Integral propagator method as a kinetic operator to describe discontinuous plasmas

Abstract

We present a path-integral-like method to numerically solve drift-diffusion equations for plasma physics. The algorithm uses short-time propagators as approximate Green's functions that tend to smooth typical discontinuities arising in plasma dynamics as, for instance, the effects of plasma-wall interaction or localized particle flows. The usual numerical schemes based on differences may fail to represent these abrupt conditions by inducing numerical viscosities and instabilities. However, the robust mesli-free computational integral method has been proved to be unconditionally stable in the simple case of no imposed restrictions by boundary conditions. The extension of the method to deal with boundary value problems is analysed. The advancing scheme is also useful to deal with the merging of natural discontinuities in the system as those induced by the effects of electromagnetic fields generated by charge separation as well as for the existence of two differentiated plasma regimes. In any case, the kinetic equation may have drift and/or diffusion coefficients that are likewise discontinuous. The method works almost being numerically insensitive to these discontinuities, leading to feasible physically meaningful solutions. The scheme works as an effective integral kinetic operator even for Fokker-Planck equations connecting two different dynamical statistics, like Maxwell-Bolt.zmann and Fermi- Dirac ones. It is robust to describe spatially heterogeneous plasmas.