Moment method applied to gaseous electronics

The five-moment method in gaseous electronics is based on a model velocity distribution function with position-dependent parameters, such as density (one moment), average velocity (three moments), and average energy (one moment). Temporal and spatial dependence of these parameters is determined by solution of velocity moments of the Boltzmann equation, which are coupled, partial differential equations in time and space. In this paper velocity moments of the Boltzmann equation, including moments of the collision integral for elastic and inelastic collisions, are given for two model distribution functions---shifted Maxwellian and shifted shell---and solved for the case of a planar Townsend discharge in helium, including nonequilibrium regions near electrodes. Based on a comparison between calculated and measured values of {α}/N versus E/N, it is concluded that five-moment theory based on a shifted Maxwellian distribution is superior to either the five-moment theory based on a shifted shell distribution, or the two-moment theory based on a monoenergetic beam distribution.