High-Beta Equilibria In Tokamaks With Pressure Anisotropy And Toroidal Flow

We extend previous analytical calculations of 2D high-beta equilibria in order-unity aspect ratio tokamaks with toroidal flow to include pressure anisotropy, assuming guiding-center theory for a bi-Maxwellian plasma and the ideal MHD Ohm's law. Equilibrium solutions are obtained in the core region (which fills most of the plasma volume) and the boundary layer. We find that pressure anisotropy with p(parallel to) > p(perpendicular to) (p(parallel to) < p(perpendicular to)) reduces (enhances) the plasma diamagnetism relative to the isotropic case whenever an equilibrium solution exists. Sufficiently fast toroidal flows (Omega > Omega(min)) were previously found to suppress the field-free region (diamagnetic hole) that exists in static isotropic high-beta equilibria. We find that all equilibrium solutions with pressure anisotropy suppress the diamagnetic hole. For the static case with a volume-averaged toroidal beta of 70%, plasmas with max (p(parallel to) / p(perpendicular to)) > alpha(1) = 1. 07 have equilibrium solutions. We find that alpha(1) decreases with increasing toroidal flow speed, and above the flow threshold Omega(min) we find alpha(1) = 1, so that all p(parallel to) > p(perpendicular to) plasmas have equilibrium solutions. On the other hand, for p(parallel to) < p(perpendicular to) there are no equilibrium solutions below Xmin. Above Omega(min) (where there is no diamagnetic hole in the isotropic case), equilibrium solutions exist for alpha(2) < min(p(parallel to) / p(perpendicular to))< 1, where alpha(2) decreases from unity with increasing flow speed. The boundary layer width increases and the Shafranov shift decreases for p(parallel to) < p(perpendicular to), while the converse is true for p(parallel to) < p(perpendicular to). (C) 2015 AIP Publishing LLC.