OpenFRC

A GPU-Accelerated 2D FRC MHD Solver

OpenFRC A GPU-Accelerated 2D FRC MHD Solver

A lightweight, research-grade simulation framework for studying Field-Reversed Configuration (FRC) dynamics, built for plasma physics education, algorithm development, and fusion interview preparation (Helion Energy, CFS, General Fusion, etc.).

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Overview

OpenFRC is a 2D Magnetohydrodynamics (MHD) solver implementing:

• Helion-style FRC magnetic topology
• Strong axial magnetic field reversal
• Poloidal flux function initialization
• FFT-based ∇·B cleaning (projection method)
• Hybrid NumPy/CuPy backend for GPU acceleration
• Multiple physics modes:
  ✓ FRC formation
  ✓ Magnetic reconnection
  ✓ Alfvén wave propagation
• Visualization + MP4 animation exports

The solver is intentionally compact, readable, and modular — ideal for:

• learning plasma & MHD theory
• testing numerical algorithms
• fusion interview preparation
• use as a starting point for Hall-MHD or 2-fluid extensions

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Why This Project Exists

FRCs are among the most compact and promising fusion configurations.
Helion Energy uses Merging-FRC (MIF) to achieve fusion-relevant conditions.

This project recreates core FRC physics in a clean 2D MHD framework:

• Axisymmetric flux rings
• Strong field reversal
• Current sheet formation
• Magnetic reconnection
• Plasmoid structures
• Outward magnetic pressure balance
• Lorentz-force-driven acceleration

This is conceptually aligned with the physics in Helion’s formation region.

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Physics Model

The solver integrates the ideal MHD equations with resistive diffusion:

$$ \frac{\partial \rho}{\partial t} = 0 \quad (\text{constant density}) $$

$$ \frac{\partial \mathbf{v}}{\partial t} = -\frac{1}{\rho}\nabla p + \frac{1}{\rho} (\mathbf{J} \times \mathbf{B}) $$

$$ \mathbf{J} = \nabla \times \mathbf{B} $$

$$ \frac{\partial \mathbf{B}}{\partial t} = -\nabla \times \mathbf{E} + \eta \nabla^2 \mathbf{B} $$

$$ \mathbf{E} = -\mathbf{v} \times \mathbf{B} $$

Divergence Cleaning

We enforce:

$$ \nabla \cdot \mathbf{B} = 0 $$

using FFT-based Poisson projection:

$$ \nabla^2 \phi = \nabla \cdot \mathbf{B} \quad\Rightarrow\quad \mathbf{B} \leftarrow \mathbf{B} - \nabla \phi $$

This method is:

• fast
• GPU-accelerated
• stable
• common in modern MHD codes (Athena++, Dedner schemes)

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FRC Initial Conditions

We initialize a long, slender FRC, similar to Helion's confinement geometry.

Flux function:

$$ \Psi(x,y) = \exp\left(-\frac{x^2}{a^2} - \frac{y^2}{L^2}\right) $$

Poloidal magnetic field:

$$ B_x = -\frac{\partial \Psi}{\partial y}, \quad B_y = \frac{\partial \Psi}{\partial x} $$

Axial field reversal:

$$ B_z = B_0 \left(1 - 2 e^{-(x^2 + y^2)/R_0^2} \right) $$

This produces:

• a magnetic null line along the axis
• a strongly reversed core
• closed poloidal flux surfaces
• current sheet regions

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Project Structure

OpenFRC/
│── backend.py              # NumPy/CuPy backend (hybrid GPU/CPU)
│── config.py               # Grid parameters, timestep, resistivity
│── initial_conditions.py   # Alfven, Reconnection, FRC setups
│── solver.py               # MHD evolution + FFT divergence cleaning
│── visualize.py            # Frame generation + MP4 animation
│── main.py                 # CLI interface
│── README.md
│── LICENSE
│── requirements.txt
│── environment.yml
│── .gitignore
│── media/                  # Logo and favicon
│── frames/                 # Auto-generated output (ignored by git)
│── animation.mp4           # Optional animation output

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Installation

Clone the repo:

git clone https://github.com/Huq2090/OpenFRC.git
cd OpenFRC

Install dependencies:

pip install -r requirements.txt

Optional: GPU support

pip install cupy-cuda12x

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Running Simulations

▶ Run FRC Simulation (with divergence cleaning)

python3 main.py --mode frc --cleaning projection --animate

▶ Run on GPU

python3 main.py --mode frc --gpu --animate

▶ Magnetic Reconnection

python3 main.py --mode reconnection --animate

▶ Alfvén Wave Test

python3 main.py --mode alfven --animate

Animations will appear in:

frames/
animation.mp4

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Example Output (FRC Evolution)

(Add images/GIFs after running the simulation)
Example placeholders:

• FRC poloidal field loops
• Axial field reversal
• Magnetic island formation
• Current sheet thinning
• Reconnection dynamics

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Future Roadmap

Numerical / Physics Upgrades

• ☐ Hall-MHD (whistler waves + FRC tilt physics)
• ☐ Two-fluid / gyrofluid extensions
• ☐ Cylindrical (r-z) geometry
• ☐ Shock-capturing Riemann solvers (HLL/HLLD)
• ☐ Dedner hyperbolic divergence cleaning

Software Engineering

• ☐ Sphinx documentation
• ☐ Unit tests (pytest)
• ☐ GitHub Actions CI
• ☐ Docker image
• ☐ Jupyter notebook demos

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Citation (Optional)

If you use this project:

@software{OpenFRC2025,
  author = {Md Fazlul Huq},
  title = {OpenFRC: A GPU-Accelerated 2D FRC MHD Solver},
  year = {2025},
  url = {https://github.com/Huq2090/OpenFRC}
}

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Acknowledgements

Developed by Md Fazlul Huq
As part of self learning of Computational plasma physics of Field-Reversed Configuration (FRC) in MHD.

Special thanks to open-source plasma physics projects and the wider fusion community.

May your fields stay divergence-free and your plasmoids stable!