**10. Results and the discussion**

The different aspects of the Hall thrusters have been reviewed in this chapter along with future challenges related to the performance and efficiency. The different types of turbulence and oscillation with frequency ranges are also summarized. Hall thruster Plasma support electrostatic and electromagnetic waves under the influence of resistive effects. Therefore the waves (electrostatic and electromagnetic) 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 theoretical model for the propagation of electromagnetic instability is derived in a Hall thrusters. The dispersion relation for the electromagnetic instability is derived analytically. The dispersion relation is solved numerically with the help of MATLAB to study the growing and propagating modes. The dominated modes are plotted to observe the behaviors of the instability.
