Magnetic reconnection

Abstract

A review is given of the theory of magnetic reconnection in the framework of resistive magnetohydrodynamics (MHD). Since interest is primarily in explaining the rapid release of magnetic energy in weakly resistive plasmas, such as in tokamak disruptions or solar flares, the theory is concerned with the problem of fast reconnection, which is basically a nonlinear process. The fundamental reconnecting structure, the Sweet-Parker current sheet, is introduced. The main approaches of conventional reconnection theory are critically reviewed, Petschek's slow shock model and Syrovatskii's current sheet model. While Petschek's model is now known to be invalid in the limit of small resistivity, Syrovatskii's theory accounts for many properties observed in fully dynamic resistive systems. The scaling properties of stationary current sheet configurations in driven reconnection are discussed and a refined picture of dynamical current sheets is given. Though these current sheets are significantly more stable than static sheets, tearing instability sets in at sufficiently large aspect ratio, limiting the Reynolds number range where stationary configurations are possible. The theory is applied to several self-consistent reconnecting systems, the nonlinear tearing mode, the nonlinear evolution of the resistive kink mode, the coalescence of magnetic islands and the process of plasmoid formation. While the main part of the review is restricted to two-dimensional systems, also some concepts for reconnection in three-dimensional systems are presented. At sufficiently high Reynolds number turbulence is expected to develop. After a brief introduction to MHD turbulence the dissipation properties in 2-D systems pertinent to strongly magnetized plasmas are discussed and some properties of weakly magnetic 3-D turbulence and the turbulent dynamo effect are outlined.