Adiabatic electron heating in the magnetotail current sheet: Cluster observations and analytical models

We consider the electron distribution in current sheets observed by Cluster mission in the Earth magnetotail. We use the statistics of 70 fast (less than 20 minutes) and 12 slow (more than one hour) crossings of horizontal current sheets. We demonstrate that for both types electron temperature decreases with increase of magnetic field |B-x| away from the current sheet center. We use the approximations T-e perpendicular to/T-e perpendicular to (max) approximate to 1 - alpha(T perpendicular to)(B-x/B-ext)(2) and T-e parallel to/T-e parallel to (max) approximate to 1 - alpha(T parallel to)(B-x/B-ext)(2), where B-ext is value of B-x in the lobes. For statistics of thin current sheets (fast crossings) we obtain mean values approximate to approximate to 1. For thick current sheets (slow crossings) we also obtain approximate to , but , > 1. The electron temperature anisotropy is about T-e parallel to/T-e perpendicular to = 1.1 - 1.2 and vertical profiles T-e parallel to/T-e perpendicular to approximate to const. Observed vertical distributions of T-e parallel to and T-e perpendicular to are described by the analytical model of electron heating in the course of the earthward convection in thin current sheets with (B-x(z), B-z(x)) and in thick current sheets with (B-x(x, z), B-z(x, z)). We also show that the observed electron temperature anisotropy is provided by the electron population in the energy range between 50 ev and 3 keV. The cold core of electron distribution (<50 eV) is isotropic and the hot tail (>5 keV) has T-e parallel to/T-e perpendicular to similar to 1 or even T-e parallel to/T-e perpendicular to < 1. We consider electron pressure tensor in observed thin current sheets and demonstrate that electron velocity distribution is gyrotropic with high accuracy.