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.
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