Description
Infernal modes are pressure-driven MHD instabilities that arise in high-$\beta$ tokamak plasmas characterized by weak magnetic shear and flattened or reversed q profiles. Such configurations are typical of advanced steady-state scenarios with a large bootstrap current fraction. Because infernal modes can be excited at $\beta$ values lower than the stability limit of high-$n$ ballooning modes, they can become the dominant pressure-driven instability, thereby limiting the maximum $\beta$. When they grow to sufficiently large amplitude, these modes may trigger a rapid loss of confinement and are considered one of the primary causes of the $\beta$ collapse observed in tokamak experiments. A quantitative understanding of their nonlinear saturation behavior is therefore crucial for reliable prediction of achievable plasma performance.
In our previous work [Nucl. Fusion 64, 076021 (2024)], nonlinear simulations were performed for two equilibria with different $\beta$ values using the MIPS code (MHD model) and the MEGA code (kinetic–MHD hybrid model) including kinetic thermal ion (KTI) effects. The results revealed a strong dependence of the saturated state on both $\beta$ and kinetic effects. In the higher-$\beta$ case, pressure collapse occurs in both models, and the overall nonlinear behavior remains qualitatively similar. In contrast, in the lower-$\beta$ case, the inclusion of KTIs in the MEGA simulations significantly reduces the saturation level and suppresses pressure flattening, leading to a markedly different nonlinear outcome. These findings indicate that KTI effects can modify the maximum $\beta$ value limited by infernal modes.
In the present study, we extend the analysis using these codes by performing a systematic scan over $\beta$ values spanning the region between these two regimes. Our central objective is to clarify how the nonlinear saturation level evolves as $\beta$ is varied. In particular, we examine whether the saturation level changes gradually with $\beta$ or whether a sharp transition occurs at a certain threshold value. By clarifying this behavior, we aim to elucidate how the maximum $\beta$ value limited by infernal modes is established through nonlinear dynamics and modified by KTI effects.