Monte Carlo simulation of resonance effects of electron transport in a spatially modulated electric field in Ar, N$_2$ and their mixtures

Abstract

The relaxation of the distribution function of the electrons drifting under the influence of a homogeneous electric field in noble gases is known to take place over an extended spatial domain at `intermediate' values of the reduced electric field, $E/N$. We investigate the transport of electrons in Ar and N$_2$ gases, as well as in their mixtures at such $E/N$ values ($\sim$ 10-40 Td). After discussing briefly the basic scenario of relaxation in a homogeneous electric field, the major part of work concentrates on the properties of transport in an electric field that is spatially modulated within a finite region that obeys periodic boundaries. The spatial distribution of the mean velocity, the mean energy, and the density of the electrons, the importance of the excitation channels, as well as the electron energy distribution function are obtained from Monte Carlo simulations for various lengths of the computational domain, at different mean values and degrees of modulation of the reduced electric field. At low modulations, the spatial profiles of the mean velocity and mean energy are nearly harmonic, however their phases with respect to the electric field perturbation exhibit a complex behaviour as a function of the parameters. With increasing modulation, an increasing higher harmonic content of these profiles is observed and at high modulations where an electric field reversal occurs, we observe trapping of a significant population of the electrons. The effect of mixing a molecular gas, N$_2$, to Ar on the transport characteristics is also examined. Transition to local transport at high N$_2$ admixture concentrations and long spatial domains is observed.