Self-consistent hybrid neoclassical-magnetohydrodynamic simulations of axisymmetric plasmas

Abstract

Neoclassical effects (e.g., conductivity reduction and bootstrap currents) have a profound impact on many magnetohydrodynamic (MHD) instabilities in toroidally-confined plasmas, including tearing modes, edge-localized modes, and resistive wall modes. High-fidelity simulations of such phenomena require a multiphysics code that self-consistently couples the kinetic and fluid models. We review a hybrid formulation from the recent literature<super>AB</super> that is appropriate for such studies. In particular, the formulation uses a set of time-dependent drift-kinetic equations (DKEs) to advance the non-Maxwellian part of the electron and ion distribution functions (<italic>fNM</italic>) with linearized Fokker-Planck-Landau collision operators. The form of the DKEs used were derived in a Chapman-Enskog-like fashion, ensuring that <italic>fNM</italic> carries no density, momentum, or temperature. Rather, these quantities are contained within the background Maxwellian and are evolved by a set of MHD equations which are closed by moments of <italic>fNM</italic>. We then present two DKE solvers based upon this formulation in axisymmetric toroidal geometries. The Neoclassical Ion-Electron Solver (NIES) solves the steady-state DKEs in the low-collisionality limit. Convergence and benchmark studies are discussed, providing a proof-of-principle that this new formulation can accurately reproduce results from the literature in the limit considered. We then present the DK4D code which evolves the finite-collisionality DKEs time-dependently. Computational methods used and successful benchmarks to other neoclassical models and codes are discussed. Furthermore, we couple DK4D to a reduced, transport-timescale MHD code. The resulting hybrid code is used to simulate the evolution of the current density in a large-aspect-ratio plasma in the presence of several different time-dependent pressure profiles. These simulations demonstrate the self-consistent, dynamic formation of the ohmic and bootstrap currents. In the slowly-evolving plasmas considered, these first-principle simulations are shown to verify a simpler, steady-state neoclassical model that is commonly used in transport codes. Future work will involve coupling DK4D to a spatially three-dimensional, extended MHD code, generalizing DK4D to nonaxisymmetric geometries, and simulating more quickly-evolving and realistic plasmas. The ultimate goal of this work is to perform self-consistent, hybrid simulations of complex tokamak instabilities and calculations of neoclassical toroidal viscosity.

<super>A</super> J. J. Ramos, Phys. Plasmas <bold>17</bold>, 082502 (2010).

<super>B</super> J. J. Ramos, Phys. Plasmas <bold>18</bold>, 102506 (2011).