The China Fusion Engineering Test Reactor (CFETR) is the next device in the Chinese roadmap for the realization of fusion energy, and is currently in the design phase. In this work, the stability of alpha particle-driven Alfvén eigenmodes (AEs) is investigated using a gyrokinetic ion/fluid electron hybrid code. It is found that the toroidal mode numbers of the most unstable modes are n = 7, 8, 10 and the linear growth rate of the n = 10 mode is slightly higher than that of the n = 7 and n = 8 modes. The excitation threshold in central alpha particle beta of the most unstable mode is found to be about β crit,α = 0.2%, which is substantially below the expected value of alpha particle beta (β α = 1.065%) in CFETR. This result indicates that the high-n alpha particle-driven AEs are strongly unstable in CFETR, with many toroidal mode numbers simultaneously destabilized, at least for the CFETR design parameters considered in this work. Furthermore, a systematic study of parameter dependence has been carried out. It is found that the stability of AE with a single toroidal mode number is sensitive to the safety factor profile. However, the overall stability of AEs is much less sensitive to the value of q min when different toroidal mode numbers are considered simultaneously. It is shown that the normalized alpha particle gyro-radius and the alpha particle speed are two important parameters determining the alpha particle drive. The alpha particle drive is maximized for CFETR values of these two parameters. Finally, it is found that the alpha particle-driven AE's growth rate decreases as the thermal ion temperature/density decreases/increases at fixed plasma pressure.
In DIII-D hybrid discharges, the intense Alfvén eigenmode (AE) activity driven by Neutral Beam Injection that is typically observed can be suppressed and replaced by fishbone modes when Electron Cyclotron Current Drive (ECCD) is centrally applied. Simulations have been carried out with the kinetic-magnetohydrodynamic hybrid code M3D-K based on DIII-D discharges #161401 without ECCD and #161403 with ECCD, respectively. In both cases, unstable modes are found—the mode frequency and the mode structure indicate that the instability excited in #161403 is of fishbone type, while that in #161401 is identified as the beta-induced Alfvén eigenmode-like mode. Moreover, we find that the calculated mode frequencies of these two shots are consistent with experimental observations. A systematic scan has been performed to study the instability region of n=1,2,3 modes in (q0,βhot) parameter space, where n is the toroidal mode number, q0 is the safety factor value at the magnetic axis, and βhot is the energetic particle beta. It is found that the transition between AEs and fishbone modes can occur when q0 is changed. In addition, the modes of n=1,2,3 are stable or weakly unstable in the region of Phot/Ptotal≤0.5 and 1.2<q0<1.3, where Phot is the central energetic particle pressure and Ptotal is the central total pressure. These results provide useful guidance for future experiments for minimizing energetic particle-driven instabilities and associated transport.
Linear stability and non-linear dynamics of the fishbone instabilities with reversed safety factor profile have been investigated by the global kinetic-magnetohydrodynamic (MHD) code M3D-K. For the consideration of the fishbone instability with a reversed q profile, there are two different types of the fishbone instability: dual resonant fishbone (DRF) with double q = 1 surfaces and non-resonant fishbone (NRF) with the minimum value of safety factor a little larger than unity. Based on EAST-like parameters, linear simulations show that the DRF is excited by the trapped beam ions when the fast ion pressure exceeds a critical value, and the mode structure of DRF exhibits splitting radial structure due to double q = 1 surfaces. When increases from below unity to above unity, the fishbone instability transits from the DRF to the NRF, and the mode frequency of the NRF is higher than the DRF as the NRF is resonant with fast ions with larger precessional frequency. Nonlinear simulations show that the saturation of the DRF is due to MHD non-linearity with a large n = 0 component. However, the saturation of the NRF is mainly due to the non-linearity of fast ions, and the frequency of the NRF chirps down nonlinearly. The fast ions are redistributed and become flattened due to the DRF or the NRF, and the transport level of the fast ions due to the NRF is weaker with more centrally radial redistribution region in comparison with that of the DRF.
Linear and nonlinear simulations of high-order harmonics q=1 energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics (m=n>1) driven by energetic trapped particles can be higher than the m/n=1/1 component. The high m=n>1 modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonics modes, whereas there is only one precessional resonance for the m/n=1/1 harmonics. The fluid nonlinearity reduces the saturation level of the n=1 component, while it hardly affects those of the high n components, especially the modes with m=n=3,4. The frequency of these modes does not chirp significantly, which is different with the typical fishbone driven by trapped particles. In addition, the flattening region of energetic particle distribution due to high-order harmonics excitation is wider than that due to m/n=1/1 component, although the m/n=1/1 component has a higher saturation amplitude.
Significant variations in MHD activity and fast-ion transport are observed in the DIII-D high-beta, steady-state hybrid discharges with a mixture of electron cyclotron (EC) waves and neutral beam injection (NBI). When electron cyclotron heating (ECH) or current drive (ECCD) is applied, Alfvén eigenmodes (AEs) are usually suppressed and replaced by low-frequency bursting modes. The analysis of a recently compiled database of hybrid discharges suggests that the change of the fast-ion pressure especially the perpendicular pressure is the main factor responsible for the instability transition although the transition in some discharges can also be explained by a slight drop of the safety factor . The lower ratio of fast-ion injection speed vinj to Alfvén speed valfven and slight drop of during ECCD also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction is less than 0.53 and is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. Here, Pf and Ptotal are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The correlation with is weaker, and is around unity in all the cases. The reason why the instability transition correlates with and is that they can significantly modify the drive of low-frequency bursting modes and AEs. The explanation is supported by the observation that low-frequency bursting modes are rarely seen in the hybrids with NBI only, with EC waves and counter-NBI, or with high plasma density. A careful check of the low-frequency bursting modes suggests that they are mainly chirping (neoclassical) tearing modes (referred to as chirping (N)TMs), i.e. the mode frequency firstly jumps up from the steady (N)TM frequency, then chirps down, and finally returns to the steady (N)TM frequency. Occasionally, the (N)TMs are fully stabilized and replaced with pure fishbones. The resonance condition calculation and ‘Kick’ model simulations suggest that (N)TMs and fishbones can interact through modification of the fast ion distribution in phase space, which influences the drive.
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