Electron energy distribution function in a Hall discharge plasma

Abstract

The role of inelastic collisions in Hall thruster operation is studied through simulation of the electronenergy distribution function (EEDF) inside the thruster channel. The electron Boltzmann equation is solvedusing the Lorentz approximation (two-term expansion) and the local-field approximation. The resultantzero-dimensional Boltzmann equation takes into account inelastic losses due to ionizing collisions andwall-collisions. Secondary electrons from ionization and wall-collisions are also included in the model.Electron continuity is used to calculate the sheath potential at the insulator walls. Results show an EEDFcut off at high energy due to electron loss to the walls. Secondary and scattered electrons from ionizationprovide a large population of low-energy electrons. The calculated EEDFs agree well with experimentalelectron temperature data when an experimentally-determined effective collision frequency is used forelectron momentum transport. Predicted values for the wall-sheath potential agree with results from acharge-balance model, except where said model predicts sheath collapse.I. INTRODUCTIONHall discharges (Hall thrusters) are presently underdevelopment for use in space propulsion applications. TheHall thruster is essentially a shaped-field accelerator, usingapplied potentials and magnetic fields to produce a highspecific impulse, low-density plasma flow. The shape of theelectric field, the Ohmic losses, and the locations of theionization zone and acceleration zone inside the thruster arecoupled to the applied fields through the plasmaconductivity. The electrons in Hall discharges exhibitcharacteristic cross-field transport, which is believed to beenhanced by fluctuations in the electric field and plasmadensity [1]. Collisions with the thruster channel walls alsoplay an important role in discharge operation.Several researchers have had success modeling theplasma inside the Hall discharge (and similar discharges)with hybrid fluid-particle codes [2-5] and full particle codes[6]. With the hybrid fluid-particle in cell (PIC) codes, someinvestigators have used an anomalous Bohm conductivity inorder to accurately reproduce discharge operation [5], whileothers have relied on a model for electron-wall scattering[3,4]. Many of these efforts have had difficulty reproducingthe location of the ionization zone inside the thrusterchannel. We believe that this may be due to a non-Maxwellian electron energy distribution function (EEDF) inthe discharge plasma. Electrostatic probe measurements ofthe EEDF have shown significant departures fromMaxwellian behavior [7-10.]. We [11] and others [10] havealso observed behavior that may be attributable to a non-Maxwellian EEDF in optical emission experiments.