Turbulent Eddies in High Density SparkChannels in Helium

Heinz Fischer and Karlheinz Sch6nbach

Turbulent eddies in high pressure microsecond spark channels in helium were photographed by means ofa 20-nsec Kerr cell shutter. Current densities exceeded 106 A/cm2. It was shown that turbulences areinitiated from plasma jets originating at the electrodes. The cathode jet is explained by Compton'saccommodation theory as extended by Haynes. The observed anode shock wave appears to be the resultof a dynamic magnetic pinch.

Background

The optical emittance of high pressure microsecondspark channels in argon and helium as produced in a40-nH, 2.75-/uF spark discharge was studied by meansof a 20-nsec Kerr cell shutter. It was confirmed thatsaturation emittances" 2 were not observed in heliumwith a gap larger than 1.5 mm because of turbulent insta-bilities within the channel. These appear as clearlydefined areas of reduced emittance and are called eddiesin this paper; in addition the channel appears twistedand discontinuous. The argon channel on the otherhand remains homogeneous within the complete rangeof observation which was gap = 1-4 mm, p = 1-9 atm,U = 2-6.5 V.

In argon, the emittance profile across the channelwas observed to become rectangular with increasingcurrent density, indicating an increase in opacity.2

Figure 1 demonstrates the differences in appearancebetween the argon and helium spark channel; thecathode is at the top of the figure. Similar instabilitiesin spark channels were observed in 1950 by Holthamand Prime,3 1954 by Cundall and Craggs,4 and 1963 byJohansson and his associates.5 It was understoodthat such phenomena originated from electrode jets4 ;however, the gas influence upon the instabilities was notdiscussed. Other authors did not try to analyze thephenomena, although it had become obvious that suchinstabilities would be observed most frequently withlarge current densities in light weight gases such ashelium and hydrogen.

The authors are with the Lehrstuhl fur Angewandte Physik derTechnischen Hochschule, Hochschulstrasse 2, 61 Darmstadt,Germany.

Received 7 July 1967.

Method and ApparatusThe circuit and apparatus have been described

previously",2 and is called Unit 2 in this paper. Gatesof the Kerr cell shutter were 8 nsec, 20 nsec, and 100nsec wide. All photographs of the spark channelswere taken with a Wratten Filter No. 65 which trans-mits from 4500 A to 5500 A.

The spark current oscillates and has its first maximumafter approximately 540 nsec. The spark channelwas observed from 140 nsec to 830 nsec after zero timeof the breakdown. Gaps were altered between 1 mmand 4 mm and the breakdown voltages were between2-6.5 kV depending upon gas pressure and gap length:maximum current density was approximately 3 X 106A/cm2 .

Results

With a gap d = 1 mm in width, a pressure of 35 atm,and a breakdown voltage U of 6 kV, the helium channeldemonstrates a uniform emittance approaching sat-uration condition.2 However, with a gap d = 1.5 mmwide, the channel already loses its cylindrical geometryand becomes inhomogeneous; now eddies may be ob-served. These instabilities become more pronouncedas the gap increases. Hence, d = 4 mm was chosen forthe detailed investigations.

The following results are obtained with a relativelysmall breakdown voltage of 3.0 kV and a gas pressure of3.5 atm (Fig. 2). Observing the time development, onenotices that the channel is still cylindrical with t = 140nsec. However, parabolic-shaped dark spaces at theelectrodes are recognized and the cathode dark spaceis much larger. Also, the anode spot is less pronouncedthan the cathode spot. The cathode dark space growsrapidly with time and after 250 nsec appears to joinwith that of the anode. After 300-400 nsec, the cath-ode spot begins to grow rapidly. At that time the

February 1968 / Vol. 7, No. 2 / APPLIED OPTICS 311

Fig. 1. Homogeneous spark channel in argon (gap = 4 mm, p =2 atm, U = 6 kV, gate at 675 nsec) and turbulent eddies in helium

(gap = 4 mm, p = 8.75 atm, U = 6 kV, gate at 675 nsec).

cathode dark space has assumed the shape of a half-sphere and is sharply separated from the bright zoneadjoining the plasma away from the cathode. Theanode spot on the other side has grown only slightly.Bright branches extend into the plasma from the brightregion of the channel close to the cathode. Theyborder small sized dark emittance eddies within thechannel. The emittances become more uniformtoward the end of the first current pulse and the eddieslose their sharp boundaries. A flare develops at theanode.

With large breakdown voltages (U = 6 kV) for com-parison, the following results may be observed (Fig.3):

Here, also, the channel is cylindrical at the beginningof its development. The anode spot, however, is nowmore pronounced than the cathode spot and growscontinuously with time. Dark spaces at the electrodesnow are approximately equal in size. The constric-tion of the channel before the anode is noticeable andexists from the beginning. After approximately 250nsec-which is earlier than with a small breakdownvoltage-there appear half-sphere-shaped dark spacesat the cathode as well as within the constriction at theanode. Eddies develop afterwards just as in the case ofsmall breakdown voltages. Again the contrasts withinthe channel fade away toward the end of the firstcurrent pulse. The anode flare is more stronglydeveloped at large voltages.

Figure 4 shows a twisted channel in helium and theanode flare which appears toward the end of the firstcurrent oscillation.

The described phenomenon is reproducible in itsgeneral appearance, S-nsec and 20-nsec exposures showthe same details and degree of definition. Longerexposure times of 100 nsec, on the other hand, demon-strate considerable blur due to channel motion. Thedark space boundaries are also blurred. The electrodespots appear less affected, as may be expected. Theinstabilities appear the same with and without thespectral filter.

AnalysisAdditional experiments are required in order to

understand fully the observed instabilities, however,one may start with the assumption that jets do startfrom the electrodes with small or large breakdownvoltages.

According to Haynes6 (he observed electrode jets in ahydrogen spark), the dark spaces are regions where theparticles have a large directed velocity and a relativelysmall thermal energy. Hence there will be a relativelysmall number of radiation emitting collisions. Alsoin Haynes' case,6 the dark spaces grow with increasingcurrent and time.

After 400 nsec (3 kV) and 250 nsec (6 kV) a shockwave starts from the cathode as was concluded frommm

I40nsec 4O0nsec

18O n sec 530 n sec

22 n sec 675nsec

29 n sec 830 nsec

Fig. 2. Spark channel development in helium with d =4 mm,U = 3.0 kV, p = 3.5 atm, and maximum current density approxi-mately 106 A/cm2 . Cathode is at the top of the figure. Numbers

under figures are gate times after breakdown.

312 APPLIED OPTICS / Vol. 7, No. 2 / February 1968

ou n sec

bn sec

-QVII b. - ou sec

Fig. 3. Spark channel development in helium with increased gaspressure and breakdown voltages (d = 4 mm, p = 8.7 atm, U =6.0 kV, maximum current density approximately 3 X 106 A/cm2).

Numbers under figures are gate times after breakdown.

the sharp contrast in emittance.8 This shock wavewould cause the channel turbulence and would producethe eddies.

Also, a shock wave starts at the anode in the case ofa large breakdown voltage and is obviously initiated bythe local constriction of the anode spot. This con-striction probably is the result of a dynamic magneticpinch.

Discussion

There is a large amount of literature, within the lastforty years, that deals with the disturbances beinginitiated at the electrodes of a gas discharge plasma.However, most authors do not consider the influencewhich the nature of the gas itself may have. Yet thegas apparently is of great importance in our case.

Some explanation for the cathode dark space, observedat the beginning of the channel development may begained from a theory proposed by Compton.7

Compton assumes that only a part of the kineticenergy of the ions is transmitted to the electrodes.

The ratio of transmitted kinetic energy to total ionenergy is called the accommodation coefficient a; it is afunction of the atomic weight of the ions and related tothe electrode material. In the literature, a valueof a of 0.06 is given for He on tungsten; a is a factorof ten larger for Ar on tungsten.

As a result, the atoms after neutralization andreflection from the cathode will have a directed velocitytoward the anode and thus will be able to produce ajet. This effect would be more pronounced in Hethan in Ar because of the differences in a.

Haynes6 confirmed in principle Compton's accom-modation theory experimentally; however, the assump-tion is added that negative ions are formed close to thesurface of the cathode. These negative ions would bestrongly accelerated within the cathode drop.

Compression and refraction waves will develop insupersonic jets and will be predominant in cases oflarge pressure gradients p between the jet and itssurrounding medium. On the other hand, the largestpressure gradients will develop during the rise of thecurrent pulse; the maximum Ap may shift towardearlier times with increasing current density.

The anode jet is assumed to be caused by the acceler-ation of the positive ions in the anode drop. Thisexplanation was also given by Haynes.6 Increasingjet velocity with current may be deduced from theincreasing constriction at the anode. The shock waveinitiated by this assumed magnetic squeeze had beenmentioned previously.

A comparable constriction phenomenon was observedby Folkierski and others8 in a low pressure dischargein argon. They assumed that the constriction wouldresult in an extremely high pressure along theaxis. This overpressure would initiate shock waves,one of which would propagate in the direction of thecathode. The opposite shock wave would result in aflatting of the anode spot, as can be observed in ourexperiment (see Fig. 3).

Thus, two effects apparently are superimposed,leading to channel turbulence and subsequent eddies.The main cause appears to be the shock wave from

Fig. 4. Twisted spark channel and anode flare in helium towardthe end of the current pulse at 830 sec (gap = 4 mm, p = 9 atm,

U = 6.2 kV).

February 1968 / Vol. 7, No. 2 / APPLIED OPTICS 313

-ft. c_ ar-,

the cathode, which is initiated by the cathode jet.At high pressure additional shock waves originate fromthe anode and are caused by the constriction of thechannel in front of this electrode. Such constrictionsapparently have not been observed in our kind of highpressure arc discharge.

Initial effects in the development of jets and com-pression waves cannot be observed with the presentapparatus because of our trigger delay of 140 nsecafter zero time of the breakdown.

Fischer9 recently has studied high density sparks ofnanosecond duration and was able to photograph theinitial development of electrode phenomena which hetentatively identified as erosion jets. We assume thatthese observations parallel our present observationsand would expect a confirmation from a study of thedevelopment of the channel in Unit 2 from the begin-ning. In addition we plan studies of low inductancespark discharges of approximately 50-100 nsec duration.

The support of the Air Force Cambridge ResearchLaboratories is acknowledged with great appreciation.

References1. H. Fischer, in Conference on Extremely High Temperatures,

H. Fischer and L. C. Mansur, Eds. (John Wiley & Sons, Inc.,New York, 1958), p. 11.

2. H. Fischer and L. Michel, Appl. Opt. 6, 935 (1967).

3. A. E. Holtham and H. A. Prime, in Electrical Breakdown ofGases, J. M. Meek and J. D. Craggs, Eds. (Clarendon Press,Oxford, 1950), p. 359.

4. C. M. Cundall and J. D. Craggs, Spectrochim. Acta 7, 149

(1955).

5. R. B. Johansson, E. A. Smars, and B. E. Wilner, in 6e con-

ference international sur les phenomenes d'ionisation dansles gaz, Paris (SERMA, Facult6 des Sciences, Paris, 1963),

Vol. 2, p. 611.

6. J. R. Haynes, Phys. Rev. 73, 891 (1948).

7. K. T. Compton, Phys. Rev. 36, 706 (1930).

8. A. Folkierski, P. Frayne, and R. Latham, Nucl. FusionSuppl. 2, 627 (1962).

9. H. Fischer, in Report on 26th Annual Conference on Physics

and Electronics, R. E. Stickney, Ed. (MIT Press, Cambridge,Mass., 1966), p. 385.

OSA Detroit

Alan M. Laties University of Pennsylvania Hospitalgiving a paper at the October Meeting.

photos D. L. MacAdam

D. G. Collins Radiation Research Associates (left) and E. V.Loewenstein AFCRL, with J. R. Meyer-Arendt Pacific Univer-

sity in the background.

314 APPLIED OPTICS / Vol. 7, No. 2 / February 1968