An Improved Calculation Scheme of Electron Flow in Propagator Method for Solving the Boltzmann Equation

An improved technique to solve the Boltzmann equation by the propagator method (PM) has been investigated. In the previous PM, the time evolution of electron velocity distribution function (EVDF) due to the electron acceleration was calculated using the upwind scheme. This scheme needed very fine cells to obtain an acceptable calculation accuracy at low electric fields. In the improved PM, the upwind and the central differences are blended in a certain ratio to calculate the electron flow stably. The PM calculations for the EVDF in a gas mixture of Ar and Ar metastable species under RF electric fields have been carried out to verify the improved scheme. Unlike the previous PM, the present results are little affected by the cell resolution. At low electric fields below 1 Td, the improved calculation can provide satisfactorily accurate results even with cells an order of magnitude larger than the upwind case. Considering the acceptable error, the total calculation time of PM can be reduced because larger cells are allowed and the complexity of the blending scheme is compensated by the reduction of the number of cells. The robustness against coarse meshes makes the PM calculation much more efficient. This feature has been built into a new user-friendly program named BOSPROM^® to enable the accurate and practical electron swarm analysis under RF electric fields.