2014/02/28 by Benjamin Cambon, Xavier Leoncini, Michel Vittot +2 · 1 citation
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Chaotic #Charged particle #Constant of motion #Hamiltonian (control theory) #Hamiltonian system #Magnetic field #Magnetosphere particle motion #Numerical methods for differential equations #Phase space #Quantum chaos and dynamical systems #nlin.CD #physics.plasm-ph
paper · pdf · doi:10.1063/1.4885103
published as Chaos, American Institute of Physics (AIP), 2014, 24 (3), pp.033101
openalex publication_date 2014/07/02 · arxiv created 2014/12/04 · arxiv updated 2014/12/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron gyration using Hamiltonian formalism. We take advantage of a symplectic integrator allowing us to make long-time simulations. First considering an idealized magnetic configuration, we add a nongeneric perturbation corresponding to a magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed and opens questions about the link between chaos of magnetic field lines and chaos of particle trajectories. Second, we return to an axisymmetric configuration and tune the safety factor (magnetic configuration) in order to recover chaotic motion. In this last setting with two constants of the motion, the presence of chaos implies that no third global constant exists, we highlight this fact by looking at variations of the first order of the magnetic moment in this chaotic setting. We are facing a mixed phase space with both regular and chaotic regions and point out the difficulties in performing a global reduction such as gyrokinetics.