Stationary electron velocity distribution function in crossed electric and magnetic fields with collisions

Abstract

Analytical studies and numerical simulations show that the electron velocity distribution function in a Hall thruster discharge with crossed electric and magnetic fields is not Maxwellian. This is due to the fact that the mean free path between collisions is greater than both the Larmor radius and the characteristic dimensions of the discharge channel. However in numerical models of Hall thrusters, a hydrodynamic approach is often used to describe the electron dynamics, because discharge simulation in a fully kinetic approach requires large computing resources and is time consuming. A more accurate modeling of the electron flow in the hydrodynamic approximation requires taking into account the non-Maxwellian character of the distribution function and finding its moments, an approach that reflects the properties of electrons drifting in crossed electric and magnetic fields better than the commonly used Euler or Navier-Stokes approximations. In the present paper, an expression for the electron velocity distribution function in rarefied spatially homogeneous stationary plasma with crossed electric and magnetic fields and predominance of collisions with heavy particles is derived in the relaxation approximation. The main moments of the distribution function including longitudinal and transversal temperatures, the components of the viscous stress tensor, and of the heat flux vector are calculated. Distinctive features of the hydrodynamic description of electrons with a strongly non-equilibrium distribution function and the prospects for further development of the proposed approach for calculating the distribution function in spatially inhomogeneous plasma are discussed.