2 pm, April 30 - 1 pm, May 2, 1997
Madison, Wisconsin, USA
(following the Sherwood Theory Conference)

To PROGRAM

To OVERVIEW and SUMMARY

Numerical and Analytic studies using Nonlinear MHD, and Nonlinear Extended-MHD such as Kinetic-MHD, Neoclassical-MHD, Two-fluids, Hybrid Particle/MHD etc, with emphasis on application to experiment.

Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas.

• Current state of nonlinear MHD and extended-MHD simulations
• Comparisons to experimental data
• Discussions between experimentalists and theorists
• Equations for extended-MHD models, closures
• Computational techniques such as unstructured mesh and new algorithms
• Paths toward more comprehensive simulation models, etc.

W. Kerner (JET, EU)
W. Park (PPPL, USA)
S. Tokuda (JAERI, Japan)

This was a lively workshop with 46 registered participants from throughout the world. The presentations and discussions at the workshop gave the following picture of the status and prospect for nonlinear MHD and extended-MHD studies.

Nonlinear MHD simulations can reproduce many qualitative phenomena observed in experiments; for example, disruptions, resistive interchange modes, double tearing sawteeth, locked modes, etc. These simulations provide valuable insights and understandings of these phenomena in present and future experiments. However, the dissipation parameters, in particular the Lundquist number S, in the simulations are still about three orders of magnitude away from the actual values in large tokamaks. As this gap narrows with increasing computer capabilities, effects that are higher order than MHD become even more important for quantitatively realistic simulations.

A full particle model or Vlasov fluid model including collisions contain such effects, but the computational requirements are currently prohibitive for global electromagnetic simulations of large tokamaks, even when a gyrokinetic formalism with a delta-f method is used. Therefore, a fluid moments formulation or a particle/fluid hybrid picture has to be used, at least for the near future. Such models can be called extended-MHD models since they support MHD waves in a fluid or a partially fluid picture, and the MHD physics still provides the dominant potential structure.

Fluid extended-MHD models encounter closure questions. In multi-fluid models, approximate neoclassical and Landau closures have been devised. The neoclassical closure has been used to explore the importance of the bootstrap-current-driven neoclassical tearing modes, and experimental comparisons presented showed strong correlations. More accurate schemes, including double adiabatic type equations with collisional and Landau damping, and a nonlinear Landau closure, were proposed. However, further study would be needed to reduce the difficulties involved in the actual usage.

Particle/fluid hybrid schemes use particles to close the fluid moment equations. Such particle closure schemes are more accurate but also computationally more expensive compared to fluid moments formulations. Gyrokinetic delta-f particle/fluid hybrid results presented showed successful simulations of nonlinear saturation of TAE modes and fishbone oscillations, m=1 reconnection, and drift Alfven-ballooning modes in a space physics context. A possibility was mentioned that the computational requirements could be significantly reduced by a mixed particle-fluid closure scheme, e.g., with a reduced dimensionality for the particle space.

The consensus was that we have to pursue the various approaches described above to progress toward efficient quantitatively predictive simulations. It was also pointed out that by incorporating multi-level physics models in one code package, one can better understand the physics involved and the soundness of the results.

As for numerical techniques, unstructured mesh MHD code results were presented, and a structured/unstructured hybrid mesh scheme was proposed. Discretized dispersion relations for various representation and discretization schemes were presented. Although possible only in a simple geometry, such dispersion relations give valuable insight.

The rapidly increasing computing power should substantially increase the realism of simulations and therefore their usefulness in the future, especially if coupled with more innovative methodologies such as more efficient mesh schemes or closure schemes.

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