The mechanism of air ionization by a single nanosecond discharge under atmospheric conditions is studied using numerical simulations. The plasma kinetics are solved with ZDPlasKin and the electron energy distribution function is calculated with BOLSIG+. The model includes the excited electronic states of O and N atoms, which are shown to play the main role in plasma ionization for ne > 10 16 cm -3 .For electric fields typical in nanosecond discharges, a non-equilibrium plasma (Te > Tgas) is formed at ambient conditions and remains partially ionized for about 12 nanoseconds (ne < 10 16 cm -3 ). Then, the discharge abruptly reaches full ionization (ne ≈ 10 19 cm -3 ) and thermalization (Te = Tgas ≈ 3 eV) in less than half a nanosecond, as also encountered in experimental studies. This fast ionization process is explained by the electron impact ionization of atomic excited states whereas the fast thermalization is induced by the elastic electron-ion collisions.

The prediction of a flame response to plasma assistance requires extensive knowledge of discharge-induced plasma kinetics. Detailed studies of nanosecond discharges are common in N2/O2 and fresh combustible mixtures but are still lacking in burnt gases. To fill this gap, we define a combustion reference test case and investigate the effects of Nanosecond Repetitively Pulsed (NRP) discharges placed in the recirculation zone of a lean (Φ = 0.8) CH4-air bluff-body stabilized flame at atmospheric pressure. In this zone, the plasma discharge is created in a mixture of burnt gases. Quantitative Optical Emission Spectroscopy (OES), coupled with measurements of electrical energy deposition, is performed to provide temporally (2 ns) and spatially (0.5 mm) resolved evolutions of the temperatures and concentrations of N2(B), N2(C), N2 +(B), OH(A), NH(A), and CN(B) in the discharge. At steady state, the 10-ns pulses deposit 1.8 mJ at a repetition frequency of 20 kHz. Spatially resolved temperature profiles are measured during the discharge along the interelectrode gap. The temperature variations are more pronounced near the electrodes than in the middle of the gap. On average, the gas temperature increases by approximately 550 K. The heat release corresponds to about 20% of the total deposited electric energy. The electron number density, measured by Stark broadening of Hα, increases up to about 1016 cm-3. These characteristics allow to classify the discharge as a non-equilibrium NRP spark, as opposed to the thermal NRP spark where the temperature can reach 40,000 K and the degree of ionization is close to 100%. These measurements will serve (i) as a reference for future studies in the Mini-PAC burner at the same conditions, (ii) to test discharge kinetic models, and (iii) to derive a simplified model of plasma-assisted combustion, which will be presented in companion paper.