A new branch of the m/n = 2/1 fishbone-like mode is found to be excitated by trapped energetic ions when the tearing mode is unstable. An energy-principle-based dispersion relation is derived and analyzed, which incorporates the wave-particle resonance and the resistive layer physics. Once the beta amplitude of trapped energetic ions exceeds a critical value, 2/1 fishbone-like instabilities would appear. The mode transition from tearing mode to 2/1 fishbone-like mode will be triggered with the increasing beta of trapped energetic ions. The total effects of the ideal magnetohydrodynamic potential energy and the adiabatic contribution of trapped energetic ions on the real frequency and growth rate of 2/1 fishbone-like modes are investigated; the effects of magnetic Reynolds number and magnetic shear are also studied. Both resistivity and magnetic shear play a stable role on 2/1 fishbone-like modes. An implication of the theory is conducive to understanding the 2/1 fishbone-like activities observed recently in HL-2A.
撕裂模不稳定时，发现了一种新的m/n = 2/1鱼骨模分支，由捕获高能粒子激发。推导并分析了基于能量原理的色散关系，其中包含了波-粒子共振和电阻层物理。当捕获高能粒子的β值超过临界值时，2/1鱼骨模不稳定性将出现。随着捕获高能粒子β值的增加，模将从撕裂模转变为2/1鱼骨模。研究了理想磁流体力学势能与捕获高能粒子绝热贡献对2/1鱼骨模实频率和增长率的综合影响，同时考察了磁雷诺数和磁剪切的作用。电阻率和磁剪切对2/1鱼骨模均起稳定作用。该理论的意义有助于理解近期在HL-2A上观测到的2/1鱼骨模活动。