Jñānābha‎, Vol. 51 (1) (2021), (114-124)



Saty Prakash Bharti, Sukhmander Singh

Department of Physics, Central University of Rajasthan, Ajmer, Kishangarh-305817, India,


Sanjeev Kumar and Shravan Kumar Meena

Department of Physics, Motilal Nehru College University of Delhi, Near South campus, Delhi-110021


(Received : April 01, 2021 ; Revised in final form : May 06, 2021)


Hall thrusters are frequently used by geostationary satellites and long range mission from Earth to Moon. Hall thruster has higher fuel efficiency, less fuel consumption, therefore less propellant storage is required on-board. The stream of electrons are used from the virtual cathode to neutralize the outer surface of the Hall thruster to overcome the charging related problems. This electron beam alter the density of the plasma inside the Hall thruster channel. It affects the oscillations of plasma and triggers the instability called as electron beam instability. In this paper, we use magnetohydrodynamics theory to obtain the modified dispersion relation under the presence of electron beam with the help of the Poissons equation. We obtain dispersion relation as polynomial of the order of five under the various parameters. The real part of the root give phase velocity of the wave and the imaginary part give growth rate of the instability. The growth rate and the real frequency depend on the various parameters like magnetic field, density of electron, ion and electron beam, mass of the electron, ion and electron beam, initial velocity. The density and velocity of the electron beam affect the growth rate and real frequency of the wave. Therefore the electron beam play important role to control the growth rate and phase velocity of the wave. The effect of various parameters on the growth rate and phase velocity are investigated.

2010 Mathematics Subject Classifications: 76D10, 76E25, 76S05, 76W05, 80A20.

Keywords and phrases: Dispersion equations, Electron collisions, Growth rate, Hall thruster, Ion temperature, Low frequency waves, Resistive instability

[Download full paper]