Fishbone instability excited by the supra-thermal circulating electrons in tokamaks is investigated. It is found for first time that the procession of all the circulating electrons is in ion diamagnetic direction if magnetic share is neglected. The circulating electrons, which experience both high field side and low field side, play bigger role on the modes than the barely trapped electrons. The analyses show that the mode frequency is close to the procession frequency of circulating electrons comparable with experiment observations. The correlation of the theory with experiments is discussed.
Fishbone instabilities, driven by trapped and barely passing energetic particles (EPs), including electrons and ions (EEs or EIs), are numerically studied with the spatial distribution of EPs taken into account. The dispersion relations of the modes are derived for slowing-down and Maxwellian models of EP energy distribution. It is found that the modes with frequency comparable to the toroidal precession frequency ω d of EPs are resonantly excited. Electron and ion fishbone modes share the same growth rates and real frequencies but rotate in opposite directions. The frequency of the modes is found to be higher in the case of near-axis heating than that of off-axis heating. The fishbone instabilities can only be excited by barely trapped or barely passing and deeply trapped particles in positive and negative spatial density gradient regions, respectively. In addition, the most interesting feature of the fishbone modes induced by barely passing particles is that there exists a second stable regime in the higher β h (pressure of EPs/toroidal magnetic pressure) region, and the modes exist in the range of β th1 < β h < β th2 (β th is threshold or critical beta of EPs) only. The results are well confirmed with Nyquist technology. The possible physical mechanism for the existence of the second stable regime is discussed.
Fast ion prompt loss induced by resonant magnetic perturbations (RMPs) is simulated by solving Hamiltonian equations strictly in the guiding center coordinate system. Full orbit simulations show that the prompt loss rate can increase significantly in resonant regions when RMPs are added. Furthermore, the prompt loss rate is larger in the low-field side than in the high-field side in tokamak plasmas. Detailed analyses show that a number of trapped ions which lie near the center of the trapped region can be lost, because of the enhancement of radial orbit drifts induced by the resonance between RMPs and the unperturbed orbit. Meanwhile, orbit conversion from counter-passing orbit to trapped orbit occurs near the trapped-passing boundary in the low-field side, while it occurs near the co-counter boundary in the high-field side, both of which play an important role in prompt loss. Simulations also demonstrate a periodicity for orbit drifts, and the mechanism of drift periodicity results from the resonance between RMP and the equilibrium magnetic field.
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