Neoclassical toroidal viscosity for an axisymmetric toroidal equilibrium with multiple trapping of particles

A method is illustrated on how to apply existing formulas to the neoclassical toroidal plasma viscosity for an axisymmetric toroidal equilibrium with an arbitrary aspect ratio that has multiple trapping states. The effect of the energy scattering on the viscosity in the regime is presented using an approximate collision operator. Here, is the collision frequency. The explicit expressions for the steady state toroidal flow speed resulting from the neoclassical toroidal flow damping in both the 1 and the regime are also presented. The physics origin of the toroidal viscous force is the broken toroidal symmetry induced by the error fields and the amplification of these fields by stable or unstable resistive wall modes, or other asymmetric magnetic field perturbations.