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

We extend previous analytical calculations of 2D high-β 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_∥ >p⊥ (p_∥ <p⊥) reduces (enhances) the plasma diamagnetism relative to the isotropic case whenever an equilibrium solution exists. Sufficiently fast toroidal flows (Ω>Ω_min) were previously found to suppress the field-free region (diamagnetic hole) that exists in static isotropic high-β 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_∥ /p⊥)>α1=1.07 have equilibrium solutions. We find that α₁ decreases with increasing toroidal flow speed, and above the flow threshold Ω_min we find α1=1, so that all p_∥ >p⊥ plasmas have equilibrium solutions. On the other hand, for p_∥ <p⊥ there are no equilibrium solutions below Ω_min. Above Ω_min (where there is no diamagnetic hole in the isotropic case), equilibrium solutions exist for α2<min(p_∥ /p⊥)<1, where α₂ decreases from unity with increasing flow speed. The boundary layer width increases and the Shafranov shift decreases for p_∥ >p⊥, while the converse is true for p_∥ <p⊥.