NPA/Int. 67 - 7 19.3.1967

Laser Induced Breakdown of Gases and the Interaction of Radiation with Gases

by

C. Grey Morgan

Introduction

1 Since the first announcement by Terhume only four years ago that electrical breakdown of gases can be caused by focusing the out• put of a giant pulse , there has been a tremendous growth of interest in the phenomenon.

Very many papers dealing with various aspects df ~he bre4k~ down have been published and already a healthy controversy appears to

be in existence concerning the mechanism by which ~ases can become almost perfect conductors in times of a few nanoseconds under the in­ fluence of relatively long wavelength light alone.

The observed phenomena are quite fascinating and may have far reaching consequences in our understanding of the mechanism of the interaction of radiation with matter.

The properties of the gaseous plasmas created by laser induced breakdown have also been studied extensively during the last few years~'J Laser produced plasmas offer several distinct advantages over those produced by conventional means. They can be created at very high den­ sities in gases or from pellets of materials of interest, for example, lithium hydride, under clinically clean,conditions in vacuo. These plasmas have a unique set of properties including isotropy and initial electronic and ionic equilibrium with zero rnomentun and current in the . These properties are of considerable practical importance in plasma physics and controlled thermonuclear research studies.

Q-switched and non-Q-switched laser beams have also been used to initiate electrical discharges between electrodes in . 4,5,6. switches. This is an application of laser induced discharges which may have several distinct advantages over more conventional triggered spark gap switches and impulse generators, especially at - 2 -

high . They offer good synchronisation prospects and are ?, 8 currently being applied, together with a form of laser radar in a search for clumps or microparticles 9 which are sometimes considered to be the cause of breakdown in vacuum 1nsu. l at1on. . 10

To gain some idea of the magnitude of the parameters involved we may take a typical experimental result, say the case of laser in­ duced breakdown in neon at 2000 torr. It is found experimentally 11 5 2 to require a ruby laser beam power density of about 10 Megawatts/cm •

Using Poynting 1 s theorems it can readily be shown that the associated electric vector field is a little less than lo7v/cm and the radiation pressure is 6 x 10 6 Newtons I m2 , i.e. about 10 12 times. grea t er th an th e solar radiation pressure on the earths surface. It is not surprising then that something violent happens.

Apparatus and Experimental Observations

The type of apparatus commonly used to study laser induced breakdown in gases is shown in figure 1. It consists essentially of a ruby or neodymium rod, an optical pumping system and a Q-switch, in this caso a Kerr cell shutter. This serves to suppress lasing action in the rod so that a very large population inversion, far above the threshold level, is achieved in the laser element. The shutter is then opened and coherent radiation, reflected between the mirrors, builds up rapidly and all the excess excitation is discharged in an extremely short time. The intensity of this giant pulse of radiation exceeds by several orders of magnitude that obtainable from an ordinary non-Q-switched laser flash.

The giant pulse is focused by a lens to a point in the gas con- tained in a vessel. The vessel is provided with electrodes for charge collection and windows for visual observation and to enable measure- ments of the optical characteristics of the breakdown plasma to be made. Breakdown in atmospheric air, for example, is observed as a bright blue flash at the focus of the lens and is accompanied by a distinctive cracking noise. Figure 2 shows an example of laser in­ duced breakdown in air at atmospheric pressure in which four closely spaced plasmas were photographed. In some of our work at CERN wo have observed two very widely spaced breakdowns from tho same laser pulse. - J -

In common with nll types of pulsed electrical discharges in gases, laser induced breakdown can. be divided into three distinct stages initiation, growth and extinction.

The initiatory stage is tha time which elapses between the arrival of the laser radiation pulse in the focal region of the lens and the initiation, by the release of and , of the growth of free and concentration in the gas.

The formative growth stage is the subsequent period of amplif­ ication in the number of charged particles until the state of break- down is reached. Breakdown is arbitrarily defined as the attainment of a. certain electron concentration. The combined duration of the initiatory and formative growth times is exceedingly small and may be only a few nanoseconds.

The final or extinction phase lasts for a time which may be

two, or three orders of magnitude longer than the duration of the la~~~ flash, - 50 microseconds compared to about 30 nanoseconds. During

this phase the plasm~ gradually dies away as a result of several pro~

cesses radiation, diffusion, recombination, attachment and s6 on~ 1

Initiation and Growth Mechanisms

Several physical processes have been proposed by various workers as the mechanism.s of initiation and orowth. These include

"cascade 11 or 11 avnlanche 11 growth by the quantum process of inverse

. t .b. . t • L • l • 1" • 11 • . 1 ,,_ 13 B remss rahl ung a sorp·ion w111c1 is pacysica y equiva~en~ t o exci• t - ation and ionisation caused by inelastic collisions between gas and the free electrons which draw en(ffgy from the electromagnetic

fi~ld Of the l~ser beam. Thfs is essentially an extrapolation to op- 1 '' tical frequencies (""10 ° Hertz) of well known microwave discharge l~, 15, 16, 17. th eory.

"ff t . . -" b t 18, 19. 20, .21, A d ~ eren view is proposeu y o her workers . ' 22, 23, who suggest that the observed growth of ionisation is the result of multiphoton absorption, that is the practically simultaneous ab­ sorption by ~n of several quanta, each having energy hV much less than the atomic ·excitatio!1 and ionisation energy. In th<:: case of heliti~ for example, no fewer than fourteen quanta from a rµby laser would' have to be absorbed simultaneously to release an elE;)ctron. The. process has been treated in terms of semi-classical field emission - 4 -

theory in which the electron is regarded as tunneling out of the atom in a tim0; which is small compared with the period of oscillation . . . 24, 25. of the laser electromagnetic radiation. An alternative proposal 26 is. that the initiatory electrons are released as a result of Thermal of the gas following

heating of the gas by non-linear absorption.

Most workers appear to prefer the cascade or avalanche growth of ionization which involves the absorption to radiation by electrons in free-free transitions and either collisional ionization or collie- ional excitation followed by photo-ionization.

The cascade processes require for their initiation, the presence of at least one free electron in the focal volume early in the duration of the laser flash. To fix ideas, consider breakdown -9 in air at atmospheric pressure:- the focal volume may be about 10 -8 to 10 cc, so that the presence of an electron requires an equilibrium concentration in the atmosphere of about 109/cc. This is comparable to that obtained in a and is certainly about a million times greater than the equilibrium density of ionization produced in the atmosphere by natural causes such as the passage of cosmic rays or the presence of local radioactivity and so on.

In the absence of an initic:::l electron, no breakdown can occur by the cascade process alone however large the intensity of the laser radiation. Consequently, if natural phenomena are relied upon to pro­ vide the initial electron,breakdown will be erratic and will occur only when an electron is fortuitously liberated at the focus during the laser pulse. The breakdown time lag will then be statistically distributed as in conventional discharges. 27 However, no significant randomness is observed in the onset of laser induced breakdown. Ob- . 28 29 served fluctuations ' 'are far too small, indeed, by.several orders of magnitude to be attributable to a random appearance of initiatory electrons and in fact there does not appear to be a significant init­ iatory time lag.

In view of these facts it follows that laser induced gas break­ down is unique insofar as it apparently requires no (~xternal source of ionization to initiate the breakdown process. This implies that the laser flash itself supplies the initiatory electrons in times of the order of a nanosecond. - 5 -

This conclusion at once raises tho important question of h~w the laser radiation interacts with the atoms to release electrons.

We will defer seeking an answer to this question for the time being and turn to examine some of the characteristics of the so-called cascade or avalanche processes of growth.

Cascade Processes extrapolation to optical frequencies

It is not· unnatural to rittempt to explain laser induced br,;ak~ down in. terms of an extrapolnt1on. of class1ca. 1 14' 30' -31 m1.crowave. br.eakdown, theory. Indeed, many of the characteristics of laser induced breakdown bear a strong r<;semblance to pulsed microwave clischarg.es.

In treating the problem 1 we can tak;.i advantage~ of the fact that although five parameters c:.re involved, namely the ionisation potehtial of the gas atoms, the associated with the laser beam, the wavelength of the laser light, the mean: free path of the charged

particles in the gas and the size pf the focal region. there ~re bnly two basic variables, namely and centimetres.

We can thus introduce the concept of 11 proper variables 11 which are found to be so useful in direct current and high frequency elec• trical discharges, namely E/p or E/N and pA or N/W in which E,N,p,A and W are respectively the electric fi6ld, the number of gas atoms per cubic centimetre, the gas pressure, the wavelength and the angular fre- quency of the laser light.

We can also introduce an effectiv0 electric field E which e produces the same energy transfer as a steady electric field and which is given by

~----- i ; I' Erms I Ve Erms Ve ' Ee/N /N ,'- ~ ,I I i laser i' "'I./. - I 1--- i laser i I (1) I ! N __ l l Jv2+w2 w _J _j For,some of the noble gases (Vc/N), the ratio of electron collision frequency to atomic concentration, takes on various charac- teristic approximately constant values, so that in the case of helium at atmospheric pressure, for example, the effective field E and the e field of ruby laser radiation are related by

Er ms (2) ruby

If we now assume that during the lnser flash the electrons very rapidly - 6 -

acquire the same electron energy distribution as they would under the equivalent static field, i.e. if we assume that the electron energy distribution function is the same for static and optical frequency fields, we can relate measurements of the Townsend primary ionization coefficient x/p and excitation coefficient 8/p and excitation made with static fields E to the optical frequency ionization coefficients (~ Vi/N and Vex/N under the corresponding optical frequency field 1.55 x 103 E and similarly for the electron diffusion coefficient D.N. e These data may be used quantitatively in evaluating the laser radiation intensity or electric field required to produce ionisation and breakdown if we can derive a suitable breakdown criterion, i.e. if we can deduce what conditions must be satisfied to ensure that some initial arbitrary electron concentration will grow under the influence of the laser radiation. Figure 3 shows values of excitation, ioniz­ ation and collision frequencies as well as electron diffusion co- 32 efficients obtained from measurements using Neon.

Breakdown Criterion for Laser Produced Discharges

The dynamic characteristics of electrons in any type of elec­ trical discharge can be expressed as lO.

)n ( q - Rn2 - anN) av - ( (DVn + nW ) dS (3) ! )t which represents the balance between generation and loss of electrons in a volume V bounded by a cloud surface s. The factor q represents 2 the rate of electron generation by any means, the term Rn represents the rate of reduction in electron concentration n by recombination with ions and the term anN represents the loss of electrons by attach- ment to n0utral gas atoms. The term - D grad n is of course the diffusion loss rate and, if there is a unridirectional drift of elec- trons with mean velocity W the term involving W represents electron loss by drift through the closed surface s.

This integral equation can be transformed using Gauss' theoreum to a differential equation, which for our present purposes we will deliberately over-simplify by the neglect, during the very earliest stages of growth, of the drift, attachment and recombination terms - these can readily be included in the analysis but complicate the analysis. - '1 -

On this basis we can express the rate of change of electron concentration as dn -· ·1r2 2 :::: q + :Uv n I ( t, r) i N + Vi 1I ( t, r )i n + DV n .) t in which (I) is the photoionization frequency to allow for the poss­ ibility of ionization by first or second harmonics of very low ioniz­ ation im)uri ty atoms and Vi is the total ionization frequency by electron impact and includes collisional excitation followed by rapid pho t 01on1za. · · t'ion 16 - 1n· th e no bl e gases, resonance ra a·ia t· ion 1s· 1.,1Ke 1 y to be trapped in the focctl volume for significantly lone times. Es­ timates bc_sed on the Holst,.oiin-Bikerman theory show, for example in .the case of helium, ultra-violet radiation can be trapped for about 50 nanoseconds in a focal volume of about lo-9cc there is no effec- tive loss of excitation energy.

The coefficients and Vi are non~linear functions of the beam

intensity,. which itself i..s o._ function of spc1ce and time in the focal volume even in the diffraction limited case there will be a pro- nounced spatial distribution of laser beam intensity and hence electric

field in accordance with the Airy pattern. The electron diffusion.. coefficient D will also be a function of position and time as the elec- tron and ion concentrations grow, becoming smaller as the charge den- si ty incre£~ses.

For the very earliest stages of growth, we raay write an app­ roximate solution of the continuity equation (4) in the for~

n (r, t) n 0 exp (A.t) ( 5) in which the tenpor.::i.l growth constcmt A is given by

Vi D/ 2 (6) where. ·.. is the diffusion length cui.d ]•. •'c.• n me.:1sure of the ~verage dis- tance, en electron will travel from the point c.t which it is created to the point nt which it lceaves the region where the

Clearly when Vi D/ 1 \ 2 any initial electron distribution will increase temporally and so, for the oversioplified case we have con­ sidered, we can write the following bre~cdown critereon - - 8 -

-2 Vi/D ,~, (?)

We can also express the time taken for the initinl electron concen­

tration n 0 to increase to some particular final value nf by

b = ). (8)

Clearly r~ will always be less than the duration of the laser flash.

Using the breakdown critereon (7) and the collision frequency excitation and ionization frequency data as well as diffusion co­ efficients of figure 3 we can estimate threshold fields and growth constants for various values of Figure 4 shows the balance bet-

ween ionization, excitation and diffusion loss rates for differentA 1 s for Neon at atmospheric pressure. The points of intersection give the threshold field and illustrate how the threshold field should increase as the diffusion length decreases. Figure 5 shows the variation of the growth constant A with laser field. It is interesting to note

that the values of A are about eight orders of ~ngnitude larger than those observed for growth of ionization currents in the noble gases between electrodes involving secondary ionization processes.

We can, in addition to estimating threshold levels and growth constants, also deduce other characteristics of a more general nature from our extrapolation of classicnl microwave breakdown theory to optical £requencies. We can, for example in the case of the noble gases, obtain an expression for the laser beam intensity required for the <,;;.nac:t of breakdown by equating the number of collisions needed to gain ionizing energies to the average number of collisions made by an electron before it diffuses out of the region of high field. In this way it is possible to deduce a relation which predicts a threshold dependence on the ionization potential of the gas Ei and upon the square of the ratio of radiation angular frequency W to the collision frequency Ve and an inverse dependence on the square of the diffusion length i.e. I 1 as er =

Again we can show that the lowest threshold field will occur when the radiation frequency resonates with the electron collision frequency. This follows by noting that the rate of gain of energy de/dt is given by

2 d£ w Ve -dt = 2 2 W + Ve - 9 -

and that this function has a maximum when w = Ve. Consequently we would expect a minimum in the graph of threshold or breakdown field versus gas pressure when tho pressure is large enough to make Ve = w.

While these arguements may seen plausible, it is nevertheless exceedingly difficult to test them to a high degree of precision by making a comparison of the theoretical predictions with experimental results. Most of the work using has been carried out using

commercial grade gases while relevant data on excitation, ionization and diffusion coefficients have been obtained with carefully. purified samples. The coefficients, especially for the nubl0 gases are exceed- ingly sensitive to suall traces of impurities.

Again, the analysis is based upon the assumption of constant spatinlly and tempornlly invarinnt mean fields wh.c}roas the output of the high power lasers used is complex there are several ~ossible laser modes in which the beam en13rgy is spr,:;ad in a complicated way and between which thore is an unknown degree of coupling. (Neverthe-

1 ass· th ere is· some ev1·a ence 33 wh' ic h in· a··ica t es th a t 1·t ~·is the mean power which is the important factor governing breakdown, i.e. tho on­ set of breakdown appears to be independent of instantaneous fluctua- tions).

Despite these uncertainties, we will proceed to make compar­ isons between experiment and the predictions of tho cascade theory which may bo summarized as follows : (1) We would expect the breakdown threshold to be higher for neon than for helium. This is confirmed by the experimental results of Haught, Meyerand and Smith 34 as well as other workers.

(2) We would expect a minimum in the threshold field versus pres~ure curve, i.e. in the Optical frequency Paschen Curve. This conclusion too is confirmed by experinent, for example 35 in the work of Gill and McDoug~'.11.

(3) If the cascade process is active we would ex~ec~ a dependence of E on the diffusion length, i.e. we would expect E to diminish as the focal diameter increases. This is confirmed experhwntally by Minck and Rndo 36 whose results show the correct forn of the depundence required by - 10 -

our extrapolation of classical microwave thoory to optical frcH1uenci es.

(~) We would expect an rate. There does not appear to be n very clear or convincing demonstration of this, but work at the Westinghouse Laboratories by Waynaut and Ramsey is in broad agreement with the calculated times of Phelps on the basis of the cascade process.

(5) If the cascade process is responsible for the growth we would expect a functional dependence of the threshold intensity on 2 the parameter si w 2 2 Ve . and approximate calculations show that this agrees reasonably well for the noble gases. i.e. the dependence is of the right form. Thus all these results can be said broadly to support the view that laser induced breakdown is describable in terms of the cascade type of process.

However, there are some results which contradict this view.

If the cascnde process occurs we would .:.~xpect, as WG he.ve shown n mono­ tonic increase in laser intensity at breakdown with the angular fre-

quency of the laser radiation. This is ~ observed experimentally.

A cc.reful s t uayi b y T om 1.inson 37 and his co-workers, using the fun- damental and first harmonic radiation from ruby and neodymium lasers showed a pronounced mnximum in the dependence of the breakdown field on frequency.

We may conclude from this comparison that extrapolation of microwave breakdown theory to optical frequencies goes a long way towards explaining most of the observed characteristics of laser in- duced breakdown but not all of them. Certninly it leaves unanswered

the question of the origin_..2}'_ _!..he initial c;_l~~ which is essential to the whole of the theory.

Let us now examine the main alternative proposal - the so-called rnultiphoton absorption mechanism. The rnain predictions of this theory 18 may be summarized as follows -

(1) The threshold photon intensity should be almost independent of pressurG. - 11 -

(2) The threshold photon flux density should vary with focal -1/N volume V and V v where NV is the number of photons which must be absorbed by an atom to excite it to the first excited state, 12 in the case of helium.

(J) Since the number of atoms ionized per unit time in u given photon flux depends on the number of gas atoms the growth will be approximately linear in time.

None of these predictions appear to be confirmed by experiments - the calculated braakdown intensities Clre o.11 one or two orders of magnitude greater than those £ound experimentally. Thus there is little or no experimental support for the many photon treatmeµ.t. Nevertheless there appears to be general, if tentative agrQeme?t, that

multiphoton absorption might conceivably account for the es~ential initial electron required by the cascade process. i.e. the multiphoton process provides the initiation mechanism and the cascade process is responsible for the subsequent growth. Even so many workers find it necessary to assume the presence, in the very small region of intense electromagnetic field at the lens focus, of small traces of low ioniz­ ation potential impurities or even dust particles, to support the multiphoton treatment.

Thus we are faced with a most unsatisfactory state of affairs insofar as neither the cascade nor raultiphoton theories, either singly or jointly, adequately account for all the observed experimental facts concerning laser produced breakdown of gases. Neither gives a satis- factory account of the interaction of rndiation with matter.

However there is a further alternative theory of the interaction 38 of rndiation with matter which was proposed by Davidson some twenty years ago in which lw draws attention to the many inconsistencies in the theory of quantum electrodynamics. These are notably concerned with the appearance of divergent integrals and modern quantum electro­ dynamics has the important drawback that in order to remove the diver­ gences which arise additional concepts have to be introduced which are neither contained in the fundamental formulation of the theory nor reflected in its basic equations.

Davidson has pointed out that the Scllrodinger or Dr·iac equations are incomplete only in that they neglect the force on tho electron due - 12 -

to its own field and he develops a theory which avoids the difficulties which are inherent in the concept of a quantized radiation fieldo His non-photon theory leads to precisely the same formula for tran- sition rates for various processes as well as the same predictions, e.g. the Planck black body radiation formula, the relativistic Compton Scattering formula and others which are often quoted as evidence of the quantized nature of radiation fieldso

It is thus of considerable interest to note the work of Keldysh 39 and of Bunkin and Prokhorov in which they develop the concepts of how a non-quantized radiation field l.eads to excitation and ionization. They show that if the interaction time between the atom and the elec­ tro-magnetic wave is sufficiently large, atomic ionization is much more probable than excitationo This might well account for the release of the initial electron required by the cascade theories.

Clearly, many more careful experiments under clean conditions must be carried out, and further detailed theoretical analysis, in which due attention to the coherent nature of laser light and the possibility of photon coupling, are needed before we can arrive at a complete understanding of the fascinating phenomenon of laser in­ duced breakdown in gases.

c. Grey Morgan

PS/63.-32 cas. n E F E R E N C E S

1. Terhune, R.W. (1963), Third International Symposium on Quantum Electronics, Paris.

2. Meyorand, R.G. and Haught, A.F., (1963), Phys. Rev. Letters,

1:2:. 1 L101 •

3. Haught, A.F. and Polk, D.H., (1965), Report on Conference on Plasma Physics and Controlled Thermonuclear Research, Culham, September 1965.

4. Pendleton, W.K., (1964), AF-WP-O., Sep.63.M. U.S.A.F. Report. Pendleton, W.K. and Geunther, A.H., (1965), RGv.Sci.Inst.36, 11.

5. Bleeker, J., Morgan, C.Grcy (1965), CERN Reports, NPA/Int.65-30 NPA/Int.65-31

6. Deutsch, F., (1967), CERN Report MPS/Int.MA 67-2.

7. Morgan, C.Grey (1967), To be published in Lasers et Optique non conventionelle. Rappori; (iu Premier Congres au Lasers, Paris, July (1967).

8. Morgan, C.Grey (1966), CERN Report NPA/Int. 66-24.

9. Cranberg, L. (1952), J.Appl.Phys., 23, 518.

10. Morgan, C.Grey (1965), 11 Fundamentals of Electric Discharges in Gases 11 Vol,. I I, Part 1, Handbook of Vacuum Physics, Editor - A.H. Beck, Pergamon Press, Oxford.

11. Smith, D.C. and Haught, A.F., 1966, Phys.Rev.Letters, 16, 2~, 1085.

12. Wright, J.K. (196l.t), Proc.Phys. Soc., 84i 41. lJ. Browne, P.F., (1965), Proc.Phys.Soc., 86, 132J.

14. See for example - ~rown, Sanborn, c. (1959), Basic Data of Plasma Physics, John Wiley, New York.

15. Tomlinson, R.G., (1964), Proc. I.E.E.E., 52j 721. (1964), Ohio State Unive'i7Sity, Antenna Laboratory Report 1579.

16. Phelps, A.V. (1966), "Physics of Quantum Electronics", McGraw-Hill, 1966.

17. Zel 1 dovich, Ya.B. and Raizer Yo.P, (1965), J.E.T.P., (u.s.s.R.), Translation, 20, 772.

18. Tozer, B.A., (1965), Phys.Rev., 137, A 1665. - 2 -

19. Zernik, w., (196"-!), Phys.Rev., 135, A51.

20. Ibmeka, H.F., (1966), Physica, _32, 779.

21. Bebb, H.B. cmd Geld, t..• 1 (1966), Phys.Rev. H,3, 1.

22. Lielich, s., (1966), AeL2. Physica Polonica 30, 393.

23. Nelson, P. (1965), Rapport C.E,A., R2888.

24. Pc;rressini, E.R., (1966), 11 Physics of Qu.::mtum Electronicsn, P499, McGraw Hill, New York.

25. Keldysh, L.V., (1965), J.E.T.P., 20, 130/'.

26. Chalmeton, V and Papoular, R., (1966), C.R. Acad Sci., Paris 262.B, 177.

27. Morgan, C.Grey and Harcombe, D. (1953), Proc.Phys.Soc.B66, 665.

28. Tomlinson, R.G. and Daman, E.K., (1963), Applied Optics, 2 1 546.

2,9. Rizzo, J.E. and Klewe, R.C., (1966), Brit.J.Appl.Phys. ,l"?,1137·

JO. Allis, W.P., (196 ), Ifondbuch der Experimental Ph.ysics, Vol.22, Springer Verlag, Berlin.

Jl, Francis, G. (1960), Ionisation Phenomena in Gases, Butterworth, London.

32. Hughes, M.H., (1967), Ph.D. Thesis, University of Wnles.

33. Breton, C., Capet, M., Chalmeton, v. and Papoular, R., (1965) Proceedings of the Eighth International Conf. on Phenomena in Ionized Gases, Belgrade.

J1±. Haught, A.F., Meyerand, R.E. and Smith, D.c.,1966 "Physics of Qmmtum Electronics" p. 509 (McGraw-Hill, New York).

35. Gill, D.H. and Dougal, A.A. (1965) Phys.Rev.Letters, 15 1 22 V

524:, BL.cl) 0

J6. Minck, R.W. o.nd Rado, W.E. (1966), 11 Physics of Quantum Elec­ tronics11, p. 527 (McGraw-Hill 1 New Yo,rk).

37. Bus6her, H~T., Tomlinson, R.G. and Damon, E.K. (1965), Phys.Rev. Letters, 15, 22, 847.

JB. Davidson, P.M., 194:7, Proc.Roy.Soc., A.191, 542.

39. Bunkin, F.V, cmd Prokhorov 1 A.M., J.E.T.P. 19, 739. Back mirror Front mirror Focussing_ fens gp_ticaf £_umg_{Xenon flash tube} Electrodes Q-5W itch 5hulter

7 -----+---.,..-.,.

"Ruby or neodymium rod _}jjgl]_ p_ressure ionisation chamber

=Fig=.'=

.£&. 2 - Photograf2_h of 4 blobs o[{J_/asma

SIS/R/15520

Yi/N Yex/N cm~s~- 1

Neon

DN DN ___ ---}~-----

10-12-+------1------f- 10 21 10-IG 10-15 10- 14

E./N vcm.2

Fig,.5

D/A~ D jA2 (A= ID Jl.·) Y..t., Yex, Neon at 760 torr. sec.- 1 Idealized sPl!.erical tocus

DjA2 (A=IOOp)

10 7 -L------t------~ 10~ 10 7 10 8 E ruby. V cm_, Fiq. 4

IQ II

Neon at 760 torr A= JOO )1

10 10

Asec~'

Includes effect of~ excitation followed Direct ionisafla 10 9 bJ ionisation only

IOe-+--~~~~~~~-+--~~~~~~---1 10 6 10 7 108

£ruby Vcm-'

Fig. 5