Magnetic flux coordinates are constructed from an analytic solution (Ito and Nakajima 2009 Plasma Phys. Control. Fusion51 035007) for the reduced magnetohydrodynamics (MHD) equilibrium equations for high-beta tokamaks in the presence of poloidal and toroidal flows comparable to the poloidal sound velocity. The analytic solution indicates non-circular magnetic flux surfaces and transition between sub- and super-sonic poloidal flows. The magnetic flux coordinates for such non-circular magnetic flux surfaces are obtained for stability analysis. The flux coordinates are numerically obtained from the high order polynomial equations for the relation with the geometrical coordinates. As applications, pressure profiles in the poloidal direction on each flux surface, which become non-constant due to flow, and the flux average of the pressure are obtained. The transitions of the pressure profiles and the flux average of the pressure between sub- and super-sonic poloidal flows are discussed in relation with the radial force balance. The flux coordinates are also obtained analytically by expanding the coordinate relations with respect to the inverse aspect ratio.
Analytical models of axisymmetric toroidal magnetic fields withnon-circular flux surfaces