PLASMA PHYSICS
`
`ionization relaxation in a plasma produced by a pulsed inert-gas
`discharge
`
`A. A. Kudryavtsev and V. N. Skrebov
`A. A. Zhdmzou State Universim Leningrad
`
`(Submitted September 29, 1981; resubmitted January 29, 1982)
`lb. Tekh. Fiz, 53, 53-61 [January 1983)
`
`A model is developed for the initial stage of ionization relaxation in a pulsed inert-gas discharge plasma at
`moderate pressures for EMI values corresponding to ionization levels nf/rzf’le“. It is shown that the
`electron density increases explosively in time due to accumulation of atoms in the lowest excited states, An
`approximate analytic solution is found for describing the behavior of the time and spatial increase in he as a
`function of the specific conditions. The proposed model is verified experimentally.
`
`PACS numbers: 52.25.Lp, 51.50. + v, 52.80.Dy
`
`The study of ionization relaxationin a plasma when
`the external electric field suddenly increases is of great
`importance in many areas of gas discharge physics and
`its applications.
`Interest in ionization relaxation in inert
`gas discharges has been stimulated recently by the rapid
`development of excimer lasers excited by pulsed electri—
`cal discharges (see, e.g., Ref. 1).
`In the present work
`we study ionization relaxation in an inert gas plasma at
`moderate pressures when the electric field strength in—
`creases discontinuously and the ratio E/ni and degree of
`ionization ne/n1 vary over a wide range.
`
`In this paper we consider the initial stage of ioniza—
`tion relaxation when the ionization ne/n, increases from
`the initial value “co/“1 = 10‘3-~10"7 to 10‘5—10‘4. We are
`mainly interested in analyzing the buildup of he and the
`behavior of the spatial distribution of ne during the relaxa—
`tion process. We report experimental data on ionization
`relaxation in the range 8 < E/nt '6 30—40 Td.
`
`THEORY
`
`In general, the increase in the electron density lie in
`a plasma when the electric field E increases abruptly is
`described by a nonlinear system of kinetic balance equa—
`tions which cannot be solved analytically because of the
`usual difficulties.
`
`In this section we derive an approximate dynamic
`model of ionization that is based on theoretical results on
`various aspects of ionization relaxation in Refs. 2—9.
`
`1. When E/n, increases discontinuously, the relaxa-
`tion time for the electron energy distribution function for
`E/h1 S 3 Td is much less than the characteristic ioniza—
`tion growth times (tr < 1 us).2!3 Therefore, the kinetic
`electron coefficients do not depend on time explicitly but
`are functions of the parameters E/ni, rte/n“ and the na—
`ture of the ionized atoms.
`In what follows, we assume that
`these parameters are known either from published ez'rperi—
`mental data or from numerical solution of the Boltzmann
`
`kinetic exudation.“6
`
`2‘. If we use k to label the excited states (with k : 2
`corresponding to the first excited state), the populations
`
`of the excited states with k > 2 are almost always quasi—
`stationary. However, quasistationarity may be violated
`for the lower metastable or resonancelcvcls when [13 is
`small and radiation capture predominates. The balance
`equation for these levels must therefore be formulated
`in differential form after first combining the states into a
`single effective level characterized by an average energy
`and total statistical weight.
`
`3. Because of the importance of the transition k 2 ks
`1 in the collisional transition kinetics between excited
`states, it is helpful when describing the atomic distribu—
`tion over the excited states with k > 2 to use the machinery
`of the modified diffusion approximation (MDA) theory,“i5
`which gives the quasistationary populations in terms of
`he and n2.
`
`4. Since for E/n, in the range of interest the ioniza—
`tion rig/n? is much greater than 10“, we may neglect ra—
`diative processes and three—body collisions.
`
`5. The data in Refs. ’7, 8 on the rate constants for
`formation of molecular ions and excimer molecules show
`that we may assume that these processes have little in—
`fluence on the ionization growth rate when an electric field
`is suddenly applied to a weakly stabilized inert gas at mod-
`erate pressures [r11 < (5—7) '10” cm'a].
`It can be shown
`using the arguments in Ref. 4 that under these conditions
`the associative ionization channel is of minor importance
`compared with the stepwise ionization channel.
`
`Using the above remarks, we can desoribe the ioniza-
`tion relaxation using the following system of equations:
`
`.
`(3
`_% : fungi?” + ”Ensign + ulna?“ — VP“
` ‘
`(7712
`npzak,u
`71.275329
`nazzafist
`nzzlmli21
`V1,.
`.m— __ 21,21,152
`
`(1)
`
`(2)
`
`Here 11,, n2, and ne are the atomic densities in the ground
`and first excited states and the electron density, resper
`tively; km k2, are the rate constants for the collisional
`transitions 1 2'— 2; [he and 52e are the rate coefficients {01'
`
`30
`
`Sov. Phys. Tech. Phys. 28(1),.lanuaiy 1983
`
`0038-5662/83/0l 0030—06 $03.40
`
`GILLETTE 1106 .30
`
`GILLETTE 1106
`
`

`

`
`
`
`FIG. 1. Diagram showing the relative sizes of the electron
`fluxes in terms of the atomic energy levels for the slow (a)
`and fast (b) stages. The width of the arrows indicates the
`magnitude of the electron flux. The horizontal arrows give
`the diffusion fluxes of electrons and excited atoms reaching
`the walls of the discharge tube.
`
`direct ionization from the ground state to the first excited
`
`.1”ve1‘fist is a generalized coefficient for stepwise ioniza—
`’
`n from the quasistationary levels (k > 2); A21 is the
`
`taneous transition probability 2 —~ 1; 921 is the capture
`tor for resonance radiation, calculated using the Biber—
`
`"n—Holstein equations4; VI‘e and V 1"2 are the diffusion
`
`. es of the electrons and excited atoms, and are given
`proximately by Vl"k~.- nkVDk [for a cylindrical geometry,
`
`12(2 .4)2D1he}.
`L It can be shown using the MDA theory4 that
`
`a
`1 (my e-Elee
`23
`Ilznelagtz’h’hp37:52.17: T 75:.1-)1
`
`Estimates using the equations in Ref 4 show that
`under typical conditions (R > 1 cm, [11>>1016 cm 3,) the
`radiation capture factor is 621 —~10‘3—1O 4. Therefore, the
`effective radiative lifetime of level 2 is long and the level
`may be regarded as quasimetastable,
`Under these same conditions, the characteristic ex—
`cited atom diffusion times are TDZ u 10'3—10”2 s, so that
`we may neglect V F2 compared with ngnefi2e in (2).
`
`The above arguments Show that the three-level approx-
`imation can be used to describe ionization buildup under
`our assumptions.
`In dimensionleSS variables, the equa—
`tions for the ionization kinetics take the form
`
`(WV/0*. : DNM --{-- (31V ~ dN,
`0111/61: :- N _._ bNM,
`
`M: “2/”«01 N : ”ll/”wt
`b : ’140625/n1k12'
`
`t : till/1‘12,
`C Sign/km:
`
`M E“:o —_Mm
`d—_ van/711A}?
`
`(5)
`
`(6)
`
`Equations (5)-(6) easily yield the following relation
`between N and M:
`
` . 1 ' ~d 1— M
`
`
`
`N_1"lmM°' M‘IJ TCb
`”HUI—(211113)]
`
`('7)
`
`so that the solution reduces to a quadrature.
`
`Using the rate constant data in Ref. 5, we find that
`b << 1 and 0 << 1 in all cases of practical interest (E/ni <
`300 Td, ne/nl < 10—5).
`In a steady—state plasma, we usually
`have M0 ‘6 1 {Ref. 9].
`
`Using the smallness of b and c, we find from (5)~(7)
`that dN/dM m o — d + bMfl << 1 in the initial stage, i.e., the
`number of atoms in the first excited states increases
`
`rapidly for a relatively slow change in the electron density.
`The rate of ionization then increases with time and rises
`most steeply for M > c/b. For nearly stationary in values
`(M = l/b), so that n2 is changing slowly, there is an ex~
`p10sive increase in ne. The subsequent increase in he then
`reaches its maximum value, equal to the rate of excitation
`dN/dr = N(1 + c r d), which is several orders of magnitude
`greater than the ionization rate during the initial stage.
`
`The behavior of the increase in 118 with time thus
`enables us to arbitrarily divide the ionization process into
`two stages, which we will call the slow and fast growth
`stages. Figure 1 illustrates the relationships between
`the main electron currents in terms of the atomic energy
`levels during the slow and the fast stages.
`
`Since ne rises at an ever increasing rate (which is
`several orders of magnitude larger than the initial rate)
`
`Sov, Phys. Tech. Phys. 28(1), January 1983
`
`A. A. Kudryavtsev and V, N. Skrebov
`
`31
`
`e a
`
`mong/rt),
`
`(719/45- 10“)“ Ty”! (no—in cm’a. T — .in'eV),
`
`0.2, Hy:13.6 eV, x(m)—:§.485’’z‘hdp
`EV;
`0
`
`4V2se‘ F1 .-7 10-7
`(4)
`cm3/s.
`“Rf/1
`To facilitate comparison, we have retained the nota—
`used in Ref. 4.
`
`The nonlinear system (1)—(2) can be solved numerical—
`the coefficients and initial conditions are specified.
`gthe rate constants given in Refs. 5-8 for the various
`esses, we can make a series of simplifications making
`ssible to solve (1)--(2) analytically for E/ni and ne/nl
`\e range of interest.
`
`'Since 328 2 10—8—10"7 cm3/s [Reis. 5, 8], we see from
`lid (4) that the ratio 529/13 st of the coefficients for
`and stepwise ionization from the first excited level
`ds on I16 and on the electron temperature Te. For
`'1013 cm"3 and Te 3 1 eV, the stepwise ionization
`nel from levels with k > 2 is unimportant (fist << [126)
`Ruse most of the radiation escapes.
`
`

`

`1017
`
`rs,us
`
`e
`
`s
`
` FIG. 3. Duration T5 for a discharge in argon. p = 11.4 (a) and 3.7 [on
`
`1) at0 =1.s-1o” cm'“;2)2.7v10‘°; 3) 4.540”; 4) 6.4- 10‘";
`a:
`(b).
`5)10”; 6) 1.6-10”; b:
`1). 9.7- 109; 2) 3-10”; 3) 5-8'101°;4) 1.6-10”
`
`once steady conditions have been reached during the fast
`stage, ionization builds up explosively when the external
`field is constant (the kinetics of gas-phase reactions are
`classified in Ref. 10).
`
`We can solve Eqs. (5)-(7) analytically and thus analyze
`in more detail the behavior of ne(t) and n2(t) as ionization
`develops,
`
`Since bM < 1 during the slow stage, if we keep only
`the linear terms in bM in (7) we find from (5)—(7) that
`
`N :: bile/2 + (c _ (1)11! + '1 .— mug/2 ~ (c — d) Mo,
`T:
`N
`b\/|A|
`
`(8)
`
`x
`
`\
`
`(b:11+c~.z_b\/;‘A[)(t.v +c—d—i—nga—M_ o
`ii
`
`i
`2 n W+c~d+WiADM/He“aw-Wm).’ A<0’
`(
`bill
`'
`93)
`+c—d]_amg[bilo+cwd
`arctg[
`bVl'Tl
`mm ],
`.4>0,
`(9b)
`
`where A is given by
`
`A 3 (21/12) H [Mo + (c — Lima]?
`
`(10)
`
`and describes the relative contribution from the various
`processes in (5) for small times.
`
`The conditions for ne to increase with time are that
`ionization should always develop eventually if A > 0; if
`A s O, the condition is that bM0 + c > d,
`
`It can be shown using (6), (7) that the curve M(T) has
`an inflection point at M1 = N1 - (c - d)/b 2 0.8/b, after
`which M changes slowly. Since M1 differs from the sta—
`tionary value by 20% and the various rate constants are
`only known to within a factor of two,5 may assume without
`any loss of accuracy that at subsequent times the ioniza—
`tion has become stationary:
`
`1
`
`-~_
`
`lnN
`1
`7V?
`(Hue—d)
`The rate constants for the elementary processes are
`known accurately enough to permit Eqs. (9) above to be
`used to describe the time changes in he and n2 as far as
`the inflection point M = N11.
`
`(11)
`
`and taking the first arctangent in (9b) equal to 77/2. Equa~
`tion (11) shows that the characteristic time for the fast
`stage is 7 k1 ln(N/Ni) << 7's. We see by inspecting the fem
`of the above solutions that n0 builds up explosively with
`time.
`
`It should be emphasized that the reason for this be-
`havior in ne(t) is quite universal and can be traced to the
`fact that we almost always have {3m << km-
`
`The explosive increase in ne(t) is most apparent when
`A > 0, which correSponds to early times and small direct
`ionization.
`In this case, he does not increase more than
`tenfold prior to the onset of explosive growth [M > «1275],
`
`These expressions can be used to determine the limits
`of applicability of the two simplest ionization models which
`are often used in practical calculations.
`'These are the
`direct ionization model, in which the ionization is deter—
`mined by the appropriate rate constant or by the first
`Townsend coefficient, and the “instantaneous ionization"
`model, in which the ionization rate is taken equal to the
`rate of excitation. Equations (8)—(11) imply that direct
`ionization predominates only for times 7‘ < T1 (M = V275)
`after the field is applied, and that the "instantaneous ioni-
`zation" approximation does not become valid until times
`t m Ts after the field was first switched on.
`
`E XPERIMENTAL RESULTS
`
`We studied ionization relaxation in He, Ne, Ar, and Kr
`for initial gas densities n, = (0.5—5) - 10” cm‘3 by applying
`an additional electric field to the preionized gas. The
`discharge occurred inside a cylindrical tube of diameter
`2R = 2.5 cm and the distance between the electrodes was
`L = 52 cm. The gas was preionized by applying a dc cur-
`rent ip = 0.5—20 mA. The parameters of the positive plas'
`ma column were calculated using the theory deveIOped
`in Ref. 9 from the experimentally recorded current denSiL‘j
`and ED/n, values. The initial density net) on the axis varid
`in the range 5.1094 .10“ cm-3.
`
`A voltage pulse with rise time (1 ~2) - 10"7 s of positivc’
`polarity with respect to the cathode was applied to the
`tube using a specially designed electrical circuit. The
`electric field was measured using several detectors
`soldered into the tube along its axis. The total voltage
`across the tube and the voltage between the probes were
`recorded byacapacitative divider (C1: 2 pl“ and C2 .—-- 100
`pF) capable of transmitting rectangular pulses with rise
`time ~ 10"7 8 without appreciable distortion. The dis~
`charge current was recorded using a zero~inductance
`
`Equations (9), (11) derived above readily yield expres—
`sions for the characteristic times of the slow and fast
`stages. Since we have bM + c — d >> bfW prior to the
`start of the abrupt rise in ne, the duration T3 of the slow
`stage can be found with sufficient accuracy from (9) by set—
`ting the first quotient in the logarithm in (9a) equal to one
`
`32
`
`Sov. Phys. Tech. Phys. 28(1), January 1983
`
`A. A. Kudryavisev and V. N. Skrebov.
`
`3?
`
`

`

`
`
`
`
`16'
`
`72
`
`11;
`
`75
`
`18
`
`07
`
`43
`
`FIG. 4. Curves for ‘rS vs. E/iu for a discharge in krypton; p =
`10.5 (a) and 6 ton (b). a:
`1.) na0 = 4.10” cm‘a; 2) no“; 3)
`1.5~1o”; 4) 3.3-10“; b: 1) 3,5-10‘”; mas-101°; 3) 1.6-
`101°;4) 3.2210”.
`
`.._._im.
`......1 ,.__l_.1_1._l_.._1 . i_i_..
`78
`Z0
`22
`2’!
`25
`36
`30
`w 15
`
`E/n, , Td
`
`:‘resistor connected in series with the cathode—to—ground
`section of the tube. The local dependences ne(t) were re—
`eorded by Observing the plasma emission intensity, which
`is proportional to 11% (p a 1). The density of the neutral
`*g‘as was monitored using the interferometric technique
`described in Ref. 11 and adual-trace oscilloscope was used
`for all the measurements. Special experiments were con-
`ducted to verify the unimportance of such factors as the
`.proximity of the shields and grounded objects or the shape
`and composition of the electrodes (we had pL > 200 cm -
`tdrr [Ref. 12]), which do cause appreciable effects during
`breakdown of a Cold gas”,13 We were also able to repro-
`duce the experimental conditions with high accuracy. We
`(measured E and the plasma emission intensity at different
`distances along the tube axis in order to find how the pa—
`'rameters of the gas discharge plasmavary along the tube
`{and ascertain the importance of various mechanisms in—'
`'yvolved in discharge formation after an abrupt increase in
`"the field strength.
`
`Figure 2 shows some typical measured curves. The
`Oscilloscope traces of the current (a), tube voltage (b),
`"voltage differences between the probes (c, d), and the emis-
`ésion from different regions along the length of the dis—
`"charge (e, i) show that after a high—voltage pulse is sud-
`rd'enly applied, the discharge current rises very slowly
`flflii' times t < ”('5 and the tube voltage remains almost con—
`r‘fstant. This is followed by a sudden rise in the current, ac—
`i'cOmpanied by a voltage drop across the tube. We also see
`t the field increases almost simultaneously (to within
`
`. 0‘7 s) over the entire length of the positive column and
`then remains constant for t < TS. The plasma emission
`{intensity from different regions along the length of the tube
`false starts to increase almost simultaneously and repeats
`the current trace.
`
`Our measurements revealed that for t < rs, ne/n1
`“creases by less than a factor of 102, i.e., we have ne/n1<
`5 at the end of the slow stage.
`
`A similar delay in the current increase has been noted
`many other workers when an electric field is suddenly
`lied (see e.g., Ref. 12). This lag might be caused by
`
`small velocity of the ionization wave down the tube from
`high—voltage electrode to the grounded electrode,”"4
`by onset of instability in the uniform quasistationary
`, Charge when the field is applied [possibly caused by
`
`:Pli‘deesses near the electrodes; of. Ref. 15]. Taken to—
`
`' Ether the above findings show that in any case, neither
`pagation of an ionization wave nor processes at the
`
`leotrodes determine the duration Ts of the slow stage.
`
`
`
`
`
`
`
`70
`
`70? 5‘
`kx’;
`r!“
`
`70
`
`
` ....._...
`
`l “i.
`.
`0 0.2 0.9 0.5 0,6
`r/fl
`Radial distribution nelr) as a function of time for A > 0 in an argon
`discharge.
`p = 11.4 tori“, neo = 1010 cm"
`3. rs = 39 us.
`
`FIG. 5.
`
`attributed to the finite time required for growth of ther—
`mal -lonization instability. Interferometric measurements
`show that for t < TS the gas density does not drop by more
`than 1%. Estimates using the equations in Ref. 16 reveal
`that for such small changes in hi, the growth time for
`thermal-ionization instability is much larger than 7'5.
`
`Thus, under our conditions the slow increase in he
`during the initial stage is due to the combined effects of
`kinetic processes occurring in the bulk of the discharge
`for constant E/nl, quasistationary electron energy dis~
`tribution functions, and ne/n1 values < 10"5.
`
`We now compare the experimental results for Ar and
`Kr with the theory developed above.
`
`The points in Figs. 3, 4 give the experimental values
`as a function of the Specific conditions (n1, neg, E/n1).
`Since in our experiments we had A > 0 [cf. (10)], Eq. (9b)
`implies that the duration of the slow stage is given by
`i
`
`Tszl/Ti"
`
`c—d2
`Vi — 7210;. + ”“5"“
`
`~___V172l1llo + (c ~ dub] ”
`
`'
`b
`c~d2 '
`
`__V1—7<m+—.-—>-
`
`The lag in rapid current buildup has often”’” been
`
` Sov. Phys. Tech. Phys. 28( l ), January 1983
`
`A. A. Kudryavisev and V. N. Skrebov
`
`33
`
`

`

`
`
`
`i
`l
`lJ-i—L g] L_l._1
`>__i
`.9
`75
`Z7
`Z7
`33
`.79
`1/5
`
`N.
`E
`0%:I:
`
`’7
`
`70
`
`70"
`
`67/7an
`1) “go/“1 =
`FIG. 6. The behavior of “e in the bulk of an argon discharge.
`10-3; 2) 10-7. Stepwise ionization predominates in region 1. direct ioniza—
`tion processes predominate in region 11, and ne does not increase in region
`111.
`
`The solid curves in Figs. 3, 4 give rs calculated from
`(12) using values for k”, 31c: and Bze from numerical cal-
`culations in Ref. 5.
`
`Equation (12) shows that for small E/np when A »—
`2/b, we have 7‘s =71/fT It follows that (nineo)12/ TS—
`(k12fi23)‘1/2-~ const for a fixed value of E/n1. For large
`E/nl we have A a 0, and 7’s -* 2/(neo,828 + nifiie- VDa)
`is only weakly dependent on neg.
`
`Figure 3a alsogives experimental values of the pa—
`rameter (n1neo)1/2'rs, which for 13/11,— const remains con»
`stant to within the experimental error for n80, hi, and Ts
`varying over wide limits. For large E/n‘ (Fig. 3b, Fig.
`4b] TS becomes almost independent of neo, as predicted
`by our theory.
`
`We also note that the function ne(t) calculated using
`(8)—(9) accurately describes the experimentally observed
`increase in the current and plasma emission. We thus
`conclude that theory and experiment are in both qualita-
`tive and quantitative agreement.
`
`The above equations can be used to analyze the time
`change of the radial distribution ne(r, t) when an electric
`field is suddenly applied to a gas for which the initial dis-
`tributions neo(r) and n20(r) are known. This problem is of
`interest in terms of understanding the mechanism re~
`sponsible for formation and constriction of the current
`channel in a pulsed discharge.17
`
`The solutions of system (5), (6) show how the initial
`distribution neo(r) is deformed when a field is switched on.
`In the situation discussed above (corresponding to A > 0)
`Eqs. (8)—(9) imply that the growth rate of ne(t) depends
`strongly on “em particularly for large values of A (A a
`2/b). This results in a sudden increase in the magnitude
`of the initial irregularities in ne(r) for t < 78. As an il—
`lustration, Fig. 5 shows curves giving the time dependence
`of ne(r) calculated from (9b) for E/n, = 12 Td and neo =
`1010 cm“3 for an argon discharge. According to Ref. 9,
`the initial neo and can distributions in a glow discharge
`at moderate pressures can be approximated by Bessel
`functions, and we took M0 = 0.1. Under these assumptions,
`we see that the theory predicts that the distributions will
`become highly nonuniform at times t S 7's after the field is
`turned on.
`
`For large E/ni. A < 0 and the growth of he during the
`slow stage [cf. (9a)] is determined by direct ionization.
`
`The form of the radial distribution ne(r) will then be Simi.
`lar to the initial distribution and no well—defined plasma
`column is produced. Our model thus predicts slight de-
`formation of the initial distribution 1160(1‘) for A < 0 but
`substantial deformation when A > 0.
`
`Experiments (of. Refs. 18, 19) have shown that ioniza.
`tion Occurs uniformly over a cross section of the dischapge
`tube when a field is applied to a preionized gas; however,
`if p > p0 the ionization is highly nonuniform and a narrow
`plasma column forms on the axis.
`In particular, for argon
`p0 = 1 torr for R 2 2—4 cm (R is the tube radius) [Ref, 13]
`and p0 = 2—3 torr for R = 1 cm [Ref. 19]. For discharge
`in helium, the experiments indicate that ionization is uni-
`form for pressures 6 10 torr when R = 1 cm.
`
`Our model accounts well for these experimental find.
`ings. Figure 6 shows calculated curves for a discharge in
`argon. We see that for pH < 1 cm ~torr, He cannot in—
`crease unless A < O.
`In this case ionization develops more
`uniformly in the bulk, in good agreement with experiment.
`Since for the heavy inert gases (Ne, Ar, Kr, Xe), 1‘12, file,
`{329, VDa all have the same order of magnitude, the cor—
`responding curves behave similarly for similar values of
`pH. Helium is an exception, since under our conditions
`VD“ is much larger and file much smaller than for the
`heavy inert gases. The region A < 0 Will therefore cor—
`respond to larger products pR, and this is also in agree—
`ment with the experimental findings.
`
`We have thus deveIOped a model for the initial stage
`of ionization relaxation in a pulsed inert—gas discharge
`plasma at moderate pressures for 13/11, values correspond-
`ing to equilibrium ionizations hoe/n? >> 10". We conclude
`from a comparison of the experimental Spatial and time
`dependences of ne that-the model is quite accurate. We
`have shown that the increase of he with time is explosive
`because atoms accumulate in the lowest excited states.
`Our results are important for analyzing the role of step—
`wise ionization processes in the buildup of instabilities
`('1’.or;
`in self—sustained and externally maintained discharges.
`Under our conditions, the above equations have the ad—
`vantage that they clearly exhibit the various ionization
`mechanisms, so that their specific effects can be studied
`as a function of the experimental conditions. Since the
`effects studied in this work are characteristic of ioniza-
`tion whenever a field is suddenly applied to a weakly
`ionized gas, they must be allowed for when studying emis-
`sion mechanisms in pulsed gas lasers, gas breakdown,
`laser sparks, etc.
`
`Phys. 22.
`
`‘A. V. h‘letskil, Usp. Fiz. Nauk 12g, 2'79 (1.078) [Sov, Phys. Usp. _2_1_. 502
`(1978)].
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`562 (1977)].
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`4I. M. Bibsrman, V. S Vorob' ev. and l. T. Yakubov, Usp F17 Nauk 1_0_'7
`353 (1972), 128, 233 (1979) [Sov. Phys Usp _1_5, 375 (1973) 22. 411 (19791
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`481 (1980) [Sov Phys. Tech Phys 25, 291 (1980)].
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`
`34
`
`Sov, Phys. Tech. Phys. 28(1), January 1983
`
`A. A. Kudryavtsev and V, N. Skrabov
`
`34
`
`

`

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`
`ahka. Moscow (1971).
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`
`:‘
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`i981).
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`
`'oscow (1975).
`
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`5:5 (1980) [Sov. Phys. Tech. Phys. 2E, 44-9 (1980)].
`
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`'feplofiz. Vys. Temp. lg, 1309 (1978).
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`in: Plasma Chemistry. B. M.
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`l’zD, N. Novichkov.
`in: Topics in Low-Temperature Plasma Physics [in
`Russian], Nauka i Tekhnika, Minsk (1070), p. 459.
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`
`Translated by A. Mason
`
` Sov. Phys. Tech. Phys. 28( 1 ), January 1983
`
`0038‘5662/83/01 0035-04 $03.40
`
`35
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