Electron-Vibrational Energy Exchange in Nitrogen-Containing Plasma: a Comparison Between an Analytical Approach and a Kinetic Model

This paper investigates the electron-vibrational (e-V) energy exchange in nitrogen-containing plasma, which is very efficient in the case of gas discharge and high speed flow. Based on Harmonic oscillator approximation and the assumption of the e-V relaxation through a continuous series of Boltzmann distributions over the vibrational states, an analytic approach is derived from the proposed scaling relation of e-V transition rates. A full kinetic model is then investigated by numerically solving the state-to-state master equation for all vibrational levels. The analytical approach leads to a Landau-Teller (LT)-type equation for relaxation of vibrational energy, and predicts the relaxation time on the right order of magnitude. By comparison with the kinetic model, the LT-type equation is valid in typical electron temperatures in gas discharge. However, the analytical approach is not capable of describing the vibrational distribution function during the e-V process in which a full kinetic model is required.