Analytical solution of Rayleigh-Taylor instability in a Hall thruster having double-ionized ions

Abstract

A modified Rayleigh-Taylor (RT) instability equation is derived using a three-fluid Hall thruster plasma model by including multi-ionized ions to study the growth rate of the RT instability. For a simplified plasma density and electron drift velocity axial profile, the growth rate for an unstable wave and the condition leading to this instability are discussed. A possible analytical solution for the modified Rayleigh-Taylor equation is discussed along with the condition that leads to it. For double-ionized ions, the behavior of growth rate and perturbed potential for different densities of double-ionized ions are studied.