Kinetic effects in a Hall thruster discharge

TLDR

Hall‑thruster electrons exhibit a non‑Maxwellian, anisotropic velocity distribution with much higher kinetic energy parallel to the channel walls, and are stratified into distinct groups, a behavior not captured by current fluid or hybrid models. The authors derive practical analytical expressions for plasma flux to the wall, secondary electron fluxes, plasma potential, and cross‑field electron conductivity. These formulas reproduce simulation results, show that elastic electron scattering governs the velocity distribution and potential, and reveal that wall secondary emission boosts cross‑field conductivity but only slightly alters sheath insulation.

Abstract

Recent analytical studies and particle-in-cell simulations suggested that the electron velocity distribution function in E×B discharge of annular geometry Hall thrusters is non-Maxwellian and anisotropic. The average kinetic energy of electron motion in the direction parallel to the thruster channel walls (across the magnetic field) is several times larger than that in the direction normal to the walls. Electrons are stratified into several groups depending on their origin (e.g., plasma or channel walls) and confinement (e.g., lost on the walls or trapped in the plasma). Practical analytical formulas are derived for the plasma flux to the wall, secondary electron fluxes, plasma potential, and electron cross-field conductivity. Calculations based on these formulas fairly agree with the results of numerical simulations. The self-consistent analysis demonstrates that the elastic electron scattering in collisions with atoms and ions plays a key role in formation of the electron velocity distribution function and the plasma potential with respect to the walls. It is shown that the secondary electron emission from the walls may significantly enhance the electron conductivity across the magnetic field but only weakly affects the insulating properties of the near-wall sheath. Such self-consistent decoupling between the secondary electron emission effects on the electron energy losses and the electron cross-field transport is currently not captured by the existing fluid and hybrid models of Hall thrusters.