Frequency chirping of neoclassical tearing modes by energetic ions

The strong interaction between energetic particles and neoclassical tearing modes (NTMs) have been observed in tokamaks. Energetic ions can affect NTM, while NTM would induce the redistribution and loss of energetic ions. The frequency chirping of NTMs has been observed in TFTR, ASDEX-U, HL-2A and DIII-D. Accompanying it, the losses of energetic ions have also been measured. However, the physics is still unclear. Here, the mechanism of fast frequency chirping of NTMs is studied. On one hand, the resonance between tearing modes and trapped energetic ions can excite a fishbone-like mode. When  exceeds to a critical value, tearing mode would transit to fishbone-like mode[1]. The result is consistent with HL-2A experimental results. On the other hand, the resonance can provide an additional torque to change the evolution of frequency of NTMs[2]. Whether enhancing or damping effect on the frequency depends on the direction of island propagation. If island propagates in the ion diamagnetic drift direction, the frequency would be enhanced dramatically and quickly. As the frequency increases, the resonance intensity increases since the population of resonance energetic ions increases. Then, the torque is enhanced. So the frequency is enhanced quickly. The predicted chirping time (few ms) and island propagation direction (ion diamagnetic drift direction) are well consistent with DIII-D experimental results. If island propagates in the electron diamagnetic drift direction, the frequency is damped to a lower value. Hence, it can be predicted that the resonance effect can affect the locking dynamics of island, and may avoid the island locking and the explosive growth of island to cause disruption.