# Cross-field chaotic transport of electrons by $\vec E \times \vec B$ electron drift instability in Hall thrusters

## TL;DR

This paper investigates how collision-less chaotic electron transport caused by $
abla imes extbf{E} imes extbf{B}$ drift instability explains high electron flux in Hall thrusters, highlighting the role of electrostatic modes in electron heating and transport.

## Contribution

It demonstrates that electrostatic modes from $ extbf{E} imes extbf{B}$ drift instability induce chaotic electron dynamics, significantly increasing cross-field electron transport in Hall thrusters.

## Key findings

- Electron dynamics become chaotic due to electrostatic modes.
- Electron temperature perpendicular to magnetic field increases by a factor of about 4.
- Significant cross-field electron transport observed along the axial direction.

## Abstract

One special interest for the industrial development of Hall thruster is characterizing the anomalous cross-field electron transport observed after the channel exit. Since the ionization efficiency is more than 90%, the neutral atom density in that domain is so low that the electron collisions cannot explain the high electron flux observed experimentally. Indeed this is 100 times higher than the collisional transport. In Hall thruster geometry, as ions are not magnetized the electric and magnetic field configuration creates a huge difference in drift velocity between electrons and ions, which generates electron cyclotron drift instability or $\vec E \times \vec B$ electron drift instability. Here we are focusing on collision-less chaotic transport of electrons by those unstable modes generated by $\vec E \times \vec B$ drift instability. We found that in presence of these electrostatic modes electron dynamics become chaotic. They gain energy from the background waves which increases electron temperature along perpendicular direction by a significant amount, $T_{\rm perp}/T_{\rm parallel}\sim 4$, and a significant amount of crossfield electron transport is observed along the axial direction.