Calculation of electrical conductivity of fast discharges in nitrogen gas using the performance of a transversely excited N2 laser

Rate equations of a low pressure transversely excited (TE) nitrogen laser with variable electrode lengths and gap separations, along with the relevant equations for the electrical circuit, drift velocity, and Townsend ionization coefficients, are used to study the electrical conductivity of the low-ionized nitrogen gas. Two different functional dependencies of drift velocity and the Townsend coefficient of nitrogen gas on the ratio of the electric field to gas pressure, E/p, are used for the calculation. The results show that the electrical conductivity in the fast electric discharge of a few nanosecond time-scales is time and space dependent. For the low selected range of the E/p-value, the electrical conductivity and small-signal-gain behave similarly. For the high selected range of the E/p-value, on the other hand, it is observed that by increasing time and electron temperature, the electrical conductivity, corresponding to the discharge between two electrodes, enhances highly near the cathode for any excitation lengths. The dependencies of the electrical conductivity on gas pressure, electron temperature, gap separation, and electrode length are illustrated. The time behavior of the electrical conductivity and the gas resistance are also presented. This is the first report on the calculation of the electrical conductivity, where the performance of a TE gas laser is used to obtain the transient as well as the steady state behaviors of the electrical conductivity corresponding to a few ten nanosecond electric discharge in nitrogen gas. Details of the numerical calculation will be given in this report.