Development of a model for the near-exit plume of a Hall thruster

Abstract

This thesis presents a fluid model for electron behavior in the near-exit plume of a Hall thruster. The model provides 3D results and allows to study the azimuthal asymmetry induced by the hollow cathode. The model is composed by the charge and energy conservation equations and is intended to solve for the electrostatic potential and the electron temperature. It relies on the results of an external model for the ion behavior. The fluid equations are diffusive and are justified in the limit of small electron Larmor radius. They include the Hall transport, which is usually ignored in 2D approaches due to symmetry. The transport along magnetic field lines is high enough to convert the 3D problem into a 2D problem, where only the directions perpendicular to the magnetic field matter. In such a 2D formulation, the basic structure of the solution for the potential is studied analytically, with the result that the lines of constant potential can be approximately predicted. The potential can be found numerically after transforming the charge conservation equation into a convective-diffusive equation. The numerical results agree approximately with analytical predictions. The results suggest that the asymmetry induced by the hollow cathode mainly depend on how much the cathode perturbs the plasma density distribution.