Theoretical study of long-lived mode in tokamaks

Long-lived mode (LLM) in rotating plasmas is studied by using a alternative dispersion relation. This work offers a theoretical interpretation of LLM observed in experiments [Heidbrink, Phys. Rev. Lett. 57, 835 (1986)10.1103/PhysRevLett.57.835; Chapman, Nucl. Fusion 50, 045007 (2010)10.1088/0029-5515/50/4/045007]. It is found that in rotating plasmas, LLM can transform from the fishbone mode. The real frequency of LLM, independent of the characteristic frequency of energetic ions (EIs), is proportional to the on-axis rotation frequency of bulk plasma. The key conditions to cause transition between the fishbone mode and LLM are weak magnetic shear (for both monotonic and nonmonotonic safety factor profile) and plasma rotation. The fishbone mode can evolve into LLM only when rotating speed is bigger than a critical value in low shear plasmas. The critical beta of EIs to induce LLM is very low. LLM is nonresonantly excited by EIs, and the driving sources mainly come from plasma inertia.