MRX documentation

MRX is a framework for performing 3D MHD equilibrium solves without the assumption of nested flux surfaces.

The design of MRX is guided by several principles:

• Thorough unit testing, regression testing, and continuous integration.

• Extensibility: It should be possible to add new codes and terms to the objective function without editing modules that already work, i.e. the open-closed principle. This is because any edits to working code can potentially introduce bugs.

• JAX-based: Everything is written in a way that is compatible with JAX and jit-compilation.

MRX is fully open-source, and anyone is welcome to use it, make suggestions, and contribute. We gratefully acknowledge funding from the Simons Foundation’s Hidden symmetries and fusion energy project.

MRX is one of several available codes for performing stellarator optimization. Others include VMEC, DESC, and SPEC. The main difference is that MRX does not assume nested flux surfaces, and is designed to be used in a JAX-based optimization framework.

Contents

• Overview
  • Ways to use mrx
  • Mathematical Formulation
  • Finite Element Discretization
  • Geometry and Coordinate Transformations
  • Magnetic Relaxation Method
• Installation
  • Requirements
  • Installing MRX
  • Optional Packages
  • Post-Installation
• Generating the Documentation
• Source code on GitHub
• Publications

API Reference

• MRX API Reference
  • Module contents
    • DESCWrapper
    • DerivativeSpline
    • DifferentialForm
    • DiscreteFunction
    • LazyBoundaryOperator
    • LazyDerivativeMatrix
    • LazyDoubleCurlMatrix
    • LazyDoubleDivergenceMatrix
    • LazyExtractionOperator
    • LazyMassMatrix
    • LazyMatrix
    • LazyProjectionMatrix
    • LazyStiffnessMatrix
    • Projector
    • Pullback
    • Pushforward
    • QuadratureRule
    • SplineBasis
    • TensorBasis
    • append_to_trace_dict()
    • converge_plot()
    • curl()
    • div()
    • get_1d_grids()
    • get_2d_grids()
    • get_3d_grids()
    • get_xi()
    • grad()
    • interpolate_B()
    • inv33()
    • is_running_in_github_actions()
    • jacobian_determinant()
    • l2_product()
    • newton_solver()
    • picard_solver()
    • poincare_plot()
    • pressure_plot()
    • project_desc_equilibrium()
    • trace_plot()
    • update_config()

Indices and tables

• Index

• Module Index

• Search Page

Tutorials

Tutorials:

• Poisson equation on the unit disk
• Mixed Poisson equation on the unit disk
• Poisson equation on a toroid
• Harmonic fields in a hollow torus
• GVEC mappings
• A simple tokamak equilibrium
• Helicity minimization

Examples

Tutorial Scripts

Tutorial Scripts:

• Poisson Problem on a disc
• Mixed Polar Poisson Problem
• Toroid Poisson Problem

Configuration Scripts

Configuration Scripts:

• Solovev Configuration
• Stellarator Configuration
• Iterative Island Calculation
• Hopf Configuration

Interactive Scripts

Interactive Scripts:

• GVEC Tokamak Interface Test
• GVEC Stellarator Interface Test
• Toroid Poisson (Interactive)
• Toroid Cavity
• Cylinder Cavity
• Cylinder Vector Poisson
• Drum Shape Optimization