Flux-force relation for non-axisymmetric tori in general flux coordinates and neoclassical toroidal plasma viscosity

Flux-force relation, a fundamental relation that relates transport fluxes to forces, for non-axisymmetric tori in general magnetic flux coordinates that are not Hamada coordinates, is derived. The derivation is based on kinetic theory instead of fluid theory. It is shown that pressure force also contributes to the relation in non-Hamada coordinates in general to make the relation compatible with kinetic theory and to make it coordinates invariant. The results are applied to the theory for the neoclassical toroidal viscosity in tokamaks that have error fields or resistive magnetohydrodynamic (MHD) modes.