The Near Axis Expansion in a General Curvilinear Frame for computing Quasi-Isodynamic Stellarators

The near axis expansion is a powerful tool capable of rapidly computing quasi-symmetric stellarators through a direct solution to the magneto-hydrodynamic equations [1]. This formulation is limited by its use of the Frenet Serret frame, which is discontinuous when curvature approaches zero, making it incompatible with quasi-isodynamic (QI) stellarators. QI stellarators have promising confinement properties as show by the W7-X device. Discontinuity in the Frenet Serret frame can be circumvented by using a distinct curvilinear frame, as has previously been accomplished in coil optimization [2]. In this work we rederive the near axis expansion using a generalized curvilinear frame to second order. We create a code package based on the PyQSC code [3] using the rederived near axis expansion and capable of QI optimization. In addition, a novel method of optimizing for QI is introduced relying on omnigenity conditions within the near axis expansion.

[1] Landreman & Sengupta, J. Plasma Phys. 85 (2019) 815850601

[2] Singh et al., J. Plasma Phys. 86 (2020) 905860404

[3] GitHub repository, github.com/landreman/PyQSC