Research Note

Linear force-free field of a toroidal symmetry

¹ Center for Plasma Astrophysics, K.U. Leuven 3001, Belgium
² Solar Observatory, Prairie View A& M University, Prairie View 77446, USA e-mail: eromashets@pvamu.edu
³ Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation of Russian Academy of Sciences, Troitsk 142190, Russia
⁴ Astronomical Institute, Academy of Sciences of the Czech Republic, Boční II 1401, 141 31 Praha 4, Czech Republic

Received: 22 January 2009
Accepted: 1 March 2009

Abstract

Context. Interplanetary flux ropes are often described by linear force-free fields. To account for their curvature, toroidal configurations valid for large aspect ratios are used. However, in some cases, flux ropes need to be approximated by a toroid with a low aspect ratio.

Aims. The aim is to find an analytical description of a linear force-free magnetic field of toroidal geometry, not restricted to large aspect ratios.

Methods. The solution is found as a superposition of fields given by linear force-free cylinders tangential to a generating toroid.

Results. The obtained solution describes toroidal flux ropes with reasonable shapes and magnetic field values. The field is exactly linear force-free for arbitrary aspect ratios. The new solution can be applied for solar and interplanetary flux ropes, astrophysical objects, and laboratory plasma.