Nonlinear simulation studies of tokamaks and STs

Abstract

The multilevel physics, massively parallel plasma simulation code, M3D has been used to study spherical toris (STs) and tokamaks. The magnitude of outboard shift of density profiles relative to electron temperature profiles seen in NSTX under strong toroidal flow is explained. Internal reconnection events in ST discharges can be classified depending on the crash mechanism, just as in tokamak discharges; a sawtooth crash, disruption due to stochasticity, or high-β disruption. Toroidal shear flow can reduce linear growth of internal kink. It has a strong stabilizing effect nonlinearly and causes mode saturation if its profile is maintained, e.g. through a fast momentum source. Normally, however, the flow profile itself flattens during the reconnection process, allowing a complete reconnection to occur. In some cases, the maximum density and pressure spontaneously occur inside the island and cause mode saturation. Gyrokinetic hot particle/MHD hybrid studies of NSTX show the effects of fluid compression on a fast-ion driven n = 1 mode. MHD studies of recent tokamak experiments with a central current hole indicate that the current clamping is due to sawtooth-like crashes, but with n = 0.

Beta-limiting MHD Instabilities in Improved-performance NSTX Spherical Torus Plasmas

“…Initial calculations using the M3D code for NSTX [37] find that for self-consistent MHD equilibria with flow included, linear growth rates of n=1 internal pressure-driven kink modes with q(0) < 1 can be reduced by as much as a factor of 3 due to flow shear. Fast particle effects, two-fluid effects, and having q(0) > 1 are all further stabilizing, and non-linearly saturated states with β values significantly above ideal-marginal values may be possible.…”

Internal Kink Mode Dynamics in High-beta NSTX Plasmas

“…Nonlinear simulations of the 1/1 mode using the M3D code in the single-fluid resistive MHD approximation [30] did find saturated states under some conditions. Such states…”

“…For a high aspect ratio tokamak with circular flux surfaces, the internal kink instability growth rate including sheared rotation can be expressed as [19]: The potential stabilizing effect of sheared toroidal flow on the 1/1 mode in NSTX has previously been studied with the M3D code [30]. For typical parameters in NSTX, M3D studies find that nonlinear saturation of the 1/1 mode is not possible via shearedflow alone for fixed momentum source rate.…”

Finite element and higher order difference formulations for modelling heat transport in magnetised plasmas

“…As most of the existing non-linear MHD codes (see e.g. [2,3]) are based, however, on a finite element approach it is desirable to develop also a finite element scheme with similar properties as our finite difference formulation.…”