameter of the screen is small enough so that the fre-quencies of interest lie below the cutoff frequency of the empty waveguide, and hencethe quasistatic analyses apply. The arrangement of the waveguide in the dischargechamber is shown in Fig. XI-2.RF COUPLING LOOP / "MAGNETICSHIELD-- 6"COPPER SCREEN WAVEGUIDEBEAMCOLLECTOR 1 1/2" DIA.ELECTRONGUN'ARC CATHODE DC ARC DISCHARGELONGITUDINAL MAGNETIC FIELDFig. XI-2. Arrangement of components in discharge chamber.The spectrum of radiofrequency energy is observed by feeding a Panoramic ModelRF 4a spectrum analyzer with the output from the coupling loop shown in Fig. XI-2 atthe left end of the waveguide. The output of the analyzer, used as a receiver, is sampledat the time of the electron-beam pulse by a boxcar generator, and the output of this gen-erator is used to drive the y-axis of an x-y recorder. The x-axis of the recorder isdriven at a constant velocity, and the spectrum analyzer tuning is changed at a constantrate. With this procedure, curves of rf power versus frequency in the range 350 mc-10 kmc may be obtained.These curves have been plotted for various values of plasma density and magneticfield strength. Although no conclusive results have yet been obtained, there appear tobe frequencies present which are nearly linearly related to the electron-cyclotron(XI. PLASMA ELECTRONICS)frequency. More experiments are planned to correlate the findings with the resultspredicted from the theory of plasma-filled waveguides containing electron beams.D. L. MorseReferences1. D. L. Morse, Electron-beam plasma interaction experiments, Quarterly Prog-ress Report No. 64, Research Laboratory of Electronics, M.I.T., January 15, 1962,pp. 93-94.E. ELECTRON-CYCLOTRON HEATING OF A PLASMAThe experimental arrangement was described in Quarterly Progress Report No. 64(pages 103-104).A preliminary series of tests with the high-power pulsed microwave source has beeninitiated. The diagram of the rf apparatus is shown in Fig. XI-3, and a section of thecavity is shown in Fig. XI-4. The cavity has been designed to sustain the TE 0 1 1 modein the absence of plasma. The magnetic field produces a containment mirror configura-tion and also determines the conditions for cyclotron resonance.Fig. XI-3. Diagram of the microwave system.Experiments have been conducted in air at a pressure 5 X 10-4 mm Hg, for the fol-lowing conditions of the rf source: incident peak power, ~ 0. 3 Mw; pulse length, 10 4sec;pulse repetition frequency, 100-500 cps; and frequency, 2780 kmc. Production of X-rayshas been observed, with average levels of radiation equivalent to 1. 5 roentgens/hour atCavity configuration with lines of constant magnetic field in theabsence of plasma, for Imagne t = 4. 3 amps.magnet100 KEVTIME0.5 MSEC 0Fig. XI-5. X-ray production as indicated by scintillator output.Fig. XI-4.(XI. PLASMA ELECTRONICS)0. 25 meter from the cavity (brass walls, 4 mm thick), as measured with an ionizationchamber.The bremsstrahlung radiation is also being studied with a scintillation spectrometer.Photons with energy up to 100 kev were obtained during the rf pulse, and an appreciableamount of radiation with energy extending to 30 kev was still detected 400 1sec afterthe application of the rf pulse. Figure XI-5 is a photograph of the scintillator outputshowing the decay of X-ray energy with time. The electron density, during the pulse,exceeds 1017 electrons/m 3AB'TIME TIMEI I I -I0 10 pSEC 0 10 pSECFig. XI-6. Streak photograph of ini- Fig. XI-7. Streak photograph of ini-tial transient of discharge tial transient of discharge(slit along AA'; exposure (slit along BB'; exposuretime, 10 [sec). time, 10 isec).Some streak photographs of the initial transient discharge have been obtained.The discharge is visible through a Plexiglas window covered by a copper screen.Figures XI-6 and XI-7 show the discharge during a 10-psec pulse; the orientations ofthe slit for the two pictures were parallel and perpendicular, respectively, to the axisof the magnetic field, as indicated by lines AA' and BB' in Fig. XI-4.G. FioccoF. INVESTIGATION OF THE PENNING IONIZATION DISCHARGEThe dependence of the voltage-current characteristics of a Penning discharge onmagnetic field, gas pressure, and tube geometry is being studied. Probe measurementsof the plasma column formed in the tube and measurements of cyclotron radiationgenerated by the discharge are being made.The discharge tube consists of a cylindrical anode and two discs at the ends of thecylinder for cathodes. A filament is mounted in the center of each disc to supply elec-trons to the discharge (Fig. XI-8). A positive voltage is applied to the anode, and anPenning discharge tube.B = 100 GAUSSB = 0 GAUSSPRESSURE = 5 x 10- 6750VOLTAGETube characteristics.'1 MAU1Fig. XI-8.Fig. XI-9.(XI. PLASMA ELECTRONICS)axial, dc magnetic field is applied. Current collected at the anode is plotted versus platevoltage on an x-y recorder. A variable leak allows adjustment of gas pressure from3 X 10- 6 mm Hg to 10 microns. Voltage in these experiments is varied from zero to1500 volts, and magnetic field from zero to 600 gauss. The current collected is in therange zero to 5 ma.Tubes with two anode geometries have been tried. The anode of one tube con-sisted of a cylinder 3. 5 inches long and 2 inches in diameter, while the anode of anotherFig. XI-10.2I-ZzUTop view o tube. (Pressure, 5 X 10-4 mm Hg; voltage,650 volts; B field, 400 gauss; gas, argon.)200PLATE VOLTAGE300Fig. XI-11. Current-voltage characteristic for magneticand for argon at 4 X 10-4 mm Hg pressure.field of 300 gauss(XI. PLASMA ELECTRONICS)tube consisted of two loops of wire spaced 3. 5 inches apart and 2 inches in diameter.The current-voltage characteristics of the tubes were investigated in the pressure range5 X 10-5 mm Hg to 10-3 mm Hg. At all pressures, a typical current-voltage curve withzero magnetic field is similar to a temperature-limited diode. However, with the mag-netic field at approximately 100 gauss, the I-V curve changes, as Fig. XI-9 shows. Thesame curve occurs regardless of whether voltage is increasing or decreasing.It was found that the current maxima (peaks) occurred at different voltages as themagnetic field was changed. The voltage at which the peaks occurred appeared to fol-low a relationship V/B = constant. The peaks appear to be associated with rf oscilla-tions or instabilities. In the regions between the peaks the plasma is usually visible asa reasonably well-defined column, as in Fig. XI-10. At the peaks the plasma appearsto "blow out" and fill the entire tube.Figure XI-11 is an I-V curve for the cylindrical anode tube at a moderately high pres-sure. No evidence of the current peaks appears here.A. R. Cooke, G. C. Hartmann100

Plasma Electronics

http://dspace.mit.edu/bitstream/1721.1/53690/1/RLE_QPR_065_XI.pdf

Plasma Electronics

Abstract

Similar works

Full text

Available Versions

DSpace@MIT