Monte Carlo analysis of the electron thermalization process in the afterglow of a microsecond dc pulsed glow discharge

A Monte Carlo model is utilized for studying the behavior of electrons in the afterglow of an analytical microsecond dc pulsed glow discharge. This model uses several quantities as input data, such as electric field and potential, ion flux at the cathode, the fast argon ion and atom impact ionization rates, slow electron density, the electrical characterization of the pulse (voltage and current profiles) and temperature profile. These quantities were obtained by earlier Monte Carlo - fluid calculations for a pulsed discharge. Our goal is to study the behavior of the so-called Monte Carlo electrons (i.e., those electrons created at the cathode or by ionization collisions in the plasma which are followed by using the Monte Carlo model) from their origin to the moment when they are absorbed at the cell walls or when they have lost their energy by collisions (being transferred to the group of slow electrons) in the afterglow of the pulsed discharge. The thermalization of the electrons is a phenomenon where the electron-electron Coulomb collisions acquire a special importance. Indeed, in the afterglow the cross sections of the other electron reactions taken into account in the model are very low, because of the very low electron energy. We study the electron energy distributions at several times during and after the pulse and at several positions in the plasma cell, focusing on the thermalization and on the behavior of the electrons in the afterglow. Also, the time evolution of the rates of the various collision processes, the average electron energy, the densities of Monte Carlo and slow electrons and the ionization degree are investigated.