Excitation of 2/1 fishbone-like modes by trapped energetic ions

Abstract

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.

The influence of electron cyclotron resonance heating on ion-driven fishbone instability

“…When S M > 10 5 , the critical beta β cr TEI0 is almost unchanged as S M increases. This further confirms the above result and is consistent with previous theoretical work [9,10,30]. As pointed out above, the value of S M from experimental parameters is sufficiently large that the critical beta, β cr TEI0 , remains unchanged with increasing S M .…”

“…√ m e 2/3 T e ( r) [34] is the slowingdown critical energy and β TEI ( r) = β TEI0 exp(− r/ σ i ) [30].…”

“…Namely, the effect of onaxis TEEs is weak. This is because the real part of δ W is related to the growth rate, since δ W R = −iωs 2 s /ω H for the small-resistivity limit [7,9,30], and the growth rate represents the mode's stability. From figure 7, Im[δ W TEE ] is much smaller than Im[δ W TEI ] for both off-axis and on-axis cases, namely the resonance between TEEs and fishbone instability can be neglected.…”

Frequency chirping of neoclassical tearing modes by energetic ions

“…Recently, frequency chirping up and back down of NTMs has also been observed on DIII-D, where the chirping time is a few milliseconds, and has been suggested that trapped energetic ions may be responsible for this [21]. Some efforts [22][23][24] have been made to theoretcially understand the underlying physics. In [22], it was pointed out that resonance between trapped energetic ions and rotating NTMs provides a torque to accelerate the rotation of the NTMs; however, the estimated chirping time is much longer than that observed in the experiments.…”

“…In [22], it was pointed out that resonance between trapped energetic ions and rotating NTMs provides a torque to accelerate the rotation of the NTMs; however, the estimated chirping time is much longer than that observed in the experiments. Two recent articles [23,24] have described the bursting and chirping of tearing modes on HL-2A. In [23], it was shown that resonance between trapped energetic ions and tearing modes can drive a fishbone-like mode.…”