PLASMA PHYSICS
`
`Ionization relaxation in a plasma produced by a pulsed inert-gas
`discharge
`
`A. A. Kudryavtsev and V. N. Skrebov
`A. A. Zhdanov State University, Leningrad
`(Submitted September 29, 1981; resubmitted January 29, 1982)
`Zli. Tekh. Fiz. 53, 53—6l [January 1983)
`
`A model is developed for the initial stage of ionization relaxation in a pulsed inert—gas discharge plasma at
`moderate pressures for E/n. values corresponding to ionization levels nf/n{’>10““. 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 its as a
`function of the specific conditions. The proposed model is verified experimentally.
`
`PACS numbers: 52.25.Lp, 51.50. + V, 52.80.Dy
`
`of the excited states with k > 2 are almost always quasi-
`stationary. However, quasistationarity may be violated
`for the lower rnetastable or resonance levels when ne 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 "1 k-1
`1 in the collisional transition kinetics between excited
`states, it is helpful when describing the atomic distribu-
`tion over the excited states with l: > 2 to use the machinery
`of the modified diffusion approximation (MDA) theory,“s5
`which gives the quasistationary populations in terms of
`ne and n2.
`
`4. Since for E/n, in the range of interest the ioniza-
`tion ng/ni’ is much greater than 104, 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 [n1 < (5—’?) - 10” cm'3].
`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 describe the ioniza-
`tion relaxation using the following system of equations:
`
`1% : ninel3la ‘l‘ ""anrp2= ‘i’ ”2".l3st ““ vre»
`
`(1)
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`U —
`
`[;'l—’,n,)z,I(w
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`
`(2)
`
`Here 11,, n2, and tie are the atomic densities in the ground
`and first excited states and the electron density, respec—
`tively; km, kg, are the rate constants for the collisional
`transitions 1 -.+_ 2; file and p28 are the rate coefficients fol‘
`
`The study of ionization relaxation in 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/n1 and degree of
`ionization ne/n, 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 neg/n1 = 104-10-7 to 1o'5—1o‘4. We are
`mainly interested in analyzing the buildup of ne 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/n1 6 30-40 Td.
`
`THEORY
`
`In general, the increase in the electron density ne 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/n1 S 3 Td is much less than the characteristic ioniza-
`tion growth times (tr < 1 ;ts).2’3 Therefore, the kinetic
`electron coefficients do not depend on time explicitly but
`are functions of the parameters E/n1, ne/n1, and the na-
`ture of the ionized atoms.
`In what follows, we assume that
`these parameters are known either from published experi-
`mental data or from numerical solution of the Boltzmann
`kinetic equation?!“
`2'. If we use k to label the excited states (with k : 2
`corresponding to the first excited state), the populations
`
`130
`
`Sov. Phys. Tech. Phys. 28(l ), January 1983
`
`0038-5662/83/01 003006 $03.40
`
`30
`
`
`
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