Methods for Direct Solution of the Boltzmann Equation for Gas Discharges

Single-collision Monte-Carlo coupled with an electromagnetic particle-in-cell (PIC) code is being used to solve the Maxwell-Boltzmann equations for many applications including gas switches, electrical discharges, and modeling gas breakdown from an intense electron beam. In these and other applications, collisions with a weakly-ionized gas are handled on a collision-by-collision basis. To be accurate, the cross-section set must have a complete set of inelastic cross sections in addition to cross sections for elastic scattering and ionization. To avoid numerical plasma heating either the plasma Debye length must also be resolved or an energy-conserving particle push must be employed. Some way of also limiting an exponentially growing number of PIC particles must be implemented. Accurate representation of the ionization process requires a sufficient number of PIC particles in the tail of the electron-energy distribution function (eedf). This makes it necessary to have hundreds to thousands of PIC particles per cell which makes detailed modeling of complex 3D geometries computationally intensive.