Electrostatic mode associated with the pinch velocity in reversed field pinch simulations

The existence of a new phenomenon in reversed field pinch (RFP) simulations related to the equilibrium pinch flow is discussed. This behavior is due to the inward equilibrium flow, but is strongly affected by boundary conditions on the perturbed azimuthal flow. It is important to understand and control this mechanism in single helicity simulations of RFPs. This mechanism can be explained in terms of an electrostatic instability related to a mode which can occur in fluid dynamics. In a simple linear model, it is shown that the mode, which is related to the inward advection of angular momentum from the edge, can be stabilized by using homogeneous Dirichlet (no-slip) boundary conditions at the wall. Behavior due to this mode is present in nonlinear simulations with zero-viscous-stress boundary conditions on the tangential velocity at the wall and, even in the presence of the usual magnetohydrodynamic modes, this mode can dominate the nonlinear dynamics of the velocity. In nonlinear simulations with Dirichlet boundary conditions on the tangential velocity, behavior associated with this electrostatic mode is not observed.