Three-dimensional current sheet tearing in the Earth's magnetotail

Evidently, reconnection takes place in the Earth's magnetospheric tail. The question is, however, what disrupts the tail current sheet and how. A major hypothesis is that of a spontaneous collisionless tearing instability. Past theoretical investigations have revealed, however that the small residual magnetic field at the geomagnetic equator stabilizes the current sheet pretty much against collisionless tearing. We have now revised this problem focusing on the main stumbling block - the effect of electron compressional stabilization. In contrary to past considerations of two-dimensional sheet tearing, we have recalculated the main terms of the variational principle for a sheared tail current sheet against shorter wavelength perturbations (WKB approach). In contrast to previous investigations, however, we have investigated truly three-dimensional perturbations. As a result we have found conditions, for which the stabilizing influence of the electron compression becomes reduced. Our results imply that a localized in all three spatial dimension tearing of the current sheet in the Earth's magnetotail is much more probable rather than the quasi- two-dimensional ones, considered in the past.