A numerical solution of the Boltzmann equation for high-powered short pulse microwave breakdown in nitrogen

Abstract

A theoretical formulation that provides a basis for generating approximate solutions of the Boltzmann equation for the study of high-powered microwave pulses interacting with a background atmosphere is given. A numerical scheme is implemented using realistic cross sections for electron–nitrogen collisions, including excitation and ionization. It is found that the numerical results agree well with previous experimental and theoretical values when α is less than about 0.1 kV/cm Torr, where α is the effective electric field divided by the pressure (α=Ee/P). Results are presented providing a simple fit for the time averaged momentum transfer rate and the ionization rate as a function of the microwave electric field E, wavelength λ, and gas pressure P, for 0.1≤α≤1.0 kV/cm Torr. This fit is compared with recent experimental data for breakdown times.