Theory for island induced neoclassical toroidal plasma viscosity in tokamaks

Error fields and resistive magnetohydrodynamic modes are ubiquitous in real tokamaks. They break the toroidal symmetry in |B| in tokamaks. Here, B is the magnetic field. There are two mechanisms that break the symmetry on the perturbed magnetic surface: one is the perturbed field itself and the other results from the distortion of the magnetic surface due to the perturbed field. The broken toroidal symmetry leads to enhanced neoclassical toroidal plasma viscosity and consequently the rate of the toroidal flow damping. The neoclassical toroidal plasma viscosity also results in a steady-state toroidal plasma flow. In addition, the neoclassical toroidal plasma viscosity in the vicinity of the magnetic islands provides a mechanism to determine the island rotation frequency, which is an important quantity for the island stability. Here, the theory for neoclassical toroidal plasma viscosity in the vicinity of the magnetic island is extended to include the effects of the collisional boundary layer that lead to scaling in the transport fluxes, where ν is the collision frequency.