J. Phys. D: Appl. Phys. 22 (1989) 623-631. Printed in the UK
`
`
`
`J Vléek
`
`Department of Physics, institute of Mechanical and Electrical Engineering,
`306 14 Plzeh, Nejedlého sady 14‘ Czechoslovakia
`
`Received 12 July i988, in final form 28 November 1988
`
`Abstract. A collisional—radiative model with an extended region of applicability is
`developed for an argon atom plasma. Atom—atom inelastic collisions and diffusion
`losses of the metastable states along with the electron—atom inelastic collisions
`and radiative processes are considered in this model, taking into account 65
`effective levels. Among the analytical expressions used for the corresponding
`cross sections. special attention is paid to those determining the set of cross
`sections for excitation by electrons from the ground state, owing to the possibility
`of utilising the formulae recommended in kinetic modelling studies of discharges in
`argon or in mixtures including argon atoms. The numerical method developed
`makes it possible to investigate the mechanisms by which the excited levels are
`populated in a non-equilibrium argon plasma characterised (even in the case of a
`non-Maxwellian electron distribution) by a set ct parameters, such as the electron
`kinetic temperature T9, the atom temperature T2, the ion temperature T,, the
`electron number density ne, the ground state atom population n,_, the discharge
`tube (or the plasma column) radius Fl and the optical escape factors /tmn and Am,
`which are dependent only on the quantities Ta, n, and R in many cases of
`practical interest.
`
`1. Introduction
`
`One of the simplifying assumptions made in basic
`equations describing the extensive collisional~radiative
`(CR) models (see eg. Bates et al 1962, Drawin and
`Ernard 1977, Fujimoto 1979, Biberman er at? 1982, van
`der Sijde er al 1984) is the use of the Maxwellian elec-
`tron energy distribution function (EEDF). However, it
`has been shown by many authors that this assumption
`is unjustified for a wide range of physically interesting
`conditions in various gases.
`In our recent papers (Vlceli and Pelikan 1985,
`1986). we presented a numerical method which enabled
`us to extend the applicability of the existing extensive
`CR models for the argon atom plasma with the Maxwel-
`lian distribution function (Giannaris and Incropera
`1973, Katsonis 1976. Gomés 1983, Van der Sijde et al
`1984. Hasegawa and Haraguchi 1985) to the region
`in which the actual EEDF differs appreciably from the
`Maxwellian form.
`A substantial feature of this method is a numerical
`solution of the Boltzmann equation (Vlcek and Pelikan
`1985) for the EEDF in a non—equilibrium argon plasma
`
`0022-3727/89/050623 + 09 $02.50 © 1989 IOP Publishing Ltd
`
`characterised by a set of parameters, such as the elec-
`tron kinetic temperature T3. the atom temperature T3,
`the ion temperature T3, the electron number density rte
`and" the ground state atom population n1, which are in
`accordance with the usual input parameters of the basic
`equations for the CR models.
`Here. our objective is to present an extensive CR
`model which may be applied to argon discharges in a
`wide range of practically interesting conditions.
`We have used the slightly corrected argon atom
`model of Drawin and Katsonis (1976) which includes
`65 discrete effective levels and refiects the actual atomic
`structure.
`
`In addition to the possibility of using a realistic
`EEDF. two further modifications have been carried out
`in the usual formulation of the basic equations for the
`CR models: the atom—atom inelastic collisions and the
`diffusion losses of
`the two metastable states are
`considered.
`
`In choosing the analytical expressions for the cross
`sections, we have taken into account the most recent
`experimental and theoretical results available for argon
`in the literature. In particular. we have used extensively
`
`623
`
` ILLETTE 1411
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