The breathing mode is the best known low-frequency longitudinal bulk instability of Hall thrusters, capable of generating very wide, regular discharge current oscillations in the 10-30 kHz range. This study extends a recent theory of breathing mode oscillations to the case of a non-ideal voltage source. A simple equivalent circuit modeling the AC behavior of the thruster is derived, using R, L and C components. The equivalent circuit explains in a straightforward way why an impedance in series with the generator is usually able to damp oscillations. More generally, the derived equivalent circuit can be expected to greatly improve the understanding of interactions between the thruster and the power processing unit, and in turn to help the design of robust filters.
Using the fluid equations of Hall thruster plasma we analyze the influence of the electron energy balance on the stability of ion sound modes. For sufficiently low frequencies (ω < 5 • 106^6 s-1 in the case of SPT-100) the gains and losses in the source term are approximately equal, thus the temperature can be in principle determined in terms of other dependent variables. This permits one to reduce the number of equations by one. It appears however, that the new system can have in some regions complex characteristics. This in turn implies instability of certain modes with frequencies lower than the critical frequency.