Time dependent multi-term solution of Boltzmann's equation for magnetised low-temperature plasmas

Abstract

We present details of the first time dependent multi-term solution of Boltzmann's equation for charged particles in gases under the influence of electric and magnetic fields. A Sonine polynomial representation of the velocity distribution function requires a time dependent weight function to accommodate arbitrary initial conditions and/or time dependent fields. The theory and code are benchmarked against an independent time resolved Monte Carlo simulation for both dc and rf orthogonal electric and magnetic fields. The results support the numerical integrity of the technique.

A multi term Boltzmann equation analysis of non-conservative electron transport in time-dependent electric and magnetic fields

“…For illustrative purposes we chose an applied electric field of 100 Td (1Td = 10 −21 Vm −2 ) to ensure the average energy of the swarm is in the range where some interesting kinetic phenomena may be induced. The theory and associated code have been benchmarked against an independent time-resolved Monte Carlo simulation [13].…”