Electromagnetics simulation library for moving point charges built on JAX

• ⚡️ Point Charge Electrodynamics: Compute relativistically-correct electromagnetic potentials and fields generated by moving point charges.
• ⚛️ Self-Consistent N-Body Electrodynamics: Simulate the dynamics of electromagnetic sources—such as free charges and dipoles—interacting through their self-generated fields.
• 🔥 Powered by JAX: Leverage JAX's just-in-time (XLA) compilation for GPU/TPU acceleration, vectorization, and scalable parallel execution.
• 🛠️ Fully Differentiable: End-to-end differentiability enables gradient-based optimization, control, and inverse design workflows.

Learn more about PyCharge in our research paper published in Computational Physics Communications and available on arXiv

PyCharge is available on PyPI and can be installed with:

pip install pycharge

Read the full documentation at pycharge.readthedocs.io.

This example shows how to simulate an oscillating charge using PyCharge, computing and visualizing the scalar potential along the x-y axis at z=0 and t=0:

import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt
from scipy.constants import e

from pycharge import Charge, potentials_and_fields

# Define an oscillating point charge with charge +e.
oscillating_charge = Charge(lambda t: [2e-9 * jnp.sin(7.5e16 * t), 0.0, 0.0], e)

# Define 1D axes for the observation points (x, y) and fix z, t.
lim, grid_size = 50e-9, 1000
x = jnp.linspace(-lim, lim, grid_size)
y = jnp.linspace(-lim, lim, grid_size)
z = jnp.array([0.0])
t = jnp.array([0.0])

# Form the full 4D spacetime grid (X, Y, Z, T).
X, Y, Z, T = jnp.meshgrid(x, y, z, t, indexing="ij")

# Build and JIT-compile a function that returns potentials and fields.
quantities_fn = potentials_and_fields([oscillating_charge])
jit_quantities_fn = jax.jit(quantities_fn)

# Evaluate all quantities on the grid (returns a `Quantities` object).
quantities = jit_quantities_fn(X, Y, Z, T)

# Extract and plot the scalar potential on the x–y plane at z=0, t=0.
scalar_2d = quantities.scalar[:, :, 0, 0]
plt.imshow(scalar_2d.T, vmax=0.2)
plt.colorbar(label="Scalar Potential (V)")

For more examples and detailed usage, please refer to the documentation.

We welcome contributions! See our Contributing Guide for details.

If you use PyCharge in your research, please cite our paper.

  @article{filipovich2022pycharge,
     title={PyCharge: An open-source Python package for self-consistent electrodynamics simulations of Lorentz oscillators and moving point charges},
     author={Matthew J. Filipovich and S. Hughes},
     year={2022},
     journaltitle = {Computer Physics Communications},
     volume = {274},
     pages = {108291},
     issn = {00104655},
     doi = {10.1016/j.cpc.2022.108291},
     url={https://doi.org/10.1016/j.cpc.2022.108291},
   }

PyCharge is distributed under the MIT License. See the LICENSE file for more details.