The space-time-averaging procedure and modeling of the RF discharge

Journal Article · Mon Apr 01 04:00:00 EST 1991 · IEEE Transactions on Plasma Science (Institute of Electrical and Electronics Engineers); (United States)

DOI:https://doi.org/10.1109/27.106806· OSTI ID:5709112

Smirnov, A S; Tsendin, L D ^[1]

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1. Dept. of Plasma Physics, Leningrad State Technical Univ., 195251 Leningrad, Politechnichesaya 29 (SU)

This paper reports that one of main difficulties in modeling of RF discharges consists in the great distinction between the characteristic space and time scales of electron and ion motions. Straightforward modeling demands calculations of high accuracy over large space and time intervals. Great simplifications are obtained if the analysis of the fast motions and the averaging over them can be performed analytically and if numerical modeling of relatively simple, averaged slow-scale equations is to be performed. As an example of such an approach, the problem of electrode sheaths in the high-pressure RF discharge is discussed. Time-averaging over fast electron motions with the applied voltage frequency gives analytic expressions for the average electric field and average ionization density. The resulting, relatively simple equations for the ion density profile describe drift, diffusion, ionization, and recombination process. The simple scaling rules, the approximate expressions for the density profile in various regions, the sheath length, the ion density at the plasma-sheath boundary, and the dimensionless criteria for various discharge regimes can be deduced. For the nonself-sustained discharge, it is demonstrated that the ion drag towards the electrode and the diffusion results in significant lowering of the ion density in the sheath compared with the positive column at not too high a pressure. The analytic transition criterion from {alpha} to {gamma} formed of the self-sustained discharge is obtained. The numerical solution of the averaged ion equations yields the result which practically coincide with the results of full-scale modeling.

• OSTI ID: 5709112
• Journal Information: IEEE Transactions on Plasma Science (Institute of Electrical and Electronics Engineers); (United States), Journal Name: IEEE Transactions on Plasma Science (Institute of Electrical and Electronics Engineers); (United States) Vol. 19:2; ISSN 0093-3813; ISSN ITPSB
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
426000* -- Engineering-- Components
Electron Devices & Circuits-- (1990-)
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ACCURACY
BOUNDARY LAYERS
CORRELATIONS
DIFFERENTIAL EQUATIONS
DIFFUSION
ELECTRIC DISCHARGES
ELECTRON DRIFT
EQUATIONS
EQUATIONS OF MOTION
HIGH-FREQUENCY DISCHARGES
ION DENSITY
ION DRIFT
IONIZATION
LAYERS
MATHEMATICAL MODELS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA SHEATH
PRESSURE DEPENDENCE
RF SYSTEMS
SPACE-TIME
TIME DEPENDENCE