JULY, 1936 1&EVIEWS OF MODERN PHYSICS VOLUME 8

The Problem of the Mechanism of Static Spark Discharge

LroNARn B.LQEB, University of California, Berkeley

TABLE OF CONTENTS

I. Introduction 26?A. Processes in the gas itself . 267B. Processes at the cathode 267

II. Possible Secondary Processes. . . . . 268III. Mechanisms of Classical Theory 271IV. Other Mechanisms Proposed. 272V. Modification of Townsend's Theory by Other Secondary Mechanisms. . . . . . 272

VI. Effect of Variables on the Sparking Potential in Normal Static Breakdown . . 276A. Paschen's law 276B. Variation of sparking potential with pressure and gap length. . . . , . . . . 276C. Effect of cathode material 279D. Influence of illumination or initial ionization. . . . . . . . . . . . 280E. Role of space charge formation. . . . . . . . . , . . . , . . . . . . . . . . , . . . . . . . . . . 282F. Time lag of sparking 284

VII. Occurrence of the Different Secondary Sparking Mechanisms. . . . . . . . . . , . . 289A. High vacuum sparks and field emission 289B. Sparks at low pressures including corona discharge 290C. Influence of metastable atoms. 291D. Summary of the sparking mechanism under ordinary conditions. . . . . . 291E. Sparking in long gaps and at high pressures. 292

VIII. Conclusion 293

which, through a transition which is sometimesexplosive, the current readjusts itself to operateunder a set of conditions where it is self-main-taining, i.e. , it changes to an arc, glow discharge,corona or brush. In order to reach a self-main-taining condition the gas-intensified photoelectricor ionization current must develop a mechanism

by which new electrons are generated in suf-ficient number by secondary processes in a sen-sitive portion of the gap to replace the externallyimposed ionization. Thus' to understand theproblem of spark breakdown, one must list anddiscuss the various mechanisms of secondary ionliberation possible in a gap.

I. INTRODUCTION

F OR the understanding of the mechanism ofspark breakdown one must recall to mind

that conduction currents in gases depend on thepresence in the gap of electrons or ions createdby some agent. If no electrons are produced thereis no current. In the presence of photoelectrons,or those produced by radioactive processes, thatis by outside agents, currents are observed thatincrease with the field, eventually tending towardsa saturation value which in some cases is reached,in others not. ' Application of still higher fieldsproduces an ultimate increase in the current dueto the multiplication of the electrons present bythe primary process of ionization by collision inthe gas (gas-intensified photoelectric or ioniza-tion current). This current of itself 'does notusually lead to a spark and is entirely dependentfor its maintenance on the ionization imposedfrom outside. At some point in the increase ofthe field, the increase of the current may becomevery rapid. It leads to an unstable regime in

A. Processes in the gas itself

1. Ionization and excitation by electron impact.2. Ionization by positive ion impact in the gas,3. Photoelectric action in the gas.4. Action of metastable atoms in the gas.

B, Processes at the cathode

1, Electron bombardment.2. Positive ion bombardment.3. Photoelectric effects.4. Impact of metastable atoms.5. Field currents,

' Loch, Kinetic Theory of Gases, 2nd edition, p. 623 ff. ;N. E. Bradbury, Phys. Iiev. 40, 980 (1932).

267

268 LEONARD B. LOEB

II. POSSIBLE SECONDARY PROCES'SES

A. 1. The ionization by electrons in the gasis essentially the primary process in all sparkdischarge. ' In general outline it is determined bythe rate of gain of energy of the electrons in thefield and on their ability to produce ionizationonce they have sufficient energy. ' The energygain depends' on the free path of the electrons,which, aside from pressure and character of thegas, depends on the energy of the electrons. 4

The energy gain depends on the field strengthexisting and on the rate of loss of energy ofelectrons in impact with gas atoms or molecules.In monatomic gases the fractional loss of energybelow the radiation or ionization potentials canbe approximately calculated from classicalconservation laws. I t is quite low. ' ' In moleculargases which have vibrational energy levels theloss is materially greater. ' Above the radiationpotentials there is again additional loss of energyof electrons to radiation. As the probability ofthis loss is not too high, electrons can gain enough

energy to ionize. Once having the ionizing energy,the probability of ionization or loss to radiationdetermines the ultimate destiny of the process.As free paths, rate of energy loss to elastic and

inelastic impacts and the probabilities of ioniza-

tion and radiation are all functions of the energyof the electron, and as the free paths at lower

energies are not accurately known, 4 a quanti-tative theory of this process cannot be derived,

largely owing to the mathematical complexityinvolved. ' It must be added that while thenumber of excited and radiating molecules pro-

' duced may not parallel ionization closely, thenumbers, will be roughly proportional in any

'Townsend, Electricity in Gases (Oxford, 1914), chapterVI I I.' Compton and Langmuir, Rev. Mod. Phys. 2, 204(1930); L. B. Loeb, Kinetic Theory of Gases, 2nd edition(McGraw-Hill, 1934), p. 628 tf, ; K. T. Compton, Phys.Rev. 7, 489, 501, 509 (1916).' R. B. Brode; Rev. Mod. Phys. 5, 257 (1933),

s Cravath, Phys. Rev. 36, 248 (1930); Morse, Allis andLamar, ibid. 48, 412 (1935).

6 H. Baerwald, Physik. Zeits. 26, 868 (1925); W. Harries,Zeits. f. Physik 42, 26 (1927); H. Lohner, Ann. d. Physik24, 349 (1935).

'A recent attempt in this direction was made byM. J. Druyvesteyn, Physica 3, 65 (1936), for Ne gasbetween values of X/P from 5 to 30. He assumed a linearvariation of the excitation and ionizing probabilities inthis region and electron impacts with no energy loss at a]lper impact.

region of energy. At the lower electron energiesand thus at lower gradients there will be agreater proportion of excitation acts relative toionization.

Fortunately, while one cannot calculate theprimary ionization by electrons in a field, onecan measure it quite simply by a proceduredeveloped by Townsend. ' The quantity deter-mined is a, the number of electrons created byionization of molecules by electron impact percm of advance in the field direction by a singleelectron. It turns out that ot/p=f(X/p). Here pis the pressure in mm of Hg and X is the field

strength in volts/cm. Only recently have thevalues of ot/p been investigated in the whole

region from X/p=20 (15,200 volts/cm p=760mm) to X/P=200 where Townsend's accuratemeasurements begin. ' It is the results oi theseinvestigations that make the present paperpossible. The exact values of a/p for the inertgases are not at hand since Penning' has foundthat owing to the effect of metastable atoms in

ionizing unbelievably small traces of impurity,previous investigations have not been conductedunder proper conditions. In general, however,the curves of Xjp against ot/p=f(X/P) areessentially similar in form for all gases.

A. 2. Recent researches have proven con-

clusively that, except for certain special types ofresonance ionization observed especially in theoctette groups of the inert gases, the positive

ions do not ionize perceptibly, if at all, under 300volts of energy. " The neutral inert gas atomsamong their own kind ionize at energies as low

as 35 volts, "and alkali ions in inert gases in themost propitious cases as low as 60 volts. " Thuspositive ions in a gas can hardly ionize gasmolecules or atoms in fields where they gain less

than about 50 volts per mean free path in theinert gases, or more nearly 200 volts per freepath for other gases. The ionization by positive

F. B. Sanders, Phys. Rev. 41, 667 (1932); 44, 1020(1933); M. Paavola, Archiv f. Elektrotechnik 22, 443, 450(1929); K. Masch, ibid. 26, 589 (1932); D. Posin, Phys.Rev. 47, 258 (1935);48, 483 (1935).

9 F. M. Penning, Phil. Mag. 11, 961 (1931).' 0, Beeck, Physik. Zeits. 35, 36 (1934); R. M. Sutton,

Phys. Rev. 32, 364 (1929); R. N. Varney, ibid. 47, 483(1935)."O. Beeck, Ann. d. Physik 19, 121, 129 (1934);Rostagni,Zeits. f. Physik 88, 55 (1934); R. N. Varney, Phys. Rev.49, 204A (1936);49, 889A (1936); 50, 159 (1936).

MECHANISM OF SPARK DISCHARGE 269

ions is thus definitely ruled out in all ordinarydisckarge pkenomerta.

A. 3. Ultraviolet radiations in gases are known

to produce ionization if of sufficiently shortwave-lengths. " Such radiations are relativelynot as effective as ionizers in the body of the gasas they are in producing photoelectrons froman electrode surface owing to their relativelylow absorption coefficients. Recent results ofCravath" have shown radiations from coronadischarges to be eRective as ionizers in air atatmospheric pressure. Cravath estimated that 1

such photoelectron was produced for every 104

ions generated in the discharge. The absorptioncoefficient of the radiations causing this effectwas about 10 cm ' in air at 760 mm pressure.Ions can electively be produced, in this fashionunder the usual high pressure sparking conditionsonly in heterogeneous gases. In such cases theradiating potentials V„ for one gas must begreater than the ionization potential V; for someother constituent, It is possible that at highelectron energies some electrons belonging toinner shells can be excited to radiation at apotential V„which is greater than V, for outerelectrons in the same molecular species. In thisevent a homogeneous gas might be ionized by aphotoelectric process generated within itself.Such a mechanism is practically ruled out as animportant factor owing to the rarity of its occur-rence at low electron energies and the highprobabilI ty of autoionization removing suchexcited states before they radiate. The onlyother mechanism by which a homogeneous gasmay be ionized by a photoelectric process in thegas is by means of the continuous recombinationspectrum of the ionized molecules or atoms whichwill give radiations capable of ionizing the gas.The emission of such spectra is feeble even inmost low pressure discharge tubes. It will befeeble in the extreme in the dark discharge pre-ceding spark breakdown.

Thus unless a gas is heterogeneous with V, forone constituent greater than V, for another, thephotoelectric processes in the gas can be ruledout as an important mechanism in spark pro-

"R. C. Williamson, Phys. Rev. 21, 107 (1923);Lawrenceand Edlefsen, Phys. Rev. 34, 233 (1929); O. Oldenburg,Zeits. f. Physik 38, 370 (1926).

'3A. M. Cravath, Phys. Rev. 47, 254 (1935); Varneyand Loeb, ibid. 48, 822 (1935).

duction. It is probable that in mixed gases likeair at high pressures and with long gaps thismechanism may be of importance as Cravath haspointed out.

A. 4. Metastable atoms have not only beenshown to be effective in ionizing a gas havingadmixtures of traces of gases of lower ionizingpotential than the metastable state of the gas,but their presence has been shown materially toinfluence the sparking potential of the gas. '4

Their ability to diffuse against an electricalgradient makes them an important factor indischarge phenomena at lower pressures. Theiraction is in a large measure limited to therelatively pure inert gases as they are easilydestroyed. In these gases, how'ever, great caremust be used to avoid complications produced bytheir action.

B. 1. Electron bombardment of surfaces, whilehighly efficient in liberating secondary electrons"cannot be considered here, as there is no mechan-ism by which electrons can be driven up to acathode, with sufficient energy to liberate elec-trons under spark discharge conditions.

B. 2. Positive ion bombardment of metal sur-faces has long been considered an importantmethod" for the secondary production of elec-trons in spark discharge. The data to date havebeen most discouragingly contradictory asregards the efficiency and even the possibility ofsuch action at low positive ion energies. "Theexperimental difhculties encountered are largelyresponsible for the diversity of opinion. Thedifficulties lie in getting enough positive ions oflow energies to strike different metal surfacesunder conditions where photoelectric and otherdisturbing processes do not falsify the results.More or less definite results have been obtainedabove 10 to 20 volts energy of the impactingions. ' ' These have shown that some of the

'4F. M. Penning, Zeits. f. Physik 72, 338 (1931); 78,454 (1932)."F.M. Penning and KruithoH, Physica 2, 793 (1935).

'~ J. J. Thomson, Conduction of Electricity TkrougIt Gases,3rd edition, Vol. 2 (Cambridge, 1933), p. 518. 2nd edition,p. 490 ff.

"Geiger and Scheel, Handbuck der Pkysik, 2nd edition,Vol. 22 (1933), part 2, pp. 127—133.Summarizes literatureup to 1932.

"M. L. E. Oliphant, Proc. Roy. Soc. A127, 373 (1930);Oliphant and Moon, ibid. 388 (1930); F. M. Penning,Konigl, Akad. Amsterdam 31, 14 (1928); 33, 841 (1930);Physica 8, 13 (1928)."W. J.Jackson, Phys, Rev. 28, 524 (1926);30, 473 (1927).

270 LEONAR D B. LOE B

diversity of opinion lay in (1) the really unknownconditions of the surfaces of different metals usedas regards their work function due to gas films,and (2) a neglect in considering the possibleeffects of differences in the ionization potentialV; of the ion used in bombardment relative tothe work function p of the surface. The fact thatmetastable atoms having an excitation energyV„greater than p for a metal surface do liberateelectrons from such a surface even when theystrike the surface with their energy of thermalagitation only" leaves no doubt in one's mindthat positive ions are capable of doing thesame. " This action of positive ions has beenasserted for many years by Hoist and Oosterhuis"on the basis of image forces, by James Taylor~by some sort of photo-effect near the cathode,by A. von HippeP' on the basis of a local ther-mionic effect at the cathode. The process ofliberation has been treated from the moremodern point of view on the basis of the Sommer-feld electron theory of metals by Oliphant andMoon. " Experiments both by Oliphant andMoon and by Penning appear to have establishedthe fact that positive ions of as low as 10 to 20volts can liberate electrons from metals if V;,their ionizing potential, is greater than p. Thisapplies then to ions of the inert gases and thecommon permanent gases with clean surfacesof Fe, Cu, Zn, Pt, W, etc. For many of the alkaliions on these metals this mechanism does nottake place. Experiment at positive ion energiesbetween 20 and 50 volts indicates that with theinert gases the number of electrons liberated perpositive ion impact is of the order of 10 percent.At lower energies nothing is known of thisquantity, although Penning's results if extra-polated indicate a material decrease in efficiencywith energy. This is not indicated by theory, norby Oilphant and Moon's experiments in inertgases.

All positive ions at energies above 100 voltsliberate electrons from metal surfaces. The effi-

~' M. L. E, Oliphant, Proc. Roy. Soc. A124, 228 (1929);Carl Kenty, Phys. Rev. 38, 377 (1931); 43, 181 (1935);S. Sonkin, ibid. 43, 788 (1933); H. J. Couilliette, Proc.Roy. Soc. A124, 228 (1928)."L.B. Loeb, Nature of a Gas (Wiley, 1931), page 120.

~ Hoist and Oosterhuis, Phil. Mag. 46, 1117 (1923)."James Taylor, Phil. Mag. 3, 753 (1927);4, 505 (1927).

Proc. Roy. Soc. A114, 73 (1927).~'A. von Hippel, Ann. d. Physik 81, 1043 (1926); von

Hippel and Blechschmidt, ibid. 86, 1006 (1928).

ciencies increase with energy according toOliphant and Moon and Penning in a nearlylinear fashion. Extreme outgassing of metalsurfaces seems to reduce' the number liberatedper positive ion impact. Otherwise as with thephotoelectric effect the gas layers on surfacesproduce complicated effects. What the effect ofgas at atmospheric pressures will be on thismechanism is not known. As the electrons maybe ejected with high energies, one may expectsome loss of such electrons back to the plate bydiffusion processes at atmospheric pressure, aswill be outlined below. It is thus clear that verylittle is known about this secondary mechanismprecisely in the regime of positive ion energieswhich are involved in spark phenomena, i.e. ,

from 0 to 10 volts. It can definitely be assertedthat there mill be electrons Liberated by this mechan-ism and that the egciency of liberation can beexpected to increase at least slowly with increasingelectron energy.

B. 3. Photoelectric yields at the cathode re-sulting from the longer wave-length ultravioletradiations (3000—2000A) in discharge are notvery effective owing to the small intensity of suchradiations in the dark predischarge period, andtheir relatively smaller efficiency at the cathode.The photoelectric yields of the shorter wave-length radiations (formerly called entladung-strahlen), between 500 and 800A have recentlybeen shown to be quite marked. " No carefulstudy of such radiations as niight be generatedin the dark predischarge period have been made.The most significant investigation in this direc-tion is that of Cravath" on corona discharge inair who found a radiation effective on Cu ofabsorption coefficient 2 cm —' in air at atmosphericpressure. The estimated magnitude of the effi-ciency of this radiation was that it gave onephotoelectron for every 10' primary electronsproduced in the corona if all the radiationreached the electrode. If this is generally true onemust consider photoelectric sects at the cathode asone of the important secondary mechanisms innormal sjark discharge.

B. 4. Metastable atoms can produce electronson impact with electrodes much as is the casewith positive ions."The ability of metastable

"Carl Kenty, Phys. Rev. 44, 891 (1933);Cashman andHuxford, ibid. 48, 734 (1935).

MECHANISM OF SPARK DISCHARGE 271

atoms to move independently of fields is a mostimportant property. They are easily destroyedand occur only in a limited group of gases. Theireasy destruction" probably makes them moreeffective in the body of the gas than at theelectrodes to which they must diffuse.

B. 5. Field currents are essentially caused bydegenerate or by thermionic electrons whoseescape over the potential barrier of a metal isfacilitated by an externally applied field of suf-ficient magnitude. For most metals such fieldsmust reach the magnitude of 10' volts/cm ormore at local spots to cause a measurable emis-sion."At extremely low pressures, fields of thismagnitude may occur in discharge and coldemission will play a role."It is doubtful whetherspace charges ever could be maintained at anyappreciable gas pressure, even over a free pathfrom a liquid and possibly even solid cathodesurface, which could cause gradients sufficientfor field emission. " In ordinary sparking phe-nomena in gases, long before fields of such mag-nitude are reached, other secondary processesbecome so efficient that breakdown occurs andfield emission is not necessary.

B. 6. It is necessary to draw attention to onefeature of all secondary processes at a cathodewhich is often ignored. If secondary electronsescape into a gas from a surface giving a currentis, and the electrons escape with a velocity Cwell above that of thermal agitation, the currenti of such electrons measured at some distancefrom the cathode is given roughly by

E,(X/p) 760(6n) &

s —» Q'

C+ Z, (X/p) 760(6~) 1'

where X. is the electron mobility and X/p hasthe usual significance. ' It is seen that unless760K,(X/p)(6s. )& C or greater, a considerableproportion of the initial electrons will return bydiffusion to the cathode andi will be considerablysmaller than io. This does not happen for elec-

"E.W. Pike, Phys. Rev. 49, 513 (1936).»' Millikan and Eyring, Phys. Rev. 27, 51 (1926) (review

of previous work); Fowler and Nordheim, Proc. Roy. Soc.A119, 173 (1928); W. V. Houston, Zeits. f. Physik 47, 33(1928); Phys. Rev. 33, 361 (1929); R. T. K. Murray,ibid. 49, 878A (1936)."J.W. Flowers, Phys. Rev. 48, 954 (1935)."I.Langmuir, Science 58, 290 (1923); Compton, Phys.Rev. 3'7, 1077 (1931);L. Tonks, ibid. 48, 562 (1935).

Fio. 1. Circled points are Posin's. Crosses representTownsend's values. Values of Masch are close to Posin'sas far as Masch went.

trons liberated in the body of the gas. It canhappen for photoelectric and other processes atthe cathode as C may be equivalent to volts ofenergy, while 760X,(X/p)(6n) & may well be less.

III. MEcHANIsMs QF CLAssIcAL THEQRY

Townsend early showed that if one had aphotoelectric current in a gas in a field of strengthX (volts per cm), as X increased beyond a certainvalue, the current began to increase faster thanthe approach to saturation called for. This wasascribed by him to multiplication of the initialand other electrons in the gas by ionization bycollision. This increased current may be called agas-intensified photoelectric current. It is studiedby making X constant and varying the distancex between the electrodes. It transpires from sucha study that i=ioe ' where rx is the number ofnew electrons formed per electron per cm path in thefield direction in the gas. Here i is the currentat x cm from the cathode while the initial currentfrom the cathode is is. Log i/io plotted against xgives a straight line whose slope is cr. Experimentshows that n/p= f(X/p) and curves of this func-tion have been observed to be similar in generalform for different gases. Such a curve for N» isshown in Fig. 1. Townsend' worked at low ip,at low p (p expressed in mm of Hg) and smallx and found the equation to hold fairly well. At acertain p and X/p, where x passed a certain

"Townsend, Electricity sn Gases (Oxford, 1914), chapterIX.

272 LEONARD B. LOEB

or 1 —y(e"8 —1) =.0.

That is at a certain value of X/p, when a and P,or n and y, approach proper values one will havea self-sustained current when x reaches the value8 indicated above. Using his values of o. and Pat high values of X/p, Townsend was able topredict the values of sparking distance x= h atthe pressures studied. Hence the equation ap-peared proven and has until recent years beengenerally accepted.

IV. OTHER )'IEcHANISMs PRoPosED

Certain difficulties connected with the abilityof positive ions to ionize by impact, initially

"Townsend, reference 30, p. 330.

value, the logi%s .versus x curves bent sharplyupward. This he explained as being due toionization by Positive ions by imPact in the gas.He assumed that each positive ion gave P newelectrons per cm path in the field direction byionization of neutral molecules. In this event heshowed theoretically that

i%&= (a—P)e& && /(a —Pe& ~& ~). (1)

From his logi/io curves at low pressure andsmall x he evaluated P (from the approximationfor n))P, i/is ——ae */(o.—Pe )), and the valuesof P so obtained fitted this theory quite well. Hefound that P/p=F(X/p). The study of thisphenomenon extended over a very narrow rangeof p, x and X/p and the results cannot be takenas proving the postulates. It had bpen assumed

by J. J. Thomson" and also assumed as analternative by Townsend, " that positive ionscould knock secondary electrons out of the cathode.This process yields the equation

i =ioe */$1 —y(e~ —1)g. (2)

Here y is the number of electrons emitted perpositive ion impact. If one set y =P'/(a —P') onegets

i = is(o. —P') e~*/(a —P'e~~) (3)

and it is seen that this yields an equation whichis so like Eq. (1) used for calculating P in formthat it is impossible to differentiate experiment-ally between them with the present degree ofexperimental accuracy. The equations abovegive i = ~ at x=8 when ct —Pe'~ ~&'= 0 (4)

pointed out by Hoist and Oosterhuis, "have ledto doubts being cast on the first of these me-chanisms proposed by Townsend. As a result,numerous of the other secondary mechanismshave been proposed, to wit: ionization by posi-tive ions at the cathode by Hoist and Oosterhuis,Penning" J. J. Thomson" and Rogowski" byspecial photoelectric processes at the cathode forall sparks by Taylor 2s in the low pressure coronaby Werner" and Greiner" and in the gas and atthe cathode by Cravath, " by metastables byPenning, '4 and by field currents at low pressureby Flowers. '

It is seen that the list of secondary mechanismssuggested above has been pretty well covered.While some of these processes have been invokedin special cases only (corona, etc.), it transpiresthat for the normal spark breakdown in gases ator near atmospheric pressure, nearly all of themechanisms mentioned have been called upon.To what extent these are justified it is the pur-pose of this paper to determine. One may antici-pate the answer by saying that as usual wherethere are so many possible solutions put forwardwith some degree of plausibility the solution isnot the simple one to be hoped for. It is probablethat each mechanism occurs to some extent innearly all sparks, but depending on conditions,one mechanism predominates over the others.Hence the divergent results by different ob-servers. One can say that while three of theprocesses are generally possible, two of them,ionization by positive ions in a gas and the fieldcurrents, occur under such conditions of X/pand p that other more likely phenomena supplantthem under any but extraordinary conditions.

V. 1VIODIFICATION OF TOWNSEND S THEORY BYOTHER SECONDARY MECHANISMS

In 1928 R. B. Brode3' and L. J. Neumanshowed that on certain simplifying assumptions

"W. Rogowski, Archiv f. E)ektrotechnik 29, 130 (1935)."S. Werner, Zeits. f. Physik 90, 384 (1934); 92, 705(1934)."E.Greiner, Zeits. f. Physik 81, 543 (1933)."R. B. Brode and L. J. Neuman presented the equa-tions before a Seminar class at the University of Californiain the spring of 1928. The results were never publishedbefore. One result as modified by Loeb is included herewith Professor Brode's consent. It is important to notethat Brode concluded from all these processes that thegeneral form of the derived equation remains the same andit is thus impossib)e experimentally to distinguish onefrom the other.

MECHANISM OF SPARK DISCHARGE

one could for the cases of electron liberation byphotons in the gas or at the cathode, or byimpacts of metastable atoms in the gas or at thecathode arrive at equations closely similar to thetwo Townsend Eqs. (1) and (2) already cited.The assumptions made neglected processes bywhich metastable atoms or photons were re-moved from the gas without producing ionizationand assumed the ion production as strictly pro-portional to the photons or metastable atomsproduced. The similarities between the variousequations are such that within the accuracy ofpresent day measurements the resulting equa-tions are practically interchangeable by a redef-inition of the constants.

Later discussion will show that three of thecases included above, to wit: the action ofmetastable atoms (limited chiefly to inertgases), and the actions of photons in the gas(limited to long gaps and mixed gases at highpressures), are not of sufficient generality in thecommon sparking phenomena to warrant detaileddiscussion at this point. The action of photonsat the cathode does, however, merit serious con-

sideration. Accordingly the equation for this casewill be deduced as a general illustration of thestatement made with, however, certain ampli-fications which, as will be seen, do not alter theargument.

Let np electrons be liberated per second at thecathode by an outside agent. These electronsplus the qz electrons liberated at the cathode bythe e photons that are created in the gas byelectrons and reach the cathode constitute thetotal electron emission at the cathode np', i.e.,np' ——np+ gs. Thus iI is the fraction of the photonswhich produce electrons that succeed in leavingthe cathode. dz is the number of photons avail-able to the cathode produced in a distance dx ofthe gas in the field direction at a distance x fromthe cathode by electron impact. It is given byde=(np'+P)g8e &»dx. Here np' is the number ofelectrons leaving the cathode and p is the numberof new electrons created by collision in the dis-tance from the cathode to x in the field direction.8 is the number of photons produced by anelectron in advancing 1 cm in the gas in thefield direction. The quantity p is the absorptioncoefficient of the photons in the gas. These areheterogeneous in wave-length and p, therefore

represents an average value. The factor g is ageometrical factor. It represents the fraction ofthe photons created in the gas that can reachthe cathode. This is necessitated by the fact thatphotons are emitted in all directions so that onlya fraction can reach the cathode. It is clear thatg will be less than one-half. For electrodes whoselinear dimensions are small compared to theplate distance it will vary with x and its averagevalue will be less than ~2. For the sake of simplicityone can consider the case of infinite plane parallelelectrodes in which case g w'ill be 0.5 at thecenter, if the external ionizing agent acts uni-formly over the cathode.

The generation of electrons by electron impactin the gas according to classical theory allowsone to write dp = (np'+ p) Odx in conformity withprevious notation, a being the number of ionscreated per cm path in the field direction byelectron impact. If P = np' at x=0, integrationbetween 0 and x yields np'+p=np'e"*, whenceP=np'(e *—1), and ds=np'e«g8e &*dx. Thus

e=(no'8/ )ge& i*+c and c= —n '8g/ .

Accordingly

e = (np'8g/a) fe&»*—1]and

np' ——np+ np'(nq8g/o&) fe &'—» —1],

yielding

n =npe«»/[1 —(8'/o) je&«-»» —1j].Here n is the number of electrons reaching x at asteady state, i.e. , n=np'+p. The equation forthe number n of electrons set free by the np

electrons generated by an external agent at thecathode in a gap of length x is thus in this case

n = nnpe /.(a—8rtgge&—» —1]). (6)

Assuming for the present that n»p, which istrue below 10 cm pressure this equation has the

, form n=npo&e»/ja —B(e«» —1)], with 8=8rtg.This is somewhat similar in form to Townsend' sEq. (1) for ionization by positive ions in the gaswhich is

n =npee«»/f~ —P(e«») ],when e»P. It is closely similar to Eq. (2) forelectron liberation at the cathode by positiveions which reads n=npne */(a —ayfe«» —1]).In

274 LEONARD B. LOE B

fact in regions where constants such as 8, P anday can be determined e *»1, so that the equa-tions are at present experimentally indistinguish-able from each other. When x reaches some value8 a spark passes and Townsend assumes thatthis occurs approximately when the denominatorsof Eqs, (1), (2) and (6) approach 0. This givesthe sparking equation under the three differentsecondary mechanisms as

~/P =e~i (for ionization by positive ions in the gas), (7)1/y =e~d (for electron liberation by positive ion im-

pact at the cathode), (8)n/B=n/8rlg=e&~ »d (for electron liberation by

photons at the cathode). (9)

Aside from the factor p, which we shall neglect,it is seen that sparking is characterized in eachcase by a quantity a/p, 1/y or cr/8rlg becomingequal to e~'.

Thus the problem breaks itself essentially intotwo parts, a study of the change of cr with field

strength and pressure, and the variation of theleft-hand terms of (7), (8) and (9) with the samequantities. Now it is well known from Townsend' swork that rz/p=f(X/p) although the measure-ments extended over a limited range only. Morerecently a/p=f(X/p) has been experimentallydetermined over a long range of values for airand Ns. " It probably varies similarly for allother gases at somewhat different ranges of X,p and X/p. Thus while Townsend's data covereda limited range of X/p, in which f(X/p} had onlyone form, the conditions over the observed spark-ing range comprise three different regions inwhich a/p=f(X/p) has three distinct forms.

As regards the left-hand sides of the Eqs. (7},(8) and (9), some comments might be made.Townsend's original measurements enabled oneto evaluate the quantity P in Eq. (1}and yieldedthe information that p/p = Ji(X/p), where

F(X/p) for air from X/p=130 to X/p=500varied possibly exponentially and somewhatfaster than rz/p= f(X/p). Recently Posin in thislaboratory has evaluated p/p from X/p=100to X/p= 1000 in Ns and finds p/p to be givenby the curve of Fig. 2."

"Varney, White, Posin and Loeb, Phys. Rev. 48, 818(1935); Jodelbauer, Zeits, f. Physik 92, 116 (1934); D. Q.Posin, Phys. Rev. to be published."D. Q. Posin, Thesis, University of California 1935.Phys. Rev. to be published.

dd

01

—.05

l00

Fio. 2. P/p as F(X/p) from Posin's data.

Since, however, it is known that positive ionsin this region of values of X/p cannot possiblyionise gas molecules by impact one must attributethe P/p variation in the case of nitrogen asevaluated in Posin's experiments to possibly oneor the other of the two alternative mechanismscited. Thus one may interpret the P observed asapproximately giving an o.y or a 8iig by writing1/y=o. /P, or n/8rtg=o. /P. Posin has calculatedthe value of y from the values of P and a andgives p/o. =y as a p(X/p) as shown in Fig. 3.Neglecting absorption in the photon equationmakes 8rjg/p =p/p. Hence experimental datagive one a quantity in terms of which the factors

y or 8rjg can be discussed.There is one apparently striking difference

between Eq. (8) for positive ion impact on thecathode and the Eq. (9) for photon impact onthe cathode. The left-hand term of the equation.for y has no e in it while n/8rig involves an ~z.

This is due to the fact that the number of positive

ions liberating y electrons at the cathode is accu-

rately equal to the electrons liberated in the gap. 8,

the number of photons produced per cm path of

MECHAN ISM OF SPARK DISCHARGE 275

.04

.03

.02

.OI

Fio. 3. Posin's P/a for Nm, representing either a y for positive ion impact at the cathode or anq8g/a for photoelectric effect.

the electron in the field direction is, however, notaccurately proportional to a. Cravath claims tohave shown that in the range of values ofX/p=40 to X/p=100 the number of photonsliberated per electron formed by ionization bycollision does not vary by more than a factor oftwo, while a varies by a factor of 100. Thus onemight call 0/a = 8' where 8' is a factor of propor-tionality approximately constant. Then 8'pgwould also be represented by the curve of Fig. 3.

Now it is seen that the experimentally evalu-ated'p or 8'qg increases at first rapidly and thenmore slowly as X/p increases and its over-allchange in the region open to investigation is bya factor of 200. In the case of liberation of elec-trons by positive ions at the cathode this wouldmean that in a gas at values of X/p=100 toX/p=1000, where the positive ions strike thecathode on the average with from 0.5 to 10 voltsenergy the electron emission increases as ob-served. The effect of the loss of electrons bydiffusion to the cathode at these values of X/pis negligible. These data are not definitely incon-sistent with what little is so far known aboutthe process of secondary emission at the cathode

by positive ion bombardment. In the case of th»photoelectric effect at the cathode the increaseof Hqg/p with (X/p) at a faster rate than ~x/pis to be expected. The rough parallelism betweenot and 8 merely means that electrons that aremore efficient as ionizers are also in nearly thesame proportion better at exciting radiation.At very high energies of the electrons, certainlybeyond X/p=500 it is likely that the ionizationprobabilities will exceed the excitation proba-bilities and this could account for the flatteningof the curve for 8'rig as X/P exceeds 500, for ethen increases less rapidly than o.. That 8'ggincreases at first from X/p=100 to X/p=500may be in part due to the fact that 0 increasesfaster than n at very low fields for 0 appears htlower electron energies than o..* The initialincrease of 8'rig is also possibly due to the factthat at higher electron energies higher states ofexcitation give harder photons. These willincrease g, the liberation fraction at the cathode.

In the previous discussion the quantity p inthe exponent has been neglected. From corona

*Compare the excitation probabilities for electron im-pact in a gas with the ionization probabilities in the samegas when plotted as functions of the electron energy.

276 LEONARD B. LOEB

discharge in air Cravath has found ts to be about2 cm —' for the radiations acting to liberateelectrons from metals, and 10 cm ' for thoseactive in the air at atmospheric pressure. Henceit is seen that for low values of n and large x, pcannot be neglected. Aside from these experi-ments nothing is known about p, , particularly forthe short wave-length radiations most active in

liberating electrons. Little can then be concludedabout the influence of the neglect of this factorexcept that in evaluating 0' from the equationthe neglect of the factor p will make the valuesof Hsing appear smaller than they should be by thequantity e &*. Thus Prig will appear to vary asthe gap length x. Hence did this quantity play arole in Posin's experiments his .value of p/p=Hag/p would have been a function of x. Thiswas not the case. In fact Posin found betweendistances x of 4 and 6 cm in Ns that P wasconstant on a curve to within better than 2percent. This means that ts must have been atmost 0.05 or less. This was to be expected as Pwas determined at about 1 mm pressure suchthat p, as determined by Cravath would havebeen 2.6X10 ' so that its effect could not havebeen observed. It is seen then that at presentone cannot on theory differentiate between theprocesses at work. Closely analogous discussionmight be based on the equations derived fromthe action of metastable atoms and photons inthe gas. However, physical considerations rulethese out for the common static sparking phe-nomena for moderately long gaps 0.1—0.5 cm,and for all but the inert gases at or below atmos-pheric pressure. Thus in the cases of normalstatic spark breakdown one may with confidenceconsider either positive ion impact on the cathodeor the photoelectric effect at the cathode theessential mechanism, with possibly a greaterlikelihood of the photoelectric effect predomin-ating in most cases.

VI. THE EFFECT OF VARIABLES ON THE SPARKING

POTENTIAL IN NORMAL STATIC BREAKDOWN

A. Paschen's law

With the data on hand for Ns one may nowturn to a study of the application of the equa-tions discussed to the conditions for sparking. Inview of the fact that the form of the equations

yielding a spark using Townsend's original cri-terion, and assuming liberation of electrons atthe cathode by either positive ion bombardmentor photoelectric processes, are closely analogous;that is since one can write (neglecting p) that aspark occurs at a gap length 8 when 1/y=e 'or when 1/0'rlg=e ', one can for the circum-stances of spark discharge usually studied setthe conditions for a spark as 1/y=e~' without

seriously committing oneself as to nrhether the

quantity y is caused by positive ions (a true y),or by photoelectric effect, y=6'rig. In what followsthen the equation in terms of y will be usedrecognizing that it is to beinterpreted as applicablelo either process. Again it was seen that Posinfound that y as determined by measurement forN2 varied as some function of X/p where @(X/p)is given by the curve of Fig. 3. o./p is also afunction of X/p, a/p=f(X/p), Fig. 1. Thus1/y = e s can be written log, 1/g(X/P) =Pbf(X/P j.Hence log 1/p(Xb/p8) =pbf(X8/p8). Now foruniform fields Xb equals V„ the sparking poten-tial. Thus one can write

f(U, /pB) = (1/pB) log (1/+(U, /pB)). (10)

That is to say V, =F(p8), This is known asPaschen's law."It can be shown to hold equallywell where flelds are nonuniform due to geo-metrical factors. Where the nonuniformity iscaused by a space charge distortion Varney hasfound by calculations based on his equation"that it holds approximately although not accu-rately. The law has experimentally been verifiedwithin the limits of accuracy over a large rangeof working conditions.

B. The variation of sparking potential with pres-sure and gap length

Let it be assumed that the criterion for aspark which set n/P = 1/p =e"' is approximatelycorrect. Then Eq. (10) derived from it on theassumption of essentially linear potential gradi-ents f( V,/p5) = (1/pb) log (1/p( V,/p8)) shouldbe open to verification once the form of f and pare known. Townsend in his limited range fromX/p= 130 to Xjp= 500 for air and N2 did not

's For a discussion of Paschen's law consult any standardwork on spark discharge. Townsend, reference 30, p. 327;J. J. Thomson, 3rd edition, reference 16, vol. 2, p. 486;W. 0, Schumann, Durchbruchsfetdstarke son Gasen(Springer, Berlin, 1923), pp. 51, 114.

MECHANISM OF SPARK DISCHAR'GE 277

derive expressions for f and p. He used curvesof his measured values of n/p and p/p plottedagainst X/p. Taking a given p and a given X heevaluated n and P, and from the expressionn/P=e' &&' calculated the sparking distance b.

Setting his gap length at b, at the value of pabove chosen, he varied the potential across hisplates until a spark occurred at V, . The valuesof V, were in close agreement with the productXb computed from the values of X and 8 chosen.This excellent confirmation of the theory in alimited region was not applied to the greaterportion of the sparking potential curve. As aresult of his extended observations of n/p overa range of X/p from about 1000 down to X/p =20and of p/p from 1000 down to X/p=100 in N2,Posin was in a position to test the theory stillfurther. He has shown that from:X/p=20 to X/p=40, (region I), n/p=Aie ~x»

in agreement in form with a similar equationfound by Sanders' for air. Here A i =5;76X 10 ",Bi=0.245.X/p =44 to X/p = 176 (region II), n/p =A ~(X/p—B2)'. A~=1.17X10 4, B&——32.2, in analogy toan equation derived from Sanders' curve. forair by Jodelbauer. "X/p=176 to X/p=200 (region III), the formoff(X/p) changes from a relation f(X/p) (X/p)'to f{X/p) ~(X/p)& passing through a point of

7

/0

0 10 ZO 30 ~ ~g

Fio. 4. a/p =A ~e x"» in region I at low X/p.

80

./ 3 .5 7 .9' /. / /3 /S

Fia. S. a/p=A2(X/p-B~)' in region II atintermediate X/p.

inflection with f(X/p) =A3(X/p)+B3. This re-gion is such that it cannot conveniently berepresented by any simple equation.X/p = 200 to X/p = 1000 (region IV), n/p= {A4X/p)& —B4. A4=0.21, 84=3.65. The extentto which such equations hold is seen in Figs, 4,5 and 6.

In each of these regions equations could be setup to give p as a p(X/p). Placing these equationswith their constants into the functional relation-ship Eq. (10) would at once give equationsyielding in their appropriate regimes. relationsbetween U, and pb. Such relations it can readilybe seen become too complex for evaluating V,from pb with any precision except by complicatedgraphical methods. Fortunately it turns out thatexcept at lower values of p5 the equations areparticularly insensitive to changes in y. Hencefor a survey of this type it is sufficient to set yat some constant value in each of the regions I,II, and IU and putting in values of pb to calculatethe value for V, as a function of p. The values ofy chosen by Posin are as follows, in region I, yis not known but can be extrapolated for asabout 10 '. In region II a mean value of 10 'was chosen for y. In region IV y was chosen as0.02, the values ranging from 0.01 at X/p= 320to 0.04 at X/p=1000. At X/p 200 p was set

278 LEONARD B. LOEB

—10

—e,o

—20

—ao

—5.0

—30

—2,0

—I.o $X/p14 Id 1e 20 22 24 2d 2e 30 32 34

I I I I I I

F&G 6 01/p=(g, x/p)& —84 in region IV at high X!P

as 1.5X10 '. Putting in constant values of ygives the equations used in the following form.

Region Ipb 1 1

V, =—log log —,y=10 'Bt Atpb

V, =69Pb —4.08Pb log Pb. Pb from 800 to more

than 104.

Region II1 1

V, =Bspb+ —log, — (pb) &.

A2

V, =32.2pb+244(pb) &, y = 10 ', pb from 3 to 600.

Region IV

B4s 2B4 1 log 1/y 1V.=—pb+—log —+ y=10 s.

A4 A4 y A4 pb

V, =63.5Pb+73.5/Pb+137, Pb from 0.4 to 1.2.

It is better to use y = 1.5 X10 ' near X/p=200.

This changes the equation to

V, =63.4pb+203/p+ 226, p = 1.5 X 10 ',

pb from 1.6 to 2.5.

700

SOO—

400—1(I

300—

200—

100— pg (mrnxcm )

Fro. 7. Computed and observed sparking curves for N2 in regions II, I II, IV. Posin's calcu-lated values —full curve; Strutt's observed values dashed curve; Hurst's observed values dot-dashed curve.

MECHANISM OF SPARK DISCHARGE

70

00—55

30—26

20

I6

IO P$' (mm gem)

0 IOO 200 500 400 500 000 700 soo QOO ooo II00 1200 l200 l400 I500 I500 1700 ls00 IQOO 2000

FiG. 8. Posin's computed sparking curve for N~ in regions I and II. Circled pointscomputed values.

The curves resulting from this test of thetheory are shown in Figs. 7 and 8 as full lines.The upper dashed curve in Fig. 7 is Hurst'scurve for Ns and the lower dashed curve is thatof Strutt. "There are no data for V, in Ns forhigher values of X/p. It is seen that the com-puted curve falls fairly well between the twoobserved curves considering the approximationmade. It may be well to point out one or twofeatures of these equations having a bearing onspark discharge observations.

It is seen that in region I the curve of V,against ph is nearly a straight line. This is therelation so often used near atmospheric pressurein rule of thumb calculations. It results from theexponential character of f(X/p) in this region.It is worth noting how relatively unimportantchanges in y are in this region. In region II thedeparture from linearity is still not very pro-nounced and V, is still relatively insensitive to y.In region III one might expect to find theminimum sparking potential at an X/p where

f(X/p) is linear. This is not the case. The"H. E. Hurst, Phil. Mag. 11, 534 (1900); R. I. Strutt,

Phil. Trans. Roy. Soc. A193, 377 (1900).

relatively rapid change of y with X/p in thisregion together with constants in the equationshift the minimum to lower values of pb. Physi-cally the minimum is due to the fact that athigh X/p, a/p increases more slowly than pro-portional to X/p, while the number of ionsformed depends on ph. Thus larger changes in

X/p are needed to increase the efficiency of theionization process to compensate for decreases in

pb, i.e., decreases in the number of molecules inthe gap.

The minimum value of U, computed from theequation for region IV is 274 volts. This ismidway between the values observed by Struttand Hurst. There is thus no doubt but that withmore accurate values of p/p and a more carefulsolution of the equations one can get agreementsbetween observed and computed values of V, asgood as required as long as there is no fielddistortion.

C. Effect of cathode materialIf the quantity y be varied by changing the

work function of the cathode, the consequencescan be viewed as follows. ~ Consider two cathodes

'o L. B. Loch, Phys. Rev. 38, 1891 (1931).

280 LEONAR D B. LOEB

of different material such that for one y=y~ andthe other y=y», and assume that y&

——ay» wherea lies between 1 and 10,

1 1 1 1f( Vs, /pb) =—log —, and f{V42/pb) =—log —.

pb pb

Since in air and N» most measurements are madein region II where f(X/p) =A»(X/p —B»}',

V4&——pb B»+ log—

Vs, ——Pb B»+ log—

Hence

Vs& —V4» (1/A»Pb} «[(log, 1/yq) « —(log, 1/y») «j

Vs, B»+k(i/A»pb) log 1/ygj«

At X/p 120, p 1 mm, 1/y is 2000 accordingto Posin, " A» 10—4, pb 5. In this regionL(1/A»pb) log 1/yqj«300, while B» 30. ThusB» can be neglected, giving (V„—V,,)/V, , as5 percent if a=2 and 14 percent if a=5. Thatis on theory one would expect a measurablechange in sparking potential with change in y atthese pressures. In argon and inert gases this isfound to be true according to Hoist and Ooster-huis " James Taylor" and L. J. Neuman. 4'

Neuman found 20 percent change in A with ¹iand Na electrodes at 0.3 mm, and 2 percentchange at 10 mm pressure. At atmosphericpressures B» in

¹is of the order of and perhaps

ten times greater than L(1/A»pb) log 1/yQ«. Underthese circumstances the effect of the value of abecomes so small as to be negligible for mostelectrodes. Older data at atmospheric pressure4»

indicate complete independence of electrodematerial. No one has with modern techniquesstudied the effect over a pressure range in air ora molecular gas. Neuman" found in Ar that at20 mm the difference in V, for Ni and Naelectrodes disappeared. A more careful study inAr and N» for Na and Pt is being carried on inthis laboratory. In the region where f(X/p)=Aje~~&xt» the effect of electrode material will

4' L. J. Neuman, Proc. Nat. Acad. Sci. 15, 259 (1929).~ J. J. Thomson, Conduction of Electricity in Gases, 3rd

edition, vol. 2 (Cambridge), p. 476. Reference 38, p. 20.

be still less while at high X/p where f(X/p)A»(X/p)" with n&1 the electrode material

will be most significant.

D. In6uence of illumination or initial ionization

One may recall the equation

i=ipe */(1 —y(e *—1))

and assume e *»1. Previously the criterion fora spark was set by the condition that i'=. ~ as1/y' =.e ' irrespective of ip, where b is the valueof x at sparking. Now such a condition isindefinite and one must consider the effect of ip

on sparking potential. This requires that one setthe condition for a spark as a condition in whichi reaches some value», where» is not defined,and probably cannot be defined in many cases,for sparks are not equilibrium phenomena. It isprobable that under a given set of conditions aspark can materialize with a given value of z.Without setting an exact value for i furtherconclusions can, however, be drawn. It is now

possible to propose the following question. Giventwo sparks occurring, one with an initial currentdensity ip and the other one with ipp due to gapillumination, what will be the change in sparkingpotential V, in a gap exactly identical, exceptfor the change in photoelectric current density?In other words, how does sparking potentialchange with gap illumination? If the current is» for a spark in this gap, then

i= ipe"o'/(1 —yelot) = ippe~« /(1 —ye «'),

and as» is constant for a spark in the gap

ipp 1 —pe e

1 —ye~os e"00s

zpp 1 —ye «log —= e = log — + (up —npp) b.

ip 1 —ye o'

Hence

1 ipp c 1 1 —ye 04s

—log —=—=—log + (crp —~pp).b ip 'b b 1 —ye"'P

A priori one cannot say much in advance aboutthe value of the term (1/b) log f(1—ye~«)/(1—ye 0')j since the values for 1—ye p' are notknown for a spark at an undefined». Let it beassumed for further study that (1—ye~«)/

MECHANISM OF SPARK DISCHARGE

(1—pe po) approximates unity. Then log 1 =0and this equation takes the simple form s/b=no —noo If

s/A sPb = ( Vsp/Pb Bp) P —(Vspp/P& —&s)s.

Neglecting first order terms in V,/Pb one has

s/A pPb = ( Vsp/Pb —Vspp/Pb) ( Vsp/Pb+ Vspp/Pb) .

Whence approximately

( Vsp —Uspp) / Usp =orb/2A p( Vsp)

In the past no great change of V, with ip hadbeen observed. Recently H. J. White4' actuallyobserved a change in V, with illumination.Nearly simultaneously and independently Ro-gowski and Wallraff'4 observed a similar change.For this purpose a very high absolute value ofillumination about 10' times the values com-monly used was needed. This is not indicated by

the simple equation above, for log (ipo/ip) = &

depends solely on the relative values. Theabsolute value of ip would, however, enter intothe more correct equation which includes the1 —ye «' terms. White observed that U, plottedagainst i gave an hyperbola-like curve, U,decreasing about 4 percent as ip increased by afactor of 10. More significant were the curves ofe plotted against np —npp taken from the valuesof Vsp and V,„by means of Sanders' curve forair assuming a uniform gradient. White foundthat within the limits of accuracy np —npo wasproportional to e, but that the slope of the linewas not quite proportional to 1/b, being 1.7instead of 2 for one gap and 2.7 instead of 3.0for another. He ascribed this deviation to spacecharge formation on the basis of the simplifiedtheory then proposed. While space charge for-mation could have been the cause, it is essentialto note that he was omitting a quantity(1/b) log P(1 —ye «')/(1 —ye &)g which is not aconstant but can be a very active function ofnp and n.p, and may in part cause the difference.It is seen that unless e/b is commensurate invalue with np, no great change can be ex-pected. White observed V, 16,000 at Pb= 380,

4s H. J. White, Phys. Rev. 48, 113 (1935)."Rogowski and Wallraff, Zeits f. Physik 97, 758 (1935).

Ap= 10 4 and e=2.3 to give (V„—V.„)/Vss=0.04. From the simplified theory above thecalculated value of (U,,—V,„)/V,,=0.017.

The answer to the question as to why alowering is not observed at low values of io andipp does not follow from the simple theory, butcan be formulated as follows. Since s=ipe +/(1—ye p') with z fixed, if io is small one mustdecrease 1 —pe~p' by increasing ye p' to give aspark. In regions where this quantity 1 —pe " isvery small, minute changes in npb (and hence ofU,,) are needed to produce excessively largechanges. in 1—ye p'. Hence until ip reachesreasonable dimensions, and dimensions not toodifferent from c, so that 1 —ye~ps can becomelarger and less sensitive, one will have e~p'/

(1—ye ") so sensitive to slight changes in aob

and hence in X/p as not notably to alter thesparking potential for small changes of ip. Thatis changes in is are so readily compensated byminute changes in np and thus V, as to beexperimentally indistinguishable. It is obviouslyin the region of high ip where others had notworked, that White was working, otherwise thequantity log (1—pe «')/(1 —pe ") could nothave been neglected. The value of ip estimatedby White at which the denominator becameimportant was of the order of 5X10 amp. percm', while previous workers rarely exceeded5X10 "amp. per cm

In recent articles Rogowski and Fucks4o andFucks4' have developed a theory of sparkingbased on positive ion impact on the cathodewith a slowly changing y. To this they add aspace charge distortion and assume contrary to

all present knowledge that the ion velocity atsparking varies as X& as does the electronvelocity. Equations are deduced on these as-sumptions which make V, vary as the ip&, Thisvariation is observed according to Fucks forpart of the region studied. The equations derivedabove for this mechanism yield variations of V,with ip agreeing with observation fully as well

as those of Fucks. Actually the data of Rogowskiand Wallraff44 are not complete nor absolute invalue. More complete data than they give areneeded for a crucial test of any theory.

~ Rogowski and Fucks, Archiv f. Elektrotechnik 29,362 (1935).

"W. Fucks, Zeits. f. Physik 98, .666 (1936).

282 LEONARD B. L0E B

E. Role of space charge formation

Another question arises for which the simpletheory does not give the whole answer. Thisquestion involves the role of space charge for-mation in spark discharge. Actually Townsend' soriginal investigations were conducted underconditions designed to avoid this complication.It is quite clear from the values of n found byTownsend at low p, small x and low intensitiesof photoelectric illumination, that space chargeswere not seriously active. Under difIerent con-ditions the values of a observed by Sanders,Paavola, Masch and Posin' showed no indica-tions of this either. Townsend also had estimatedfrom the value of photoelectric current densityhe used that such currents should not lead tospace charge formation. It is clear, however,that as a increases with higher X/p and large x,the multiplication of charges can lead to currentdensities i which might begin to yield spacecharges. Hence it was not entirely certain thatthe up-curving of the log i%0 versus x curves atappropriate X/P and x which Townsend ascribedto positive ion ionization might not be a spacecharge effect. The fact that these curves yieldeda constant P along their length and that from thevalues of n and P at high X/p, and relativelylow P and h, Townsend could from the sparkingpotential V„assuming a uniform field, calculatea proper 8, however, confirmed his conviction ofabsence of space charge. The same applies tothe conditions of Posin's"" measurements inNs above X/P = 100, where special care was usedto avoid space charges,

That, however, space charge formation mightplay a role in sparking at the higher pressureswas first emphasized by Loeb and Rogowski4'independently. These writers in 1928 concludedthat if the ionization mechanism of Townsendby positive ions in the gas were to be maintained,it would be essential to assume the existence ofspace charges at the cathode of sufhcient magni-tude to cause positive ions to ionize. These spacecharges were assumed to be produced by positiveion accumulation and movement in the gap.Since it is now known that positive ions cannotionize in a gas, this original argument for thenecessary existence of space charges is no longer

"L. B. Loeb, J. Frank. Inst. 205, . 305 (1928); W.Rogowski, Archiv f. Elektrotechnik 20, 99 (1928).

valid. Similar conclusions were later arrived atindependently by Franck and von Hippe14' andby Schumann. " Again certain evidence fromthe Kerr cell studies of spark breakdown in airin time intervals of 10 second indicated non-uniform gradients at the cathode in short gaps,and at the cathode, in midgap, and at the anodein longer gaps. "Finally, the sparking potentialsobserved in long sparks such as lightning dis-charge yielded on the assumption of uniformfield strength gradients, fields of the order 3000to 10,000 volts per cm, which correspond to an

X/p far below any for which even an a appearsin air at atmospheric pressure. Hence. nonuniformfields in such breakdown must be postulated,and these in turn may be space charge condi-tioned.

Certain results obtained by Sanders, Paavola,and lately by Posin, ' in which the log i/is versus xcurves showed upcurvings ascribed to a P, which,however, never yielded values of P which wereconstant over the upward bent portions of thecurves, led Uarney, White, Loeb and Posin' toset up and solve the complicated differentialequation for the effect of space charges on thelogi/iI versus x curves. The results of this studyshowed that: Depending on the electrode dis-tance, pressure, potential, and intensity ofillumination in a plane parallel electrode gap,the appearance of the upcurving of the log i%0versus x curves and an ultimate spark breakdowncould be caused by space charge distortion due to

primary electron ionization alone. The possibilityof such occurrences due to primary electronionization alone. is determined by the form of thef(X/P) giving the value of o./p. If f(X/p) is ofthe form f(X/P) =(X/p)" with n&1 the spacecharge distortion will occur. The higher theexponent n the more likely such a space chargedistortion and a spark from this cause. Uarneycalculated that while with a photoelectric currentdensity of 10 " ampere per cm' notable up-curving due to space charges could not at about2 mm pressure occur in Posin's plate distance of10 cm, both marked upcurving and an ultimatespark at 8 cm distance could be expected at

"Franck and von Hippel, Zeits. f. Physik 57, 696 (1929).4'W. O. Schumann, Zeits. f. tech. Physik 11, 58, 132,

195 (1930).~0 F. G. Dunnington, Phys. Rev. 38, 1535 (1931);H. J.

White, ibid. 46, 99 (1934).

MECHANISM OF SPARK DISCHARGE 283

X/P=120 when the current density was 10 "amp. per cm'. At 10 '4 amp. per cm' thereshould be no perceptible space charge effect. Infact Posin, "using light from the positive columnof a quartz Hg arc giving an average currentdensity of 10 "amp. /cm' over an area of somecm' of cathode, found a marked distortion of thelog i%s versus x curves yielding abnormal valuesof P and leading to a spark at about 6 cm. Thisis in as good agreement as possible with thetheory in view of the impossibility of obtaininga true estimate of Posin's current density at anypoint. This density could easily have exceededthe average density by a factor of 10 or more.At values of the average current density of10 '4 amp. /cm' Posin found that the upturnedportions of the log i/is versus x curves yieldedconstant values of P along the curve with nosign of space charge distortion. Thus it appearsthat while under some circumstances space chargedistortion occurs, it did not play a role in Town-send's experimentol domain.

Further calculations by Varney" for p=760and X=30,000 volts/crn with X/P=40 (i.e.,about normal sparking conditions in Ns atatmospheric pressure between plane parallelelectrodes) yield the following data for sparkingwithout secondary ionizing effect. If the densityof photoelectric current is is ——5 &(10 "amp. /cm'sparking occurs at 8 = 1 cm. If is =5 X 10 "amp. /cms sparking occurs at o= 1.7 cm. Ifis =5 X 10 " amp. /cm' the spark occurs ataround 2 cm. This means that even withoutsecondary processes near the cathode the sparkcan occur by electron ionization alone due to theconcentration of space charge near the cathode.As actually under the above conditions sparksalways occur at 1 cm, and as no variation ofsparking potential has been observed for valuesof is between 10 "amp. /cm'and 10 "amp. /cm',it is clear that secondary and not primaryprocesses must liberate electrons in all but thefirst case. One might even be permitted tospeculate that the occurrence of a spark at10 " amp. /cm' may be aided by the chanceoccurrence as a result of some secondary localizedprocess, which in a limited micro area of cathode

~' Further ca'lculations made subsequent to the publica-tion of reference 29 are here included through the kindnessof Dr. Varney.

yields enough electrons to give is a local valueof the order of 10 " amp. /cm'. Such a picturewould explain the localized discharge streamersalways observed. A current density of 10 "amp. /cm' amounts to 6X104 electrons per mm'

per second or 6 electrons per mm' per 10 'second. This is a long period in the time scaleof spark breakdown. The spark cannot occuruntil enough photons or positive ions are liber-ated in the gap by the primary electron process(a) to make a localized secondary current of thisorder possible. All that increasing the intensityof illumination can do between 10 'r to 10 "amp. /cm' is to make the formation of thenecessary density of ionization more probableand thus decrease the time for the formationto take place. Above 10 "amp. /cm' an increasein current density will lower the sparkingpotential by making the ionization effective inshorter gap lengths than 1 cm through spacecharge formation. This. in fact was observed byWhite4' and Rogowski and Wallraff" to be thecase.

The theory makes it possible to calculate theamount of space charge distortion produced atthe cathode by the primary electron process forthe sparking value of the current density. Thisis surprisingly low at higher pressures, being but14 percent in the case above while at X/P=120the value of the field is 50 percent above thatfor a linear fall of potential taken as V,/b. Thisis interesting in that such distortion at themaximum point will not change X/P by asufficient amount so as to change the form of thefunction o./p=f(X/p) from one where f(X/P)=(X/p)" with n)1 to one where n&1. Thesignificance of such low space charge values forspark production illustrates the fact that it isnot that the field must be materially increasedto cause the spark but that the field near tice

cathode must be increased. It is the localizationof the increase that is as effective as the increaseitself. Whether under actual conditions sparkingoccurs solely due to the primary mechanismdiscussed above, becomes essentially an academicquestion. For it is clear that once such spacecharge accumulations begin, and probably well

before. they reach their maximum effectivenesssecondary processes (positive ion bombardmentat the cathode, photons at the cathode or in the

284 LEONARD B. LOE33

gas) will occur in sufficient magnitude so as toraise the current density to the sparking value.Thus the space charge formation and distortion,7vhile probably not the primary cause of breakdown,must and does under circumstances materially aidin preparing the conditions for more ejectivesecondary processes, leading in some cases to lou er

sparking potentials.

F. Time iag of sparking

If a sparking potential be applied to a given

gap it will be observed that the spark dischargemay occur at almost any interval of time afterthe gap has acquired the sparking potential V, .The delay may be exceedingly short or very long(10 ' second to 30 minutes) provided inadequateionization exists near the cathode. The timebetween the occurrence of the spark and theapplication of the potential is called the sparklag. In recent years this time lag has been theobject of considerable study, By using a veryshort gap with a small volume of effective field

strength the lag without artificially appliedexternal ionization may be indefinitely long.Laue and Zuber" studied these lags down toabout 10 ' second at normal breakdown voltageand as a function of the intensity of ionization.The lags were found to be purely statistical intime, that is, if the number of lags n out of no

that exceeded t seconds are plotted against t,then the curve of n/ns plotted against t is of theform n =noe»', where pp = 1/r and r is theaverage time lag. From the plot of log (ns/n)against t the straight line of slope 1/r =pp isobtained. Now as Laue points out, P representsthe chance that an electron is liberated by theionizing agent. In Zuber"s case the volume of thegas was ionized by gamma-rays and P dependednot only on the number of electrons liberatedper unit volume per second but also on "the

chance that they were liberated in the effectivevolume of the gap. Thus here P depends on boththe ion current and the volume. p is the chancethat one electron will start the discharge. Itdepends on the overvoltage and on the mechan-ism active. In Zuber's work the range of theinvestigation was not very extensive. He estab-lished the law and showed that r or pp was

"K. Zuber, Ann. d. Physik 76, 231 (1925); M. v. Laue,ibid. 76, 261 (1925).

dependent on the intensity of illumination.At the time no lower physical limit to r was

looked for. It was believed that the statisticallag was merely caused by the fact that a singleelectron had to be liberated at a propitious timeand/or spot in the gap to start the discharge,and that pp = 1/r marked the chance that thiswould occur for a.given set of conditions. Itwas, however, taken for granted that there mustbe a finite time r which comprised the actualtime to break down the gap (formative lag)once the electrons were produced with sufficientfrequency in the gap to get rid of the statisticallag. This formative lag was believed to be veryshort for it was thought that it corresponded tothe time taken for the charges to cross theelectrode spacing in the high fields. Alreadyrelatively early P. O. Pedersen, ' using Lichten-berg figures, estimated that this time could be ofthe order of 10 ' second.

When in 1928 Loeb and Rogowski4' inde-pendently attempted to salvage the Townsendtheory of secondary ionization by means ofpositive ions by assuming space charges in thegas, Loeb pointed out that the space chargeformation created by the movement of positiveions alone (which was the most powerful one andeasiest to invoke) required finite time intervalsof the order of 10—"second to develop in a gapof 0.1 cm at /60 mm in air. He stated that afinite limit for the statistical lags of Zuber andLaue should be found in this interval. Within ayear the papers of Torok, Beams, Tamm,Rogowski'4 and others had appeared confirming.Pedersen's short-time intervals in the sparkmechanism. These and the later results ofStrigel"' indicated that these short time lagsextended well down to 10 ' second but occurredonly under conditions of rather high overvoltage(20 percent or more) and strong illumination,and were shorter the higher the overvoltage.

"P.O. Pederson, Ann. d. Physik 71, 371 (1923).'4 J. W. Beams, J. Frank. Inst. 206, 809 (1928); J. J.

Torok, Trans, A. I. E. E. 47, 177 (1928); 48, 46 (1930);Burraway, Archiv f. Flektrotechnik 16, 14 (1926); R.Tamm, Archiv f. Elektrotechnik 20 (1928); W. Ro-gowski, Archiv f. Elektrotechnik 20, 99 (1928); Law-rence and Dunnington, Phys, Rev. 35, 396 (1930); F. G.Dunnington, ibid. 38, 1535 (1931); Street and Beams,ibid. 38, 416 (1931);L. v. Hamos, Ann. d. Physik 7, 857(1930).

~ R. Strigel; Wissenschaft, Veroffent. aus dern Siemens-Konzern ll, 53 (1932).

MECHANISM OF SPARK DISCHARGE

In consequence Loeb" modified his theory totake account of the spark discharge mechanismin high fields by which high space charges couldbe built up by single electron movements overshort distances, due to the rapid increase in cx

with X/p. Shortly thereafter von Hippel andFranck" put forward their theory of the buildingup of space charges by successive electronavalanches which occur in intervals of 10 s to10 ' second. Similar calculations were made byW. O. Schumann, " Simmer""' and Kapzov. "Whichever picture of the exact mechanism offormation of this space charge caused by electronmovement is taken, and doubtless under differentconditions the different mechanisms each comeinto play, it is clear that these give rise toformative lags of a different order from thosecausing space charge by movement of positiveions, i.e. , 10 ' in contrast to 10 second. Sincethe positive ion mechanism gives more powerfulspace charges and requires lower values of o. onewould expect that the formative lags taking 1() s

second would occur for low overvoltages. On thewriter's suggestion Tilles" undertook the prob-lem of studying the shorter lags. To this end hedeveloped an ingenious device for measuring thetime lags lying:between 10 5 and 1 second. Themethod consisted in measuring with a ballisticgalvanometer the constant output current givenby a modified vacuum tube voltmeter betweenthe time of application of the sparking potentialand its fall during the spark. Two series wererun, one with an impulse wave of short duration,another with an approach voltage of 96 percentof V, and the sudden application of a voltage Us

which was from 1 to 5 percent greater than V, .Tilles obtained linear curves for log ns/n plottedagainst t as had Zuber at low overvoltages andlow intensity of illumination (see Fig. 9, curvesa and b). The slopes of these lines varied in alinear fashion with overvoltage and with thelogarithm of the intensity of ultraviolet illumi-nation which was varied by a factor of 10'.For these statistical lags Tilles found that forstatic breakdown with 96 percent approachvoltage one may write for Cu spheres 0.952 cm

~ L. B. Loeb, Science 69, 509 (1929); J. Frank. Inst.210, 15 (1930).

'~ J. J. Sammer, Zeits. f. Physik 81, 490 (1933)."N. Kappzov, Physik. Zeits. Sowjetunion 0, 82 (1934).~' A. Tilles, Phys. Rev. 40, 1015 (1934).

~'I X

0 02 04 06 08 0 4 6 dSemis X Over voltage

Fta. 9. Tilles' curves of statistical time lags. a, sparklag distributions, percent of lags greater than given byabscissa; b, average lag vs. percent overvoltage. Approachvoltage=96 percent; overvoltage, curve 1=0.7 percent;overvoltage curve 2 =3.5 percent; overvoltage, curve3 =4.9 percent.

radius and gap length 0.0683 cm at U, =3820volts

r=P 00376-s»(arly&1001-s 76

Here b, V/V, F100 is the percent overvoltage,b, V being given by Uo —V, =b, U, U& being theapplied potential and V, that of normal sparking.This law holds from 1 to 10—4 second in his gap.I is the vacuum photoelectric current densitymeasured in the gap in units of 10 "ampere percm' from a clean Ni plate. This does not actuallycorrespond to the current per cm' from the Cusphere because of the difference in photoemissionfrom Cu and Nf. I is, however, proportional atconstant pressure and approximately constantfield strength to the actual number of photo-electrons liberated in the spark gap, and isproportional to the photoelectric current density.

It is therefore possible to apply Tilles' measure-ments to the interpretation of the statisticaltime lags given by Laue. Thus one has

1/, =PP = (1/P. PP37)

e»&aviv&/san

4.

In these experiments P is directly proportionalto I, the current density of photoelectrons.

p contains the chance that one electron sufticesand is modified by factors which increase thischance. That the overvoltage should affect Pcritically is clear and that the overvoltage shouldincrease p very rapidly is more or less to be

286 LEONARD B. LOEB

lM ge0 a~ I 0

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random at I=0.0258; c, transitional at I=0.365;d, peaked at I=5.75.

expected since changes in X/p strongly affectn/p and hence secondary electron emission,space charges, etc. The term pp is proportionalto I if one electron can suffice under properconditions to start a spark. If two electronssimultaneously were required then pp would beexpected to vary with P, etc. As in theory P isproportional to I, it is clear that since pp isobserved to be proportional to I'l4, pp mustcontain in itself other conditions that actapparently to reduce the effectiveness of increasingultraviolet illumination. Actually p would haveto contain a factor (I)'" in itself to give the ob-served change. Whether this result is spuriousor whether the formation of space charges duringthe approach voltage period and after or othereffects prolongs the time lag by making some ofthe electrons liberated less effective cannot besaid. With surge impulse breakdown at lowerilluminations the value of pp as a f(I) changes toppccI. In this case one can assume that eachelectron within the regime designated by thevalue of e"~A ~ '~ will produce a spark. Underthese conditions with weak illumination, it ispossible that action of an inhibitory sort doesnot take place.

As the illumination intensity is increased thephoto-current reaches a value such that thecurves of log (is/i) against t alter their shape ina fashion indicating the existence of a minimumvalue of r, in the shorter time intervals (seeFig. 10, a, b, c and d). At lower values of I in

this regime only a small percentage of the break-downs show the effect. At I=5X10 "amp. /cm',however, 30 percent of the lags are of a fixedlength of about 10 4 second and 70 percent arestatistical. Finally both at 3 and 5 percent over-voltage at about 2X10 " amp. /cm' the break-downs are nearly all of one time r, i.e. , 10 4

second; that is, one goes from a statistical lagof decreasing r to a formative lag of 10 4 secondfor the gap used, with sufficiently intense photo-electric emission, overvoltage being constant (seeFig. 11).In this region of time lag as overvoltagesincrease the formative lag at r remains the lag,but decreases in value as with increasing U. theelectron avalanches produce the necessary ioniza-tion density much more effectively. Thus fewerelectron avalanches are needed to produce thesame gradient and r decreases. Tilles' lags of10 4 second are not determined by the timetaken for positive ions to cross the gap. Thetime of crossing is much shorter than 10 4

second. These time lags must represent the timetaken for a series of events possibly conditionedby the very short gaps used. White's" results in

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"H. J. White, Phys. Rev. 49, 507 (1936).

FIG. 11. Summary of Tilles' results. Master curve ofaverage or peak values. Time lag of 'sparkover ss. illumi-nation

APPROACHCURVE VOLTAGE

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MECHANISM OF SPARK DISCHARGE 287

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air in intervals of 6X10 sec. show that thelags at the same overvoltage are materiallylonger for a 1 mm gap than for a 5 mm gap,Fig. 12.

It is conceivable that with increased over-voltage the electron movement either in one, orin several successive avalanches following atshort time intervals, will produce a space chargewhich is not conditioned by ion movement, andwhose minimum value will depend on the timeof electron crossing. One mode of such short-time interval space charge production has beencalculated by Franck and von Hippel. "" Itleads to lags of the order of several times 10 'second. Quantitative measurements in this regionwere begun by H. J. White. ' White used lightfrom a spark to set off the gap to be studied andby means of the Kerr cell shutter observed the

0 ZO OO 00 OO /00 /ZO /OO

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FIG. 12. White's time lag curves for air. Overvoltageagainst time lag for three gaps.

time between the flash of the initiating dischargeand the breakdown of his experimental gap.Time lags of a nonstatistical sort were observedas a function of gap length, intensity of illumina-tion and overvoltage. As White worked withvery high illumination intensities he found thatonly small overvoltages of some 14 to 15 percentwere needed to cause formative lags of the orderof several times 10 'to 10 ' second. The higherthe intensity the lower the overvoltage required.Near 5X10. ' second the overvoltages rapidlyincreased (see Fig. 12). Calculations made byWhite indicated this time to be that of the orderof an electron crossing the gap. White, however,pointed out that the same time intervals wereof the order of time taken for the rapid initialrise of intensity of light emission in tke initiatingspark source. Hence the upward bend of over-voltage versms time lag curves at about 5 X10 'second had to be ascribed to a rapidly decreasingintensity of photoelectric illumination. Helium,unlike air, and COs showed a very much higherset of overvoltages (about 30 percent) for thewhole range. This is to be expected because ofthe low potentials at which helium yieldsappreciable values of n. At such potentials n islow and the ionization process is inefficient sothat many impacts with atoms are needed togive much multiplication of ions. In short timeintervals this requires greatly increased values ofV, in a given gap.

Very recently R. R. Wilson" has carriedWhite's experiments further, using a steady,but only 10 s times as strong a source ofillumination (quartz Hg arc). Wilson used anapproach voltage about equal to the normalsparking potential and suddenly applied anovervoltage. He raised the overvoltage appliedin successive steps until a spark could be seenin his optical system, with a given time setting.He found that as overvoltage increased at firstan occasional spark was observed when a givenovervoltage was applied. He then increased theovervoltage by steps and recorded the percentageof sparks observed when the same overvoltagewas repeatedly applied. He plotted this. per-centage of sparks as a function of overvoltageas seen in Fig. 13B.From these curves he chose

O' R. R. Wilson, Phys. Rev. 49, 210 (1936).

288 I.EONARD B. LOEB

as his overvoltage for a spark in the time intervalused, the point at which 50 percent of the over-voltage applications gave a spark. A series ofsuch curves is shown in Fig. 13B and indicates.why this criterion for the value of the overvoltageat a given time was resorted to. He found thatcorroded electrodes or a decrease in the intensityof illumination produced a decrease in the slopeof the curves as shown in Fig. 13C and thusincreased the overvoltage chosen for a given timelag. He found that materially higher over-voltages were required with his weak illumina-tion than were observed by White for the sametime lags. Two of his curves for air are given inFig. 13A with weak and strong illumination.It is seen that Wilson's overvoltages decreasecontinually as the lag increases. At about 1 X 10 'second his overvoltage curves rise relativelysteeply. He found, however, no louer limit tohis lags even down to 10—' second if segcient over-

voltage boas applied. For such short time measure-ments a vacuum switch was required for applyingthe potential. Wilson also studied breakdown,

using a surge impulse with no approach voltage.He points out that with surge voltages and evenwith the application of high overvoltages abovean approach voltage, the overvoltage valuestaken from the applied potential lose muchsignificance. This follows since in the case ofbreakdowns occurring in 10 ' second it is possiblethat the actual voltage applied, owing to thereflection of the surge at the gap electrodes, maybe materially higher than the static .overvoltageapplied. An indication that this occurs in thepresent work is seen in the actual observationsof breakdowns which take place by the suddenapplication of surge potentials under the normalbreakdown voltage of the gap for the timesetting. Beams" observed similar QiAiculties inhis work. Thus while the overvoltage observedby Wilson in surge impulse breakdown was onlysome 20 percent higher than that observed withthe approach voltage, it may in reality havebeen much higher. Wilson also points out thatthe use of an approach voltage alters the gap

~2 J. W. Beanis, J. Frank. Inst. 206, 809 (1926).

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FIG. 13. A, Wilson's curves for time lag as a function of overvoltage for strong and weakillumination. B, C, curves of percentage of sparks against overvoltage for strong and weakillumination.

MECHANISM OF SPARK DISCHARGE

in that it builds up a strong gas-intensified photo-current before the overvoltage is applied. Thehigh electron densities produced by this are,however, all near the anode. With a photoelectricemission of 10 "amp. /cm' the currents achievedamount to some 10 ' amp. /cm'. In the area of5 mm' where sparking occurs the current is10 ' ampere, giving an equivalent of 10 electronscreated in the gap in the 10 ' second of observedbreakdown. What the influence on breakdownof such electron production in the gap precedingbreakdown will be is undetermined. It is possiblethat such electron distributions in a gap beforethe breakdown may produce the anode streamersobserved in Kerr cell studies. '0

It must also be pointed out that in measure-ments of time lags by the procedures outlinedthe definition of time lag varies. In Wilson'swork the lag is that between the application ofthe overvoltage and the appearance of a lightemission in part of the spark gap. In White'swork the lag is the time between the illuminationof the gap by the auxiliary spark and the firstappearance of light emission. In Tilles' work thelag was the time as measured by the linearcharging of a condenser from the instant ofapplication of the potential until the spark hadso lowered the potential that the condenserceased charging. It is essential that such differ-ences in interpretation be kept in mind in thediscussion of spark lag studies.

In the experiments of White and Wilson thelags are so short that neither positive ions norelectrons could possibly have crossed the gap in theintervals used. This is again borne out by a calcu-lation of H. J. White. "White showed that if athis observed overvoltage an electron crossedthe 5 mm gap used, the number of positive ionsleft behind by the one electron would be sogreat that the positive ypace charge would haveproduced field distortions preventing the elec-trons from ever reaching the anode. This con-dition in the time intervals investigated wouldlead exactly to the types of field distortioncausing Dunnington's mid-gap streamers, whichwere also in evidence in White's and Wilson'sgaps. Thus it is clear that there is no lower limitto the formative lags as regards the crossingtime for electrons. This agrees with the mecha-nism postulated by Loeb."At lower overvoltages

it is probable that the electrons do cross thegaps giving other durations of time lags. Thereare indications in the longer formative lags dueto the movement of the mid gap streamer withovervoltage that the successive electron ava-lanches of von Hippel and Franck" and Schu-mann4' also occur. It is further possible thattime lags can be conditioned on the movementof positive ions. Such lags have so far not beenobserved. Tilles' lags of 10 4 second cannot beinterpreted in this fashion. More work is requiredin the region of longer lags extending from 10 'to 10 ' second.

VII. THE OccURRENcE QF THE DIFFERENTSECONDARY SPARKING MECHANISMS

A. High vacuum sparks and Geld. emission

According to classical sparking theory, whenthe product p5 becomes very small in a gap thesparking potential rises sharply. At pressuresmuch below 10 ' mm with reasonably small gapsit should be virtually impossible to produce aspark breakdown owing to the absence of anymolecules in the gap which can give ions.Actually such sparks have been well known foryears. In the period 1923—25 several investi-gators arrived at an explanation of the phe-nomena on the basis of field current emission. "That is, electrons are emitted from the metalsover the potential barrier in the presence ofsuitably high applied fields. The magnitude ofthese fields for most ordinary electrode materialsas calculated from the contour of the cathodeand the potential must be of the order of some10' volts per cm, giving local fields at points orirregularities of 10' or more volts per cm.Under these conditions electrons can leak outover the potential barrier, and carry the current.The theoretical treatment of the problem bythe Sommerfeld electron theory of metals hasyielded equations in satisfactory agreement withexperiment. ~' If the field current becomes greatenough so that the minute point is heated, itvaporizes and a regular spark ensues throughthe medium of gases and metal vapors liberatedfrom this point. Even at somewhat lower fields

by increasing the temperature the thermionicthreshold can be lowered by the field so that for

290 LEONARD B. LOEB

heated electrodes the resulting currents can leadto sparks at appropriate fields, by vaporizingpoints.

While positive ion emission from metals hasbeen observed at high temperatures, there isno record to date of any field emission for positiveions either of the regular type or one wherethermionic emission is assisted by high fields.

Recent results of Flowers" on the sparkingpotentials in unsymmetrical gaps at relativelylow pressures, which gaps are swept free ofions by an auxiliary field, have inclined him tointerpret the sparks as due to a field emission.It is true that such an hypothesis would explainthe peculiar independence of gas pressure andcharacter observed by Flowers. On the otherhand, the phenomenon is observed to occurwhether the smaller electrode is positive ornegative, and when the fields at the largernegative electrode could not under any circum-stances be such as to give a field emission.It is clear that under such conditions othermechanisms should be scrutinized in seeking anexplanation for the results before resorting to anexplanation on the basis of a positive fieldemission. However, it must be realized thatunder any circumstances where the fields at localpoints can reach field emission values, one maylook for field emission at suPciently low pressures.However, there are little data at hand on the con-ditions of sparking at extremely low pressures,and the mechanisms marking the transition fromfield emission sparks to lom pressure gaseoussparks have never been investigated.

B. Sparks at low pressures including coronadischarge

1. Lom pressure sparks. At low pressures andmoderate gap lengths it is quite clear from theprevious discussions that space charges playlittle role in the phenomenon. Unless X/p issuch that the ions gain more than about 50 voltsover a free path, in most gases ionization bypositive ions in the gas cannot occur. Except ininert gases the metastable atoms cannot beseriously considered as giving the secondarymechanism. This leaves one with but two agents,to wit: positive ion impact on the cathode andphotoelectric processes. With the absorptioncoefficient of 10 cm ' found by Cravath for

radiations photoelectrically active in air atatmospheric pressure, it is clear that the actionof photons in a gas below 1 mm pressure can beneglected as a secondary agent. Thus thereremain only the action of photons or positiveions at the cathode. This fact is clearly indicatedby the effect of the work function of the cathodematerial on sparking potentials, as well as thepeculiar polarization effects often observed asthe result of discharges on electrodes at lowpressures. Whether the photon or positive ionaction at the cathode predominates cannot bedefinitely answered, although the discussion atthe end of part 5 appears to favor the photons.In one case of low pressure discharge it is possibleto gain a definite picture of the mechanism.This occurs in the case of the relatively lowpressure corona discharge with dissimilar elec-trodes.

Z. Low pressure corona. In the case of the lowpressure corona discharge with the positive mireand negative cylinder the action of photons atthe cathode has been shown to be the predomi-nating action. " '4 The large cathode surfaceand small cathode field strength militate infavor of the photons relative to the positive ionimpact as indicated by Penning. ' The photonshave been shown to be effective by Greiner. ~4

Werner" has shown that only 1 out of 3 photo-electrons produced at the cathode in vacuumescape in the presence of gas of some 16 mmpressure, Space charges create less than 1 percentof the total field according to Werner, even incorona. " In the case of the negative wire andpositive cylinder the whole picture changes. Thefine wire has so little surface that the photons aremostly absorbed by the walls, or escape from thecylinder. The positive ions are drawn to the wirein a high field. The electrons are liberated bypositive ions at the wire. The beaded appearanceof the discharge indicates points of low workfunction at which the discharge concentrates.The negative corona is more disruptive, itextinguishes easily. ' This indicates instabilityand that space charges may be active. Spacecharges will aid the secondary liberation ofelectrons as they aid in escape of electrons, givea greater field on the positive ions, and con-centrate the events near the cathode.

In the corona breakdomn studies the low'

MECHANISM OF SPARK DISCHARGE 291

pressures and shorter gap lengths easily lead tothe complications produced by the product pbbecoming too small, and this becomes particu-larly troublesome in the case of the inert gaseswhere V, is low and many collisions are requiredto give adequate ions."Werner" estimates thatPS must allow about 70 collisions in Hs and 500in He. In the case of the corona with the positivewire, it appears that the value of p, the workfunction of the cathode, makes little differencein V, . This may in part be due to the enormousefficiency of the large cathode surface. It is alsoin part due to the relatively higher pressures incorona discharges of the type studied (16 mm)compared to those where electrode dependencewith parallel plates was observed. Under theseconditions, as was seen, the cathode materialappears to exert relatively little influence. Whatthe effect of the photoelectrically inactive metalsAl and Mg as electrodes with a positive wireunder carefully controlled conditions will be isnot known.

C. The influence of metastable atoms

The influence of metastable atoms is mostbeautifully illustrated in the case of the lowpressure corona. ' If inert gases such as Ne orHe are used without any impurity (i.e. , Hg or Arfor which the excitation potential of the meta-stable state of the inert gas is greater than theionizing potential of the impurity) the startingpotentials V, are high. The starting potential U,for the corona discharge with positive wire isgreater than V, for the starting potential with anegative wire. Traces of the impurities (0,002percent of Ar) immediately lower V, for bothcases but lower V, for the positive wire muchmore. With just the correct amounts of impuritythey make V, with wire positive lower than V,with wire negative. This neglected circumstancehas falsified the results of many investigators asPenning has shown. The action depends on thelong life of the metastable atoms which arecreated in the high field near the wire andin general disuse away from it, carrying theirionizing power out into the gas. In the case ofthe positive wire the metastable atoms diffuseto the cathode cylinder or to the effective gasvolume near the cathode in which electrons

"J.S. Townsend, Phil. Mag. 28, 83 (1914).

liberated can be of great value to the dischargemechanism. The action is most effective in thegas at a distance from the cathode because herethe metastable atoms liberate electrons in thegas where the loss by diffusion to the cathode issmall. In the case of the negative wire it is onlythe few metastable atoms that diffuse into thesmall volume near the wire from the regionsfurther out in which they were created, that canmaterially aid in the discharge. For the intensefield near the wire is the only region whereelectrons created by metastable atoms can be ofvalue to the discharge. The number of metastableatoms effective in this region from the nature ofthe diffusion process and the geometry of thesystem are relatively few.

It is probable that most of the early studiesof sparking conditions in inert gases both at low

and high pressures should be repeated, usingprecautions such as indicated by Pennings ' inorder to eliminate the effects of metastableatoms on impurities of lower ionizing potential.The possibility of actions of this sort was notrecognized at the time and inadequate pre-cautions were taken to avoid impurities such asAr in Ne and He or Hg in any of these gases.

D. Summary of the sparking mechanism underordinary conditions

Granting the primary process of ionization byelectron impact as presented, with n/p= f(X/P),and that to produce a breakdown enough elec-trons must be created near the cathode to makethe discharge self-sustaining, one can concludethat a general equation of the type of Townsend' sequation will lead to an evaluation of the spark-ing potential. This applies especially to condi-tions in which X= V/8, i.e. , where no spacecharge distortion occurs. In it Paschen's law isstrictly obeyed and U, =F(pb) depends on theform of f(X/p) and @(X/p) far electrons andsecondary processes, although primarily on theformer. As to the precise character of thesecondary process mechanism the equation ofthe Townsend type cannot yield information byquantitative comparison with experiment, as thedata will probably always be too inaccurate todiscriminate between the various hypotheses.At pressures up to 100 mm and X/p greaterthan 40, the type of equation developed by

292 LEONAR D B. LOE8

Townsend is found to hold experimentally forplane parallel electrodes. While the secondaryprocess mechanism is not revealed by the equa-tions definite information is at hand concerningwhat processes can and cannot occur under givencircumstances. The following conclusions maybe stated.

The mechanism for the primary ionization isparamount and ever present. The ionization inthe gas by positive ion impact cannot and does notenter into the sparking equations at any time.It is unlikely that field currents play a roleexcept in extreme vacua. " This leaves onewith liberation of electrons at the cathode bypositive ion impact, with photoelectric effects atthe cathode, with photoelectric eRects in the gasand with the effect of metastable atoms in thegas or at the cathode. There is in addition achance that with sufficient initial ionizationspace-charge conditioned field distortion canlead through the primary process directly to aspark. " Which of these processes occurs isobviously determined by the particular condi-tions imposed by the experimental arrangements.

In the absence of inert gases and up to pres-sures of about 100 mm especially in pure gases,the action of metastable atoms and photo-electric processes in the gas are ruled out.Thus as at lower pressures the principal second-

ary mechanisms are positive ion impact at thecathode and photoelectric processes at thecathode. In this region, however, space charges

can begin to play a role.

Z. Sparking in long gaps and at high pressures

When the pressures approach atmospheric andthe gap length increases to the order of severalmillimeters both the possibility of photoioniza-tion in the gas for any but the purest gases,and the influence of space charges must beconsidered. This is indicated by the followingfacts. At gap lengths of several mm at atmos-pheric pressure, and definitely at lower pressureswith adequate illumination, the breakdown ispreceded by a space charge distortion, "which asindicated, enhances materially the processes atthe cathode and hence lowers the value of thesparking potential. The presence of distortion hasbeen definitely verified by time lag studies, " " "

by studies of the Townsend coefficients,and by theoretical considerations, " " " 't aswell as by observation of suppressed discharges 'and discharges studied visually or photographi-cally in short time intervals" including Lichten-berg figures" and recent cloud track pictures. @ "How important space charge is under the con-ditions where it first appears is not known.That it is possible that at high pressures andlong gap lengths space charge distortion cancause a spark on the basis of the primarymechanism appears to have been demonstratedmathematically. " Whether such a spark occursor not is aside'from the point, for accompanyingany large space charge formation by a primaryprocess is the presence of considerable ultravioletradiation and positive ion production. Underthese conditions the secondary process will befurnished by the photoelectric ionization of thegas or secondary emission from the cathode.

Since it is probable that the photoelectricprocess in the gas will occur at higher pressureswith and probably before one reaches the fielddistortions needed to produce a spark on thebasis of an electron ionization alone, it is obviousthat the photoionization in the gas will accountfor certain discharges whose explanation hashitherto given trouble. It must be clear that inthe static discharges of ultra-long gaps, such aslightning discharges, photoionization or positiveion impact at the cathode cannot be invoked. Thesame argument applies in the case of dischargesfrom isolated positive conductors (needle points,wires'and the high pressure corona") for thefields at the cathode are exceedingly weak andthe cathodes are too far distant to be involved.Hence the regions in which the primary processesinitiate must, have the power of not only originatingthe high potential gradients locally needed for givingthe discharge. They must also provide for themechanism by which electron supplies are main-tained and by which these gradients travel as theydo in lightning strokes. Such a mechanism in theabsence of ionization by positive ions can onlyoccur with photoelectric processes in the gas. That

'4 J. J.'Torok, Trans. A. L E. E. 13, Feb. 1928."Nakaya and Yamasaki, Proc. Roy. Soc. A148, 466

(1935); H. Kraemer, Archiv f. Elektrotechnik 28, 703(1934); Bradley and Snoddy, Phys. Rev. 47, 541 (1935).

"Flagler and Raether, Zeits. f, Physjk 99, 635 (1936).~' W. G. Hoover, Elec. Eng. 55, 448 (1936).

MECHANISM OF SPARK DISCHARGE 293

such space charge distortions must occur isindicated by the fact that the average field

strengths actually calculated in the case ofpositive point or wire corona discharges to planesat atmospheric pressure, and in the lightningdischarges are exceedingly low (e.g. , 3000 voltsper cm for lightning discharges and 4,000 voltsper cm for the positive point corona with aluminous path from point to plane at atmos-pheric pressure). These fields are 1/5 to 1/4 thefields which are required to give cr a measurablevalue at atmospheric pressure. Hence unlessspace charge distortion occurs the mechanismsconcerned cannot give rise to sparks. Further-more in some cases these distortions must havethe power of propagating themselves in order tobridge the gap. That the positive space chargedendrites emanating from the cathode can act asneedle point electrodes in propagating the dis-charge has been emphasized by von Hippel. "How such channels propagate at the enormousspeeds observed by Schonland and Collens" in

lightning discharge and by Flagler and Raether"in sparks has been shown by Cravath and Loeb'on the basis of the ionization of the gas by ultra-violet radiation which produces ions in the dis-torted field ahead of the point.

"A. von Hippel, Naturwiss. 22, 47 (1934)."Schonland and Collens, Proc. Roy. Soc. A143, 654

(1934);A152, 595 (1935);Roy. Soc. South Africa, MeetingOct. 16, 1935.

"Loch and Cravath, Physics 6, 125 (1935).

VIII. CONCLUSION

In conclusion one may say that while in detailthere is a great deal to be learned about theindividual processes of spark breakdown in manyof the cases observed, in general the nature ofthe secondary mechanisms active in most sparksare pretty well understood. The essential con-clusion to be drawn from this analysis is, how-

ever, that there is no single definite secondaryProcess ivhich occurs universally in all dischargephenomena as some would like to believe. Thereare at least five and, including very low pressures,six mechanisms by which the self-sustainingcharacter of spark discharge can occur. De-pending on the circumstances, any one or twoin combination predominate to the exclusion ofthe others. In many cases the circumstancesindicate at once the favored mechanism.

The writer desires to express his indebtednessand thanks to Dr. R. N. Varney, to ProfessorN. E. Bradbury and to Dr. H. J. White for theircareful study of the manuscript and valuablesuggestions. His thanks are also due to Dr. A.Tilles and Dr. D. Q. Posin and R. R. Wilson fordiscussions of sections cogent to their own re-searches and to Professor R. B. Brode for thenotes on the equations resulting from severalsecondary mechanisms. He is particularly in-

debted to Dr. A. M. Cravath for his verypenetrating and able criticism of many questions.