Realistic examples of chaotic magnetic fields created by wires

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

Corresponding authors: aguirreaj@inta.es dperalta@math.uc3m.es

Received: 13 June 2007
Accepted: 21 October 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.