How well can VMEC predict the initial saturation of external kink modes in near circular tokamaks and l = 2 stellarators?

Abstract

The equilibrium code, VMEC, is used to study external kinks in low β tokamaks and l = 2 stellarators. The applicability of the code when modeling nonlinear MHD effects is explored in an attempt to understand and predict how the initial saturation of the MHD mode depends on the external rotational transform. It is shown that helicity preserving, free boundary VMEC computations do not converge to a single perturbed solution with increasing spectral resolution. Additional constraints are applied to narrow down the numerical resolution parameters appropriate for physical scans. The dependence of the modeled (4, 1) kink mode on the external rotational transform and field periodicity is then studied. While saturated states can be identified which decrease in amplitude with increasing external rotational transform, alternative bifurcated states are found, which contradict this trend. As a result, it was not possible to use VMEC alone to identify the physical dependency of the nonlinear mode amplitude on the magnetic geometry. Nevertheless, the accuracy of VMEC solutions is demonstrated by showing that the expected toroidal mode coupling is captured in the magnetic energy spectrum for stellarator cases. Comparing with the initial value code, JOREK, the predicted redistribution of poloidal magnetic energy from the vacuum to plasma region in VMEC is shown to be physical. This work is a first step toward using VMEC to study MHD modes in stellarator geometry.