Numerical Calculation of MHD Equilibria with Poloidal-Sonic Flow and FLR Effects

We have developed a code for calculating MHD equilibria with poloidal-sonic flow and FLR effects in high-beta tokamaks, using an aspect-ratio expansion and the two-fluid model. We show that the equilibrium condition can be expressed in terms of differential equations for the first- and second-order poloidal flux and five free profiles of the first-order poloidal flux. We present results for sample equilibria, illustrating behaviors such as the deviation of pressure contours from the flux surfaces and the criteria for the presence of the ``poloidal-sonic singularity.''