Nonlinear dynamics of magnetic field lines generated by simple electric current elements are investigated. In general, the magnetic field lines show behavior similar to that of the Hamiltonian systems; in fact, they can be generally transformed into Hamiltonian systems with 1.5 degrees of freedom, obey the Kolmogorov-Arnold-Moser (KAM) theorem, and generate chaotic trajectories. In the case where unperturbed systems are described by two action (slow) and one angle (fast) variables, however, it is found that the periodic orbits of the unperturbed systems vanish for arbitrarily small symmetry-breaking perturbations (a breakdown of the KAM theorem) and drifting or periodic trajectories appear. The mechanism of this phenomenon is investigated analytically by weak nonlinear stability analysis. It is also shown numerically that scattering processes of the perturbed system exhibit typical features of chaotic dynamical systems.
We investigate simple three-dimensionally crossed wires carrying electric currents which generate chaotic magnetic-field lines (CMFLs). As such wire systems, cross-ring and perturbed parallel-ring wires are studied, since topologically equivalent configurations to these systems can often be found in contemporary electric and integrated circuits. For realistic fundamental wire configurations, the conditions for wire dimensions (size) and current values to generate CMFLs are numerically explored under the presence of the weak but inevitable geomagnetic field. As a result, it is concluded that CMFLs can exist everywhere; i.e., they are ubiquitous in the modern technological world.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.