Dynamic non-null magnetic reconnection in three dimensions. I. Particular solutions BY ANTONIA WILMOT-SMITH*, GUNNAR HORNIG † AND ERIC PRIEST School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK A stationary model of three-dimensional magnetic reconnection in the absence of a null point is presented, with a non-ideal region that is localized in space. Analytical solutions to the resistive magnetohydrodynamic equations are obtained, with the momentum equation included so that the model is fully dynamic, and thus extends the previous kinematic solutions. A splitting of variables allows solutions to be written in terms of a particular non-ideal solution, on which ideal solutions may be superposed. For the non- ideal solution alone, it is shown that only the field lines linking the diffusion region are affected by the reconnection process, and counter-rotating flows above and below the diffusion region are present. It is only the dimensions of the diffusion region along the reconnection line that are important for the reconnection rate. Many features of the previous stationary kinematic model are also observed here. Keywords: magnetohydrodynamics; plasma; reconnection 1. Introduction Magnetic reconnection is a fundamental process in a plasma whereby magnetic energy is rapidly converted into other forms. It is responsible for a wide range of dynamic processes in astrophysical and space plasmas, such as solar flares and geomagnetic substorms. Recently, much work on magnetic reconnection has centred on understanding the three-dimensional problem (for an overview, see Priest & Forbes 2000). The discovery that, while two-dimensional reconnection is fairly well understood, many aspects of the full three-dimensional problem are not present in two-dimensions has provided motivation for this work. Our understanding of the nature of three-dimensional reconnection has been advanced both by numerical simulations and analytical work. Recent three- dimensional numerical experiments (e.g. those by Linton & Antiochos 2005) have provided important clues to our understanding of the behaviour of such magnetic fields. Analytical work has mainly focused on the kinematic problem (i.e. examining the implications of Ohm’s law alone without the effects of the equation of motion) in a finite region. The localization of the non-ideal term in the induction equation is an important typical feature of reconnection in Proc. R. Soc. A (2006) 462, 2877–2895 doi:10.1098/rspa.2006.1697 Published online 4 April 2006 * Author for correspondence (antonia@mcs.st-and.ac.uk). † Present address: Division of Mathematics, University of Dundee, Perth Road, Dundee DD1 4HN, UK. Received 30 September 2005 Accepted 16 February 2006 2877 q 2006 The Royal Society