In this paper, the effect of electron temperature on the resistive instability has been investigated in a Hall thruster beam plasma. The dispersion relation for the axial–azimuthal propagating waves and the instabilities has been derived using the first-order perturbation technique under the effects of various parameters. The growth rate shows Gaussian-type behaviour with the magnetic field, azimuthal wavenumber and the electron temperature but it increases linearly with axial wavenumber, beam density, beam velocity and collisional frequency. The growth rate decreases with the drift velocity of electrons. The real frequencyalmost increases with the axial–azimuthal wavenumbers, electron drift velocity, electron temperature and the collisional frequency.

Bounded plasma occur in waveguide of nanodevices with dielectric boundaries and the dimension of nanodevices control the frequency of oscillation and particle acceleration. A system with cylindrical bounded quantum plasma is used to study the electrostatic wave instability in the presence of magnetic field. Bohm potential, exchange-correlation potential and Fermi pressure significantly affect thecharacteristic frequency of oscillation of particle in bounded plasma. Using quantum hydrodynamic model, basic equations of cylindrical bounded quantum plasma are constructed and linearized under the effect of ionization rate. Dispersion relation for growing waves is obtained, which shows dependence on ionization rate, magnetic field, number density, wave vector and geometry of cylindrical waveguide. We investigated that growth rate increases with magnetic field, ionization rate, number density and poles of Bessel’s function, whereas it decreases with wave vector and radius of waveguide. The present investigation is performed on the basis of numerical parameters of astrophysical plasma.

Hall thrusters have high thrust-to-power ratio, efficiency and specific impulse. Therefore, less propellant mass is required for small satellite missions compared to chemical thrusters. In electric propulsion technology, the thrust is generated by the acceleration of ions in a cross-field plasma configuration. The fast ion bombardment near the exit channel is the main cause of erosion of the walls, which limits the lifetime of Hall thruster. The magnetic field profile controls the exhaust-beam divergence, motion of the energetic particles from the plume and erosion of outer surface of the device, which affects performance of the thruster. So, it is necessary to study the effect of different profiles of the magnetic field and density, and ion velocity on the plasma plume in addition to the impact of collisions between the plasma species. In this paper, we have investigated these effects on the plasma plume potential by considering Gaussian and super-Gaussian profiles for the density. The plasma plume is found to acquire larger potential, if the magnetic field of higher strength is used. The potential of the plasma plume attains a peak value outside the accelerationchannel. The peak of the plume potential gets shifted more outside in the case of Gaussian density profile when the position of the magnetic field peak is shifted towards the cathode.