Extending the collisional fluid equations into the long mean-free-path regime in toroidal plasmas. I. Plasma viscosity

An expression for the pressure anisotropy and thus for the viscous stress in the plateau regime is derived for arbitrary toroidal magnetic configurations without assuming incompressibility or the existence of flux surfaces, without neglecting the flow components perpendicular to the magnetic surface, and without restricting the flow velocity to be a constant on the flux surface. It can be employed to study low-frequency instabilities in the long mean-free-path regime. A smoothly connected formula for the pressure anisotropy, valid in both the collisional fluid regime and the plateau regime, is given to facilitate the numerical computation. An alternative interpretation of the neoclassical transport theory is also obtained. It is found that if the effects of the temperature gradient are neglected, neoclassical transport fluxes can be interpreted as driven by the velocity stress.