Multi-region relaxed Magnetohydrodynamics model based on Hamilton’s principle of stationary action which applied to the MHD Lagrangian but using only a small subset of constraints build into ideal MHD. Unlike commonly used ideal-MHD, in 3D geometry magnetic islands and chaotic fields form whenever there is singularity ( resonant harmonic parallel current ) in magnetic differential equation. Model generalizes the Taylor relaxation principle of confined plasma by minimizing the global magnetic energy subject to magnetic flux, conservation of global magnetic helicity and thermodynamic constraints with coarse or fine-grained pressure profiles, KAM surfaces, magnetic islands and chaos.
In this talk, I show some success of MRxMHD model in describing linear stability (Tearing mode analysis ) with hessian approach in cylindrical and 3D geometry with Stepped Pressure Equilibrium Code. If time permits, I will discuss in fusion device like Wendelstein 7-X (w7-x) ,how the construction of area preserving symplectic nature of magnetic field line trajectories near separatrix useful for optimizing the heat flux within the lobes/tangles or the magnetic footprints on magnetic islands divertors plates in near edge plasma geometry.