Nonlinear frequency chirping of the energetic-particle-driven geodesic acoustic mode (EGAM) is investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic fluid. It is demonstrated in the simulation result that both frequency chirping up and chirping down take place in the nonlinear evolution of the EGAM. It is found that two hole-clump pairs are formed in the energetic particle distribution function in two-dimensional velocity space of pitch angle variable and energy. One pair is formed in the phase space region that destabilizes the instability, while the other is formed in the stabilizing region. The transit frequency of the hole (clump) in the destabilizing region chirps up (down), while in the stabilizing region the hole (clump) chirps down (up). The transit frequencies of particles in the holes and clumps are in good agreement with the chirping EGAM frequency indicating that the particles are kept resonant with the EGAM during the nonlinear frequency chirping. Continuous energy transfer takes place from the destabilizing phase space region to the stabilizing region during the spontaneous frequency chirping of the wave.

Strongly magnetized plasmas are rich in spatial and temporal scales, making a computational approach useful for studying these systems. The most accurate model of a magnetized plasma is based on a kinetic equation that describes the evolution of the distribution function for each species in six-dimensional phase space. High dimensionality renders this approach impractical for computations for long time scales. Fluid models are an approximation to the kinetic model. The reduced dimensionality allows a wider range of spatial and/or temporal scales to be explored. Computational modeling requires understanding the ordering and closure approximations, the fundamental waves supported by the equations, and the numerical properties of the discretization scheme. Several ordering and closure schemes are reviewed and discussed, as are their normal modes, and algorithms that can be applied to obtain a numerical solution.

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Optimal strategies for disruption mitigation benefit from the understanding of details both spatially and temporally. Beyond the assessment of the efficacy of a particular proposed Disruption Mitigation System (DMS), ITER's longevity will require accounting of both mitigated and unmitigated disruptions. Accurate models and validated simulations that detail multiple ITER scenarios with mitigated and unmitigated disruptions are essential for accurate estimates of load damage. The primary candidate for ITER's DMS is Shattered Pellet Injection (SPI); its efficacy must be evaluated within the next several years. To perform critical time dependent 3-D nonlinear simulations, we have developed a particle based SPI model in the NIMROD code coupled to its modified single fluid equations with impurity and radiation [Izzo, Nucl. Fusion 46(5), 541 (2006)]. SPI validation simulations of the thermal quench and comparisons to DIII-D impurity scan experiments [Shiraki et al., Phys. Plasmas 23(6), 062516 (2016)] are presented. We also present an initial ITER Q = 10 pure neon SPI simulation and compare it with the DIII-D SPI simulations. NIMROD SPI simulations demonstrate that the ablating fragment drives strong parallel flows that transport the impurities and governs the thermal quench. Analysis of SPI simulations shows that the mixed deuterium/neon SPI results in a more benign thermal quench due to the enhanced transport caused by the additional deuterium. These results suggest that an optimal pellet mixture exists for the SPI system.