Integrating the Fokker-Planck approach to vibrational kinetics in a self-consistent N₂ plasma chemistry model

The Fokker-Planck (FP) approach for the description of vibrational kinetics is coupled for the first time to a chemical kinetics model. Due to the importance of vibrational ladder climbing for the optimization of nitrogen fixation in a plasma reactor, nitrogen has been used as a test case for the validation of this method.

A self-consistent N2 plasma model is developed, including a complete description of chemical, vibrational and electron kinetics. This includes vibrational-translational, resonant and non-resonant vibrational energy exchanges, as well as electron-impact step-wise vibrational excitations.The complexity of the model has been gradually increased by adding vibrational-translational, resonant and non-resonant vibrational energy exchanges. Moreover, electron-impact step-wise vibrational excitations have been included, allowing self-consistent evolution and coupling of vibrational kinetics with electron kinetics. The model is coupled to the gas heating and vibrational energy equations, coupling with gas heating and vibrational energy has also been implemented, making the complete model suitable for investigating vibrational non-equilibrium conditions in a plasma reactor.

The time-resolved evolution and steady-state solution of the vibrational distribution function obtained through the FP approach have been benchmarked against results from the widely employed state-to-state method, showing excellent agreement and higher computational efficiency, while vibrational excitation and gas heating reproduce experimental results obtained at DIFFER.