Issue
EPL
Volume 80, Number 6, December 2007
Article Number 60007
Number of page(s) 6
Section General
DOI http://dx.doi.org/10.1209/0295-5075/80/60007
Published online 13 November 2007
EPL, 80 (2007) 60007
DOI: 10.1209/0295-5075/80/60007

Realistic examples of chaotic magnetic fields created by wires

J. Aguirre1 and D. Peralta-Salas2

1  Centro de Astrobiología, CSIC-INTA - Ctra. Ajalvir, km 4, 28850 Torrejón de Ardoz, Madrid, Spain
2  Departamento de Matemáticas, Universidad Carlos III de Madrid - 28911 Leganés, Spain

aguirreaj@inta.es
dperalta@math.uc3m.es

received 13 June 2007; accepted in final form 21 October 2007; published December 2007
published online 13 November 2007

Abstract
In this paper we study some examples of magnetic fields with hyperbolic periodic orbits and erratic behavior. The remarkable fact is that the fields under consideration are originated by configurations which consist of two thin wires. We present a rigorous proof of the chaoticity of these magnetic fields, in the sense that they possess KAM islands and homoclinic tangles, and we also provide numerical simulations. In particular we illustrate, contrary to folk wisdom, that magnetic lines originated by current filaments can show a very complex nature. Finally, we propose a simple experimental verification of these results, as well as possible fields of application.

PACS
05.45.Ac - Low-dimensional chaos.
41.20.Gz - Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems.

© EPLA 2007