Conditions and growth rate of Rayleigh instability in a Hall thruster under the effect of ion temperature

Abstract

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<sqrt[Y{i}T{i}k{y}²/M+ω{p}{i}²(Ω²+Y{e}T{e}k{y}²/m)/(ω{p}{e}²+Ω²+Y{e}T{e}k{y}²/m], where u₀ is the drift velocity of the electrons, Ω is their gyration frequency under the effect of the magnetic field, k{y} is the wave propagation constant, n₀ is the plasma density together with ∂n₀/∂x as the density gradient, and T{i}(T{e}), M(m), Y{i}(Y{e}), and ω{p}{i}(ω{p}{e}) are the temperature, mass, specific heat ratio, and plasma frequency of the ions (electrons), respectively. A relevant Rayleigh equation is derived and solved numerically using the fourth-order Runge-Kutta method for investigating the perturbed potential under the effect of electron drift velocity, channel length, magnetic field, ion temperature, and electron temperature. The instability grows faster because of the magnetic field, ion temperature, and drift velocity of the electrons but its growth rate is reduced because of the electron temperature, channel length, and also its far distances from the anode.