Fluid theory of radial angular momentum flux of plasmas in an axisymmetric magnetic field

The fluid equations of Mikhailovskii and Tsypin have been applied to the problem of radial transport of angular momentum of plasmas in an axisymmetric magnetic field with flux surfaces of arbitrary shape [P. J. Catto and A. N. Simakov, Phys. Plasmas 12, 012501 (2005)]. In this paper, compact expressions for the radial angular momentum flux for both up down symmetric and asymmetric flux surfaces are obtained by utilizing the ratio of poloidal to toroidal magnetic fields as an additional small parameter. A systematic expansion of the fluid equations in the ratio of gyroradius over plasma and magnetic field scale length is performed, followed by a subsidiary expansion in the ratio of collisional mean free path to the scale length. A derivation of the equations of Mikhailovskii and Tsypin is also presented in a form that facilitates application to the transport problem.