@article{136,
  keywords = {quasisymmetry, magnetic fields, particle dynamics, Hamiltonian mechanics},
  author = {J Burby and N Kallinikos and R MacKay},
  title = {Approximate symmetries of guiding-centre motion},
  abstract = {<p>In a strong, inhomogeneous magnetic field, charged particle dynamics may be studied in the guiding-centre approximation, which is known to be Hamiltonian. When the magnetic field is quasisymmetric, the first-order guiding-centre (FGC) Hamiltonian structure admits a continuous symmetry, and therefore a conserved quantity in addition to the energy. Since the FGC system is only an approximation, it is also interesting to consider approximate symmetries of the guiding-centre Hamiltonian structure. We find that any approximate spatial symmetry coincides with quasisymmetry to leading order. For approximate phase-space symmetries, we derive weaker conditions than quasisymmetry. The latter include {\textquoteleft}weak quasisymmetry{\textquoteright} as a subcase, recently proposed by Rodr{\'\i}guez et\&nbsp;al. Our results, however, show that weak quasisymmetry is necessarily non-spatial at first order. Finally, we demonstrate that if the magnetic field is constrained to satisfy magnetohydrostatic force balance then an approximate symmetry must agree with quasisymmetry to leading order.</p>
},
  year = {2021},
  journal = {Journal of Physics A: Mathematical and Theoretical},
  volume = {54},
  number = {12},
  pages = {125202},
  month = {03/2021},
  publisher = {IOP Publishing},
  url = {https://doi.org/10.1088/1751-8121/abe58a},
  doi = {10.1088/1751-8121/abe58a},
}