Nonlinear MHD simulations of external kinks in quasi-axisymmetric stellarators using an axisymmetric external rotational transform approximation.

Reduced magnetohydrodynamic (MHD) equations are used to study the nonlinear dynamics of external kinks in quasi-axisymmetric (QA) stellarators with varying fractions of external rotational transform. The large bootstrap currents associated with high beta plasmas typically make QA configurations susceptible to low n external modes, limiting their operational space. The violence of the nonlinear dynamics, and, in particular, when these modes lead to a disruption, is not yet understood. In this paper, the nonlinear phase of external kinks in an unstable QA configuration with an edge safety factor below two is simulated. The nonlinear MHD code JOREK is used, validating the linear dynamics against CASTOR3D. The external rotational transform is approximated axisymmetrically, and varied from the tokamak limit to understand its influence on the nonlinear dynamics. The violence of the kink instability is quantified, and shown to reduce with the increasing external field. At the same time, the external kink triggers (9, 5) and (7, 4) internal modes that exacerbate the loss in confinement during the nonlinear phase, such that it remains large over much of the parameter space. It is only with a significant fraction of external rotational transform that these subsequent modes are stabilised.