Effect of viscous dissipation on the generation of shear flow at a plasma edge in the finite gyro-radius guiding center approximation

Abstract

A numerical simulation is performed to study the effect of a viscous dissipation term on the generation of shear flow at a plasma edge in the guiding center approximation. The guiding center model includes the effects of finite Larmor radius corrections and polarization drift. The numerical code applies the method of fractional steps to the fluid guiding center equations. We attempt to discriminate between the smoothing of the microstructure by a small viscous dissipation term to control numerical instabilities, and the modification of the macroscopic physical results introduced by this small viscous dissipation term. The finite Larmor radius effect allows for a charge separation to exist, which can be further accentuated by the polarization drift. A difference in the viscous term between electrons and ions can add to the charge separation effect at the plasma edge, which can modify the physical results. The numerical calculation is effected using a slab model, periodic in one direction and finite in the other direction, with an inhomogeneous density of guiding centers to simulate a plasma edge. The evolution of the system shows the potential evolving to a shape characterized by the longest wavelength associated with the transverse dimension of the system, an evolution characteristic of an inverse cascade. We present an analysis of the effect of different values of the viscous term on the time evolution of this guiding center system, and on the formation and existence of a charge separation and an electric field at the edge of a plasma and the associated shear in the E × B flow.