Particle method for mathematical models with allocated ionization front

The kinetic equation for recoil electrons, which appears in the gas behind the photons’ front as a result of Compton scattering and photoabsorption, is considered. The electrons interaction with self-consistent electromagnetic field and ionizing scattering in the approximation of small energy transfer in collisions are taken into account. The self-consistent electromagnetic field is described by Maxwell equations. The conversion to ionization front proper time from laboratory time is done. The problem with initial conditions on the ionization front is considered. The process of the conduction current is considered. The delta-substitution, which reduces equation into identity, is constructed. So, the applicability of particle method for numerical simulation of ionized medium in ionization front proper time is justified.