Analytical models for electron-vibration coupling in nitrogen plasma flows

A model for the electron-vibration energy exchange in nitrogen based on a Landau-Teller-type rate equation is presented. Analytical expressions of relaxation times are derived for cutoff harmonic oscillator and Morse oscillator approximations, assuming that the relaxation proceeds by way of a continuous series of Boltzmann distributions over the vibrational states. Comparisons with the direct numerical integration of the master equation have shown that the use of a two-temperature relaxation time allows accurate modeling of the nitrogen vibrational energy relaxation rate for various conditions encountered in high-enthalpy flows with electron and vibrational temperatures up to 40, 000 K.