Weak and reversed magnetic shear effects on internal kink and fishbone modes

TL;DR

The paper tackles how weak and reversed magnetic shear shapes internal kink and fishbone instabilities in tokamaks under energetic particle driver. It uses a hybrid kinetic-MHD model implemented in NIMROD to perform linear simulations in a circular limiter configuration, varying q profiles, energetic particle beta fractions, and internal transport barrier parameters. The results show a nonmonotonic stabilization of the resonant kink by reversed shear, EPs can shift the balance between kink and fishbone and even promote double kink/double fishbone structures, and nonresonant modes follow a Delta q stabilization with a beta_f–dependent threshold; ITB shaping further strengthens stabilization. These findings provide actionable insights for optimizing q-profile shaping and ITB formation to suppress deleterious MHD activity in advanced tokamak scenarios.

Abstract

Advanced tokamak scenarios often feature weak or reversed magnetic shear configurations. In this study, the hybrid kinetic-MHD model implemented in the NIMROD code is used to investigate the effects of reversed magnetic shear on internal kink and fishbone mode in a circular shaped limiter tokamak. In the absence of energetic particles (EPs), the mode growth rate initially increases and then decreases as the magnetic shear changes from positive to negative, indicating stabilizing effects of the reversed magnetic shear on the internal kink mode. In the presence of EPs, when the reversed magnetic shear region is sufficiently narrow, the transition from internal kink/fishbone modes to double kink/fishbone modes takes place, and the stabilizing effects of the reversed magnetic shear can significantly dominate the destabilization of EPs. For non-resonant modes, the EP beta fraction $β_f$ for excitation increases with $q_{min}$, concurrent with progressively lower growth rates in non-resonant fishbone modes. When the equilibrium profile has an internal transport barrier (ITB), broader ITB widths suppress internal kink modes more effectively, whereas steeper temperature gradients strengthen EP stabilization.

Figures (12)

• Figure 1: (a) Equilibrium pressure profile and (b) $q$-profiles as functions of normalized minor radius $\rho$ with various magnetic shear $\hat{s}$ at $q=1$ surface. (c) Equilibrium magnetic flux-aligned mesh for poloidal plane used in NIMROD simulations.
• Figure 2: Normalized growth rates of the $(m,n)$=$(1,1)$ mode as functions (a) the magnetic shear $\hat{s}$ at $q=1$ surface and (b) the minimum of $q$ profile $q_{min}$ in absence of EPs.
• Figure 3: Pressure perturbation contours of the $1/1$ kink mode in absence of EPs for the magnetic shear (a) $\hat{s} =-0.8$, (b) $\hat{s} = -0.2$, (c) $\hat{s} = 0$, (d) $\hat{s} = 0.7$, (e) $\hat{s} = 0.8$ at $q=1$ surface.
• Figure 4: (a) Normalized growth rates and (b) real frequencies as functions of the magnetic shear $\hat{s}$ at $q=1$ surface for $\beta\rm_f=0.1, 0.5$.
• Figure 5: Normalized growth rates and real frequencies as functions of the EP beta fraction $\beta\rm_f$ for (a) $\hat{s}=-0.2$, (b) $\hat{s}=0$, (c) $\hat{s}=0.2$ at $q=1$ surface.