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The influence of energetic particles and plasma resistivity on the n = 1 ( n is the toroidal mode number) internal kink and fishbone modes in tokamak plasmas is numerically investigated, using the full toroidal, resistive magnetohydrodynamic-kinetic hybrid stability code MARS-K [Liu et al., Phys. Plasmas 15 112503 (2008)]. The results show that energetic particles can either stabilize or destabilize the ideal internal kink mode, depending on the radial profiles of the particles' density and pressure. Resistive fishbones with and without an ideal wall are investigated. It is found that, in the presence of energetic particles as well as plasma resistivity, two branches of unstable roots exist, for a plasma which is ideally stable to the internal kink instability. One is the resistive internal kink mode. The other is the resistive fishbone mode. These two-branch solutions show similar behaviors, independent of whether the initial ideal kink stability is due to an ideal wall stabilization for high-beta plasmas, or due to a stable equilibrium below the Bussac pressure limit. For a realistic toroidal plasma, the resistive internal kink is the dominant instability, which grows much faster than the resistive fishbone. The plasma resistivity destabilizes the resistive internal kink while stabilizes the resistive fishbone. Systematic comparison with an analytic model qualitatively confirms the MARS-K results. Compared to analytic models based on the perturbative approach, MARS-K offers an improved physics model via self-consistent treatment of coupling between the fluid and kinetic effects due to energetic particles. [ABSTRACT FROM AUTHOR]

Features of fishbone-like trapped energetic electrons driven modes (TEEMs), which are a particular manifestation of the fishbone gap modes, are investigated taking into account model radial profile and the pitch angle distribution of the energetic electrons (EEs). The TEEMs are found unstable only when the beta values of EEs βh (¼pressure of the energetic electrons/pressure of magnetic field) are higher than certain critical values which are proportional to perturbed energy δWc of background plasma and much lower than that for traditional fishbone modes. In addition, TEEMs become stable again and enter a second stable regime whenβh values are higher than second critical values. Furthermore, the modes can only be excited in plasmas which are stable for MHD instabilities. The real frequency and growth rate of the modes are approximately linear and parabolic functions of βh, respectively. The real frequency is very low but not zero in the vicinity of lower beta region, whereas it is comparable to the toroidal precession frequency of the EEs in higher critical beta region. The numerical results show that the second stable regime is easy to form when q=1 flux surface is close to the magnetic axis. Suitable density gradient of EEs and magnetic shear are other two necessary conditions for excitation of the TEEMs. [ABSTRACT FROM AUTHOR]

A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does not contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects. [ABSTRACT FROM AUTHOR]