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The electrostatic and electromagnetic low frequency waves propagating in azimuthal direction in a Hall thruster channel are found to be unstable due to the resistive coupling to the electrons' closed drift in the presence of collisions. The thermal motion of the electrons and their collisions significantly affect the growth of these waves. With respect to the collision frequency, wave number, electron temperature and plasma density, both the instabilities grow in a similar fashion but they behave oppositely under the effects of magnetic field and electron drift velocity. In both the cases, smaller wavelength oscillations are found to be most unstable, and magnitude of the growth rate of the electrostatic wave supersedes that of the electromagnetic wave. The electrostatic instability is more sensitive to the electron collisions in comparison with the electromagnetic instability. On the other hand, the electromagnetic instability is suppressed in the presence of larger ion drift velocity.

Resistive Instabilities in a Hall Thruster Under the Presence of Collisions and Thermal Motion of Electrons