The question of how to proceed toward ever more realistic plasma simulation studies using ever increasing computing power is addressed. The answer presented here is the M3D ͑Multilevel 3D͒ project, which has developed a code package with a hierarchy of physics levels that resolve increasingly complete subsets of phase-spaces and are thus increasingly more realistic. The rationale for the multilevel physics models is given. Each physics level is described and examples of its application are given. The existing physics levels are fluid models ͑3D configuration space͒, namely magnetohydrodynamic ͑MHD͒ and two-fluids; and hybrid models, namely gyrokinetic-energetic-particle/MHD ͑5D energetic particle phase-space͒, gyrokinetic-particle-ion/ fluid-electron ͑5D ion phase-space͒, and full-kinetic-particle-ion/fluid-electron level ͑6D ion phase-space͒. Resolving electron phase-space ͑5D or 6D͒ remains a future project.Phase-space-fluid models are not used in favor of ␦ f particle models. A practical and accurate nonlinear fluid closure for noncollisional plasmas seems not likely in the near future.

Global hybrid simulations of energetic particle effects on the n=1 internal kink mode have been carried out for tokamaks. For the Internationa Thermonuclear Experimental Reactor (ITER) [ITER Physics Basis Editors et al, Nucl. Fusion 39, 2137.], 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.

Saturated internal kink modes have been observed in many of the highest toroidal beta discharges of the National Spherical Torus Experiment (NSTX). These modes often cause rotation flattening in the plasma core, can degrade energy confinement, and in some cases contribute to the complete loss of plasma angular momentum and stored energy. Characteristics of the modes are measured using soft X-ray, kinetic profile, and magnetic diagnostics. Toroidal flows approaching Alfvénic speeds, island pressure peaking, and enhanced viscous and diamagnetic effects associated with high-beta may contribute to mode non-linear stabilization. These saturation mechanisms are investigated for NSTX parameters and compared to experiment.

Off-axis sawteeth are often observed in reversed magnetic shear plasmas when the minimum safety factor q is near or below 2. Fluctuations with m/n = 2/1 (m and n are the poloidal and toroidal mode numbers) appear before and after the crashes. Detailed comparison has been made between the measured Te profile evolution during the crash and a nonlinear numerical magnetohydrodynamics (MHD) simulation. The good agreement between the observation and simulation indicates that the off-axis sawteeth are due to a dou ble-tearing magnetic reconnection process.

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A nonlinear numerical model for the two-fluid (electron and ion fluid) description of the evolution of a plasma in toroidal geometry, MH3D-T, is described. The model extends the “drift” ordering for small perturbations to arbitrary perturbation size. It is similar, but not identical, to the collisional Braginskii equations. The ion gyroviscous stress tensor, Hall terms, temperature diamagnetic drifts, and a separate electron pressure evolution are included. The model stresses the (fluid) parallel dynamics by solving the density evolution together with the temperature equations, including the thermal equilibration along the magnetic field. It includes the neoclassical, collisional parallel viscous forces for electrons and ions. The model has been benchmarked against the stabilizing effects of the ion diamagnetic drift ω*i on the m=1, n=1 reconnecting mode in a cylinder. The stabilization mechanism is shown to be poloidal rotation of the global kink flow of the plasma mass vi within q<1, relative to the location of the magnetic field X-point within the reconnection layer. The ion ω*i-drift is also shown to cause frequency-splitting for the toroidal Alfvén eigenmode (TAE). Basic diamagnetic and neoclassical magnetohydrodynamic (MHD) effects on magnetic island evolution and rotation are discussed. The dynamics of the plasma along the magnetic field, when compressibility, parallel thermal conductivity, plasma density evolution, and full toroidal geometry are kept, are found to have strong effects on both linear growth rates and nonlinear evolution. The nonlinear coupling of magnetic islands, driven by perturbations of different toroidal mode number, is enhanced by the density evolution in both MHD and two-fluids.

Gyrokinetic-magnetohydrodynamic hybrid simulations have been carried out to study the nonlinear saturation of the torodicity-induced Alfven eigenmode driven by energetic particles in a tokamak plasma. It is shown that wave-particle trapping is the nonlinear saturation mechanism for the parameters considered. The corresponding density profile flattening of the hot particles is observed. The saturation amplitude is proportional to the square of the linear growth rate. In addition, a new n = 1, m = 0 global Alfven eigenmode is shown to be excited by the energetic particles.