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Nonlinear simulations of sawteeth and related energetic particle transport are carried out using the kinetic/magnetohydrodynamic (MHD) hybrid code M3D-K. MHD simulations show repeated sawtooth cycles for a model tokamak equilibrium. Furthermore, test particle simulations are carried out to study the energetic particle transport due to a sawtooth crash. The results show that energetic particles are redistributed radially in the plasma core, depending on pitch angle and energy. For trapped particles, the redistribution occurs for particle energy below a critical value in agreement with existing theories. For co-passing particles, the redistribution is strong with little dependence on particle energy. In contrast, the redistribution level of counter-passing particles decreases with increasing particle energy. [ABSTRACT FROM AUTHOR]

A set of scalar variables and projection operators for the vector momentum and magnetic field evolution equations is presented that has several unique and desirable properties, making it a preferred system for solving the magnetohydrodynamic equations in a torus with a strong toroidal magnetic field. A “weak form” of these equations is derived that explicitly conserves energy and is suitable for a Galerkin finite element formulation provided the basis elements have C1 continuity. Systems of reduced equations are discussed, along with their energy conservation properties. An implicit time advance is presented that adds diagonally dominant self-adjoint energy terms to the mass matrix to obtain numerical stability. [ABSTRACT FROM AUTHOR]

The sawtooth instability is one of the most fundamental dynamics of an inductive tokamak discharge such as will occur in ITER [R. Aymar et al., Plasma Phys. Controlled Fusion 44, 519 (2002)]. Sawtooth behavior is complex and remains incompletely explained. The Center for Extended MHD Modeling (CEMM) SciDAC project has undertaken an ambitious campaign to model this periodic motion in a small tokamak as accurately as possible using the extended MHD model. Both M3D [W. Park et al., Phys. Plasmas 6, 1796 (1999)] and NIMROD [C. R. Sovinec et al., Phys. Plasmas 10, 1727 (2003)] have been applied to this problem. Preliminary nonlinear MHD results show pronounced stochasticity in the magnetic field following the sawtooth crash but are not yet fully converged. Compared to the MHD model, extended MHD predicts plasma rotation, faster reconnection, and reduced field line stochasticity in the crash aftermath. The multiple time and space scales associated with the reconnection layer and growth time make this an extremely challenging computational problem. However, these calculations are providing useful guidelines to the numerical and physical requirements for more rigorous future studies. [ABSTRACT FROM AUTHOR]

Global hybrid simulations of energetic particle effects on the n=1 internal kink mode have been carried out for tokamaks. For the International Thermonuclear Experimental Reactor (ITER) [ITER Physics Basis Editors et al., Nucl. Fusion 39, 2137 (1999)], it is shown that alpha particle effects are stabilizing for the internal kink mode. However, the elongation of ITER reduces the stabilization effects significantly. Nonlinear simulations of the precessional drift fishbone instability for circular tokamak plasmas show that the mode saturates due to flattening of the particle distribution function near the resonance region. The mode frequency chirps down rapidly as the flattening region expands radially outward. Fluid nonlinearity reduces the saturation level. [ABSTRACT FROM AUTHOR]

Extensive linear and nonlinear simulations have been carried out to investigate the energetic particle-driven fishbone instability in spherical tokamak plasmas with weakly reversed q profile and the qmin slightly above unity. The global kinetic-MHD hybrid code M3D-K is used. Numerical results show that a fishbone instability is excited by energetic beam ions preferentially at higher qmin values, consistent with the observed appearance of the fishbone before the 'long-lived mode' in MAST and NSTX experiments. In contrast, at lower qmin values, the fishbone tends to be stable. In this case, the beam ion effects are strongly stabilizing for the non-resonant kink mode. Nonlinear simulations show that the fishbone saturates with strong downward frequency chirping as well as radial flattening of the beam ion distribution. An (m, n) = (2, 1) magnetic island is found to be driven nonlinearly by the fishbone instability, which could provide a trigger for the (2, 1) neoclassical tearing mode sometimes observed after the fishbone instability in NSTX. [ABSTRACT FROM AUTHOR]

We offer a response to the claims of L. E. Zakharov. [ABSTRACT FROM AUTHOR]