Theoretical investigation of pulsed microwave discharge in nitrogen

A pulsed microwave discharge burning close to the centre of a cylindrical chamber (omega/2 pi = 2.45 GHz) in pure nitrogen at low pressure (5 mbar) has been investigated theoretically. Boltzmann equation analysis is applied for the description of the breakdown and the consecutive maintenance phase of the discharge. The breakdown electric field is estimated using the calculated ionization frequency and the losses by the free electron diffusion. A self-consistent model for electron and heavy-particle kinetics coupling the rate master equations for the vibrational levels N-2(X, v) of the electronic ground state of the nitrogen molecule to the Boltzmann equation of electrons has been developed. Besides the momentum transfer, inelastic as well as superelastic e-V collisions, ionization and free diffusion of electrons have been taken into account in the Boltzmann equation. The balance of the populations of the vibrational levels includes e-V, V-V and V-T exchanges, dissociation, atom re-association, vibrational deactivation on the walls and the effect of molecular diffusion. A further relation used is the global energy balance of electrons. The calculated breakdown electric field strength and the temporal course of the population of vibrational levels have been compared with experimental breakdown data and CARS measurements. Calculations and measurements are found to agree well.