Growth of Low-Frequency Electrostatic and Electromagnetic Instabilities in a Hall Thruster

Resistive instabilities corresponding to the electrostatic (ES) and electromagnetic (EM) waves are investigated in a Hall thruster under more realistic situation, where the ions and electrons carry finite temperatures and collisions are also taken into account. Relevant dispersion equations are obtained and solved numerically in order to investigate the growth rates of these waves. Based on analytically obtained expressions for the growth rate and real frequency of the ES wave, limiting cases are discussed for the propagation of this wave and the importance of finite temperature of the ions. An application of magnetic field is found to support the instabilities together with the enhanced growth rates of the ES and EM waves. In both the cases, smaller wavelength oscillations are found to be most unstable. The ion (electron) thermal motions are found to have negative (positive) effect on the growths of both the instabilities, though the EM instability shows stronger dependence. The magnitude of the growth rate of the ES wave supersedes that of the EM wave, but its growth shows weak dependence on the ion temperature, collision frequency, and drift velocity of the electrons.