Symplectic integration of guiding-center equations in canonical coordinates for general toroidal fields
Abstract
Symplectic integrators with long-term preservation of integrals of motion are introduced for the guiding-center model of plasma particles in toroidal magnetic fields of general topology. An efficient transformation to canonical coordinates from cylindrical and flux-like coordinates is discussed and applied using one component of the magnetic vector potential as a spatial coordinate. This choice is efficient in both, theoretical and numerical developments and marks a generalization of magnetic flux coordinates. The transformation enables the application of conventional symplectic integration schemes formulated in canonical coordinates, as well as variational integrators on the guiding-center system, without requiring magnetic flux coordinates. Symplectic properties and superior efficiency of the implicit midpoint scheme compared to conventional non-symplectic methods are demonstrated on perturbed tokamak fields with magnetic islands and stochastic regions. The presented results mark a crucial step towards gyrokinetic models that conserve physical invariants.
Keywords
Cite
@article{arxiv.2503.15278,
title = {Symplectic integration of guiding-center equations in canonical coordinates for general toroidal fields},
author = {Christopher G. Albert and Georg S. Grassler and Sergei V. Kasilov and Markus Markl and Jonatan Schatzlmayr},
journal= {arXiv preprint arXiv:2503.15278},
year = {2025}
}