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.

Global Stability Analysis of Azimuthal Oscillations in Hall Thrusters

“…However, all these local stability studies suffer from the problems mentioned above. On the other hand, the few studies that do account globally for the axial variations of the inhomogeneous plasma focus on the high frequency range [36]- [40]. The current study fills the gap of global stability analyses in the low frequency range, where the ionization process plays a very important role.…”

Low frequency azimuthal stability of the ionization region of the Hall thruster discharge. I. Local analysis

“…The few studies that do account globally for the axial variations of the inhomogeneous plasma are focused on the high frequency range. [44][45][46][47][48] The local stability analyses covering the low and medium frequency ranges may be grouped according to whether or not they include ionization in the formulation. Let us start our discussion with those that do not take it into account.…”

Numerical Study of Instabiities in Magnetized Inhomogeneous Plasmas under the Effect of Ionization

“…Vranjes and Poedts [12] studied the kinetic instability in inhomogeneous partially magnetized plasma containing both the positive and negative dust grains. Malik and Singh [13] have recently studied the Rayleigh Taylor instability in a plasma under the effect of finite temperature of ions and crossed electric and magnetic fields. Many other types of instabilities and propagating waves have been studied by Jain group [14][15][16], Nishida group [17][18][19][20] and Malik group [21][22][23][24][25][26].…”