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.

We present an ultrafast neural network (NN) model, QLKNN, which predicts core tokamak transport heat and particle fluxes. QLKNN is a surrogate model based on a database of 300 million flux calculations of the quasilinear gyrokinetic transport model QuaLiKiz. The database covers a wide range of realistic tokamak core parameters. Physical features such as the existence of a critical gradient for the onset of turbulent transport were integrated into the neural network training methodology. We have coupled QLKNN to the tokamak modelling framework JINTRAC and rapid control-oriented tokamak transport solver RAPTOR. The coupled frameworks are demonstrated and validated through application to three JET shots covering a representative spread of H-mode operating space, predicting turbulent transport of energy and particles in the plasma core. JINTRAC-QLKNN and RAPTOR-QLKNN are able to accurately reproduce JINTRAC-QuaLiKiz T i,e and n e profiles, but 3 to 5 orders of magnitude faster. Simulations which take hours are reduced down to only a few tens of seconds. The discrepancy in the final source-driven predicted profiles between QLKNN and QuaLiKiz is on the order 1%-15%. Also the dynamic behaviour was well captured by QLKNN, with differences of only 4%-10% compared to JINTRAC-QuaLiKiz observed at mid-radius, for a study of density buildup following the L-H transition. Deployment of neural network surrogate models in multi-physics integrated tokamak modelling is a promising route towards enabling accurate and fast tokamak scenario optimization, Uncertainty Quantification, and control applications.

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