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arXiv · 1509.04141

Arnold diffusion of charged particles in ABC magnetic fields

Alejandro Luque·Daniel Peralta-Salas
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Abstract

We prove the existence of diffusing solutions in the motion of a charged particle in the presence of an ABC magnetic field. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of these parameters, we obtain a normally hyperbolic invariant manifold and we apply the so-called geometric methods for a priori unstable systems developed by A. Delshams, R. de la Llave, and T.M. Seara. We characterize explicitly sufficient conditions for the existence of a transition chain of invariant tori having heteroclinic connections, thus obtaining global instability (Arnold diffusion). We also check the obtained conditions in a computer assisted proof. ABC magnetic fields are the simplest force-free type solutions of the magnetohydrodynamics equations with periodic boundary conditions, so our results are of potential interest in the study of the motion of plasma charged particles in a tokamak.

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Alejandro Luque, Daniel Peralta-Salas. 2015-09-14. Arnold diffusion of charged particles in ABC magnetic fields. https://doi.org/10.1007/s00332-016-9349-y

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