- 13-43 Alejandro Luque; Daniel Peralta-Salas
- Motion of charged particles in ABC magnetic fields
May 10, 13
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Abstract. In this paper we study the motion of a charged particle under the action of ABC magnetic fields. In particular, we analyze bifurcation diagrams and stability of the equilibrium points, existence of periodic and quasi-periodic trajectories near these equilibria, analytic integrability and existence of chaotic invariant sets. Our approach makes use of diverse tools from the theory of Hamiltonian systems, like Birkhoff normal form, KAM theory, Morales-Ramis theory and splitting of separatrices. Two interesting consequences of our study are the existence of confinement regions of charges near some magnetic lines and that ABC fields give rise to non integrable and chaotic motions. The analysis of the motion of a charge in ABC fields can be interpreted as a toy model for the motion of plasma charged particles in a tokamak, thus showing the potential interest of this work in applications.