Low-frequency model of breathing oscillations in Hall discharges

A paradigm for Hall discharge modeling is presented whereby only the time scale of the lowest-frequency mode is explicitly resolved. The ability of such a low-frequency model to reproduce with excellent accuracy the breathing mode is demonstrated through comparisons with a fully time-dependent numerical model. Based on this formalism, an approximate linearized model is derived which essentially constitutes a one-dimensional generalization of the classical zero-dimensional predator-prey model. The model highlights the interaction of standing plasma waves with the transport of neutral species, which involves standing and convective waves of similar magnitude. It predicts a frequency which is in close agreement with the frequency of the small perturbation modes observed in simulations. Finally, it is shown that unstable modes are in general strongly nonlinear and characterized by frequencies obeying a scaling law different from that of linear modes.