Ion Beam Instability in Hall Thrusters

Stability of an ion flux, bounded with an anode and cathode, in Hall thrusters is investigated by theoretical and numerical modeling. Two-fluid magnetohydrodynamic approximation with cold magnetized electrons and cold nonmagnetized ions is used. The inertia of the electrons is taken into consideration. The perturbations are assumed to be quasi-neutral, potential, and dependent on a single spatial coordinate only. For simplicity, the magnetic field is assumed to be uniform. It is shown that the presence of the boundaries, where the potential of the ion beam is fixed, can cause instability of the beam. The growth rate of instability and frequency excited oscillation is of the order of the reciprocal of the ion crossing time between the anode and cathode. In the limit of a uniform unperturbed state of plasma, the instability is analogous to the Pierce instability of an electron beam with the fundamental distinction that here, the perturbations are quasi-neutral. It is shown that the instability is alternately a periodical and oscillating depending on the range of the α_lh parameter, which includes induction of the magnetic field (through lower hybrid frequency), thickness of the acceleration layer, and velocity of the ion flux.