One-dimensional model of the plasma flow in a Hall thruster

Abstract

A macroscopic model which accounts for the complex interactions between electrostatic, thermal, and kinetic effects in a Hall thruster is presented. The analysis establishes the one-dimensional steady structure of the flow as consisting of an anode sheath, a long electron free-diffusion region, with reverse ion flow, a thin ionization layer, and the acceleration region, which extends into the plume. The ion flow presents a forward sonic point around the exit of the ionization layer, which can be either internal, with a smooth sonic transition, or localized at the channel exit. The supersonic plume is included via a simple expansion model, allowing closure of the formulation and calculation of thruster performance. The results indicate good agreement with experimental data for the case of an internal sonic point, and they delineate the existence and nonexistence regions in the space of externally controllable parameters. They also unveil the importance of the electron pressure, the reverse flow of ions, and the ionization rate in shaping the plasma structure, whereas, contrary to common perception, the details of the magnetic field profile influence weakly that structure.