Two-dimensional numerical model of plasma flow in a Hall thruster

TLDR

The model couples an electron diffusion equation with an ion kinetic equation, using an assumed ion‑production distribution in the first step and a self‑consistent determination via energy conservation in the second, to compute electrostatic potential contours and ion‑beam trajectories. The model shows that electric‑field distortion from magnetic‑field curvature and radial ion‑production nonuniformity drives ion loss, that the ion‑production distribution shape—and thus ion‑loss flux—depends strongly on magnetic‑field geometry, with computed loss fractions of 0.30–0.55 agreeing with measurements, confirming its usefulness for Hall thruster design.

Abstract

Two-dimensional numerical model of plasma flow in a Hall thruster has been made to estimate analytically the ion-loss flux to the walls of an acceleration channel, and to obtain information about desirable configurations for good thruster performance. The model presented herein is comprised of an electron diffusion equation and an ion kinetic equation, which enables one to compute electrostatic potential contours and ion-beam trajectories. In the first step ion-production distribution was assumed. From the results it was found that electric-field distortion, which is a main cause of ion-loss to the channel walls, is induced not only due to the curvature of magnetic field lines, but also due to the radial nonuniformity of ion-production distribution. In the second step, the ion-production distribution was self-consistently determined by combining an energy conservation equation with the previous two basic equations. The results indicate that the shape of ion-production distribution largely changes with the magnetic field geometry, and hence, the field geometry significantly influences the ion-loss flux to the channel walls. The computed ion-loss fraction (a fraction of ions produced that are lost to the walls) ranges from 0.30 to 0.55, and shows good agreement with the measured values. Therefore, this model should be an effective tool in both the design and improvement of Hall thrusters.