Rayleigh instability is investigated in a Hall thruster under the effect of finite temperature and density gradient of the plasma species. The instability occurs only when the frequency of the oscillations ω falls within a frequency band described by k{y}u₀+1/k_{y}∂²u_{0}/∂x²+Ω/k_{y}n_{0}∂n₀/∂x≪ω
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