Effect of axial and radial components of the magnetic field on the electrostatic resistive instabilities in Hall thruster plasma

A two-fluid model is used to investigate the influence of the axial component of the magnetic field on the growth rate of electrostatic resistive instabilities with cross field electron transport in a Hall thruster. The axial component of the magnetic field plays an important role in instabilities. It provides additional confinement to electrons and ions near the channel axis. Also, it helps to protect the walls from the direct impacts of particles, thereby reducing erosion and extending the operational lifetime of the system. A fourth-order dispersion equation is derived using plasma perturbed densities into Poisson's equation to observe the various effects on the growing waves in plasma. It is observed that the growth rate and the real frequency increase with axial and radial components of the magnetic field, respectively. The order of the real frequency of the wave is found to be 10(6) / s. For the fixed value of the azimuthal wavenumber ( k(y) = 500 / m), the amplitude of the growth rate of the instability dropped to almost 40% if the axial component of the magnetic field is considered. Similarly, the amplitude of the real frequency increases by almost 74% (at k(y) = 500 / m) by incorporating the contribution of the axial component of the magnetic field. In addition, it is also observed that the amplitude of the growth rate increases with low values of radial and axial components of the magnetic field, but it decreases at the higher value of the magnetic field due to the resonance of electron cyclotron frequency with plasma frequency.