Simulation of filamentation dynamics of microwave discharge in nitrogen

Abstract

The present study deals with numerical simulations of microwave discharges in nitrogen based on extended fluid-dynamic model. The set of governing equations for non-equilibrium gas-discharge plasma includes conservation equations for species number densities, electron energy density, Poisson equation for the electric field coupled to the multi-temperature Navier--Stokes fluid-dynamic equations taking into account thermal nonequilibrium; the power transmitted from microwave radiation to electrons is determined from the Helmholtz equation. The kinetic scheme includes 62 reactions involving neutral molecules and atoms in the ground and electronically excited states, ions and electrons. The set of equations is solved for a two-dimensional problem under conditions of experiments at a pressure of 40 and 50~Torr and different electromagnetic wave frequencies and pulse duration. The dynamics of discharge formation and transition from the diffuse to the filament form is studied. The results are compared with experimental data, and a good agreement is shown for the time larger than 10~$\mu$s. The possible reasons for discrepancies at a shorter time are discussed and the effect of small oxygen impurities on the quantitative characteristics of the discharge are evaluated. The presence of a small oxygen impurity and seed electrons in the region of discharge formation yields a better agreement between numerical and experimental data.