References

The analytic field models in magpylib_jax come from the magnetostatics literature. This page collects the primary sources; each is cited from the relevant kernel in Equation models and, where useful, from the source code.

Field models

  • Magpylib (the reference library and conventions). M. Ortner and L. G. Coliado Bandeira, Magpylib: A free Python package for magnetic field computation, SoftwareX 11, 100466 (2020). doi:10.1016/j.softx.2020.100466

  • Cuboid / rectangular prism magnet. R. Ravaud and G. Lemarquand — analytic prism fields; see also J. M. Camacho and V. Sosa, Alternative method to calculate the magnetic field of permanent magnets with azimuthal symmetry, Rev. Mex. Fís. E 59(1), 8–17 (2013).

  • Cylinder (axial + diametral). N. Derby and S. Olbert, Cylindrical magnets and ideal solenoids, Am. J. Phys. 78(3), 229–235 (2010). doi:10.1119/1.3256157

  • Cylinder segment / general cylinder tile. P. Slanovc, M. Ortner, M. Moridi, C. Abert, and D. Suess, Full analytical solution for the magnetic field of uniformly magnetized cylinder tiles, J. Magn. Magn. Mater. 559, 169482 (2022). doi:10.1016/j.jmmm.2022.169482

  • Current loop (circle). J. Simpson, J. Lane, C. Immer, and R. Youngquist, Simple analytic expressions for the magnetic field of a circular current loop, NASA Technical Reports Server, 20010038494 (2001).

  • Triangle surface charge / polyhedral magnets. D. Guptasarma and B. Singh, New scheme for computing the magnetic field resulting from a uniformly magnetized arbitrary polyhedron, Geophysics 64(1), 70–74 (1999). doi:10.1190/1.1444531; M. Fabbri, Magnetic flux density and vector potential of uniform polyhedral sources, IEEE Trans. Magn. 44(1), 32–36 (2008). doi:10.1109/TMAG.2007.908698

Numerical methods

  • Complete elliptic integrals (Bulirsch cel). R. Bulirsch, Numerical calculation of elliptic integrals and elliptic functions, Numer. Math. 7(1), 78–90 (1965). doi:10.1007/BF01397975

  • Automatic differentiation / the JAX system. J. Bradbury, R. Frostig, P. Hawkins, M. J. Johnson, C. Leary, D. Maclaurin, G. Necula, A. Paszke, J. VanderPlas, S. Wanderman-Milne, and Q. Zhang, JAX: composable transformations of Python+NumPy programs (2018). https://github.com/jax-ml/jax

Citing magpylib_jax

If magpylib_jax supports your research, please cite this repository (with the release version you used) together with the Magpylib paper above.