Relaxed Magnetohydrodynamics with Ideal Ohm's Law Constraint
arXiv:2106.12348 · doi:10.1017/S0022377821001355
Abstract
The gap between a recently developed dynamical version of relaxed magnetohydrodynamics (RxMHD) and ideal MHD (IMHD) is bridged by approximating the zero-resistivity "Ideal" Ohm's Law (IOL) constraint using an augmented Lagrangian method borrowed from optimization theory. The augmentation combines a pointwise vector Lagrange multiplier method and global penalty function method and can be used either for iterative enforcement of the IOL to arbitrary accuracy, or for constructing a continuous sequence of magnetofluid dynamics models running between RxMHD (no IOL) and weak IMHD (IOL almost everywhere). This is illustrated by deriving dispersion relations for linear waves on an MHD equilibrium.
arXiv comment47 pages, 4 figures. Long version of condensed version accepted for publication in J. Plasma Phys. Dec 2021
References in corpus (14)
- Computation of multi-region relaxed magnetohydrodynamic equilibria
- Cross helicity and related dynamo
- Ergodic Theory and Visualization I: Mesochronic Plots for Visualization of Ergodic Partition and Invariant Sets
- Necessary and Sufficient Conditions for Quasisymmetry
- An Augmented Lagrangian Method for Optimization Problems in Banach Spaces
- Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics
- On quasisymmetric plasma equilibria sustained by small force
- Stepped pressure equilibrium with relaxed flow and applications in reversed-field pinch plasmas
- Magnetohydrodynamic motion of a two-fluid plasma
- On Magnetohydrodynamic Gauge Field Theory
- Multi-region relaxed magnetohydrodynamics with flow
- Multi-region relaxed magnetohydrodynamics with anisotropy and flow
- Time-dependent relaxed magnetohydrodynamics -- inclusion of cross helicity constraint using phase-space action
- On the non-existence of stepped-pressure equilibria far from symmetry