An improved calculation scheme of electron flow in a propagator method for solving the Boltzmann equation

Abstract

In order to accurately evaluate the electron acceleration process in the time evolution calculation of electron velocity distribution function (EVDF) based on the Boltzmann equation, an improved scheme blending upwind and central differences is introduced into the propagator method (PM). While the previous PM based on the upwind scheme needs fine cells to obtain an accurate EVDF at low electric fields, the improved PM is robust against coarse cells, which allows the reduction of the cell resolution. Calculations of the EVDF in Ar under RF electric fields demonstrated that the blending scheme can provide satisfactorily accurate results even with cells about tenfold larger than the upwind case at low reduced electric fields below 1 Td, which leads to much shorter computational time because the reduction of number of cells satisfactorily compensates the complexity of the blending scheme. This technique has been built into a new user-friendly PM software named BOSPROM.

Particle Propagation and Electron Transport in Gases

“…The ratio of the scattered electrons that a destination cell receives is proportional to the solid angle of the cell subtended at the origin v = 0 of velocity space in case of isotropic scattering, and the sold angle Ω of a cell is given from dΩ = 2πd(cosθ) = 2πsinθdθ. Such a polar-ϵ configuration has been adopted not only for f (v, t) in velocity space in pulsed Townsend (PT) mode [76,84] but also for the steady-state Townsend (SST) mode [85][86][87], for the time-of-flight (TOF) mode [76,88,89], and rf [90] and impulse [91] fields as mentioned afterward.…”

“…Another recent improvement of the PM calculation is for calculations under low E/N conditions and rf E fields [90]. The polar-ϵ configuration has a tendency that the cells around the origin become more coarse than in the polar-v configuration.…”