Stability of a magnetized Hall plasma discharge

Abstract

Using recent experimental data on the time-averaged, spatially varying plasma properties within a Hall discharge plasma, we present in this article, a theoretical study of the response of this plasma to small (linear) perturbations in its properties. As a starting point for this analysis, we assume a two-dimensional fluid description that includes a simplified equation for the electron energy, and constrain the azimuthal wave vector such that we excite only the dominant (m=1) azimuthal modes. The growth rate and frequencies of predominantly axial and azimuthally propagating plasma disturbances are obtained by numerical solution of the resulting eigenvalue problem under a quasiuniform plasma condition, along the entire discharge channel. The results identify the persistence of a low frequency instability that is associated with the ionization process, concentrated largely in the vicinity of the exit plane, where the magnetic field is at its maximum value, consistent with experimental observations for the relatively low operating voltages (∼100 V) considered in this study.