Proton velocity distribution in thin current sheets: Cluster observations and theory of transient trajectories

The structure of thin current sheets in the Earth magnetotail is studied on the basis of 43 crossings by Cluster spacecraft. Current sheet embedding is described as the ratio of the magnitudes of magnetic field at the thin current sheet boundary and in the lobe. This ratio is found to be similar to 0.4 on average. The proton population consists of the current-carrying particles with density similar to 10%-20% of the total density, and the background plasma. This current-carrying distribution is found to have a half-ring structure in the (v(x), v(y)) plane, which is consistent with the theory of transient particle motion (so-called Speiser-type trajectories). The main parameter of the thin current sheet models, the flow anisotropy epsilon, is estimated to be epsilon >= 0.3-0.5. The E x B drift of the background plasma due to the presence of an earthward ambipolar electric field can weaken the total proton current density (in the magnetospheric rest frame) by a factor of similar to(1-T(e)n(p)/T(p)n(Delta)), where T-e and T-p are electron and proton temperatures and n(Delta) and n(p) are the density of the current-carrying particles and the total plasma density, respectively.