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https://github.com/sarvesh2304/stellarator_simulation

A comprehensive Julia package for stellarator fusion reactor physics analysis featuring 3D magnetic field calculations, neoclassical transport modelling, quasi-isodynamic optimisation algorithms, and interactive 3D visualisations. Includes tokamak comparison framework and high-resolution plotting capabilities for fusion research.
https://github.com/sarvesh2304/stellarator_simulation

3d-visualisation data-analysis field-line-tracing fusion-physics fusion-research interactive-3d julia magnetic-confinement magnetic-field-calculations magnetic-surfaces matplotlib neoclassical-transport numerical-methods optimisations physics-simulation plasma-physics plotly quasi-isodynamic stellarator stellarator-optimization

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A comprehensive Julia package for stellarator fusion reactor physics analysis featuring 3D magnetic field calculations, neoclassical transport modelling, quasi-isodynamic optimisation algorithms, and interactive 3D visualisations. Includes tokamak comparison framework and high-resolution plotting capabilities for fusion research.

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README 

          

# Stellarator Physics Analysis Package



A comprehensive Julia package for stellarator fusion reactor physics analysis, featuring 3D magnetic field calculations, neoclassical transport modeling, optimization algorithms, and comparison with tokamak performance.



## Features



### 🔬 Core Physics

- **3D Magnetic Field Calculations**: Complete stellarator magnetic field modeling with Fourier harmonics

- **Neoclassical Transport**: Stellarator-specific transport coefficient calculations

- **Boozer Coordinates**: Advanced coordinate system for stellarator analysis

- **Magnetic Surface Analysis**: Calculation of magnetic surfaces and safety factors



### âš¡ Optimisation Algorithms

- **Quasi-Symmetry Optimisation**: Minimize magnetic field asymmetry

- **Quasi-Isodynamicity Optimisation**: Optimise for isodynamic magnetic fields

- **Magnetic Well Optimisation**: Maximize magnetic well depth for stability

- **Transport Optimisation**: Minimize neoclassical transport



### 🔄 Tokamak Comparison

- **Performance Metrics**: Direct comparison of stellarator vs tokamak performance

- **Transport Analysis**: Side-by-side transport coefficient comparison

- **Stability Analysis**: Comparison of stability properties and beta limits

- **Confinement Scaling**: Analysis of confinement time scaling laws



### 📊 3D Visualisation

- **Magnetic Field Lines**: Interactive 3D field line tracing

- **Plasma Surfaces**: 3D visualisation of magnetic surfaces

- **Transport Profiles**: 2D and 3D transport coefficient visualisation

- **Optimisation Results**: Real-time optimisation progress visualisation



## Installation



1. Clone the repository:

```bash

git clone 

cd "Stellarator Physics"

```



2. Start Julia and activate the environment:

```julia

julia> using Pkg

julia> Pkg.activate(".")

julia> Pkg.instantiate()

```



3. Load the package:

```julia

julia> using StellaratorPhysics

```



## Quick Start



```julia

using StellaratorPhysics



# Create a stellarator configuration

Râ‚€ = 1.0  # Major radius [m]

a = 0.2   # Minor radius [m]

N = 5     # Number of field periods

Bâ‚€ = 1.0  # Reference magnetic field [T]



stellarator_bfield = MagneticField3D(Râ‚€, a, N, Bâ‚€)



# Set up plasma parameters

T_e = 1000.0  # Electron temperature [eV]

T_i = 1000.0  # Ion temperature [eV]

n_e = 1e20    # Electron density [m^-3]

n_i = 1e20    # Ion density [m^-3]



transport = NeoclassicalTransport(stellarator_bfield, T_e, T_i, n_e, n_i)



# Calculate transport coefficients

s = 0.5  # Normalized radius

coeffs = calculate_transport_coefficients(transport, s)



# Create 3D visualization

plot_3d = plot_plasma_surfaces(stellarator_bfield, [0.2, 0.4, 0.6, 0.8])

```



## Examples



### Complete Analysis Example

Run the comprehensive example:

```julia

include("examples/stellarator_analysis_example.jl")

```



This example demonstrates:

- 3D magnetic field calculations

- Neoclassical transport analysis

- Stellarator optimization

- Comparison with tokamak performance

- 3D visualization



### Individual Module Examples



#### Magnetic Field Analysis

```julia

# Calculate magnetic field at a point

R, φ, Z = 1.2, 0.0, 0.1

B_R, B_φ, B_Z = calculate_magnetic_field(stellarator_bfield, R, φ, Z)



# Trace a field line

field_line = trace_field_line(stellarator_bfield, R, φ, Z, 10.0)



# Find magnetic surface

surface = find_magnetic_surface(stellarator_bfield, 0.5)

```



#### Transport Analysis

```julia

# Calculate transport coefficients

coeffs = calculate_transport_coefficients(transport, 0.5)



# Calculate bootstrap current

j_bs = bootstrap_current(transport, 0.5)



# Calculate radial electric field

E_r = radial_electric_field(transport, 0.5)

```



#### Optimisation

```julia

# Optimise for quasi-symmetry

result, optimal_harmonics = optimize_quasi_symmetry(stellarator_bfield, 1000)



# Multi-objective optimization

weights = Dict(

    "quasi_symmetry" => 0.4,

    "magnetic_well" => 0.3,

    "transport" => 0.3

)

result = multi_objective_optimization(stellarator_bfield, weights, 1000)

```



#### Comparison with Tokamak

```julia

# Create tokamak field

tokamak_bfield = create_tokamak_field(Râ‚€, a, 1.0, 2.0, Bâ‚€)

tokamak_transport = NeoclassicalTransport(tokamak_bfield, T_e, T_i, n_e, n_i)



# Compare performance

comparison = TokamakComparison(stellarator_bfield, tokamak_bfield, 

                              stellarator_transport, tokamak_transport)

results = comprehensive_comparison(comparison, 0.5)

```



## Package Structure



```

StellaratorPhysics/

├── src/

│   ├── StellaratorPhysics.jl      # Main module

│   ├── MagneticField3D.jl         # 3D magnetic field calculations

│   ├── NeoclassicalTransport.jl   # Transport modeling

│   ├── StellaratorOptimization.jl # Optimisation algorithms

│   ├── TokamakComparison.jl       # Tokamak comparison

│   ├── Visualization3D.jl         # 3D visualization

│   └── utils.jl                   # Utility functions

├── examples/

│   └── stellarator_analysis_example.jl

├── Project.toml

└── README.md

```



## Dependencies



- **Julia 1.8+**: Required for optimal performance

- **Plots.jl**: For 2D plotting and visualization

- **PlotlyJS.jl**: For interactive 3D visualization

- **Optim.jl**: For optimization algorithms

- **NLopt.jl**: For advanced optimization

- **DifferentialEquations.jl**: For field line tracing

- **ForwardDiff.jl**: For automatic differentiation

- **SpecialFunctions.jl**: For special mathematical functions



## Physics Background



### Stellarator vs Tokamak

Stellarators are toroidal fusion devices that use 3D magnetic field configurations to confine plasma, unlike tokamaks which rely on axisymmetric fields and plasma current. Key advantages include:

- **Steady-state operation**: No need for plasma current drive

- **Reduced MHD instabilities**: 3D field provides additional stability

- **Flexible design**: Can optimize for various physics objectives



### Neoclassical Transport

Neoclassical transport in stellarators differs from tokamaks due to:

- **3D magnetic field geometry**: Affects particle orbits and transport

- **Magnetic field ripple**: Creates additional transport channels

- **Quasi-symmetry**: Can reduce transport to tokamak-like levels



### Optimisation Objectives

- **Quasi-Symmetry**: Minimize magnetic field asymmetry to reduce transport

- **Quasi-Isodynamicity**: Optimise for isodynamic magnetic fields

- **Magnetic Well**: Maximize magnetic well depth for stability

- **Transport**: Minimize neoclassical transport coefficients



## Contributing



Contributions are welcome! Please see the contributing guidelines for details on:

- Code style and formatting

- Testing requirements

- Documentation standards

- Pull request process



## License



This project is licensed under the MIT License - see the LICENSE file for details.



## Citation



If you use this package in your research, please cite:



```bibtex

@software{stellarator_physics,

  title={Stellarator Physics Analysis Package},

  author={Stellarator Research Team},

  year={2024},

  url={https://github.com/your-repo/stellarator-physics}

}

```



## Acknowledgments



- Based on stellarator physics theory and VMEC code

- Inspired by the work of the stellarator research community

- Built with the Julia scientific computing ecosystem



## Support



For questions, issues, or contributions:

- Open an issue on GitHub

- Contact the development team

- Check the documentation and examples



---



**Note**: This package is designed for research and educational purposes. For production fusion reactor design, consult with fusion physics experts and use validated codes.