DATA

The stellarator database that is used in this repository can be found in Zenodo: Stellarator Database

PIC-STELLARATOR

The PIC-STELLARATOR repository aims to establish a database for a comprehensive assessment of the conditions under which functional and efficient stellarators can be created and also for posterior analisation with machine learning.

The repository comprises three main folders:

• data, which contains the file that serves as a template to the creation of stellarators, a SQL database Python file (to origin the latter) and the actual database.

• data_base_support, which contains three files which generate the template of stellarator VMEC_database.py and qi_functions.py, as well as plotting useful data that comes with the previous files -> vmecPlot2.py. Additionally, this folder has the file that creates random stellarators and transports them to the database auxiliary_functions.py.

• data_analysis: Contains files for interpreting the database. This folder has two subfolders, one for quasi-symmetry and one for quasi-isodynamic properties within the database. For each of these quantities, LightGBM was used to create binary classification and regression models, and LightGBM LSS was used to train a regression model.

Folder Structure

data_analysis/
│── quasi_isodynamic/
│   ├── non_probabilistic_models/
│   │   ├── qi_study_nn.ipynb  # Generates neural network plots
│   │   ├── qi_study.ipynb     # Generates LightGBM plots
│   │
│   ├── probabilistic_models/
│   │   ├── plot_lss.ipynb  # Generates plots for LightGBM_LSS
│
│── quasi_symmetric/
│   ├── non_probabilistic_model/
│   │   ├── lightgbm_classification_model/
│   │   │   ├── plot_class.ipynb  # Generates VMEC convergence section plots (e.g., confusion matrix)
│   │   │
│   │   ├── lightgbm_regressor/
│   │   │   ├── qs_study_nn.ipynb  # Generates neural network plots
│   │   │   ├── plot.ipynb         # Generates LightGBM plots
│   │
│   ├── probabilistic_models/
│   │   ├── plot_lss.ipynb              # Generates LightGBM_LSS plots
│   │   ├── lgbm_boxplot_errors.py      # Generates CSV with LightGBM errors
│   │   ├── lgbmlss_boxplot_errors.py   # Generates CSV with LightGBM_LSS errors
│   │   ├── boxplot.ipynb               # Uses CSVs to create a boxplot figure

Instalation

Clone the repository and install the necessary packages. In the file requirements.txt, you will find all the packages required to run files from the repository.

git clone https://github.com/laiarodrigo/PIC-STELLARATOR.git
cd PIC-STELLARATOR
pip install -r requirements.txt

Usage

Loading Data

Some configurations and their respective results are provided in case the user prefers not to create new stellarators. Otherwise, it is possible to run the

 main.py 

file. This file will generate database containing the columns:

Column	Column Name	Description
x1, x2, ..., xN	The input parameters (RBC's and ZBS' values)	These Fourier coefficients collectively define the stellarator surface, enabling the calculation of the other columns.
y1	Quasisymmetry	symmetry found in toroidal magnetic fields that aid in the confinement of charged particles by reducing the radial drifts that lead to particle losses.
y2	Quasiisodynamic	A quasiisodynamic field is omnigenous and has poloidally closed contours of constant field strength which helps eliminate the bootstrap current in the limit of low collision frequency, being beneficial for avoiding current-driven instabilities.
y3	Rotational Transform	Measures how magnetic field lines wind around the toroidal plasma confinement device, defined as the number of times a field line wraps poloidally for each complete toroidal circuit.
y4	Inverse Aspect Ratio	Inverse of the ratio of the major radius (distance from the torus center to the tube center) to the minor radius (radius of the tube).
y5	Mean Local Magnetic Shear	The local rate of rotation of the magnetic field direction and is another equilibrium quantity that plays an important role in the stability.
y6	Vacuum Magnetic Well	Defined as the second derivative of the volume enclosed by a flux surface with respect to the toroidal flux, measuring how the volume of the plasma changes as it moves through different layers of the magnetic field.
y7	Maximum Elongation	Refers to the shape of the plasma cross-section being stretched, increasing the plasma’s area-to-volume ratio.
y8	Mirror Ratio	Ratio of the maximum to the minimum magnetic field strength along the magnetic axis.
y9	Number of Field Periods NFP	Indicates the number of times the magnetic field pattern repeats itself as one moves around the toroidal direction.

Reference Papers about Database columns

Acknowledgements

Thanks to Gonçalo Abreu and Rogério Jorge for kickstarting this project.