Nonlinear magnetohydrodynamic modeling of ideal ballooning modes in high- β Wendelstein 7-X plasmas

We present nonlinear magnetohydrodynamic (MHD) simulations of high-β Wendelstein 7-X plasmas using the stellarator extension of the M3D-C 1 code, building on the recent work that shows benign saturation of ideal ballooning modes above the designed β limit in the standard configuration [Zhou et al., Phys. Rev. Lett. 133, 135102 (2024)]. First, we examine the results' sensitivity to the parallel thermal conductivity. It is found that while an increased parallel conductivity reduces the linear growth rate, the saturated pressure profile is barely affected. Second, we consider the dependence on the profile shape. It is shown that an equilibrium with a peaked pressure profile and lower β is subject to more significant change than a broad profile with higher β and a larger growth rate, suggesting that benign saturation, or nonlinear stability, is not guaranteed and not dictated by linear growth. Third, we study the influence of the magnetic configuration, with the equilibrium rotational transform varied by adjusting the planar coil current. With similar growth rates, similar magnitudes of profile change are found regardless of the presence of a low-order resonance, which implies that the saturation mechanism is not specific to a resonant or nonresonant mode. These results indicate that MHD stability should still be treated seriously in stellarator operation and design, for which nonlinear modeling using tools like M3D-C 1 can play an instrumental role.