Application of Nonlinear Equilibria to Inform Open Questions in Tokamak Perturbed Equilibrium Modeling

The prediction of perturbed equilibrium models for tokamaks with small 3D fields is strongly dependent on which reference frame for axisymmetry is assumed - for example, the toroidal field (TF) coil vs the poloidal field (PF) coil centroid. We use fully 3D equilibria generated by VMEC to determine the correct reference frame in these models when subject to n=1 coil asymmetries. We analyze a case for SPARC and find that the appropriate frame can be well approximated by the centroid of the TF coil set. We also consider the case of NSTX-U and find that the frame can be approximated by the radial location of the TF coil inboard legs at the midplane. We determine the correct frame by analyzing the shifted magnetic axis in the nonlinear equilibria. We also analyze the field line displacement to identify where the linearized MHD theory begins to break down, and compare that to typical coil tolerances in existing tokamaks. We find that linear theory is valid for existing tolerances, but with a sufficiently small margin to be of note for future devices with relative tolerances larger than approximately 1% of the minor radius. This study enables confident use of 3D perturbative models for determining tokamak assembly geometric tolerances.