Island instability as a mechanism of destabilization and collapse of current sheets

Abstract

The work shows that a single elongated island immersed in the quasi-neutral current sheet makes it MHD unstable. Typical values of growth rate are found to be several per cent of inverse Alfven time for broad sheets. Hall dynamics greatly enhance instability and growth rate reaches one-tenth of ion cyclotron frequency when sheet width is comparable to ion inertia length. A weak square-root dependence of increment on island width and length is derived both from numerical simulation and analytical analysis. At the non-linear phase of evolution a phenomenon of fast impulsive intensification of current is found. After finite time of about 10 ion-cyclotron periods it ends by a collapse of the sheet. It is shown that Hall dynamics is responsible for such a behaviour. Possible implications for magnetotail substorms are discussed.