Tokamak magneto-hydrodynamics and reference magnetic coordinates for simulations of plasma disruptions

Abstract

This paper formulates the Tokamak Magneto-Hydrodynamics (TMHD), initially outlined by X. Li and L. E. Zakharov [Plasma Science and Technology 17(2), 97–104 (2015)] for proper simulations of macroscopic plasma dynamics. The simplest set of magneto-hydrodynamics equations, sufficient for disruption modeling and extendable to more refined physics, is explained in detail. First, the TMHD introduces to 3-D simulations the Reference Magnetic Coordinates (RMC), which are aligned with the magnetic field in the best possible way. The numerical implementation of RMC is adaptive grids. Being consistent with the high anisotropy of the tokamak plasma, RMC allow simulations at realistic, very high plasma electric conductivity. Second, the TMHD splits the equation of motion into an equilibrium equation and the plasma advancing equation. This resolves the 4 decade old problem of Courant limitations of the time step in existing, plasma inertia driven numerical codes. The splitting allows disruption simulations on a relatively slow time scale in comparison with the fast time of ideal MHD instabilities. A new, efficient numerical scheme is proposed for TMHD.

Electromagnetic thin-wall model for simulations of plasma wall-touching kink and vertical modes

“…In 2008 the triangle based electro-dynamic model of the thin wall was implemented into the numerical Shell simulation code (SHL), mentioned in Ref. and used for simulations of eddy currents in the Lithium Tokamak Experiment (LTX) (Berzak Hopkins et al 2012). Earlier, the triangle based wall model was implemented in STARWALL code of P. Merkel (Merkel et al 2004(Merkel et al , 2006Strumberger et al 2008;Merkel et al 2015) for resistive wall mode studies.…”

“…The TMHD disruption model splits the equation of motion into an equilibrium equation and the plasma advancing equation. The splitting allows disruption simulations on a relatively slow time scale in comparison with the fast time of ideal MHD instabilities (Zakharov & Li 2015). In a thin HSoL approximation (the -functional Hiro currents) the equilibrium equation determines the shape of the contact zone, the contour of the entrance and the amplitude of the Hiro currents along this contour.…”

“…Another, , part of is associated with the Evans currents in the conventional SoL (Zakharov et al. 2012; Zakharov & Li 2015) created by the plasma particles released from the shrinking plasma core when the plasma touches the material surface. The toroidal loop voltage drives the current in this SoL along the open field lines.…”

“…Another significant advantage of this geometrical model is the existence of analytical formulas for the magnetic field of a uniform current in a single triangle. The 3-dimensional thin wall model complements the Tokamak Magneto-Hydro-Dynamics (TMHD) disruption model (Zakharov et al 2015) by the wall response.…”

“…All new physics effects related to a direct contact of the plasma with the wall, and to current sharing, require implementation into plasma-wall simulations. This paper provides an initial step in implementation of the 3-D wall into the TMHD model (Zakharov & Li 2015). The units used in the paper are: m, T, MA, MN, MPa, , for lengths, magnetic fields, currents, forces, pressure, electric conductivity and magnetic permeability, respectively.…”