Accelerated solution of the Boltzmann equation
- Univ. of Wisconsin, Madison (United States)
Methods are presented for accelerating a numerical procedure for self-consistent solution of a kinetic equation and Poisson's equation in Plasma simulation. The kinetic equation is solved using a propagator technique, although other approaches would also benefit from the accelerated procedure. The kinetic equation is solved in a phase space of at least one spatial variable and two velocity coordinates, (Z, V[sub z], V[sub p]). V[sub p] is in the direction perpendicular to Z. In these variables it is possible to advance the reduced distribution function g(Z, V[sub z]) in time very efficiently using several [open quotes]short[close quotes] time steps within a desired [open quotes]long[close quotes] step. We can then use the results of the [open quotes]short[close quotes] steps to find the quantities needed to calculate the change in the full distribution f (Z, V[sub z], V[sub p]) during a single [open quotes]long[close quotes] time step. In the case studied here, the electric field and,/or transition matrix in the (Z, V[sub z]) space are calculated from the reduced distribution, at each of C time steps of roughly one tenth of the plasma period. The full step is then for C/10 plasma periods, thus removing the limit on the integration imposed by the plasma period. Applications to an rf discharge are presented. 11 refs., 6 figs., 1 tab.
- OSTI ID:
- 5200512
- Journal Information:
- Journal of Computational Physics; (United States), Journal Name: Journal of Computational Physics; (United States) Vol. 106:1; ISSN 0021-9991; ISSN JCTPAH
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
700330 -- Plasma Kinetics
Transport
& Impurities-- (1992-)
99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
BOLTZMANN EQUATION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
EFFICIENCY
ELECTRIC DISCHARGES
EQUATIONS
MONTE CARLO METHOD
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
SIMULATION