Publications and citation

If you use SIMPLE in a publication, cite the method papers that apply to your work. The software itself is archived on Zenodo; the badge in the repository README links to the current version.

Method papers

1. C. G. Albert, S. V. Kasilov, W. Kernbichler, Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices, J. Comput. Phys. 403, 109065 (2020), https://doi.org/10.1016/j.jcp.2019.109065

2. C. G. Albert, S. V. Kasilov, W. Kernbichler, Accelerated methods for direct computation of fusion alpha particle losses within stellarator optimization, J. Plasma Phys. 86, 815860201 (2020), https://doi.org/10.1017/S0022377820000203

3. C. G. Albert, R. Buchholz, S. V. Kasilov, W. Kernbichler, K. Rath, Alpha particle confinement metrics based on orbit classification in stellarators, J. Plasma Phys. 89, 955890301 (2023), https://doi.org/10.1017/S0022377823000351

4. C. G. Albert, G. Grassler, J. Lion, J.-F. Lobsien, J. Schatzlmayr, F. Warmer, Symplectic methods for optimization of wall heat loads by fusion alpha particles in stellarator reactors, Nucl. Mater. Energy 48, 102200 (2026), https://doi.org/10.1016/j.nme.2026.102200

5. C. G. Albert, G. S. Grassler, S. V. Kasilov, M. Markl, J. Schatzlmayr, Symplectic integration of guiding-center equations in canonical coordinates for general toroidal fields, arXiv:2503.15278 (2025), https://arxiv.org/abs/2503.15278 (preprint).

Related work used by SIMPLE

• J. D. Meiss, R. D. Hazeltine, Canonical coordinates for guiding center particles, Phys. Fluids B 2, 2563 (1990), https://doi.org/10.1063/1.859380

• R. G. Littlejohn, Variational principles of guiding centre motion, J. Plasma Phys. 29, 111 (1983), https://doi.org/10.1017/S002237780000060X

• H.-S. Bosch, G. M. Hale, Improved formulas for fusion cross-sections and thermal reactivities, Nucl. Fusion 32, 611 (1992), https://doi.org/10.1088/0029-5515/32/4/I07 (D-T reactivity of startmode = 7)

• J. D. Huba, NRL Plasma Formulary, NRL/PU/6790–19-640, Naval Research Laboratory (2019) (Coulomb logarithms of the collision operator)

• E. Hairer, C. Lubich, G. Wanner, Geometric Numerical Integration, 2nd ed., Springer (2006), https://doi.org/10.1007/3-540-30666-8 (backward-error analysis of the symplectic schemes)

• M. Landreman, M. Czekanski, A. Giuliani, B. Jang, R. Conlin, Bayesian optimization of stellarator alpha-particle confinement using data-informed parameter spaces and dimensionality reduction, arXiv:2606.19523 (2026), https://arxiv.org/abs/2606.19523 (segmented loss objective of the GPU backend)

• M. Landreman, E. Paul, Magnetic fields with precise quasisymmetry for plasma confinement, Phys. Rev. Lett. 128, 035001 (2022), https://doi.org/10.1103/PhysRevLett.128.035001 (equilibria used in the tutorials)

The FIRM3D-compatible tracing path has separate provenance information in LICENSES/FIRM3D-MIT.txt.