We discuss the processes underlying the excitation of fishbone-like internal kink instabilities driven by supra-thermal electrons generated experimentally by different means: Electron Cyclotron Resonance Heating (ECRH) and by Lower Hybrid (LH) power injection. The peculiarity and interest of exciting these electron fishbones by ECRH only or by LH only is also analyzed. Not only the mode stability is explained, but also the transition between steady state nonlinear oscillations to bursting (almost regular) pulsations, as observed in FTU, is interpreted in terms of the LH power input. These results are directly relevant to the investigation of trapped alpha particle interactions with low-frequency MHD modes in burning plasmas: in fact, alpha particles in reactor relevant conditions are characterized by small dimensionless orbits, similarly to electrons; the trapped particle bounce averaged dynamics, meanwhile, depends on energy and not mass.
Phases of nonlinear double tearing modes are studied numerically. The first two phases lead to the formation and growth of magnetic islands and are followed by a fast reconnection phase to complete the process, driven by a process of neighboring magnetic separatrices merging and magnetic islands coupling. The fast growth can be understood as a result of the island interaction equivalent to a steadily inward flux boundary driven. Resistivity dependences for various phases are studied and shown by scaling analysis for the first time. It is found that after an early Sweet-Parker phase with a eta(1/2)-scale, a slow nonlinear phase in a Rutherford regime with a eta(1)-scale is followed by the fast reconnection phase with a eta(1/5)-scale.
Sheared flow layers driven by magnetic energy, released in tearing-reconnection processes inherent in dissipative magnetohydrodynamics, are proposed as a triggering mechanism for the creation of the internal transport barrier (ITB) in tokamak plasmas. The double tearing mode, mediated by anomalous electron viscosity in configurations with a nonmonotonic safety factor, is investigated as an example. Particular emphasis is placed on the formation of sheared poloidal flow layers in the vicinity of the magnetic islands. A quasilinear simulation demonstrates that the sheared flows induced by the mode have desirable characteristics (lying just outside the magnetic islands), and sufficient levels required for ITB formation. A possible explanation is also proffered for the experimental observation that the transport barriers are preferentially formed in the proximity of low-order rational surfaces.
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.
The linear behaviors of the double tearing mode (DTM) mediated by parallel electron viscosity in cylindrical plasmas with reversed magnetic shear and thus two resonant rational flux surfaces is numerically investigated. The distance between the two surfaces is found to play an important role for modes with poloidal mode number m>1. Two modes, one of which is centered at the inner rational surface and the other is located between the two surfaces, are simultaneously unstable and the growth rates show the standard single tearing mode (STM) scaling as γ∝R−1/3 when the distance is large (here, the Reynolds number R≡τυ/τh, τυ, and τh are, respectively, the viscosity penetration time of the magnetic field and the Alfvén time for a plasma sheet of width a). The latter is unstable only and the growth rate transits to the standard DTM scaling as γ∝R−1/5 for low-m (e.g., m<4) modes and keeps the STM scaling γ∝R−1/3 for high-m (e.g., m∼10) modes, which are found dominant, when the distance is decreased. In contrast, two unstable modes extending from plasma center to the two rational surfaces, respectively, coexist and the growth rates always show the scaling of γ∝R−1/5, independent of the distance, when the poloidal mode number m=1. The DTMs mediated by electron viscosity are enhanced by plasma resistivity of the range where the growth rate of the mode induced by the latter alone is comparable with that mediated by the former alone and vice versa. Otherwise, the growth rate of the mode is equal to the higher of the modes mediated by resistivity or electron viscosity alone when both of them are taken into account.
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.
The internal kink (fishbone) modes, driven by barely passing energetic ions (EIs), are numerically studied with the spatial distribution of the EIs taking into account. It is found that the modes with frequencies comparable to the toroidal precession frequencies are excited by resonant interaction with the EIs. Positive and negative density gradient dominating cases, corresponding to off- and near-axis depositions of neutral beam injection (NBI), respectively, are analyzed in detail. The most interesting and important feature of the modes is that there exists a second stable regime in higher βh (=pressure of EIs/toroidal magnetic pressure) range, and the modes may only be excited by the barely passing EIs in a region of βth1<βh<βth2 (βth is threshold or critical beta of EIs). Besides, the unstable modes require minimum density gradients and minimum radial positions of NBI deposition. The physics mechanism for the existence of the second stable regime is discussed. The results may provide a means of reducing or even preventing the loss of NBI energetic ions and increasing the heating efficiency by adjusting the pitch angle and driving the system into the second stable regime fast enough.
The effects of energetic ions on the electric field structure and the energy deposition of kinetic Alfvén wave (KAW) in a tokamak plasma are considered. A cylindrical geometry is adopted and a linearized kinetic model including the bulk plasma and the energetic ions is established. These effects of fusion alpha particles (abbreviated, alphas) in deuterium–tritium (D–T) tokamak plasmas are numerically analyzed. The energetic ions tend to alter the wave structure and the energy deposition. The absorption of the kinetic Alfvén wave by the bulk plasma depends sensitively on both the velocity distribution of alphas and the spatial profile of the alpha particle density, as well as on the frequency of the injected wave. Numerical results of the wave structure and the power absorption are given for the parameters of D–T plasmas. The present studies lead to the following discoveries: (1) The slowing-down alpha particle distribution reduces the KAWs energy deposition and the Maxwellian alphas have hardly any influence over it; (2) the more the (slowing-down) alphas near the resonant layer, the more heavily they prevent the KAWs power absorption by the bulk plasma; (3) the lower frequency of the injected wave within the range of KAWs continuum, the more heavily the KAWs structure and power absorption by the bulk plasma are affected by alpha particles; and (4) the energy deposition decreases rapidly as the total number of alphas increases.
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