Energy balance in nanosecond pulse discharges in nitrogen and air

Kinetic modeling is used to analyze energy partition and energy transfer in nanosecond pulse discharges sustained between two spherical electrodes in nitrogen and air. The modeling predictions are compared with previous time-resolved temperature and N 2 ( X 1 Σ g + , v = 0 − 9 ) vibrational population measurements by picosecond broadband coherent anti-Stokes Raman spectroscopy (CARS) and phase-locked Schlieren imaging. The model shows good agreement with experimental data, reproducing experimental discharge current pulse waveforms, as well as dominant processes of energy transfer in the discharge and the afterglow. Specifically, the results demonstrate that the temperature rise in the plasma occurs in two stages, (i) ‘rapid’ heating on sub-acoustic time scale, dominated by N 2 ( A 3 Σ u + ) energy pooling processes, N 2 ( B 3 Π g ) and N( 2 P, 2 D) quenching (in nitrogen), and by quenching of excited electronic states of N 2 molecules by O 2 (in air), and (ii) ‘slow’ heating due to N 2 vibrational relaxation by O atoms (in air), nearly completely missing in nitrogen. Comparison of the model predictions with N 2 vibrational level populations confirms that the N 2 vibrational temperature rises after the discharge pulse is caused by the ‘downward’ vibrational–vibrational exchange depopulating higher vibrational levels and populating vibrational level v = 1. The model reproduces temporal dynamics of vibrational level populations and temperature in the discharge and the afterglow, indicating that energy partition among different modes (vibrational, electronic, dissociation, and ionization) is predicted accurately. At the present conditions, energy fraction coupled to the positive column of the discharge filament in air is approximately 50%, with the rest coupled to the cathode layer. Nearly 10% of the total pulse energy is spent on O atom generation, and about 10% is thermalized on a sub-acoustic time scale, producing a strong compression wave in the radial direction. The experimental wave speed is considerably higher compared to the model predictions, by approximately 30%. The reason for this difference may be due to interaction between the cylindrical and spherical compression waves generated in the discharge filament and in the cathode layer, respectively.