Benign Saturation of Ideal Ballooning Instability in a High-Performance Stellarator

To examine the robustness of the designed 5% $\ensuremath{\beta}$ limit for high-performance operation in the W7-X stellarator, we undertake nonlinear magnetohydrodynamic (MHD) simulations of pressure-driven instabilities using the m3d-c1 code. Consistent with linear analyses, ideal ballooning instabilities occur as $\ensuremath{\beta}$ exceeds 5% in the standard configuration. Nonetheless, the modes saturate nonlinearly at relatively low levels without triggering large-scale crashes, even though confinement degradation worsens as $\ensuremath{\beta}$ increases. In contrast, in an alternative configuration with nearly zero magnetic shear, ideal interchange modes induce a pressure crash at $\ensuremath{\beta}=1%$. These results suggest that the standard W7-X configuration might have a soft $\ensuremath{\beta}$ limit that is fairly immune to major MHD events, which enhances the appeal of the stellarator approach to steady-state fusion reactors.