Computational modeling of neoclassical and resistive MHD tearing modes in tokamaks

Abstract

Numerical studies of the linear and nonlinear evolution of magnetic tearing type modes in three-dimensional toroidal geometry are presented. In addition to traditional resistive MHD effects, where the parameter {Delta}{prime} determines the stability properties, neoclassical effects have been included for the first time in such models. The inclusion of neoclassical physics introduces and additional free-energy source for the nonlinear formation of magnetic islands through the effects of a bootstrap current in Ohm`s law. The neoclassical tearing mode is demonstrated to be destabilized in plasmas which are otherwise {Delta}{prime} stable, albeit once an island width threshold is exceeded. The simulations are based on a set of neoclassical reduced magnetohydrodynamic (MHD) equations in three-dimensional toroidal geometry derived from the two-fluid equations in the limit of small inverse aspect ratio {epsilon} and low plasma pressure {beta} with neoclassical closures for the viscous force {del} {center_dot} {leftrightarrow}{pi}. The poloidal magnetic flux {psi}, the toroidal vorticity {omega}{sup {zeta}}, and the plasma pressure p are time advanced using the parallel projection of Ohm`s law, the toroidal projection of the curl of the momentum equation, and a pressure evolution equation with anisotropic pressure transport parallel to and across magnetic field lines. The equations are implemented in an initial value code which Fourier decomposes equilibrium and perturbation quantities in the poloidal and toroidal directions, and finite differences them radially based on a equilibrium straight magnetic field line representation. An implicit algorithm is used to advance the linear terms; the nonlinear terms are advanced explicitly. The simulations are benchmarked linearly and nonlinearly against single and multiple helicity {Delta}{prime} tearing modes in toroidal geometry in the absence of neo-classical effects.