This work investigates energy transfers between electrons, vibrational and translational degrees of freedom and their effect on dissociation mechanisms in a N2 microwave plasma in the pressure range between 50 and 400 mbar. A novel self-consistent 0D plasma chemistry model describing vibrational kinetics via the vibrational energy equation and the Fokker-Planck approach is developed. It is used to simulate conditions achieved experimentally, providing good agreement with measured values of vibrational and gas temperature and electron density. Above 100 mbar energy efficiency of dissociation increases with power density, due to the significant contribution of collisions between vibrationally excited N2 and electronically excited molecules. Energy transfer to vibrations is maximum at low power density and low pressure due to reduced gas heating.

The Fokker−Planck (FP) approach for the description of vibrational kinetics is extended in order to include multiquanta transitions and time dependent solutions. Due to the importance of vibrational ladder climbing for the optimization of plasma-assisted nitrogen fixation, nitrogen is used as a test case with a comprehensive set of elementary processes affecting the vibrational distribution function (VDF). The inclusion of the vibrational energy equation is shown to be the best way to model transient conditions in a plasma reactor using the FP approach. Results are benchmarked against results from the widely employed state-to-state (STS) approach for a wide parameters range. STS and FP solutions agree within ∼10% for the lowest vibrational levels, while time dependent VDFs are in agreement with the STS solution within a ∼ 5% error. Using the FP approach offers the possibility to parametrize drift and diffusion coefficients in energy space as a function of vibrational and gas temperature, providing intuitive and immediate insights into energy transport within the vibrational manifold.