Investigation of finite aspect ratio effects in axisymmetric magnetic equilibria with toroidal rotation and pressure anisotropy

The inverse equilibrium formulation and numerical code described in [L.L. Lao Phys. Fluids 24, 1431–1440 (1981)] are extended in a new `exact' fixed boundary equilibrium code that accounts for plasma toroidal rotation and pressure anisotropy. The formulation precisely captures deviations from an inverse aspect ratio $\epsilon:=a/R_0$ expansion, at various orders, with $a$ a minor radius and $R_0$ the major radius at the magnetic axis. We show that for experimentally relevant elongation $\kappa\lesssim 2$ and moderate aspect ratio $\epsilon \sim 0.3$, Next to Leading Order (NLO) effects driven mainly by elongation and triangularity are important especially for the Shafranov shift. For the plasma diamagnetism, order unity deviations are seen at moderate pressures, even though the NLO contribution is weak. The impact of strong perpendicular anisotropy on shaping is investigated, as it was theoretically proposed in [N.A. Madden and R.J. Hastie Nucl. Fusion 34 519 (1994)] that temperature ratios such that $\epsilon T_\perp/T_\parallel \sim 1$ would lead to leading order modifications of the shaping through the strong poloidal localization of the perpendicular pressure. We show through a near-axis analysis that the leading order distribution function must be chosen carefully for consistency, and we verify numerically that shaping modifications due to the anisotropy or rotation remain small for conventional poloidal betas $\beta_p \sim 1$.