Prebreakdown electrical conductivity of nearly

saturated caesium vapour

C. Christopoulos, M.Sc, D.Phil., and V.G. Endean, M.A., D.Phil., C.Eng., M.I.E.E.

Indexing terms: Arcing, Conductors and conductivity, Breakdown and gas discharges

Abstract: Comprehensive measurements of the electrical conductivity of mixtures of nearly saturated caesiumvapour and xenon prior to the transition to the glow or arc are shown to fit an empirically derived analyticalformula- As saturation is approached, the electrical conductivity exhibits a regular double-exponentially-growing periodic oscillation as a function of the degree of saturation. Experimental points cover the rangefrom 12 periods to 3 periods from saturation. Extrapolation of the empirical curve to saturation predictsa change in electrical conductivity from a metallic level to an extremely low level between the last peakand the last trough of the oscillation. This behaviour is quite different from that predicted by Saha equilibriumanalysis for example, and is thought to be a new effect Possible approaches to a theory are discussed. Ifsimilar behaviour is confirmed in other metallic vapours, e.g. copper, mercury and sodium, it will shedconsiderable light on puzzling phenomena that have been observed in industrial arcs and discharge tubesfor many years without satisfactory explanation.

List of symbols

e = electron charge/ ' = discharge currentk — Boltzmann constantm — electron massn - charge number densityna = neutral number densityQ - electron momentum transfer collision cross-sectionTg — gas temperature, KTi = reservoir temperature, Kvth ~ electron thermal velocityK' = discharge voltageV = voltage constantVi = ionisation potentialVB = electrode voltagea)Q{ = constantso = electrical conductivity, ft"1!™*"1

a0 = electrical conductivity constant

1 Introduction

Metal-vapour arcs are of considerable practical importancein the electric lighting and power industries and in manyother applications, e.g. welding. They have been intensivelystudied both experimentally and theoretically.1"4 There ishowever still no agreement as to how the very high currentdensities and low temperatures that are observed near thecathode can occur. Thermionic emission on its own cannotaccount for the measured current densities, because theappropriate cathode temperatures given by the Richardsonformula are often well above the boiling points of the metalcathodes. Alternative explanations have invoked fieldemission, thermionically enhanced field emission, tunnelling

Paper 575A, first received 25th October 1979 and in revised form7th January 1980Dr. Christopoulos is with the Department of Electrical & ElectronicEngineering, University of Nottingham, University Park, NottinghamNG7 2RD, England, and Dr. Endean is with the Department ofEngineering Science, University of Durham, Science Laboratories,South Road, Durham DHl 3LE, England

IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980

of electrons through oxide layers on the cathode surface,5

and many other mechanisms. But detailed quantitativeverification of any of these theories has not yet beenachieved.

One of the assumptions invariably made in metal-vapour-arc cathode theories is that metal vapours at the lowtemperatures of interest must be very poor conductorsof electricity. Theoretical electrical conductivities maybe worked out using equilibrium considerations and Saha'sequation, and these are very low. Experimental supportfor electrical conductivities of metal vapours based onSaha's equation has been obtained for much higher tem-peratures6'7 at which appreciable ionisation is expected,but not at the low temperatures observed at vapour arccathodes. Indeed, apart from some measurements previouslyreported by the present authors,8'9 there appear to be nomeasurements at all of electrical conductivities of metalvapours at these lower temperatures recorded in the litera-ture.

The work reported here was motivated by the obviousneed to fill in this gap in the experimental evidence. Caesiumwas chosen as the working metal vapour because it has thelowest ionisation potential in the periodic table (3-89 V)and is therefore the metal vapour most likely to producemeasurable electrical conductivities at low temperatures. Italso has the advantage of a low boiling point (943 K) sothat vapour pressures in the medium range may be obtainedwithout going to excessively high temperatures. Its pro-perties however are very similar to those of sodium, andalthough mercury and copper have very much higherionisation potentials (10-4 V and 7-7 V, respectively), theresults of this investigation are such as to suggest thatthe value of the ionisation potential may not after allbe too important a parameter.

2 Test procedure

Measurements were carried out on mixtures of caesiumvapour and xenon over a gas temperatures range 600—HOOK. The caesium vapour pressure was varied between0-3 and 2103 Pa, corresponding to liquid caesium reservoirtemperatures (T{) between 400 and 670 K. Xenon pressures

95

0143-702X/80/020095 + 8 $01-50/0

were in the range 102 to 104 Pa. Measured electrical con-ductivities varied between 310~7 and KT1 £l~lm~l.

This range of measurements presented some experimentaldifficulties. With reservoir temperatures well above roomtemperature it was found to be necessary to enclose theentire experimental assembly in a vacuum chamber in orderto prevent oxidation of the discharge tube electrodes andto eliminate thermal convection currents around thedischarge tube. It was not practical to use a remote caesiumreservoir. One end of the discharge tube was kept at thelower temperature 7} so that it retained a small depositof.liquid caesium, while the bulk of the tube was kept atthe higher temperature Tg. This meant that the dischargetube wall had to withstand a very sharp temperaturegradient.

Wall leakage resistance was a continuing problem. It wascaused by the caesium vapour reacting with the internalsurface of the discharge tube and by deposition of materialfrom the oven coils and the radiation shields onto theexternal surface of the discharge tube. Eventually theleakage resistance would become too large for accuratereadings of the discharge resistance to be taken and thedischarge had to be discarded. Five tubes were used alto-gether.

-o I

Fig. 1 Experimental assembly

AB, C

D, EFGHI I

= discharge tube= lower tube containing hypodermic

caesium= ovens= thermocouples= aluminium block= radiation shields= electrode connections

needle filled with

2. /. Experimental arrangement

Two tubes made of sapphire (tube d) or sintered alumina(tubes b-e) (>99-9% A12O3) were joined by a hollowniobium tube (Fig. 1). The upper tube (10 cm long, ~ 1 cmdiameter) was used as the discharge tube. Hypodermicneedles containing approximately 0-3 g of caesium wereplaced inside the lower tube (6 cm long, ~ 1 cm diameter).The free ends of the two tubes were sealed with niobiumelectrodes and remained vacuum tight up to 1200K. Fortechnical reasons it was necessary to carry out the sealingprocess in an atmosphere of xenon. Xenon could not there-fore be eliminated from the discharge tube, but it waspossible to vary the xenon pressure with different tubesover a limited range. The nominal xenon pressures given forthe different tubes (Table 1) may only be treated as veryrough estimates however because they could have beenconsiderably affected by the sealing process.

The two tubes were mounted inside two cylindricalovens constructed of resistance wire mounted on recrystal-lised alumina tubes. The oven temperatures could becontrolled independently. A system of thin stainless-steelradiation shields was used to maintain the bulk of the uppertube at the temperature Tg. A small amount of caesiumwas distilled from the lower tube through the hollow niobiuminterconnecting tube and deposited at the lower end of theupper tube. Chromel-alumel thermocouples were used tomeasure the temperature Tg and the temperature Tt of thelower niobium electrode of the upper tube and the liquidcaesium in contact with it. In the latter case, care was takento ensure full metallic contact between electrode andthermocouple. Radiation shields were used to obtain asharp temperature gradient just above the lower electrode,thus ensuring that the rest of the upper discharge tube wasmaintained at temperature Tg. An aluminium block placedin thermal contact with the lower electrode provided furthercontrol of the reservoir temperature.

The complete assembly was placed inside a Pyrex tubewhich was then, evacuated. The upper and lower electrodesof the upper discharge tube were brought out to an externalcircuit to enable voltage-current characteristics to beobtained. Tests were carried out to ensure that leakagecurrents other than through the discharge tube itself werenegligibly small. Leakage currents through the walls of thedischarge tube itself however were difficult to eliminate,particularly as saturation was approached. However, whenleakage currents through the walls were significant, theywere subtracted from the measurements.

c* - reduced scalecurrent

96

Fig. 2 Typical discharge voltage/current characteristic

IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980

2.2 Voltage/current characteristics

A typical voltage/current characteristic is shown in Fig. 2.Voltages up to approximately 100 V were applied, andcurrents ranging between a few mA and several mA weremeasured depending on the conditions. For small appliedvoltage the discharge tube behaved as a constant resistance.The resistance was the same whether the upper (hot) eiec-trode or lower (cold) electrode was treated as the cathode,and there was no measurable voltage step when the polaritywas reversed. As the applied voltage was increased, with thehot electrode as cathode, a point P was reached (transitionvoltage VB) at which the slope of the characteristic suddenlyincreased. With further increase in voltage the characteristicfollowed a new straight line until, at Q, the current startedto increase more rapidly. Beyond this point the dischargewould undergo a transition to a glow or an arc. Sometimes itwould jump straight to the arc mode without going throughthe glow. With the cold electrode as cathode the character-istic would rarely depart from the initial straight line exceptat high values of Tt when the behaviour was similar to thatwith the hot electrode as cathode. The slope of the linePQ would then be very nearly the same, but usually therewas a larger value of transition voltage VB.

The initial straight line at low applied voltage wasassumed to be due entirely to wall leakage currents. Theslope of the straight line PQ was interpreted as the resistanceof the discharge itself in parallel with the wall leakageresistance. The resistivity of the discharge only was obtainedfrom the ratio V'/l' X(tube cross-section/electrode separ-ation). It was assumed that the effect of sheath resistancein the PQ portion of the V/I characteristic was negligible.The transition voltage VB was interpreted as an electrodevoltage drop which had to be exceeded before the dischargewould conduct. For one of the tubes (tube a), while thecharacteristic was observed to undergo the transition to theglow as with all the other tubes, the value of VB was verysmall. This made it difficult to be sure that wall leakage wasnot shorting out the discharge especially as saturation wasapproached. Results for electrical conductivity were how-ever repeatable to within a factor of 2, which was not con-sistent with appreciable wall leakage, since with all theother tubes, the wall leakage currents were observed toincrease with time. Nevertheless, to be on the safe side,results close to saturation for this tube have been excluded,even though they show reasonable agreement with theformula which all the other results fit.

It may be noted that the.voltage/current characteristicsof these discharge tubes differ from normal in that theyexhibit a constant discharge resistance before enteringthe Townsend prebreakdown region instead of the moreusual constant current independent of voltage. The measur-able range of electrical conductivity was limited at thelower extreme (~310~7fZ"1m"1) by the fact that the wallleakage predominated and the change of slope at P couldnot be reliably detected, and at the higher extreme(~lO~l£l~lm~l) by the discharge going straight intothe Townsend region or even directly into the glow orarc from the wall conduction region.

3 Results

Readings were taken of the electrical conductivity a andthe electrode voltage VB for different values of 7} and Tg.Large variations in 0 and VB were frequently observed to

IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980

occur for quite small changes in 7} and Tg with no obviouspattern. Repeat runs were carried out to make sure thatthe variations were real and not just the result of spuriousexperimental errors of a random nature.

It was expected that the results for a, even if theydid not show full agreemet with theoretical predictionsbased on Saha's equation and equilibrium considerations,would at least be reconcilable in some way with such atheory. This proved not be the case. Plots for each tubeof In a + (eViJ2kTg) against 1/7} with ^ = 3 -89 V, theionisation potential of caesium, did not produce the setof straight lines parallel to the 1/7} axis expected theor-etically. They did not even produce recognisable curves.The experimental points were distributed apparently atrandom and with no obvious relation between the resultsfor the different tubes. Two facts did stand out, however.One was that if (1/7}) — (l/Tg) was treated as one of thevariables instead of 1/7}, the data did appear to collapsemore readily onto single curves for each tube. The secondwas that In a + (eV/2kTg) was a suitable choice for asecond variable provided that V was chosen to be approxi-mately 1 -1-5V rather than _3-89 V. The final choiceof In (a/a0) + (eV/2kTg) and (eV/k){(\IT{) - (HTg)}, withV = 1-34V and a0 taking on fixed values for each tubeas the appropriate variables to plot against each other,was obtained as a result of a lengthy trial and iterationprocess using the criterion that all the data should collapseonto a single curve.

3.1 Electrical conductivity measurements

The experimental points obtained for the five dischargetubes a—e are shown in Figs. 3a-e respectively. Thecurves superimposed on the plots are in fact all partsof the same curve which is shown in Fig. 4. Some datawere obtained with tube a for values of (eV/k){(1/Ti) —(l/Tg)} < 6-5, but are not shown despite thefact that it also provided a reasonable fit to the empiricalcurve. This is because the electrode voltage VB was verysmall for this tube and for Tx close to Tg, i.e. near saturation,the results could have been significantly affected by wallleakage resistance. It may be noted that it would be possible,for this tube on its own, to replace the curve through theexperimental points by a straight line with a small positiveslope, and attribute the deviation from the straight line eitherto experimental- errors, or to a weak dependence on Tx.Without the data from the other four tubes and the realis-ation that (l/Ti) — (l/Tg) was a similarity variable, thiswould in fact be the natural interpretation to place on thedata. In fact the data from this tube wer.e published pre-viously9 at a time when the data for the other four tubeshad not yet been obtained, and they were interpreted inthis way, the discrepancy between the data and theoreticalSaha predictions being noted. Other data obtained muchearlier8 lacked separate measurements of Th but werealso interpreted on similar lines.

The data for tubes b-d show more of the oscillatorystructure of the empirical curve. There is a shortage ofexperimental points near the troughs of the empiricalcurve, particularly for the smaller values of (eV/k){(1/7}) — (l/Tg)}. This was not caused by failure to attemptto take readings near these troughs. Attempts were madebut the discharge resistance was too high to be separatedreliably from the wall leakage resistance.

97

The data obtained on tube d for (eV/k) {(1/7}) -between 3 and 5 are worth particular comment. The highdensity of experimental points on the left-hand side of thelobe between 4 and 5 was obtained deliberately. Thevariation in a with small variations in 7} and Tg was observedto be particularly rapid and several runs over the sameregion were made to ensure that the variation was real.The data on the lobe between 3 and 4 are truncated. Thisoccurred because wall leakage currents prevented readingsbeing taken lower down on the lobe, while, towards thepeak of the lobe, transition to the glow or arc was occurring

before or as soon as the transition voltage VB was reached,and no linear prebreakdown characteristic could beobtained.

With tube e, acceptable data were obtained closer tosaturation than with any of the other four tubes. Wallleakage was less of a problem with this tube and somedata were obtained well down on the empirical curve.The fit to the empirical curve for values of (eV/k){(l/T{)-(l/Tg)} < 4 is not particularly good, but it doesshow the very rapid variations in a with small variationsin 7} and Tg, and as with tube d, it also shows the effects

A

2

0

Ms?c- -2

10

a

12

8r

0 -

-2

11 (1.1. )

*L5?

-2

10r

8 -

6 -

-2

-U •

f\

-f?

ev /i j _ \k U " Tj

Fig. 3 Electrical conductivity measurements

Tube a only:10 3

o 1Q 1

X 1

/Tg values:•6 +•44 A•35 v

Tubes b—e:10 3

•1- 2t 2 -o 2-

jT\ values:•5 o 2•4 x 23 +2

111

•2•1•0

•25•1707

A 1v 1o 1

> 13 00 0

•9•8• 7

00• 9 4

•90

<a 1-60 1-5

98 IEEPROC. Vol. 127, No. 2, Pt. A, MARCh 1980

Tube

ao,i7"' m~'Xenon pressure. Pa

a

1-6 X 10'2X 103

Table 1: Nominal xenon pressure and a0

b

10X 10'< 5 X 102

c

10104

values

X 10'

d

5 X 1 0 '3 X 103

e

4X 10" '104

of wall leakage currents and early transition to the glowor arc in truncating the acceptable data as saturation isapproached.

3.2 The empirical formula

The curve which fits all the data for electrical conductivityas a function of 7} and Tg shown in Fig. 4 is an exponentiallygrowing sine wave. The analytical formula corresponding tothe curve is

a = a0 expeV\ eV I 1

+ B exp — a —lKlg I K W, lg

sin2-neV 1

(1)

where V = 1 -34 V, a = 0-39 and |3 = 42. o0 is a constant foreach tube and is tabulated with nominal xenon pressure inTable 1. There is considerable experimental uncertainty inthe values of xenon pressure and appreciable tolerances inthe curve-fitting procedure on the values of a0. It would

therefore be unwise to draw any conclusions from thisTable. The accuracy of the curve fit to the experimentaldata also juggests ±15% possible error in a and Q. Thevalue of V is much more accurately fixed. With the dataconvering 9 periods, an error in V of 1% would seriouslydegrade the fit. There remain possible systematic errorscaused for example by the thermocouple readings beingconsistently high or low either because of the physicallocation of the thermocouples, or, less likely, becauseof calibration errors. The total possible error in Pis estimatedto be ±3%; i.e. V= 1-34 ± 0-04 V. The validity of theempirical equation is limited by these possible errors in theparameters. Clearly it is not the only possible interpretationof the data, but alternative interpretations cannot be verydifferent.

If the empirical formula is extrapolated to the firstpeak and first trough from saturation it gives approximately108 and 10~19 O"1 m"1 as maximum and minimum valuesof o, respectively, with a spread of approximately 10 ± 2 onboth values depending upon a0 and Tg. The maximumvalue may be compared with the electrical conductivityof solid caesium at room temperature, 5x 106r2~1m"1.The minimum value is much less than that of solid insulating

1 0 r

c 2

-2

10 12

Fig. 4 Empirical curve for electrical conductivityx tube aa tube bo tube c+ tube dO tube e

IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980 99

materials such as A12O3 at room temperature (approximately

3.3 Electrode voltage measurements

Measurements of the electrode voltages showed littlecorrelation with any of the other measured quantities orbetween tubes. All readings were taken with the upper(hot) electrode as cathode. When VB could be measuredwith the lower (cold) electrode as cathode, it was generallylarger. All the electrodes were made of niobium. However,the conditions of the electrode surfaces may well have beenvery different. The effects of surface impurities, possiblecaesium monolayers (in the case of the cold electrode adeposit of liquid caesium), and different sizes of surfaceprotrusions could all have contributed to the erratic natureof the electrode voltage readings.

4 Discussion

The results for electrode voltage do not permit any positiveconclusions to be drawn about electrode-emission mech-anisms in this type of discharge. Clearly the behaviour atthe electrodes depends very much on electrode conditions,and classical cathode-fall theories10 are unlikely to be ofmuch relevance until the effects of electrode conditionshave been fully investigated. One important negativeconclusion may be drawn from these results however.The electrical conductivity of the discharge does notappear to depend on what happens at the electrodes.The fact that all five discharge tubes produce results fora which fit the same empirical curve, while the resultsobtained for VB show little correlation between electrodevoltage and the other measured quantities, indicates thatalthough the conditions in the main volume of the dischargemay sometimes have an effect on what happens at theelectrodes, the reverse is not the case. Therefore in orderto explain the electrical conductivity results, it is necessaryto consider volume effects or discharge wall effects orboth, but to exclude electrode effects.

While there does not appear to be any theory in existencewhich would help to explain the observed dependence ofthe electrical conductivity on Tt and Tg, what can be saidis that the observed dependence would help to explainsome well known characteristics of metal-vapour arcs. Ifsolid metal levels of electrical conductivity are possible inmetal vapours, then the very high current densities observedat the cathodes of metal-vapour-arcs become much easierto explain. If rapid transition to a highly insulating stateoccurs for very small changes in temperature and pressure,the observed instability of the metal-vapour-arc cathodespot becomes more easily understood. Conduction ofcurrent can only occur where the temperature and pressureof the vapour are appropriate, and quite small temperaturevariations will therefore be sufficient to cause rapid motionof the cathode spot. One of the problems with theoriesof the cathode spot which utilise tunnelling of electronsthrough an insulating layer on the cathode surface5 toexplain the high emission current densities is that theyneed an insulating layer of an appropriate thickness to bepresent and this has seemed unlikely for liquid-metalcathode surfaces. The empirical formula, eqn. 1, however,predicts a very low level of electrical conductivity,

- l O ' ^ f t ^ m " 1 , for (eV/k) {( l /7 | ) - ( l /7 i )} = i , anda layer of vapour approximately satisfying this conditionwill presumably exist immediately adjacent to a liquid-metal surface at which Tg -> 7J. The required insulatinglayer will therefore be present and a detailed analysismight establish that it automatically takes on an appropriatethickness.

4.1 Accuracy and reliability of results

An important aspect of the results obtained is concernedwith the accuracy of measurement of the quantity (eV/k){(l/Ti) — (l/Tg)} for which error bars (not shown on theplots for reasons of clarity) of approximately ±0-15 wereestimated. Consider for example values of 800 K and 500 Kfor Tg and Th respectively, which give (eV/k) { ( 1 / r , ) -(l/Tg)} - 5. A measurement error of 0-25 in this quantitywould give a reading 90° out of phase with the phase of theoscillation in the empirical formula. This would be causedby an error of approximately 15 K in the measurementof the difference between Tg and 71,. In practice, the fit ofthe data to the empirical formula implies an r.m.s. errorappreciably smaller than this, which implies in turn that themeasurements of the difference between Tg and Tt have anr.m.s. error of 10 K or less,and those of Tg and Tx separately,nearer 5 K r.m.s. error. _

the fact that the fit improves for larger values of(eV/k){(1/7}) — (l/Tg)} may be explained on this basis. With alarger difference between Tg and 7), smaller errors in(eF/A:){(l/7i)-(l_/7^)} are to be expected. [The errorsin {/«(a/a0) + (eV/2kTg)} are expected to be much smallerby comparison.] The quality of the fit is thus consistentwith r.m.s. errors of approximately 5 K in the measurementsof 7} and Tg. Given that the steps taken to ensure a sharptransition between the cold end of the discharge tubeand the rest of the tube at the higher temperature Tg wereeffective, errors of this order are what might have beenexpected. It is interesting to note that changes of temperatureas small as 30 K were sufficient to alter the electricalconductivity by several orders of magnitude.

No difficulties were experienced with the measurementsof voltage and current and hence of a and VB. Values forthese quantities were therefore considered to be accurateand reliable. The posibility that conduction through thewalls of the discharge tube constituted a major source oferror is considered to be most unlikely. It is difficult toimagine how a wall conduction mechanism could give riseto the transition voltage VB and to conduction in onedirection only. It may also be noted that while the dischargedid not emit light observable with the naked eye in theprebreakdown region, it certainly did so when it wentover into the glow or arc. It would have been useful toobtain spectroscopic evidence of discharge activity inthe prebreakdown region but this was impractical withthe existing experimental rig. Finally, measurementshave been reported of leakage resistance across aluminasufaces exposed to caesium vapour.11 These showed thatthe leakage resistance falls off rapidly and is a monotonicfunction of Tg and 7) for values of Tg > 600 K. Also, poorreproductibility of results was reported. These characteristicsare consistent with the behaviour of the wall leakageresistance detected in these experiments, but not at allconsistent with the conduction attributed to the discharge.

100 IEEPROC. Vol. 127, No. 2, Pt. A, MARCH 1980

4.2 Theoretical considerations

The electrical conductivity of a weakly ionised gas may bewritten

a = (ne2)/(mnavtnQ) (2)

If the charged particle number density n is that given bySaha's equation based on equilibrium volume ionisation andit is assumed that the other quantities in eqn. 2 are bycomparison weak functions of Tg, then to a good approxi-mation

aa exp - (eVJlkTg) (3)

Since the experimental results obtained here are in totaldisagreement with this prediction, it is necessary to lookfor reasons.

One possibility is that the momentum transfer collisioncross-section for electrons Q is in fact a very strong andoscillating function of (eV/k) { ( l / r , ) - ( l /7^ )} . TheRamsauer-Townsend effect2 operates at low electrondrift velocities and would be an interesting possible expla-nation of the large oscillations in a except that the effectdepends on electron drift velocity and not on (1/7^) — (\/Tg).A second possibility is that the effective ionisation potentialVi is much altered by the close proximity of neighbouringparticles. This would require a new theory which tookinto account the degree of saturation as an importantparameter. Thirdly there is the possibility of interactionsbeween excited atoms and molecules producing some formof charge exchange mechanism. It may not be entirelycoincidental that the lowest excitation potential of caesiumatoms, 1-38 V, is close to the measured value of V, 1-34V.On the other hand it is likely that there is a significantconcentration of caesium molecules in the discharge whichhave excitation potentials12 as low as approximately 1 V.Furthermore a simple theory based on excited atomswould be unlikely to produce a strong dependence on(eV/k){(llTd-(\lTg)}.

Finally it may be that volume equilibrium ionisation isnot reached in the discharge and that it is dominated bycollisions with the walls. (The experimental evidenceappears to rule out the possibility that the electrodes havean important effect on the discharge electrical conductivity).This could be possible if account is taken of the very longtime required to attain equilibrium at the temperaturesused in these experiments.2 Clearly there are several possi-bilities for constructing a theory, but the observed depen-dence of the electrical conductivity on the degree ofsaturation is quite new and will necessitate a radically newapproach.

5 Conclusion

Measurements carried out on discharges consisting ofmixtures of nearly saturated caesium vapour and xenonhave demonstrated the existence of a discharge regimecharacterised by an electrical conductivity and an electrodevoltage, which occurs prior to the Townsend region and

subsequent transition to the self-sustaining glow and arcdischarges. The electrical conductivity and electrode voltagehave been measured for different values of gas temperatureand vapour pressure in five different tubes containingvarying amounts of xenon.

The electrode voltage showed little correlation with theother measured quantities. The electrical conductivitymeasurements on all five tubes fitted an empirical formulawhich related the electrical conductivity to the gas tempera-ture and the caesium reservoir temperature. The qualityof the fit in relation to the anticipated experimental errorshas been discussed and shown to be consistent. The empiri-cal formula cannot be reconciled with a simple theorybased on equilibrium volume ionisation of the dischargebut possible approaches to new theory to account for theresults have been suggested.

Extrapolation of the empirical formula to saturationpredicts that the electrical conductivity varies from asolid-metal level to an extremely low level and the roleof such behaviour in accounting for metal-vapour-arcphenomena has been discussed. Further work is neededto see if other metal vapours of practical interest behavein a similar fashion, to improve the accuracy of temperaturemeasurements, and to obtain corroborating spectroscopicevidence.

6 Acknowledgments

The authors thank P. Molesdale and his colleagues ofThorn Lighting, Leicester, for supplying the dischargetubes, and the UK Science Research Council for partialsupport of this work.

7 References

1 ECKER, G.: 'Electrical components of the arc discharge',Naturwiss., 1961, 33, pp. 1-104

2 von ENGEL, A.: 'Ionized gases' (Oxford University Press,1965, 2nd edn.), pp. 33-34, 81-85, 273-280

3 HOYAUX, M.F.: 'Arc physics' (Springer, New York, 1968)4 GUILE, A.E.: 'Arc-electrode phenomena', Proc. IEE, 1971,

118,(llR),pp. 1131-11545 RAGEH, M.S.I., GUILE, A.E., MORGAN, D.V., and HITCH-

COCK, A.H.: 'Initiation of arc cathode emission in Cu2 O films',ibid., 1978, 125, (1), pp. 81-84

6 HARRIS, L.P.: 'Electrical conductivity of caesium-seededatmospheric pressure plasmas near thermal equilibrium', J.Appl. Phys., 1963, 34, pp. 2958-2965

7 KRASNIKOV, Yu:G., KULIK, P.P., and NORMAN, G.E.:'Non-ideal plasmas''in '10th international conference on phenom-ena in ionized gases' (Oxford, 1971), pp. 405-435

8 ENDEAN, V.G.: 'Stable cold cathode arc', Nature, 1975, 254,pp. 131-132

9 CHRISTOPOULOS, C: 'The electrical conductivity of caesiumplasma', Posies Letters, 1979, 71A, pp. 227-230

10 ENDEAN, V.G.: 'Cathode voltage of the stable cold cathodearc' in 'Gas discharges', IEE Conf. Publ, 143, 1976, pp. 102-104

11 WESTBROOK, J.H.: 'Electrical leakage across alumina insulatorsexposed to caesium vapor', Electrochem. Soc. Ext. Abstr., 1974,74-1, pp. 418-419

12 HUBER, K.P., and HERZBERG, G.: 'Constants of diatomicmolecules' in 'Molecular spectra and molecular structure',1979,4, pp. 188-189

IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980 101

Christos Christopoulos was born inPatras, Greece, on September 171946. He received the Diploma inElectrical & Mechanical Engineeringfrom the National Technical Univer-sity of Athens in 1969 and the M.Sc.and D.Phil, from the University ofSussex in 1970 and 1974, respect-ively.

In 1974 he joined the Arc ResearchProject of the University of Liverpool

and spent two years working on vacuum arcs and breakdownwhile on attachment to the UKAEA Culham Laboratories.In 1976 he joined the University of Durham as a seniordemonstrator in electrical engineering science, and sinceOctober 1978 he has been a lecturer at the Departmentof Electrical & Electronic Engineering, University ofNottingham. His fields of interest include power, gasdischarges and high-voltage breakdown.

Geoffrey Endean was born in Liverpoolon April 24th 1938. He received aB.A. degree from Cambridge Univer-sity in 1960 having read engineeringwith the electrical option. From 1960to 1968 he was an engineering officerin the UK Royal Navy, specialisingin electrical and control engineering.In 1968 he joined the Department ofEngineering Science at Oxford Univer-

1 sity. He was awarded the Diploma inElectrical Plasmas in 1969 and the D.Phil, in 1973. From1971 to 1973 he was an IBM research fellow at UniversityCollege. In 1973 he joined the Department of EngineeringScience at Durham University as a lecturer and was pro-moted to senior lecturer in 1978. His present researchinterests are in gas discharges and rotating electromagneticfields.

102 IEE PROC. Vol. 127, No. 2, Pt. A, MARCH 1980