M3D-K simulations of low-n instability under neutral beam injection conditions in EXL-50U

Global kinetic-magnetohydrodynamic (MHD) hybrid simulations based on representative EXL-50U design parameters are carried out with the M3D-K code to investigate low-n kink-type instabilities driven by passing energetic beam ions under neutral beam injection (NBI) conditions. For the n=1 fishbone mode, phase-space diagnostics show that the perturbed energetic-particle (EP) distribution aligns with the p=-1 resonance, indicating a dominant passing-ion resonance \omega=\omega_\phi-\omega_\theta. By scanning the beam injection energy, we find that the mode frequency follows \omega\propto\sqrtE_0, consistent with the dependence of passing-ion transit frequencies on particle speed. By scanning the EP beta, we observe that the linear growth rate shows an overall increasing trend with \beta_\rmhot0 within the unstable range considered, reflecting a stronger EP drive at higher fast-ion pressure. At sufficiently high beta, the same passing-ion drive mechanism can also excite n=2 and n=3 instabilities, whose structures are dominated by the n/m=2/2 and n/m=3/3 components, respectively. The corresponding phase-space analysis confirms the generalized resonance condition \omega=n\omega_\phi-n\omega_\theta for n=1–3. These results provide a resonance-based interpretation of NBI-driven low-n activity and offer reference for planning and interpreting forthcoming EXL-50U protium-phase experiments.