Solver for Astroparticle Equation of Transport Analysis in Spherical Symmetry

A Python library for simulating cosmic-ray transport in spherically symmetric astrophysical environments using a finite volume method approach.

Overview

SAETASS numerically solves the astroparticle transport equation in spherically symmetric astrophysical environments; this is, the fundamental equation governing the propagation and energy losses of energetic particles within astrophysical environments such as stellar wind bubbles.

The package decomposes the full transport equation into independent physical operators: diffusion, advection, energy losses and source. It evolves them via mathematically robust operator-splitting schemes. Each operator is implemented as a dedicated finite-volume solver, ensuring modularity, testability and physical transparency.

For comprehensive documentation, visit the SAETASS Documentation.

Key Features

Feature	Description
Modular solvers	Independent numerical schemes for advection, diffusion energy losses, and source injection; combined via operator splitting
Flexible grids	Dedicated grid object with support for diverse spatial and momentum grid configurations
Physical accuracy	Deep integration with astropy.units and astropy.constants for strict dimensional analysis
Extensibility	Plug in custom diffusion coefficients, velocity fields, loss functions and source terms

Installation

A quick simple installation to get started using SAETASS can be simply done via pip:

pip install saetass

This will install the latest stable version of SAETASS from PyPI.

See the full Installation Guide for additional installation options and troubleshooting.

Quickstart

For step-by-step guides to get started with SAETASS, check the Tutorials section of the documentation.

For complete, more advanced examples, check the Examples section of the documentation.

Mathematical background

SAETASS solves the following astroparticle transport equation in spherically symmetric geometry:

$$\frac{\partial f}{\partial t} + \frac{1}{r^2}\frac{\partial}{\partial r}\left(r^2 u_\mathrm{w}f\right) + \frac{\partial}{\partial p}\left( \dot{p} f \right) = \frac{1}{r^2} \frac{\partial}{\partial r} \left(r^2 D\frac{\partial f}{\partial r}\right) + Q.$$

Where:

• $f(t,r, p)$ is the particle distribution function,
• $u_\mathrm{w}(t,r,p)$ is the advection (wind) velocity,
• $\dot{p}(t, r, p)$ is the rate of energy loss,
• $D(t, r, p)$ is the spatial diffusion coefficient,
• $Q(t, r, p)$ is the source term.

The equation is discretized using a finite volume scheme and solved by an operator-splitting routine, which decomposes the full PDE into simpler, independently solvable subproblems.

References

For a detailed derivation of the numerical schemes, see the technical paper.

Citation

If you use SAETASS in your research, please cite the technical paper to acknowledge the development effort:

@article{PLACEHOLDER_FOR_TECHNICAL_PAPER,
  author  = {Garcia-Morillo, J. M.},
  title   = {SAETASS: Solver for Astroparticle Equation of Transport Analysis in Spherical Symmetry},
  journal = {XXXX},
  year    = {2026},
  volume  = {X},
  doi     = {10.XXXX/XXXXX}
}

For software-specific citations, you may use the Zenodo DOI 10.5281/zenodo.19468484 citation:

@software{saetass_software,
  author       = {García-Morillo, José María and Menchiari, Stefano and López-Coto, Rubén},
  title        = "{SAETASS: Solver for Astroparticle Equation of Transport Analysis in Spherical Symmetry}",
  month        = apr,
  year         = 2026,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.19468484},
  url          = {https://doi.org/10.5281/zenodo.19468484}
}

Contributing

Contributions, bug reports and feature suggestions are welcome! Whether you want to fix a typo, improve a solver or add a new physical module: we'd love your help!

Please read the Contributing Guidelines and our Code of Conduct before getting started.

License

SAETASS is released under the BSD 3-Clause License.

Acknowledgements

SAETASS is developed within the VHEGA research group at the Instituto de Astrofísica de Andalucía (IAA-CSIC), Granada, Spain.