High-beta equilibria in tokamaks with pressure anisotropy and toroidal flow

Abstract

We extend previous analytical calculations of 2D high-b 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 pk > p? (pk < p?) reduces (enhances) the plasma diamagnetism relative to the isotropic case whenever an equilibrium solution exists. Sufficiently fast toroidal flows (X > Xmin) were previously found to suppress the field-free region (diamagnetic hole) that exists in static isotropic high-b 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 ðpk=p Þ > a1 ¼ 1:07 have equilibrium solutions. We find that a1 decreases with increasing toroidal flow speed, and above the flow threshold Xmin we find a1 ¼ 1, so that all pk > p? plasmas have equilibrium solutions. On the other hand, for pk < p? there are no equilibrium solutions below Xmin. Above Xmin (where there is no diamagnetic hole in the isotropic case), equilibrium solutions exist for a2 < minðpk=p?Þ < 1, where a2 decreases from unity with increasing flow speed. The boundary layer width increases and the Shafranov shift decreases for pk > p?, while the converse is true for pk < p?.