P/2536 Ukrainian SSR

Electron Cyclotron Resonance, PlasmaWave Guides and Plasmoids

By K, D. Sinelnikov, P. M. Zeidlitz, Y. B. Fainberg, L. V. Douborov,A. M. Nekrashevich, O. G. Zagorodnov, E. I. Lutsenko,B. O. Shafronov and N, V. Topolya *

ELECTRON CYCLOTRON RESONANCEInvestigations dealing with plasma resonance pro-

perties are of interest in ascertaining the possibilitiesof heating the plasma by means of a high-frequencydischarge, and in developing methods of investigatingthe plasma parameters and the physical processestaking place in it.

The present work was carried out to investigate theproperties of an electrodeless high-frequency discharge,and plasma parameters under electron cyclotron andpolarization resonance conditions.

Electron resonance in plasma has been discussed inother papers.1' 2 However, as far as we know theseinvestigations were not concerned with the plasmaparameters, i.e., its density and temperature.

The determination of the temperature and densityof a plasma produced by means of a high-frequencydischarge in hydrogen within an external magneticfield was performed by a double probe method.3' 4

The control measurements of density were carriedout by means of the method of high-frequency doubleprobes,5 the probes being located outside the dischargetube. The high-frequency signal fed to one of theprobes is propagated through the plasma and receivedby the second probe connected with the resonanceamplifier. Assuming that the probe field is approxi-mately a dipole field, it is possible to determine theplasma density by the maximum in the transmittedsignal which takes place if the measuring signalfrequency equals the Langmuir plasma frequency.

The plasma densities measured by the two-probemethod and by a high-frequency probe coincide inorder of magnitude. The maximum density valuesobtained with a 200-300 w generator at the frequencyof 30-33 megacycles lie in the range of 5 x 1011-1012 cm-3. The volume of the ionized spaec did notexceed 200 cm3. The resonance was observedby measuring the power output of the generatorigniting the discharge as a function of the magne-

Original language: Russian.* Academy of Sciences of the Ukrainian SSR, Kharkov.

tic field at various pressures. At the same timemeasurements of plasma luminescence intensity withinthe visible light region were carried out with the aidof a FEU-19t photomultiplier. The resonance curvesindicating the power expenditure and light flux coin-cide on the corresponding scale within measurementerrors (pressures being no lower than 10~3 mm Hg).

Figure 1 shows the dependence of power outputupon the magnetic field value at different pressures.As was to be expected, the width of the resonancecurve decreases when the pressure reduces. Furtherreduction of the pressure, however, causes an increasein the resonance curve width (see Fig. 2). Apparentlyit can be explained in the following way.

Under cyclotron resonance conditions the electronis accelerated by a high-frequency field within theinterval between two collisions. A pressure reductionand a corresponding increase in the interval betweentwo collisions result in an increase in the mean electronenergy and the electron orbit radius. Thus, whenan electron orbit diameter in the discharge approachesthe vessel dimensions, the electron accelerationtime is reduced due to collisions with the wallswhich lead to a broadening of the resonancecurve. To check this hypothesis, measurements atanother frequency (120 megacycles) have beencarried out. The measurements revealed that theresonance curve half-width continues to dependqualitatively upon the pressure, but the pressure atwhich the broadening of the resonance curve occursshifts towards higher vacuum.

If the above mechanism actually takes place, itbecomes possible to estimate the electron energy atpressures which are close to the value at which theabnormal growth of the resonance curve half-widthbegins. If the vessel diameter is 4 cm and themagnetic field value in resonance is 17 gauss, themean electron energy should not exceed 102 ev, whichcorresponds to the temperature of 1.2 X 106 °K.This value agrees in order of magnitude with themaximum temperature value (4 x 105 °K) obtained

t Transliteration.

292

ELECTRON CYCLOTRON RESONANCE 293

p = 1.5 X TO"4 mm Hg

Figure 1. Electron cyclotron resonance curves. Power outputW in arbitrary units as a function of magnetic field H, for various

pressures p

by the double probe method for the pressure of3 x 10-3 mm Hg (Fig. 3).

The resonance value of the magnetic field at thegenerator frequency of 120 megacycles equalled43 gauss. The vessel diameter being 10 cm, thecorresponding temperature was 1.5-4.5 x 107 °K.

10-2 10-3 10-5

Figure 2. Electron cyclotron resonance width as a function ofpressure p: (a) as determined by light measurements; (b) as

determined by power measurements

It should be noted that at the frequency of 33 mega-cycles the magnetic field value corresponding to theelectronic cyclotron resonance equals 12 gauss insteadof 17 gauss obtained experimentally. Such a diffe-rence in magnetic field intensities with an inductivecoupling between the generator and the discharge,and with an external magnetic field perpendicular tothe axis of the coil causing the discharge, was alsoobserved in other experiments dealing with cyclotronresonance in plasma. At the frequency of 120 mega-cycles resonance was observed for the magneticfield value corresponding to cyclotron resonance.However, during this experiment capacitive couplingbetween the generator and the discharge was used.The possibility of changing the resonance conditionsby changing the mode of excitation ensues fromthe relations (1), (2) given below.

When the resonance took place at the frequencyof 120 megacycles, the plasma luminescence inside

the discharge volume almost completely disappearedsimultaneously with the beginning of the increase inthe resonance half-width. This was accompaniedby an increase in generator power expenditure and theappearance of blue luminescence of the retort walls,which is usual during the bombardment of glass withsufficiently fast electrons.

Plasma ResonanceAlong with the cyclotron resonance determined by

the condition coc = eH/mc there takes place a pola-rization resonance, in which the resonance frequencyis determined not only by the magnetic field inten-sity, but by the plasma density as well. In this casethe resonance frequency and the electron velocity aredetermined by the following relations.

Low Densities:

(a) Inductive coupling between the generator andthe load {Еф(а) is given at the plasma boundary) :

vr = — ^ — ' т>ф = ivr. (1)

(b) Capacitive coupling between the generator andthe load (Er(a) is given at the plasma boundary) :

2v a mcon

4 0 0 '

300

200

100TO"2 mm H g

l O ' 1i Hg

10 20

2536.3 H gauss

Figure 3. Electron temperature T as a function of the appliedmagnetic field H, for various pressures p. Generator frequency

Г>"Э KA-= 33 Me

294 SESSION A-6 P/2536 K. D. SINELNIKOV et al.

High Densities:

cop2 (oc2; œ = cop +

(a) Inductive coupling between the generator andthe load:

coc Y еЕф{а) .

(b) Capacitive coupling between the generator andthe load :

eEr(a)vr = Ô2covv a tncoG

v, = ivr, (2)

Here œ = generator frequency, cop = Langmuir elec-tron frequency, coc = Larmor electron frequency,v = collision frequency, vr and Уф = components ofthe electron velocity in the plasma, and a = plasmacolumn radius. A photomultiplier was used toindicate the polarization resonance and to determinethe maximum plasma luminescence. The increasein the plasma density was achieved by increasing thehigh-frequency generator capacity. Figure 4 showsthe dependence of the photomultiplier indicationsupon the magnetic field intensity at differentanode currents of the high-frequency generator. Theplasma density increases with an increase in theabove current, and the resonance curve is shifted intothe region of large magnetic fields.

Investigation of noises generated by the plasmaproduced by a high-frequency discharge is of grealinterest. Measurements of noise levels as a functionof the magnetic field were carried out. For this

1.5

1.0

0.5

I = 2 0 0 m a 1 1 = 2 5 0 m a

I = 150 mol g = 100 ma •

02536.4

200 400 600 800 1000H gauss

Figure 4. Light intensity as a function of magnetic field H forvarious currents /g of the hf generator. (Photomultiplier

voltage VPm as ordinate)

purpose an insulated probe was placed in the plasma,and the induced signal was fed to an oscillograph.Oscillations at the frequency of 1 megacycle andrelaxation oscillations were discovered among thenoises. An abrupt noise decrease in the region ofthe cyclotron resonance (see Fig. 5) is characteristicof the noise level dependence on the magnetic fieldintensity.

PLASMA WAVE GUIDES

To investigate the possibilities of high-frequencyplasma heating, it is necessary to study the penetra-tion of the high-frequency field into confined plasma(plasma wave guides).

To construct linear accelerators, it is necessary tohave an effective moderating system where the phasevelocity of electromagnetic wave propagation wouldbe lower than the velocity of light, and a simultaneousphase and radial stability of accelerated particlescould be provided. Anisotropic plasma wave guidesmeet these requirements, in particular plasma waveguides in a magnetic field. 6~12

This work includes an investigation of plasma waveguides. The experiments also determined dispersionproperties, i.e., the dependence of the phase velocityupon the frequency at the given plasma density.They also determined the topography of high-fre-quency fields.

The plasma wave guide was formed with the helpof a high-frequency discharge in a quartz tube 30 mmin diameter and 1800 mm long, where the vacuumwas sustained at about 10~3 mm Hg. The highfrequency gas discharge was ignited at one end of thetube by a 500 watt high-frequency generator at thefrequency of 116 megacycles. The discharge plasmafilled the whole tube, its density falling off with thedistance from the generator.

A high-frequency signal with a frequency changingwithin 50-500 megacycles, was fed to the plasma froma separate low-power generator placed opposite theignition point.

Moving a loop connected with a resonance circuitalong the wave guide, we could observe howii^, the<^component of the magnetic field of the standing wave,propagated along the plasma wave guide. The stand-ing wave field distribution is shown in Fig. 6. Thedistance along the wave guide in cm is plotted on theabscissa axis, the Нф values in arbitrary units beingplotted on the ordinate axis. A plasma wave guidein a constant longitudinal magnetic field Ho is cha-racterized by curve I; curve II was obtained for thecase Ho = 0. The distance between the meanminimums equals a half wavelength in the plasmawave guide. The ratio of this wavelength to thewavelength Ao in the free space determines thevalue of j8 = v^/c. It should be noted that theplasma density differed somewhat from one experi-ment to another because the ignition conditionschanged. The results of measuring the dependenceof the phase velocity ¡}c upon frequency / with amagnetic field (f}¿) and without it (/30) are summarizedin Table 1.

ELECTRON CYCLOTRON RESONANCE 295

It follows from Table 1 that with frequency changesfrom 50 to 500 megacycles, the phase velocity changedfrom 0.16c to 0.33c.

The influence of the constant magnetic field uponthe phase velocity is not great in the given region ofplasma wave guide parameter variation, and this factcoincides with theoretical predictions.

Table 1. Dependence of Phase Velocity upon Frequencyin a Plasma Wave Guide

/(Me) . . .

A ....te ....n x 10~

9 .

500.140.16—

1400.1670.1699.1

1500.20.24.7

2000.1960.2834.6

3000.180.229.0

4000.3070.329.7

5000.3309

It should be pointed out that the density data givenin Table 1 refer to a plasma wave guide with noexternal magnetic field. The superposition of themagnetic field resulted in a change of the plasmadensity by 10%-15%.

The determination of the plasma density wasperformed by two methods. One method determinedthe displacement Дсо of the proper frequency of aresonant cavity along the axis of which the plasmawave guide was placed. The frequency displacementAco is determined by the plasma density n0 = kAcowhere k is a coefficient depending upon the geometryof the resonant cavity and the plasma wave guide.13

The second method was that of a high-frequencyprobe.5 The results of both methods are in accord,showing that the plasma density in the wave guidechanged from 4 x 109 to 9.8 X 109 cm-3.

Measurements along the wave guide radius of theelectric field component Ez were carried out withthe help of a wire probe. These measurementsindicate that within the phase velocities of about0.15 c-0.2 с the Ez drop from the wave guide boundaryto the centre is insignificant. Theoretical calculationsshow that within these phase velocities the field Ez

should fall off by 10-20%. Having determined theEz(r) ratio outside the wave guide we can find thephase wave velocity. For a typical case we have

1.0

20 30 40 50 60 70 80 90 100 110

Figure 5. Noise level J as a function of magnetic field H

thus obtained f} = 0.2 which agrees well with themeasurement data produced by the standing wavemethod.

PLASMOIDS

One of the possible methods of investigating therelaxation effects inside a plasma which is subject tothe external magnetic fields, is studying the behaviourof plasmoids confined in space during their movementin non-uniform magnetic fields. We attach particularimportance to cases where adiabatic conditions obtainonly for the electron component of the plasma in theinteraction with external magnetic fields.

To obtain a sufficiently fast moving plasma, amodified plasma source of the Bostick type 1 4 wasused. The modification consisted in adding a cylindernozzle 10 mm in diameter and 20 mm long to theBostick source, thus reducing the divergence of theplasmoid to 20-30°. Hereafter the term " plasmoid "will mean a neutral plasma beam, modulated indensity and stringently limited in space and time.We found in the plasmoid no self-organizing propertiesassociated with its own currents or magnetic moments.All measurements were conducted at a distance ofabout 100 cm, and if there were any currents andmagnetic fields close to the source (at <—'10 cm),as stated by Bostick,14' 1 5 they were extinguishedunder the conditions of our experiment and could notinfluence the measurements. The plasma densitymodulation was due to the presence of ions of differentmasses (chiefly of oxygen and copper) which within10 /¿sec of movement could consolidate into closelylocated, separate plasmoids. The ion density estima-tion of the leading plasmoid gave 1-5 X 109 particles/cm3. The mean plasmoid speed was ~ 8 x 106 cm/sec.

Figure 7 shows the scheme of the set-up. Theplasma, leaving the source (1), after covering acertain distance gets into a non-uniform magneticfield created by a short solenoid (2) which has amagnetic field gradient of about 7 gauss/cm.

The basic measurements were carried out at amagnetic density of /—' 100 gauss.

Different magnetic (4) and electric (3) probes wereused to measure the plasma parameters. Themagnetic probes were coils which could both encompassthe glass tube and be inserted inside, NS remainingconstant (NS is the product of the number of turns inthe coil by the area). The Faraday cylinder (3)shown in Fig. 7 served as electric probe. It con-tained a measuring electrode 8 mm in diameter placedin an isolated cylinder, which, in its turn, was sepa-rated by a copper cylinder from the bulk of the plasma.The magnetic and electric probes were connected withan oscillograph having a low resistance input (100 cm).Signals arising in the magnetic probes were caused bymagnetic field changes in the coil at the moment theplasma was crossing it. The signals were of dia-magnetic type, i.e. the magnetic field was reduced atthe moment the plasma was crossing it. The magneticprobes located on the chamber axis were helpful infinding the diamagnetic signal which was at a maxi-

296 SESSION A-6 P/2536 K. D. SINELNIKOV eî al.

H . arbitrary units

22 30

2536.6

Figure 6. Standing-wave field distribution in a plasma wave guide

mum when the plasma entered the magnetic field. Thesignal disappeared gradually as the plasma wassinking in the magnetic field, but when it left thelatter, the diamagnetic signal of the opposite signappeared again 3-4 times farther from the lenscentre. The outcoming diamagnetic signal was3-4 times lower than the corresponding entrancesignal. An investigation of the dependence of thediamagnetic signal upon the magnetic field valueshowed that the signal reached its maximum valuewhen the magnetic field intensity was 60 gauss.

An examination of the plasmoid movement througha non-uniform magnetic field carried out with the aidof electric probes leads to the conclusion that dia-magnetic signals can be observed at the moment theelectron component of the polarized plasma crossesthe magnetic probe.

As the magnetic field of a short solenoid is characte-rized by non-uniformity along z and r, the presenceof an Hz gradient must lead to the polarization ofthe plasma along the z axis and consequently to theappearance of uncompensated charges in certain partsof the plasmoid.

The character of the signals obtained from electronprobes is given in Fig. 8a, which shows that plasmacrossing a heterogeneous magnetic field becomespolarized in the longitudinal direction and has theappearance of a sign-alternating chain. Charge topo-graphy in the plasmoid during its movement through

a heterogeneous magnetic field was obtained bymeans of electric probes. Fig. 8b, c, d shows thedependence of the probe current upon time fordifferent positions of the probe in the magnetic field.The position of the short solenoid is marked by adashed line and the probe location with respect tothe chamber axis is shown to the right of each diagram.

The diagrams indicate that electrons (the firstnegative peak) entering the heterogeneous magneticfield leave the plasmoid periphery and concentratearound the plasmoid axis. This process is accom-panied by a positive charge formation over theperiphery. Thus a plasma polarization takes placein the radial direction which results from the presenceof an H gradient along r. The first negative peakdisappears at some distance in front of the magneticfield, and the plasmoid front proves to be positivelycharged. This shows that besides pressing electronstowards the axis, the magnetic field slows them down,thus enabling the ions to outstrip the electrons.Analysing the behaviour of the first and the secondnegative peaks we can see that the appearance anddisappearance of electrical polarization is asymmetricwith respect to the value of median lens density. Thisis verified by diamagnetic probe signals, as mentionedabove. The behaviour of the ion peaks is alsoasymmetric with respect to the magnetic field en-trance and exit.

Knowing the charge distribution (shown in Fig. 8b, с, d), the ion velocity, and the particle density, wecan estimate the polarization electric fields arisingduring the plasma movement through a heterogeneousmagnetic field ; such an estimate shows that an electricfield of 500 v/cm can appear between the first positiveand negative peaks. Such local fields, naturally,must cause a relative movement of plasma particlesand change the plasmoid configuration. The presenceof electric fields is also proved by an observed drastic1.5-2-fold increase of the ion velocity which occursat a certain distance from the median plane of themagnetic field. This ion acceleration approximatelycoincides with the moment of the first negative peakdisappearance when the ions come to the front. Tosummarize, the plasmoid movement through a hetero-geneous magnetic field leads to a longitudinal andtransverse plasma polarization and to a change inthe configuration of the plasma formation.

3 4

X

Figure 7. Apparatus for plasmoid studies. 1, plasma source; 2, solenoid; 3, electrostatic probe; 4, magnetic probe; 5, glasstube; 6, pump; 7, oscilloscope

ELECTRON CYCLOTRON RESONANCE 297

(b)Direction ofplasma velocity

Figure 8. Plasmoid signals

The appearance of polarization electric fields andthe movement of plasma particles inside the plasmoidcaused by them probably brings about an additionalenergy exchange between the ion and electron plasmacomponents.

REFERENCES

1. B. Koch and H. Neuert, Z. Naturforsch., 4a, 496 (1949).2. H. Neuert, H. J. Stuckenberg and H. P. Weidner, Z.

angew. Phys., 6, 303 (1954).3. Biberman and Panin, J. Tech. Phys. (USSR), 21, 12

(1951).4. J. E. Allen, R. L. F. Boid and P. Reynolds, Proc. Roy.

Soc. (London), 70, 297 (1957).5. T. H. Yeung and J. Sayers, Proc. Phys. Soc, N 451B,

70, 7, 663 (1957).

W. O. Shuman, Z. angew. Phys., 3, 178 (1951).

Y. B. Fainberg and L. M. Pyatigorsky, Doklad SessiiAN SSSR, Kharkov (1953).

Y. B. Fainberg and N. A. Khizhnyak, Otchet FTI ANSSSR (1955).

Y. B. Fainberg, Proc. CERN Symposium, v. I (1956).

L. M. Pyatigorsky, Dissertation (1954).

6.7.

8.

9.

10.

11. Y. B. Fainberg and M. F. Gorbatenko, Otchet FTI ANSSSR (1957).

12. L. B. Mullet, Report AERE (1957).13. D. J. Rose and S. С Brown, J. Appl. Phys., 23, 711

(1952).14. W. H. Bostick, Phys. Rev., 104, 282 (1956).

15. W. H. Bostick, Phys. Rev., 106, 104 (1957).

P/344 USA

The Oak Ridge Thermonuclear Experiment

By C. F. Barnett, P. R. Bell, J. S. Luce, E. D. Shipley and A. Simon

The production of a self-maintaining thermo-nuclear reaction m a mass of deuterium, or deuteriumand tritium, gas is the goal toward which manydifferent experimental programs are directed Oneof the most difficult problems to be solved is that ofignition, or the initial heating of the fuel gas to atemperature high enough to make the reaction self-maintaming The Oak Ridge Group is attemptingto solve this ignition problem by trapping an acce-lerated beam m a magnetic field container by a changeof the charge-to-mass ratio of the particles inside thefield By this means we hope to accumulate a highconcentration of energetic ions and hold them untilthey have had time to randomize into a truly thermal-îzed plasma at a high ultimate temperature

The success of the trapping method depends on theproperties of the mechanism used to induce the changeof charge-to-mass ratio We have found that certainspecialized arc discharges can cause the dissociationof energetic deuterium molecular ions into atomic ionsand neutral atoms with high efficiency The atomicions are trapped m the field by virtue of having halfthe radius of curvature of the original molecular ionsA successful device must produce efficient trapping,but at the same time it must not cause a large lossof the trapped ions through charge exchange or exerta strong cooling effect upon the resulting plasmaThe special arc discharges developed by our group г

have proved to be satisfactory m this respect as willbe shown in the following sections

The ignition method is being tested by the injectionof deuterium molecular ions at an energy of 600 kevinto a direct current mirror machine (DCX) wherethey pass through one of these special discharges, anenergetic carbon arc The 300-kev atomic ions pro-duced by dissociation are trapped into a closed orbitnear the central plane of the machine, while the resul-tant neutral atoms and the remaining undissociated

* Oak Ridge National Laboratory operated by UnionCarbide Corporation for the US Atomic Energy Commission

The work reported m this paper is the outcome of thejoint effort of the members of the Thermonuclear Expenmental Division with effective assistance from members of otherdivisions of this Laboratory Active participation in earlytheoretical work by A E Ruark and H S Snyder is greatfullyacknowledged and the continuing interest of these mentogether with other consultants is likewise recognized withgreat appreciation

beam leave the machine at once The trapped ionsare in the form of a highly organized beam The ionsof this beam cause îonization of the residual gas inthe machine and also become thermahzed by inter-action with electrons and other ions

DCX THEORY

The conditions under which an injected beam willgive rise to a thermonuclear plasma are consideredbelow The requirements for overcoming the neutralgas background are considered in the next sectionThe steady state plasma temperatures are then studiedin the section thereafter Attention is paid in this andthe succeeding sections to the effects of cold electroninflux, impurities, heat transfer to the walls and elec-trons in the arc.

BurnoutThe initial neutral gas pressure in DCX will he

somewhere in the range between 10~6 and 10~8 mmof Hg, depending upon the vacuum system usedUnder these conditions the trapped beam will remainorganized Each deuteron will lose very little energybefore being lost by charge exchange with a neutralgas atom The essential reason for this is that thecharge-exchange cross section (orCx) for 300-kev deute-rons m deuterium is about 2 x 10~18 cm2, while theeffective energy-loss cross section is less than 10~19 cm2

The effective Coulomb cross section (ac) for 90°deflection by multiple collisions is about 10~23 cm2

As a result, there will be little energy degradation ofthe input beam, and a plasma will not be formed unlessthe neutral gas density can be further reduced

The injected ions, however, tend to destroy theneutral gas atoms in two ways The first, and prin-cipal, mechanism is by îonization Since the îoni-zation cross section (cri) at 300 kev is about 4 X 10~~17

cm2, there will be about 20 neutral atoms ionized byeach hot ion before it suffers a charge exchangeThe slow ions which are produced scatter rapidly andleave the system by following the magnetic lines to theend walls or the arc cathode In addition to this,charge exchange itself also destroys a neutral atom,since the fast neutral atom which is formed will thenfly to the walls and bury itself with little sputtering

If the slow ions, which will be neutralized uponstriking a solid surface behind the mirrors, can be

298