PyBiotSavart

Overview

PyBiotSavart is a Python library designed to simulate and visualize magnetic fields generated by various coil configurations using the Biot-Savart law. It provides an easy-to-use interface for calculating magnetic fields and visualizing them in 3D space. With GPU acceleration powered by PyTorch, PyBiotSavart ensures faster computations for large-scale simulations.

Requirements

• Python 3.6 or higher
• numpy for numerical computations
• einops for tensor rearrangement
• matplotlib for plotting
• torch for gpu acceleration

Installation

To use PyBiotSavart, clone the repository and ensure the required dependencies are installed.

git clone https://github.com/your-repo/PyBiotSavart.git
cd PyBiotSavart
pip install -r requirements.txt

Usage

Example: Circular Coil in the XY Plane

import numpy as np
from PyBiotSavart import BiotSavart
from einops import rearrange
import matplotlib.pyplot as plt

# Define coil geometry
coil = np.zeros((200, 3))
coil[:, 2] = 0
coil[:, 0], coil[:, 1] = np.cos(np.linspace(0, 8 * np.pi, coil.shape[0], endpoint=False)) * 6e-2, \
                         np.sin(np.linspace(0, 8 * np.pi, coil.shape[0], endpoint=False)) * 6e-2

# Define current
current = 1

# Define mesh grid
xmin, xmax, nx = -25e-2, 25e-2, 51
ymin, ymax, ny = -25e-2, 25e-2, 51
zmin, zmax, nz = -25e-2, 25e-2, 51
x = np.linspace(xmin, xmax, nx, endpoint=True)
y = np.linspace(ymin, ymax, ny, endpoint=True)
z = np.linspace(zmin, zmax, nz, endpoint=True)
xx, yy, zz = np.meshgrid(x, y, z, indexing='ij')
mesh_grid = np.stack([xx, yy, zz], axis=-1)
vectorized_grid = rearrange(mesh_grid, "x y z p -> (x y z) p")

# Compute magnetic field
B = BiotSavart(coil, current, vectorized_grid)
mesh_B = rearrange(B, "(x y z) p -> x y z p", x=nx, y=ny, z=nz)

# Visualization
plt.figure(figsize=(10, 4))
ax1 = plt.subplot(1, 2, 1, projection="3d")
ax1.plot3D(coil[:, 0], coil[:, 1], coil[:, 2])
ax2 = plt.subplot(1, 2, 2)
im2 = ax2.imshow(mesh_B[:, :, 24, 2], cmap="bwr")
im2.set_clim(-5e-5, 5e-5)
plt.colorbar(im2, ax=ax2)
plt.show()

Examples

The repository includes a Jupyter Notebook (demo.ipynb) that demonstrates the following:

1. Circular Coil
2. Spiral Coil with Varying Radius
3. Helical Coil
4. Helical Coil with Varying Radius
5. Toroidal Coil with Sinusoidal Perturbation

Run the notebook to explore these examples and visualize the results.

License

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