Vibrational–translational relaxation in nitrogen discharge plasmas: Master equation modeling and Landau–Teller model revisited

Vibrational–translational (V–T) relaxation is quite common in molecular nitrogen discharge non-equilibrium plasmas. In this paper, the energy relaxation in V–T transition is investigated by master equation modeling on all vibrational levels below the dissociation limit. The state-to-state transition rates are calculated by a forced harmonic oscillator (HO)-free rotating model. Meanwhile, the classic Landau–Teller model based on the HO of vibrational levels is revisited. First, the V–T relaxation in a heat bath is compared between the HO model, Morse’s anharmonic oscillator (AHO) model, and realistic vibrational levels by a direct-potential-fit analysis of spectroscopic data. The relaxation of average vibrational energy using the AHO model is faster than that using the HO model. Then, the influence of more frequent vibrational–vibrational (V–V) collision on the V–T transition in the heat bath is investigated by using different numbers of vibrational levels. The anharmonic effect is significant with more vibrational levels. Finally, the V–T energy transfer is modeled by a coupled solution to master equations and gas heating. The stronger the non-equilibrium between vibrational and translational temperature in the beginning, the larger the difference that can be obtained between the HO model (Landau–Teller theory) and realistic vibrational levels.