Embedded current sheets in the Earth's magnetotail

In this investigation we introduce and discuss quantitative parameters of a thin current sheet embedded in the background plasma sheet. We use Cluster statistics and empirical models, as well as self-consistent simulations, to understand the formation and development of embedded current sheets, in particular in the course of substorms. Data and theory show that the embedded sheet thickness is of the order of a proton larmor radius, a constraint equivalent to magnetic flux conservation. The embedded sheet can be essentially described by two dimensionless parameters B-0/B-ext and F-0/F-ext. B-0 is the magnetic field at the embedded sheet boundary, B-ext is the field at the boundary of the background plasma sheet, and F-0 and F-ext are magnetic flux values. During the growth phase current density in embedded sheet and B-0 increase, while thickness decreases. Sheets with the most intense currents (large B-0) are observed after onset. The self-consistent anisotropic sheet model, including both electron and proton currents and combined with the Harris-type background shows that when the proton-scale embedded sheet becomes sufficiently thin, an electron-scale current sheet can appear inside it due to enhanced electron curvature drift.