Effect of the shear viscosity on plasma sheath in an oblique magnetic field

Abstract

In a magnetized plasma sheath, strong velocity shear exists owing to the three-dimensional nature of ion velocity. Thus, the ion viscosity should have an important effect on the sheath structure, which has not been studied. This article presents the study of the effect of ion shear viscosity on the sheath in an oblique magnetic field within the framework of classical cross-field transport. It is shown that the inclusion of the shear viscosity in the ion momentum equation results in a significant reduction in the sheath thickness. It is also shown that the “generalized Bohm criterion” is not affected by the shear viscosity within the present model. However, additional boundary conditions such as the velocity shear arise in the viscous case. The appropriate boundary conditions are formulated, accounting for E × B and diamagnetic drifts at the sheath edge, which affects the criterion and sheath profiles.