Three-dimensional particle-in-cell model of Hall thruster: The discharge channel

There are still many missing elements to complete the physical picture at the basis of the Hall thruster functioning. The origin of the anomalous electron cross-field transport often ascribed to azimuthal electron E × B drift instability remains decoupled from self-consistent ion axial acceleration and radial boundary conditions, at the same time. This study represents the first attempt to correlate the different mechanisms contributing to the electron transport by means of a fully kinetic three-dimensional Particle-in-Cell model. A geometrical scaling scheme has been used to make the simulation possible. This scheme irremediably changes what are some salient characteristics of the discharge, such as the wall interaction and the axial component of the electric field. For this reason, a critical assessment of the effects of reducing dimensions has been addressed. The present paper deals with the physics of discharge channel. Results confirm the occurrence of E × B drift instability along the azimuthal direction. The modulation is almost standing wave: it moves back and forth travelling only a short distance before being axially convected away. In addition, the dielectric floating potential nature of the lateral walls gives to the azimuthal modulation an important radial component creating an oblique pattern in the radial-azimuthal plane. As a consequence, the azimuthal electric field presents a double alternating structure: two phase-opposing waves are present in the first and second half of the radial extension between the two lateral walls. Finally, the effect of secondary electron emission from walls is not sufficient to guarantee the right electron current to neutralize the ion beam, but rather it works as an auxiliary mechanism (together with ion heating and azimuthal rotation) to saturate the electron drift instability leading to smaller amplitude oscillations.