Numerical near-axis expansion of weakly quasisymmetric MHS equilibria to all orders

Quasisymmetric stellarators can achieve tokamak-like neoclassical confinement without driven current. However, QS equilibria are notoriously hard to construct. It is widely believed that isotropic pressure MHS equilibria with global QS may not exist. When expanded in effective minor radius, the governing equations become over-determined at the 3rd order.[1] This does not forbid the existence of special solutions, as recent optimization works have indeed produced equilibria with precise QS.[2] It also does not apply to anisotropic equilibria. Rodriguez and Bhattacharjee has shown that adding a pressure anisotropy allows the expansion of global weak QS equilibria to any order.[3] This expansion is likely divergent,[4] but its optimal truncation and higher order behavior remain unclear.

We present pyAQSC, the first numerical near-axis expansion code for anisotropic QS equilibria to any order. We also present numerical correlations of the optimal truncation and divergence rate to common QS metrics. In all examined cases, the expansion diverges after the 4th order, consistent with the accuracy of scalar pressure NAE.[5] Our code explores new regions in QS configuration space by relaxing pressure isotropy. It allows the study of higher order quantities, like magnetic shear, without special parameter choices. PyAQSC supports GPU acceleration and auto differentiation. Along with a new anisotropic equilibrium solver developed for DESC, it provides an efficient tool for designing QS stellarators.