Introduction

In a conducting medium a typical current sheet tends to diffuse outward at a slow rate with a time-scale of τd = l2/η, where 2l is the width of the current sheet and η = (μσ)-1 is the magnetic diffusivity. During the process of magnetic diffusion, magnetic energy is converted ohmically into heat at the same slow rate. However, in practice, the magnitude of τd is often far too large to explain the time-scale of dynamical cosmic processes. Nevertheless, Furth et al. (1963) showed how the diffusion can drive three distinct resistive instabilities at a rate which is often fast enough to be physically significant. These instabilities occur when the sheet is wide enough that τd ≫ τA, where τA = l/υA is the time it takes to traverse the sheet at the Alfvén speed υA = B0(μρ0)-½. The instabilities occur on time-scales τd(τA/τd)λ, where, and they have the effect of creating in the sheet many small-scale magnetic loops. In other words, resistive instabilities produce current filaments in current sheets (or, indeed, in any sheared structure) subsequently, the filaments and associated magnetic loops diffuse away, releasing magnetic energy in the process.

The gravitational and rippling modes (§6.3) occur when the density or resistivity varies in the direction across the sheet. They create a small-scale structure in the sheet (Fig. 6.1) and so are relatively harmless as far as the large-scale global stability of the configuration is concerned, although they may produce a turbulent diffusivity.