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arXiv · 2503.15278

Symplectic integration of guiding-center equations in canonical coordinates for general toroidal fields

Christopher G. Albert·Georg S. Grassler·Sergei V. Kasilov·Markus Markl·Jonatan Schatzlmayr
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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.

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Christopher G. Albert, Georg S. Grassler, Sergei V. Kasilov, Markus Markl, Jonatan Schatzlmayr. 2025-03-19. Symplectic integration of guiding-center equations in canonical coordinates for general toroidal fields. https://arxiv.org/abs/2503.15278

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