Effects of critical energy on the excitation of 2/1 fishbone-like modes during tearing modes in a generalized multiphase flow system

The plasma in a tokamak can be viewed as a complex multiphase magnetohydrodynamic system composed of various "flowing components"; such as energetic ions, energetic electrons, and background plasma. The interactions and energy exchange between these different phases significantly affect the instability of the plasma. This work investigates the effects of critical energy on the excitation of the 2/1 fishbone-like mode (FLM) by trapped energetic ions in the presence of the tearing mode (TM) in a tokamak multiphase flow system. The combination of analytical theory and numerical simulations is used to analyze how critical energy modifies the interactions between different phases and affects the excitation of instabilities. The influence of parameters such as the total adiabatic potential energy, magnetic Reynolds number, and magnetic shear on instabilities in multiphase flow is examined. The results show that the critical energy has a destabilizing effect on the 2/1 FLM and can significantly reduce the beta threshold of the 2/1 FLM, significantly impacting the stability and dynamics of the multiphase system. This study provides a theoretical foundation for predicting instabilities in multiphase flow systems and holds significant implications for applications in tokamak devices and beyond.