Toroidal viscosity and ambipolarity in the neoclassical transport theory of axisymmetric tori

To self-consistently evaluate both the toroidal rotation and the radial electric field in a tokamak the two distinct constraints of toroidal angular momentum conservation and ambipolarity must be invoked. A gyrokinetic derivation of the neoclassical transport equations that permits a large toroidal rotation speed is employed. Explicit forms for the toroidal viscosity are obtained so that both constraints can be imposed. To keep the E×B drift speed smaller than the ion thermal speed and still consider large toroidal rotation, the ratio of the poloidal to toroidal magnetic field components is assumed to be small. For larger poloidal fields the derivation is restricted to small rotation. In general, it is also found necessary to retain the poloidal variations in the electrostatic potential and density. A tokamak plateau regime calculation is performed using the general formulation and illustrates the importance of retaining finite poloidal gyroradii effects.