Growth of Rayleigh instability in a Hall thruster channel having dust in exit region

Abstract

In a Hall thruster, the axial movement of ions towards the exit of the chamber and the divergence of ion beam sputter the wall and thus the maximum erosion of wall of the exit region takes place. This way the dust is generated, which is largely confined near the exit of the channel. By considering dust particles with negative charge, we derive and solve the dispersion equation for the growth of Rayleigh instability in the thruster plasma and examine its growth rate for different density, charge, mass and temperature of the dust particles. We also talk about the role of density gradient scale length on the growth of the instability.