Overview

MRX is a differentiable 3D magnetohydrodynamic (MHD) equilibrium solver that allows for magnetic relaxation of magnetic fields in perturbed/non-minimum energy states to lower energy states. The code is designed to address traditional challenges to 3D MHD equilibrium solvers, including exactly enforcing physical constraints such as divergence-free magnetic fields, exhibiting high levels of numerical convergence, dealing with complex geometries, and modeling stochastic field lines or chaotic behavior. By using differentiable Python (JAX), the numerical method provides computational efficiency on modern computing architectures, high code accessibility, and differentiability at each step.

The method is based on the concept of admissible variations of \(\mathbf{B}\) and \(p\) that allows for magnetic relaxation without the assumption of nested flux surfaces. This makes MRX particularly suitable for studying magnetic islands and chaos in stellarator fusion devices.

For more details, see the paper: MRX: A differentiable 3D MHD equilibrium solver without nested flux surfaces.

Overview Sections:

• Ways to use mrx
• Mathematical Formulation
• Finite Element Discretization
• Geometry and Coordinate Transformations
• Magnetic Relaxation Method

For more details on specific scripts, see the individual script documentation pages.