A PIC based procedure for the integration of multiple time scale problems in gas discharge physics
An efficient particle-in-cell (PIC) technique for studying electrical discharges over long periods of time is derived and validated on a train of several hundred Trichel pulses. The requirements on the time-step that particles must be displaced less than the grid spacing, and that it must be less than the characteristic times of source and sink terms, have been eliminated by deriving semi-analytic expressions for the position and density of the computational particles. The derivation assumes the electrical field to be stationary during the integration of the particles and the time-step has therefore to be less than the charge relaxation time. It must also be less than any other characteristic times present in the system. It is noted that the interaction of electrons with the background gas is the cause of the most important processes in gas discharges and plasmas in general, and these are the processes giving rise to new electrons and the other particles considered. For this reason the derived semi-analytical expression is applied only to the electrons, and the evolution of other kinds of particles is obtained from the electrons. In the test case considered with discharges between a sphere above a ground plane a speed-up of a factor of about 70 for integration particle positions and number of particles as compared to a standard PIC implementation is demonstrated, without noticeable loss of accuracy.
scientific article; zbMATH DE number 5526716