Time sequence of a simulated "reconnection event" in the NSTX at PPPL. Red and green iso-surfaces of constant pressure are shown. Some frames also show select magnetic field lines before, during, and after the reconnection process. The initial (red) high pressure region has been expelled from the center and replaced by a (green) lower pressure region in this spontaneous, self-regulating event.

S. Jardin, G. Y. Fu, W. Park, X. Tang, E. V. Belova, J. Breslau, and S. Hudson, Princeton Plasma Physics Laboratory
H. R. Strauss, New York University
L. E. Sugiyama, Massachusetts Institute of Technology

Research Objectives
The M3D (Multilevel 3D) Project consists of a multilevel comprehensive plasma simulation code package and applications of various levels of the code to increasingly more realistic fusion problems. M3D is capable of describing the nonlinear behavior of large-scale instabilities in most every magnetic fusion energy confinement configuration, including tokamaks, spherical tokamaks, stellarators, spheromaks, reversed field pinch, and field-reversed configuration. Many phenomena of interest require a plasma description that includes some kinetic effects, and thus the need for the multi-level description.

Computational Approach
The M3D code is basically a magnetohydrodynamics (MHD) code which implies a fluid description of the plasma. However, it is well known that the fluid model of a plasma leaves out many important effects, for example, due to the long-mean-free-path particle orbits and some wave-particle resonant effects. For more realistic simulations, the key factor that determines the degree of realism and also the corresponding computational requirements is the phase-space resolved in the simulation. Thus, the M3D multilevel physics code package has options to resolve increasingly larger phase-spaces, which are thus increasingly more realistic. To resolve velocity space, and hence kinetic effects, we use the df particle method, rather than a Vlasov phase-space fluid model, since as the dimensionality increases, the former becomes much more efficient than the latter model.

Accomplishments
Internal disruption events in spherical tokamaks: We have demonstrated that the spherical tokamak will be unstable to a catastrophic internal instability when the current is too broad and when the central safety factor passes through unity. There is another regime involving double tearing that can also be unstable during current ramp-up. These simulation results show good agreement with recent National Spherical Torus Experiment (NSTX) results.

Flux surfaces and ballooning modes in stellarators: The M3D code has been extensively applied to the quasi-axisymmetric National Compact Stellarator Experiment (NCSX) stellarator design. Resistive simulations, initialized with VMEC equilibria, allow the magnetic field to reconnect and develop islands. Comparisons with equilibria generated with the PIES code are under way, as are studies showing the nonlinear evolution of ballooning modes once the linear stability threshold is exceeded.

Pressure tensor effects on the stability of tearing modes: It was shown that anisotropic pressure effects strongly influence the dynamics and stability of toroidally confined plasmas through the parallel viscous stresses. Inclusion of these effects in the plasma description was shown to greatly influence the stability and evolution of resistive modes.

Nonlinear kinetic stabilization of tilting modes in the field reversed configuration: The global stability of the field-reversed configuration (FRC) has been investigated using fluid electron and kinetic ion simulations. It was shown that the resonant interaction of the tilting mode with ions for which the Doppler-shifted wave frequency matches the betatron frequency is essential for describing the saturation of that mode. At low values of the kinetic parameter s, the tilt instability will saturate nonlinearly through the lengthening of the initial equilibrium and modification of the ion distribution function.

Significance
The M3D code is one of two major extended MHD codes in the nation, the other being NIMROD. Extended MHD goes well beyond the standard MHD model to greatly improve the realism of plasma model by using increasingly more realistic physics models, including various levels of hybrid particle/fluid models. Our simulation studies have already produced many valuable results on fusion plasmas. In a few years, the realism is expected to reach such a level that the fundamental device-scale nonlinear dynamics of magnetized plasma configurations with parameters close to fusion-relevant regimes can be simulated. This capability can help reduce the ultimate cost of developing a practical fusion energy source by billions of dollars. It will also shed light on many contemporary problems in nonlinear science, including magnetic reconnection, self-organization of complex systems, and stochasticity.

Publications
L. E. Sugiyama and W. Park, "A nonlinear two-fluid model for toroidal plasmas," Phys. Plasmas 7, 4644 (2000).

H. R. Strauss and W. Park, "Pellet driven disruptions in tokamaks," Phys. Plasmas 7, 250 (2000).

E. Belova, S. Jardin, et al., "Global stability of the field reversed configuration," Phys. Plasmas (submitted); technical report PPPL-3502 (2000).

http://w3.pppl.gov/~wpark/pop99