Near-ideal relaxed MHD in slab geometry

Abstract

We investigate the solutions of the relaxed MHD model (RxMHD) of Dewar \& Qu [J. Plasma Phys. {\bf 88}, 835880101 (2022)]. This model generalizes Taylor relaxation by including the ideal Ohm's law constraint using an augmented Lagrangian method, providing a pathway to extend the multi-region relaxed MHD (MRxMHD) model. We present the first numerical solution of the RxMHD model by Dewar \& Qu, demonstrating that it is mathematically well-defined and computationally feasible for constructing MHD equilibria in slab geometry. We also show that a cross-field flow can exist without enforcing an arbitrary constraint on the angular momentum, as is done in the case of MRxMHD with flow. Our results also demonstrate the self-organization of fully relaxed regions during the optimization, which was an important motivation behind developing this model.

References in corpus (12)

• Computation of multi-region relaxed magnetohydrodynamic equilibria
• Topological Constraints on Magnetic Relaxation
• Relaxed plasma equilibria and entropy-related plasma self-organization principles
• Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics
• A minimally constrained model of self-organized helical states in reversed-field pinches
• Stepped pressure equilibrium with relaxed flow and applications in reversed-field pinch plasmas
• Multi-region relaxed magnetohydrodynamics with anisotropy and flow
• Time-dependent relaxed magnetohydrodynamics -- inclusion of cross helicity constraint using phase-space action
• Islands and current singularities in quasisymmetric toroidal plasmas
• Relaxed Magnetohydrodynamics with Ideal Ohm's Law Constraint
• Nonlinear saturation of resistive tearing modes in a cylindrical tokamak with and without solving the dynamics
• Direct prediction of saturated neoclassical tearing modes in slab using an equilibrium approach