A two-dimensional model of glow discharge in view of vibrational excitation of molecular nitrogen

A two-dimensional model is suggested of dc glow discharge with parallel electrodes. The model includes equations for electron and ion concentrations, which are related to the Poisson equation for electric potential. The collision ionization and electron-ion recombination are described using empirical relations. Processes of vibrational excitation of $\mathrm{N}_2$ molecules are considered. The vibrational kinetics of nitrogen are described in view of excitation by electron impact, vibrational exchange, and vibrational-translational relaxation. The finite-difference model used for solving kinetic equations is described. Results are obtained for a two-dimensional model of glow discharge in nitrogen at a pressure of $5$ torr and an emf of $2000$ V. The obtained fields of distribution of electron temperature and populations of vibrational levels of nitrogen are analyzed. The results enable one to estimate the fraction of electric field energy utilized for the excitation of vibrational states.