Confinement of a charged particle subjected to an oscillating magnetic field in a plane (xy) and uniform in the perpendicular direction (z)

In this paper we used a magnetic field of the form $\overrightarrow{ℬ}={ℬ}_1\left[\cos (\omega t)\widehat{i}+\sin (\omega t)\widehat{j}\right]+{ℬ}_0\widehat{k}$ as the zero order of an expansion, arising from a parabolic magnetic field, to describe the confined motion of an electrically charged particle subjected to a Lorentz force, with a dynamics valid for a specific region of space. The equations of motion obtained are nonlinear and a particular solution can be extracted, in which the particle performs a periodic motion. Moreover, through Poincaré sections and Lyapunov exponents, we find that the system is chaotic, and therefore admits different forms of quasi closed trajectories obtained by varying slightly the parameters and initial conditions, from a numerical solution.

Keywords
Oscillating fields; charged particle; chaos