NPA/Int. 67-5 19.4.67

HIGH VOLTAGE BREAKDOWN IN VACUUM *)

by

C. Germain QTI.d F. Roll~bnch

1. Introduction

The phenomeno. tho.t occur when high voltages o.re applied between electrodes

in n vo.cuum ho.ve been studied for m1::.ny ye'lrs. However, the progress in this

field ho.s only recently been speeded up under the spur of the increo.sing number

of teclmical o.pplicc,tions of v=:cuum insul,'.',tion. Dur:Lng the course of the lo.st

deco.de there has been a considerable incre'.'..se in the nuirrber of people involved

and, of course, in the number of papers they ho.ve 9ublished ~nd conferences

they kcve attended. As a result of this increG.sed effort o. progressively clern'er

picture is emerging, ct le0st on some '.~sr,ects of the lJroblem, but there is still

much to do before we can. obt::cin a coherent, clec.r c~nd. complete explo.nation of

all the relevc.nt observed phenomenn.

Let us first ex::;,mine whd we me::m by electric.

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Except in very short pulses a high voltage ca1:not be maintained between

electrodes together with a high current since we no longer have a vacuum between

electrodes. We can thus understand how vacuum breakdovm and gas discharge are

related and there is an intermediate region where curious phenomena occur as

we shall see it later.

Since we know that residual gas molecules are not involved in the init-

iation of vacuum breakdovm, what kind of limitation are we going to encounter

with the electrodes upon raising the voltage be-tween them ? At first sight we

might expect an appreciable current to appear when field values of 107 to 108 V/cm

are reached because electron field emission from the cathode metal becomes

significant at this field intensity according to Fowler-Nordheim theory. At

about the saoe field intensity the mechanical stress on the electrodes, which is

proportional to the sq_u:ire of the field intensity 1 bec.omes comparable to the

bulk tensile strength of the electrode material. A mecl:anical stress of about

5 x 108 pascals (i.e. rv 50 kg/mrn2) is generated by a field intensity of 108 v/cm.

Therefore at a field of about 107 - 108 v/cm there should be a catastrophic

breakdown between electrodes for these reasons. Is this the limitation encountered

in eq_uipment in which high voltages are applied in a vacuum ? .Anyone who has

spent hours or event days trying to bring up the performance of an electrostatic

separator or of an accelerating column to its nominal value will tell you the .. t

there is a "performance gap" of about three orders of magnitude !!

In order to lmd.erstand tho reasons for this enorwous discrepancy we must

look again more closely into conditions at the electrodes

1) The average or mo..croscopic· field, which is voltage/ gap length, is the

releV'ant par2.:-neter for particle so:r;an:tor performa.rice but for determ-

ining the current between the electrodes tho surface field is the

critical factor. This true microscwp:Lc field on the electron emitting

cathode points is much larger than tho average field because of the

enhancement produced by the point gGometry. The enhancement factor may

reach one or two orders of magnitude.

2) The microgeometry of the electrodes, that is the shape of the points,

.is continuously modified under the combined action of the electric

field and of the surface curvature gradient; this modification is

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facilitated when the local temperature is raised. Therefore perfect

polishing of the surface will not permanently reduce the field

enhancement factor. Sputtering of the electrode surface also has to

be taken into account in some cases.

3) In large scale practical devices such as separators, where ultrahigh

vacuum technology and high ternperaturebaking are not used, the

surface of the electrodes is not ~u.re metal but is contaminated by

all kinds ofl organic materials which have a much smaller work function

than perfectly clean metals. k.purities and dislocations in the metal

also enha.i.~ce electron field emission.

A fairly satisfactory theory of the electrical breakdown of small gaps

( ~ 1 mra), bnsed on a detailed analysis of the electron emission from the cathode

and on the current interaction wit:'.1 either electrode, has been developed by

1 1,2) .. th' several authors for the case of very cles.11 c8tc::.l e ectrodes • however, is

theory cl.oes not fit, in its presEmt fom., the experimental data accumulated on

the electrical breclcdown of large g:::.ps. Otl:er )henomena may become prominent in

large gaps and cause the onset of rree...~dmm at lower voltage values than expected

from this theory. We only mention briefly t~1e clunp hypothesis which we shall

discuss in more detail later. No satisfactory theory has yet been produced for

larga gaIJ brer.:kdoim .filld a completely new line of attack may perhaps be necessary

in order to develop a successful theory.

We shall start our review with 2 brief look at the theory of emission of

electrons from metals; then we shall c-:mside1· the energy exchanges between the

electrons and electrodes and discuss tbe anode versus ca.thode control of breakd01m.

We shall shoi-1 that this provides a rather satisfactory explanation of experimental

data for electrical brea_l\:down in s:.:ie.11 gs.:;is or relatively low voltages (i.e.

millimetre gap or hundred kilovolt regioE) whereas other hypotheses have to be

considered for larger gaps and voltages.

Since th8re is clearly not enough ti:ne to mention all the important

contributions in the literature, we have selected papers which are typical of the

main trends of the present state of knowledge. We also have to apologize for so·ne

over-simplifications which are inevitable for the sake of a clearer presentation.

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·2. Emission of Electrons from i'· etals

The theories cif thermionic and field erc.ission of electrons frora r'.letals

were worked out about half a century ago 3,4, 5,6 ), but lL'1til recently thsy were

considered as sepc::.rate theories, each one h'lving its own range of temperature

and field within 11hich the corrosp0nding ex-;;ression of the current i.ras valid.

However, I4urphy and Good ?) in 1956, gave a unified treat=-,ent and obtained a

general expression fo:r the cur:.r:ent as a function of electric field F, temperature T

and work-fuI1ction ~' in tl:s fora1 of a definite integral. Then they applied

approxirnating tecl:1niqi:ss for t:·,is integral e..'1d set up hro distinct formulae fOl'

thermionic and field cmfas:.on, 1d th a characteristic dependence on F, T and yl for each type of emission. Jm e.pprox:'..::,ation for :i..ow fields 2nd high temperatu:res

leads to an extension of the Richardson-Schottky formula for field assisted

thermionic efilssion. The 71.l:i_cl:'_ ty of the a~)proxlic.a tion determines the range of

temporo.ture ar;.d field within which it apylies. A si:r:il2r trGatnent of the

integr&l for high fields and low te:J.:_::eratures, gives an exter:si.on of tl1e

Fowler-Nordhei::i forrm~:ta for field emission, wi t~1 the corresponding r2nge of

temperature and field in which the o.pproxL1ation is valid. With e..nother approx-

imation they evaluated the integral in an :L'1ten:ediate region between the::'mionic

and field emission. Outside th0se three regions the emitted current is obtained

by numerical integration of the general e:z:pression for each set of values of

the paraneters.

Murphy and Good der~.ved their general ex9ression for the emitted current

from the well established. r::o:iel of e.. rr·etEcl : the Fermi-Dirac distribution for a

free electron gas in the m~tal and the clr~ssical iincEe force barrier at the

surface. This model provides c~n expression for E(T,

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Without going through the mathematical details of this interesting paper,

we shall just examine the general expression for the emitted current density

3 o 5 I ( ) in figure 2. In the expression (2) y = (e F) • I WI and v y is a tabulated function. Withj_n the regions of validity of the approximations we have mentioned,

simpler expressions can be derived as shown in figure 2, expression (3) for

thermionic emission and expression (4) for field emission. From these expressions the well-known Richardson-Schottky and Fow1er-Nordheim formulae, written with

the system of units and the symbols used by Murphy and Good, are respectively

obtained within still more restrained regions of validity.

The boundaries for the three types of emission discussed by Murphy and

Good are represented in figure 3 for a work function of 4.5 eV, a representative

value for tungsten. At current densities of about 108 A/cm2, which are typically

required for excessive heating of tungsten protrusions the emission of electrons

is mostly due to tunneling Ui..rough the barrier, i.e. the emission increnses

rapidly 1,1ith the field and is relatively insensitive to temperature 8 ), .as cnn

be seen in figure 4.

3. Exchon&:es of Energy between Electrons Emd Electrodes --· ----·------------------------

· .l..J._~ons on the co.thode surfac~

Upon raising the voltage V between plane parallel electrodes a current is

emitted at very localized points on the c:1thode surface. The value F of the field

that determines the intensity I of the electron boom is not the average value of

the field in the gap d, F = V/d, but F = yF at the apex of the emitting point. 0 0

The unhancement foctor y is determined by the shape of the point and by its

height h expressed with respect to d. Even when there are several emitting points, 11) the factor y is determined, to a first approximation, by the sharpest one •

If the emitted current follows the :B'owler-Nordheim formula, then the expression

log (r/v2-) is a linear function of l/V ~ which the factor y enters in a simple way.. In fact the current measured as a function of V, in any experiment not

interrupted by a spark which would destroy the emitting point, appears generally

to follow· the Fowler-Nordheim formula quite well so that a stra:Lght line is obtained

in the F-JIT graph, that is when log (1/v2) is reprnsented versus l/V as in figure ~ From the slope of this straight line m =A ¢1. 5 d/y, where A is a known constant,

nn experimental determination of the value y of the emitting point is easily

obtained, provided yJ is known.

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By making some assumptions on the geometrical shape of the protrusion,

for example by considering an ellipsoid or a cylindrical rod with a hemispher-

ical cap 81 9), the corresponding y values can be calculated from electrostatic

principles. Experimental values of y, deduced from F-N graphs, are currently

observed in the range 1 (for extremely small gaps) to a few hundreds (for

millimetre gaps) 9,lO)• When comparing the theoretical values with the exper-

imental values obtained as a function of the gap d the geometrical parameters

of protrusions are obtained : values of about 1 µm and 0.1 µm, within an order

of magnitude each, are generally obtained for the height and the diameter of the

protrusions respectively. These dimensions pertain to protrusions of simple

geometrical shapes but direct geometrical measurements by using electron.

microscopes have.confirmed that the dimensions thus estimated are of the right . 11 12)

order of magnitude ' •

When the emitted cu~rent density exceeds 107 P/cm2 electron space-charge effects reduce the true field F at the emitting surface appreciably below the

value calculated from electrostatics. The field emission formula is still Yalic.

provided the true value of the field is used. The space-charge effects at

current densities of about 108 A/ cm2 , which are often attained in practic«~, strongly reduce the influence of variations in the work function on the emitt'

surface 8 ).

In general the presence of protrusions on the surf ace cannot be avoided

and is primarily responsible for the limited voltage strength of vacuum gaps.

Even perfect polishing of the surface would not be of great help since the

surface condition can deteriorate quite quickly with time under the action.of

temperature, applied field and ion bombardment. It has also been shown by

:Little and Smith 13) that projections ~re removed from the anode. by the electric field and these produce craters and sharp field-enhancing protrusions on impact

with the cathode; The growth of the protrusions has been studied by Charbonnier 14) .. .

et al. , using Herring's theory, whose fundamental postulate is that the flu."?'.

of atoms b·eing transported past a certain point on the surface of a protrusion

is proportional to the product of a diffusion coefficient and the local gradient

of chemical potential at that point. ~lhen the average field exceeds a certain

value the protrusion will grow indefinitely and produce a breakdown. They have

also studied the formation and growth of protrusions by the action of sputterin;

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J.L2 E}ectron-cathode energy exchanges

The field-emission induced heating of cathode protrusions has been studied 15) . t 1 8,1~) R . t· theoretically in detail by Lee and by Charbonn1er e a • • esis ive

heating alone cannot explain the stability of field emission at current densities

high enough to raise the tip temperature to 2000° K or higher : a balance of

Jouie'heating with thermal conduction and radiation losses is impossible, leading

to an unstable situation. Furthermore with a low work function coating on the

tungsten tip ?ne can draw a higher current density while maintaining a lower tip

temperature which is impossible with heating by Joule effect alone. For these

reasons the Nottingham effect clearly comes into account in the thermal balance

of the _protrusion tip.

The Nottingham effect is due to the difference between the average

energy < E ) of the emitted electrons and that < E 1 > of the replacement electrons which is assumed to be the Fermi energy in the simple Sommerfeld free

electron model of metals. At room temperature < E > is lower than the Fermi energy so that the cathode is heated by the Nottingham effect. As the temperature

is raised the energy distribution of the··~mitted electrons is modified and

becomes symmetrical with respect to the Fermi level at the transition temperatu::.-e,

At higher temperatures the Nottinghrun effect changes its sign as < E ) becomes higher than < E' > and cooling of the cathode results from the absorption of energy by the electron beam. At these temperatures the Joule and Nottingham

effects have opposite actions on the tip temperature. The transition temperatur-;

is Ti= 5.35 x 10-5 Fjr;{J• 5, that is Ti.= 1250 °K at F = 5 x 107 V/cm for tungsten (

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1) T'11e pulse is longer than a thermal time constant \. Then the

steady-state distribution of the temperature is reached for the

protrusion standing on the cathode surface.

2) The pulse is very short : shorter than a smaller time constant t 2 •

This is the adiabatic case where no appreciable heat diffusion can

take place and the local temperature is governed by the local heat

generation.

3) The pulse duration is intermediate between t 1 and t 2 •

8,16) The values of t 1 and t 2 are given by the theory and for pulses

longer than t 1 or shorter than t 2 simple expressions for the critieal currents

as functions of the relevant parameters nre obtained. From these the corresponding

critical voltage may be calculated.

4. Breakdown across Small Gaps

A.J Cathode initiation of breakdow11

Field emission at high current density does not necessarily lead to

breakdoi:m as pointed out by Char bonnier 8 ), since de emission densities in

excess of 107 A/cm2 or pulsed emission densities in excess of 108 A/cm2 have

been maintained without instability for operating periods of several thousand

hours. However, excessive current density causes excessive heating of the tip

and evaporation of cathode material. This metal vapour has a high ·probability

of being ionized in the very high density, low-energy electron beam just outside

the emitting surface. Production of positive ions in front of the tip reduces

the electron space-charge effect and therefore increases the field erni tted

current. Furthermore the cathode tip is bombarded by these positive ions which

can liberate more electrons so that these t1vo regenerative processes lead to an

extremely rapid development of a full vacuum arc in times of the order of

10 nanoseconds. The Nottingham effect does not markedly affect these general

conclusions.

Experimental studies have shoi-m the onset of rapid instability when the

protrusion tip reaches a critical temperature corre8ponding to a metal vapour

pressure of 10-4 Torr. The critical current density jc does not differ widely

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from one material to another and is about 108 A/cm2 for a typical conical

. t• 16) pro JGC J.on •

The rate of increase of the breakdovm voltage, as pulse length t . 0

becomes smaller, is quite low since, in the adiabatic.limit, the permissible

current density jM is proportional to

·08 AA/ 2 . . t 1 v3 1 /6

cm varies approxirna e y as

t- 1 6 • Therefore the voltage increase 0

duration is reduced by a factor ton •

t- 0.5 • Now since j in the region of 0

the breakdown voltage increases as

is only 40 to 50 o/o when the pulse

.4._.J_.lin.ode versus cathode control of bL,e_a..::l\:dow.n.

We have so far discussed the emission-induced heating of the cathode

protrusions. However, there is an additionnl l1eating effect : the field emitted

electrons, accelerated by the field across the gap, cause anode heating on

impact with the anode. Breakdo1m is likely to occur when the temper2ture at

either electrode oecomes high enough loce.lly to cause significant eva~oration

of electrode mderial into the path of the electron beam. Whether this critical

condition first occurs at the cathode or at the anode depends on the gap

geometry, on the field enh::illcement factor y, on the relative electrode materials 8)

and on whether the gap voltage is de or pulsed, as discussed by Charbon..nier

Chatterton 17 ) has pointed out that in the case of de voltages and

parallel plane electrodes it is virtually certain that excessive heating will

occur at the anode well before the electron current density reaches a level

sufficient for excessive ?r9trusion self-heating at the cathode.

From the radial spreading of the electron beam emitted from a protrusion

in the case of parallel plane electrodes the beD1n power density at the anode

may be calculated as a function of the current density end of the corresponding . . . 8 10 17 18) .

fie1d on the protrusion ' ' ' j the values of these two quantities should

be smaller than the values obtained from the conditions of cathode-controlled

breakdovm since 'de are now interested in anode-controlled breakdown. If the

values corresponding to cathode-controlled brea1..cdown are used in the expression

of the anode power density the maximum possible vive heating of the anode.

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We may define two thermal time constant values t 1 and t 2, corresponding

respectively to the steady-state and adiabatic conditions of anode temperature

distribution, in order to assess the criticnl or maximum admissible anode power

density. The value of the voltage pulse duration t 0 relative to t 1 and t 2

determines which expression for critic al anode power density hclS to be Considered

· and then the corresponding criterion of anode-controlled breakdown is obtained

simply by stating that the m'UCimum possible VD.lue of the anode power density

exceeds the critical value 8119 ). This criterion turns out to be a 2imple

expression for the maximum value y," of the cathode field enhancement factor y. Fl

If no protrusion on the cathode has a y value _larger than Yr.r then the breakdmm

is induced by excessive heating of the anode. When the voltage pulse duration t 0

decreases the relevant value of y11 also becomes smaller : the breakdown which is

generally Qnode-controlled in de conditions is fina1ly cathode-controlled at

very short pulse durations.

10) Utsumi and Dalman have. studied theoretically and experimentally what

are the respective conditions for o.node versus cathode·control of de breakdown

between plane parnllel electrodes as a function of their separation. The type

of breakdown which is likely to occur can be determined from the dimensions

of the projection and the thermal andelectrical properties of the electrode

materials. Af3 the separation d is increased the clomin-::nt mode of breakdo11m is

first the anode type when the value of the enhancement factor y is small, then

the cathode type with which is associated a critic2l cu.rrer:.t of constant value,

E:nd finally, the anode type again when d reaches the 0.1 - 1 rnm region and the -·o 5 corresponding critical current varies as d • •

The nnalysis of vacuum breakdovm, which we hove just presented in

simplified form, is sufficient to provide estimates of the breakdown voltage

and indication of the necessary electrode conditions for initiahon, which are

0 f . d . t "1 lO, 19) ~ t 1 «. t f 1 c n irme experimen

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we have just presented, which is.based solely on the heating power of the field

emission-induced electron beam. The large gap studies with plane parallel

electrodes have revealed several facts which cannot be explained by this theory

at the present time ; these are :

1) 'rhe breakdown field FOB is a decreasing function of the gap d. The

experDrrental data can be fitted to the following eCTpirical expression

- ex FOB = A d with O. 3 < ex ( 0.8

2) The steady current value just below the microdischarge threshold is

strongly dependent upon the gap d in the range 1 - 6 cm: Whereas

in a 0.5 cm gap between stainless steel electrodes in ultrahigh vacuum

conditions hundreds of microamps c~n be drawn without causing

breakdown, it is impossible to obtain more tkm a few nanoamps when

the gap is increased to 5 cm 24).

3) The breakdmm field increases with pressure when gas is admitted to

the vacuum chrunber up to the region where Paschen's gas discharge law

becomes applicable 1 which is usually in the milli tor range 27 ) • This

effect, which was first demonstr~ted clearly for separators at CERL~

in 1959, had been noted in the early fifties by a few authors 29).

T'ne effect of the gas pressure on the microdischarge threshold and on

the breakdown fields is stronger the larger the gap, (figure 6).

~l.hen discussing the cathode initiation of breakdo1m we have established

the existence, in this CB.se, of a critical value of the cathode emitted current

which is independent of the gap d. Since the value of the enhancement factor y

is independent of d for large gC>.ps, the as.sociatGd critical average field FOB

sho:;.ld .lso be independent of d,

The first and second points just m::ntion'-'d, ns well ns our

- 12 -

If we now consider the possibility of breakdown controlled by the

vaporization of a small amount of anode material under the action of the field-

emi tted electron beam impinging· on the anode, we have to remember, according.

to Utsumi and Dalman lO)' that in this case the critical current varies as

d- 0 •5. This condition is obtained by ir:lposing the condition that the temperature

of the heated anode spot centre be kept constant, at the melting point for

instance, when the separation between electrodes is increased. The experimental

results mentioned in noint (2) show th2t the microdischarge threshold current . . . varies by several orders of magnitude instecd of half 2.Il order when the gap is

increo.sed from0.5 to 5 cm, which rules out also this theory for rnicrodischnrges

initiation. This conclusion is valid also for bre&1\:down initiation, since

microdischarges develop into full discharges, or brea.1\:down, at a higher voltage

and can therefore be considered as being governed by the same law .

.2_._~ The micropc.rticle brea .... ~down ini ti2tion hypothesis

In 1952 Cr2nberg 28 ) put forwa:rd ~he hypothesis that breakdown is initiated by tiny bits of material or clumps, impinging on the electrodes under the effect

of the electric field. The brdakdown, in this clump theory, is the consequence

of the electrical gas discharge taking place in the v~pour generated when a high-

speed microp~rticle collides with one of the electrodes. Assuming that the

micro-particle gets detached from one electrode, it carries along an electrical

charge q, which is proportio~al to the field, and it has an energy W = q.V after crossing the gap when it impinges on the other electrode. A criterion for breakdown

is obtained by simply stating that breakdown will ta..~e place when this energy

is larger than a critical value W · . t. cri . ,

The breakdown field-gap relationship derived from this simple clump

theory, in the case of plane parallel electrodes, is : F0B2 x d =constant.

When comparing this formula with the exµ;rimental results mentioned in point (1).

above no discrepancy appears but the range of ex?erir:lentally possible values for

a is too broad .for this to be a strong confirmation of the clump theory.

Furthermore by refining the clump theory, the theoretical value obtained for a

can be IDQde to differ slightly from 0.5, so that some direct experimental confirm-

ation not only of the existence of clumps but also of their triggering action

in the breakdovm process is necessary. Nany attempts are made in that direction

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and we only mention briefly a method.which was first proposed by C. Germain at

CERN for detecting clumps during their flight ncross the go.p in order to

establish directly their triggering action in the breakdown process. This method

is based on the detection of the light reflected by the clump when it crosses

at right angles a wide laser beam. in the gap between the electrodes.

·The microdischarges we ha.ve mentioned in the introduction are observed

at voltages lower than the breakdown voltage. 'l'hey are essentially self-

extinguishing_ bursts of current, that is they do not involve 2 complete colls.pse

of the voltage across the gap. On the basis of the clump hypothesis. a micro-

discharge 211d a full discharge can be caused by the same process, that is by a

more or less complete vaporization of the micro1xi.rticle when it impinges on

the opposite electrode. In the case of a microdischarge one can assUL~e that the

amount of material vaporized do not generate a bubble of va~our large enough to

induce a diverging gas discharge process.

In the clump theory the microdischarge and the full discharge are consiO.ered

as being unrelated to the steady current th0-t exists simultc.neously between

electrodes since no proposed clump extraction or generction process under the ::.ction

of this steady current can account for the very large variation of the micro-

dischnrge threshold current as a function of the gap in the centimetre range.

The clump can rather be considered as detached ~y the action of the electrostatic

pressure from the electrode to which it is loosely bound. The exact process of

this extraction is not yet known o.nd this is the first of a series of questions

which must be asked about the theory of brealcdovm across le.rge gaps. Little l '1)

and Smith _, have reproduced natural bre~ikdmm phenomena in a 0.25 rxn gap by

intentionally inserting nickel particles about 0.01 mm in size into a small hole

on the anode surfnce Ctncl they evaluated tho cr:i. tical clump energy to be a few

nanojoules. They demonstn1ted that in no.tu.ral breakdown clwnps had been extracted

from anode pi ts located at impurity centres near grain bou..'1daries Ei.nd had

produced sharp-field-enhancing protrusions on the cnthode surface. No sueh exper-

imental work has yet been perfo'rmed for larg"' gaps and high voltages.

A regenerative process is required for the creation of clumps, otherwise

it would be possible to condition electrodes once o.nd for all at a given voltage

provided the working voltage is kept lower than this value in a constant gap.

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The growth of protrusions under the action of the electrostatic pressure is a

possible regenerative process which is well known experimentally 12 ) but it

is only valid for small gaps since it is associated with a given field or current

level. Any proposed clump regeneration proces~, based on the effect of either

the current or the field, must account for the respective variations of the

critical values with the gap length.

The marked influence of the residual gas pressure on breakdown voltage . . 22 26)

mentioned ear~ier, which is of :i.mportance·in some practical applications ' ,

is also difficult to explain completely on the basis of the clump theory because

of- the g2.p dependence of both the microdischarge threshold current and the

breakdown field. The influence of the pressure on the breakdown voltage in small

gaps has been investigated recently 11129) and it can be explained by the

selective ion bombardment of the sharpest points of the cathode : the corresponding

values of the field enhanc8ment factor y are thus reduced by sputtering so that

a higher v2lue of the average field FOB can be sustained. Such.an expl:ination

was also attempted for large gaps but the mechanism of this.influence is not . 21)

yet completely understood

6. Conclusion

The initiation and the development of electrical discharges in vacuum

across small gaps hetween clean metal electrodes can be described satisfactorily

in terms of the gap geometry, cathode surface microgEometry and the physical

properties of the electrode material. The relevant theory is based on a detailed

analysis of· the electron field emissiorifrom the cathode and on the associated

current thermal interaction.with e:.ther. electrode. However this theory fails to

fit the experimental data obtained with large gaps: in this case the hypothesis

of breakdown initiation by microparticles which are accelerated across the gap

by the electric field, provides an explana.tion which has received some experimental

confirmation, but is not fully sntisfactory. Further investigations, both

theoretical and experimental, are required in order to develop a completely

quantitative theory of br0akdown across large gaps.

It is a pleasure to acknowledge the assistance of Dr. Colyn G. Norgan,

University College of Swansea, for revising this text.

/fv PS/5902

C. Germain F. Rohrbach

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References

1) Proceedings of the first Internation:cl Symposium on the Ins_ulation of High Voltages in Vacuum, October 19 - 21, 1964, M.I.T. Boston, referred to as 11Proc. Itt in other referencas.

2) Proceedings of the second International Sympqsium on the _Insulation of High Voltages in Vacuum, September 7 - 8, 1966, M.I.T. Boston, referred to as 11Proc. IItt in other references.

3) O.W. Richardson.- The Emission of Electricity from Hot Bodies, (Long:nans Green o.nd Company, London, 1921).

4) W. Schottky - Physik: z. 15, 872 (1914) !

5) L.W. Nordheim - Proc. Roy. Soc. -(London) A 121, 626 (192$).

6) R.H. F'owler and L.\I. Nordheim - Proc. Roy. Soc. (London) A 119, 173 (1928).

7) E.L. Nurphy and R.E. Good - Phys. Rev. 102, 1464 (1956).

8) F.M. Charbonnier - Proc. I, 23 and 477.

9) D. Alpert, D.A. LBe, E.M. Lyman and H.E. Tomaschke - Proc. I, 1.

10) T. Utsumi and G.C. Balraan - Proc. II, 151.

11) H.E. Tomaschke, D. Alpert, D.A. L€e 3nd E.iI. Lyma.Yl, Proc. I, 13

12) R.P. Little and S.T. ~nith - Proc. I, 171.

13) R.P. Little 2nd S.T. Smith - Proc. II, 41.

14) F.M. Charbonnier, E.E. Hartin, R.W. Strayer l'cnd C.J. Bennette - Proc. I 169 and 507.

15) D.A. Lee - Proc. I, 69 and 453.

16) F.N. Charbonnier, L.W. Swanson and C.J. Bennette, Proc. II, 11.

17) P.A. Chatterton - Proc. I, 25.

18) F.E. Vibrans - Lincoln Lab. Technical Report No 353, 8 Ntiy 1964,

19) C.J. Bennette, L.W. Swanson and F.r1;, Charbonnier - P-..roc. II, 21.

20) C. Germ,-:cin et F. Rohrbach - IVeme Conf6rence Internationale sur les Phenomenes d'Ionisation dans le Vide - Paris 1963 - Section Va-To:::e II.

21) F. Rohrbach - Proc. I, 393.

PS/5902

- 16 -

22) J .J. Murray - UCRL report 9506 (1960).

23) K.W. Arnold - Proc. II, 73.

24) Ji,. Hohrbach - Proc. II,· 83.

25) W.A. Smith, T.R. Mason - P1·oc. II, 97.

26) C. Germain, L. Jeanneret, F. Rohrbach, D.J. Simon et R. Tinguely -Proc. II, 279.

27) C.M. Cooke - Proc. II, 181.

28) L. Cranberg - J. Appl. Phys. 23, ·51s·- 1952.

29) E.N. Lyman, D.A. Lee, H.E. Tomaschke arid D. Alpert, Proc. II, 33.

PS/5902

· ..

Energy

! I

0 x ~~~~--~~~~~~~~~~~~~~~~~~~~~-·~

~ I

'I max. f /'"-.............. , ·1/ ............ ,

' ' -!% ,~, I. ~ ~ ~ '( - -~,,,,~":'::_-

. ' - '" I '- > ·-- "'~~. i '°' ,, -~ -..... ~ t:tl="ormi lev·... j---- .,,..,.~% t''-l --.. • '• ___,_ -- ---- - --·i .,,,,, . --. ' -~--=-=--- -·{ '

-~- -~=-;~~J ~.~ -- ----------- ----- I "' - - "~ --~-~-__ ' ~ - _, - I --------

q)

! '.I +-v~a ''1

~

V (x) = Pote1nticll ener~IY of an electron near the rneto.l surface

X = Coordinate norrnal to the surface ~ = Ferr·ni en,:rgy

(b e

rJ .. ~ ~; • ~\ 2 "i n

\!;._fa - ~;J \! \.< Er.~.::r -'1·•. '"" _,,""\''""'>-.a. t• -- 10 c·~· ron ut:l..t~\·~' cu~ ::~:nan ~·t11.;.; t l

F

l"'l-oi -:.r~·,t • ~ h .. ah. •

r- . ··-~ nr:::rli"'~!~I':" ':!~ &~:.;,II'"''"'\,.;.~~ _,. •ff'~""' ,,,, ~'4..i3 u

.,t l

i:" ~.,, '{ .o. rr ,,..,,, r~· I i "/ f-,f'\ "''- l ~ i ~---""~ ll.j

1 \.! ~~ ( • 3 t- v:--· "'"f'\{"-(«J' -· ....., c::i. f• ~ 2 -~ i ~~"·· • ,._ J -

-··o)" p•ct,., !.,) l'"" I' ,.,. VII rt'-¥ L

f"""~\.li!,

1

in~.id110. thP mpta1l ~1o1 s"-~-;1:!:""1:~·.,.,¥ i:J ~ ..... "" il: '4'!t ,

rn ~ll'"""'""'O I' t~~,,k> ~ ~~~ t

~ t . !I'• if~! •CJ,(" rRf"' ~(2 • ..., 11.·..,, ~ ~ ...... ~:

Vrnax.

'l°' 0,, ,,

\!""'"""'. r~ i ~ . ~ """"'' ' l -1'.1; a "'"~ I!':·~~ - -- !i. i~, ...... n if_\'\ - -~Ii ' ··--·'"'""~~. I! ~ ~~ ''\>,.( ~,\lf'ilo,;) ~ \4~ ~M~ ~ iv~ ~','l

Th&rmionic e mi ssicn

Field emission

f \ ' J

Cil' rd l "'"

Current density j ( F, T, ~ ) as a function of electric field F, ternperature T and , Ferrni energy J 1n Hartree uni • according to r,l1urphy and Good 7> _________________ ,

3000

~ 0

2000 c

OJ I-::i --d l-{j) 1000 0. E ~

for a

• ion ( ~ ) i.en

'7)

log. 1 ... VL

-13

-14

--i~S

-16

~~,

- . -\'' -~ \-. -----,-1 ,ff\ (X)

I \/ I ~ ! \\, I . ·r \i~

I

Typi l ( D.

m::

[ n I' q' " \ " J

( kv) A Voltage V

500 -

300

200 -

100 _l

gap d ---t--------+--· ---+-----------+--·--, --~

2 3 4 5 (cm)

£lg~_§ __ Ty . VO fc t"' v-1 ... ;o· ·ue:-.,QI .,u,, a -ii current and t t