Self-similarity in Hall plasma discharges: Applications to particle models

Abstract

Electron transport is a key process in the physics of Hall thruster discharges. Therefore, a kinetic description of the heavy particles (Xe) as well as electrons is required. The ideal numerical model would be a particle model for all the species. Nowadays, such a model is unpractical because it would need too large an amount of computation time due to the very different time scales of electrons and heavy particles dynamics. For this purpose two scalings to speed-up the execution time of a two-dimensional fully kinetic Particle-in-Cell/Monte Carlo Collision simulation of the Hall thruster SPT-100 are proposed. These two different scaling schemes generate self-similar systems of the acceleration channel including the process of secondary electron emission from the dielectric walls. Instead of using the common approach of a smaller neutral and ion mass or a larger vacuum permittivity the channel dimensions are reduced keeping the main dimensionless physics parameters constant. This leads to scaling laws for the input (magnetic field, mass flow rate, current and voltage discharge, etc.) and output parameters obeying self-similarity. This scaling methodology makes the simulation faster and allows improved modeling of electron interactions and fundamental processes. This model has demonstrated its outstanding capability in improving the physics insight into the processes in SPT-100 under the scaling constraints for the geometrical reduction. The application to particle models of different plasma based devices is suggested for such systems where a linearization of the Boltzmann equation is possible.