Modelling of the temporal evolution of the gas temperature in N2 discharges

The time-dependent evolution of the energy transfer to gas heating in a pure N2 discharge produced in a cylindrical tube at low pressures (1-10 Torr) is studied for different fixed values of the reduced electric field and electron density. We consider a model based on the self-consistent solutions to the time-dependent gas thermal balance equation coupled to the electron, vibrational, and chemical kinetic equations for the most important heavy species produced in N2 plasma discharges. The results of this model provide the temporal variation of the radially averaged value of the gas temperature, as well as the corresponding gas heating mechanisms. It is shown that the pooling reactions N2(A) + N2(A) → N2(B) + N2 and N2(A) + N2(A) → N2(C) + N2 are responsible for a smooth increase in the gas temperature before the first millisecond. For longer times, gas heating is found to be mainly caused by vibrational energy exchanges from non-resonant vibration-vibration (V-V) processes between N2 molecules and by vibration-translation (V-T) N2-N collisions. The heating rates of these different gas heating mechanisms and the gas temperature are calculated for a reduced electric field of 50 and 100 Td (1 Td = 10−17 Vcm2), an electron density of 1010 and 1011 cm−3, and a pressure of 1 and 10 Torr. The fractional power converted to gas heating from electronic and vibrational excitation is also calculated for these parameters, being respectively ∼2% and in the range 10%-35%. The effect of having a contribution of non-resonant V-V processes to gas cooling within the time interval 0.1-1 ms is analysed. The role of the gas temperature on the temporal evolution of the vibrational distribution of N2(X, v) molecules is also discussed.