Along with crossed electric and magnetic fields in a Hall thruster, a radial component of electric field is generated that takes ions toward the walls, which causes sputtering and produces dust contamination in the thruster plasma. Considering negatively charged dust particles in the Hall thruster, we approach analytically the resistive instability by taking into account the oscillations of dust particles, ions and electrons along with finite temperatures of ions and electrons. In typical Hall thruster regimes, the resistive instability growth rate increases with higher collision rates in the plasma, stronger magnetic field but it decreases with higher mass of the dust and higher temperature of the ions and electrons. In comparison with dust-free models, the presence of dust results into a drop of the resistive instability growth rate by three orders of magnitude, but the growth rate increases slowly for dust densities within the typical range.
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