Computational modeling of neoclassical and resistive magnetohydrodynamic tearing modes in tokamaks

Abstract

Numerical studies of the nonlinear evolution of magnetohydrodynamic-type tearing modes in three-dimensional toroidal geometry with neoclassical effects are presented. The inclusion of neoclassical physics introduces an 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 ⌬Ј stable, albeit once an island width threshold is exceeded. The plasma pressure dynamics and neoclassical tearing growth is shown to be sensitive to the choice of the ratio of the parallel to perpendicular diffusivity ( ʈ / Ќ ). The study is completed with a demonstration and theoretical comparison of the threshold for single helicity neoclassical magnetohydrodynamic tearing modes, which is described based on parameter scans of the local pressure gradient, the ratio of perpendicular to parallel pressure diffusivities Ќ / ʈ , and the magnitude of an initial seed magnetic perturbation.

Generalized reduced magnetohydrodynamic equations

“…For conventional reduced MHD where there is no such distinction, it is difficult to incorporate all of the relevent physics. 7,17 However, in the present formulation, the neoclassical physics is easily captured.…”

“…It is important to realize that this effect cannot be represented in conventional reduced MHD descriptions since the only perturbed flow allowed within the flux surface is poloidal. 17 Further, the presence of a viscous term in the vorticity equation in combination with the parallel momentum balance gives the neoclassical polarization-current enhancement of neoclassical MHD theory. 7 For the perturbed electron stress tensor, the form is simplified if we order the relation between the electron velocity V ជ e and the MHD variables that we are evolving:…”

Observation of spontaneous neoclassical tearing modes

“…3. Various theoretical treatments have estimated this constant to be as low as 3.17 [19] and as high as 9.26 [20]. The actual best fit of this parameter to experimental data has varied from as low as 1.7 [12,21] to 7 [14].…”

Computational modeling of fully ionized magnetized plasmas using the fluid approximation

“…The second term represents the bootstrap current. Early simulations of neoclassical tearing modes 44,71 used just this term to represent the electron stress tensor.…”

“…Using a local approximation to the Landau fluid closures would be useful and consistent with the philosophy of the heuristic closure; however all neoclassical tearing mode calculations to date have used a Braginskii heat flux closure. 44,71,74,77 The implementation of Landau-fluid models for the parallel heat flux closure would be an improvement to existing models and remains an active area of research.…”