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Time ‐ Dependent Multi ‐ Term Treatment of Plasma Electrons Acted upon by RF Electric Fields
Author(s) -
Loffhagen D.,
Braglia G. L.,
Winkler R.
Publication year - 1998
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.2150380406
Subject(s) - boltzmann equation , physics , electron , legendre polynomials , distribution function , monte carlo method , plasma , boltzmann constant , term (time) , ionization , computational physics , atomic physics , quantum electrodynamics , quantum mechanics , ion , mathematics , statistics
Using a new method for solving the time‐dependent electron Boltzmann equation in higher order accuracy, studies of the temporal behaviour of electrons in weakly ionized, collision‐dominated plasmas under the action of rf fields have been performed. The method is based upon a multi‐term approximation of the Legendre polynomial expansion of electron velocity distribution function and is applied to investigate the established periodic behaviour of the electron velocity distribution in helium, argon and CO plasmas. The results obtained in various approximation orders are discussed. The analysis has shown that the simplified treatment using only two terms of the velocity distribution expansion can fail in several conditions. In general, the four‐term approximation gives already a good representation of the convergent solution of the electron Boltzmann equation at each instant of the rf period. The discrepancies between two‐term and convergent results are found to depend sensitively on the specific atomic data, in particular on the magnitude of the various electron collision cross sections involved. Furthermore, the results obtained in the multi‐term approximation are compared with corresponding ones obtained by accurate Monte Carlo simulations. Very good agreement between convergent eight‐term Boltzmann and Monte Carlo calculations is found.