Evolution of electron current sheets in collisionless magnetic reconnection

<jats:p>An electron current sheet embedded in an ion scale current sheet is an inherent feature of collisionless magnetic reconnection. Such thin electron current sheets are unstable to tearing mode and produce secondary magnetic islands modulating the reconnection rate. In this work, 2-D evolution of tearing mode at multiple reconnection sites in an electron current sheet is studied using electron-magnetohydrodynamic (EMHD) model. It is shown that growth of the perturbations can make reconnection impulsive by suddenly enhancing the reconnection rate and also forms new structures in the presence of multiple reconnection sites, one of which is dominant and others are secondary. The rise of the reconnection rate to a peak value and the time to reach the peak value due to tearing instability are similar to those observed in particle-in-cell simulations for similar thicknesses of the electron current sheet. The peak reconnection rate scales as 0.05/ϵ1.15, where ϵ is half thickness of the current sheet. Interactions of electron outflows from the dominant and secondary sites form a double vortex sheet inside the magnetic island between the two sites. Electron Kelvin-Helmholtz instability in the double vortex sheet produces secondary vortices and consequently turbulence inside the magnetic island. Interaction of outflow from the dominant site and inflows to the adjacent secondary sites launches whistler waves which propagate from the secondary sites into the upstream region at Storey angle with the background magnetic field. Due to the wave propagation, the out-of-plane magnetic field has a nested structure of quadrupoles of opposite polarities. A numerical linear eigen value analysis of the EMHD tearing mode, valid for current sheet half-thicknesses ranging from ϵ&lt;de=c/ωpe (strong electron inertia) to ϵ&gt;de (weak electron inertia), is presented.</jats:p>