Sheath Boundary Effects on the Stability of Hall Plasmas

Abstract

Plasma devices based on the ExB- field con figuration (where the externally applied electric and magnetic fields are everywhere perpendicular) are used for a variety of applications such as electric propulsion (i.e., Hall thrusters), diagnostic tools (e.g., Penning trap) and plasma processing of materials (i.e., magnetrons). Transverse electron current due to the electric and magnetic forces as well as diamagnetic flows due to the presence of pressure and magnetic field gradients are the sources of gradient-drift instabilities which result in turbulence and anomalous transport (the transport of particles, momentum and energy that cannot be explained by theory). Most investigations into plasma instabilities for various configurations of the fields and plasma parameters have been done under the assumption that the plasma is unbounded and, therefore, in neglect of any boundary effect. However, the presence of physical boundaries may significantly alter the dynamics of the plasma by restricting the parallel electron dynamics and introducing plasma sheath regions (regions where quasi-neutrality is violated) near the walls. Previous works have shown that conservation of charge at the boundary of the plasma affects the instability criteria for the gradient-drift modes as well as result in new instabilities. Effects of the sheath boundary conditions on the instabilities of partially magnetized plasmas are further investigated in this project. It is shown, for the first time, that sheath dissipation results in the instability of the anti-drift mode (i.e. the Simon-Hoh instability) due to the plasma density gradient. It is also shown that sheath dissipation results in a strong instability in conditions where the criterion for the standard Simon-Hoh instability (which results from the difference in electron and ion drifts together with a density gradient) is not satis ed; this result is important as it may provide an explanation for anomalous transport when the Simon-Hoh instability is absent. Then, including the electric potential induced by the sheath as well as the sheath boundary condition, one arrives at a set of two nonlinear ordinary differential equations with a non-local integral condition. The boundary conditions are finally derived consistent with the sheath to fully define the boundary-value problem.