ChargedParticleDynamics.jl

General

• Normalization
• • Charged Particle Lagrangian
  • Strongly Magnetized Plasmas
• Initialization
• • Velocities
  • Gyro-radius Vector and Position
  • Guiding Center Coordinates
  • Initial Conditions
  • Example

Models

• Charged Particles in 3D
• • Canonical Formulation
  • Noncanonical Formulation
  • Modules
• Guiding Center Dynamics in 3D
• • Where the constraints come from
  • Choosing the constraint pair
  • The three formulations
  • Which symbol is which
  • Usage
  • Modules
• Guiding Center Dynamics in 4D
• • Lagrangian Formulation
  • Hamiltonian Formulation
  • Modules
• Pauli Particles in 3D
• • Relation to the Other Models
  • Slow Manifolds
  • Implementation
  • Usage
  • Modules
• Gyrokinetic Guiding Centre Dynamics in 4D
• • The characteristics
  • Rescaled time
  • Potentials and splitting
  • Noncanonical Hamiltonian structure
  • Usage
  • Status
  • Equilibria
  • Module
• Model Audit
• • Simplifications
  • Known singularities
  • Interface conventions
  • Documentation coverage
  • Interface
  • Open work
• Findings
• • The reversed field of the left-handed charts
  • Conditioning of the 3D guiding centre constraint formulations
  • The toroidal momentum of the guiding centre models
  • The gyrokinetic model is the guiding centre model in rescaled time
  • Volume preservation of the gyrokinetic splitting
  • Conservation across the model families
  • The three families on one initial condition
  • The residual scale of the ITER-size equilibria

References

• Xinjie Li, Ruili Zhang, Jian Liu, Approximately symplectic Runge-Kutta methods for the guiding center dynamics, Journal of Computational Physics 563, 115069 (2026), doi:10.1016/j.jcp.2026.115069.
• Ruili Zhang, Jian Liu, Tong Liu, Wenxiang Li, Xiaogang Wang, Canonical Hamiltonian guiding center theory and classical intrinsic magnetic moment, Frontiers of Physics 21(2), 026200 (2026).
• Jianyuan Xiao, Hong Qin, Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics, arXiv:2006.03818 (2020).
• Joshua W. Burby, Guiding center dynamics as motion on a formal slow manifold in loop space, Journal of Mathematical Physics 61, 012703 (2020), doi:10.1063/1.5119801.

Acknowledgements

Stefan Possaner contributed vitally to sorting out the appalling details of normalization and initialization.

License

Copyright (c) Michael Kraus <michael.kraus@ipp.mpg.de>

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.