Effect of negatively charged dust on resistive instability corresponding to the electrostatic wave is investigated in a Hall thruster plasma when this purely azimuthal wave is tilted and strong axial component of wave vector is developed. Analytical calculations are done to obtain the relevant dispersion equation, which is solved numerically to investigate the growth rate of the instability. The magnitude of the growth rate in the plasma having dust particles is found to be much smaller than the case of pure plasma. However, the instability grows faster for the increasing dust density and the higher charge on the dust particles. The higher magnetic field is also found to support the instability.

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.

The present study focuses on the Rayleigh equation derived in the case of a Hall thruster plasma having dust contamination, produced near the exit of the channel due to the finite divergence of the accelerated ions and the sputtering of the walls. In the presence of negatively charged dust particles, a modified form of the well-known Rayleigh equation of fluid dynamics is realized. The modified equation takes the form of the Rayleigh equation for a particular band of oscillation frequency, revealing that the Rayleigh instability shall occur in the thruster only for the oscillations having frequencies within this band. For better understanding, the variation of frequency band with various parameters, viz. dust density, dust charge number, dust mass, electron temperature and ion density, has been traced out.

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