Electric field structure inside the secondary island in the reconnection diffusion region

Abstract

Secondary islands have recently been intensively studied because of their essential role in dissipating energy during reconnection. Secondary islands generally form by tearing instability in a stretched current sheet, with or without guide field. In this article, we study the electric field structure inside a secondary island in the diffusion region using large-scale two-and-half dimensional particle-in-cell (PIC) simulation. Intense in-plane electric fields, which point toward the center of the island, form inside the secondary island. The magnitudes of the in-plane electric fields E_x and E_z inside the island are much larger than those outside the island in the surrounding diffusion region. The maximum magnitudes of the fields are about three times the B₀V_A, where B₀ is the asymptotic magnetic field strength and V_A is the Alfvén speed based on B₀ and the initial current sheet density. Our results could explain the intense electric field (~100 mV/m) inside the secondary island observed in the Earth's magnetosphere. The electric field E_x inside the secondary island is primarily balanced by the Hall term (j × B)/ne, while E_z is balanced by a combination of (j × B)/ne, -(v_i × B), and the divergence of electron pressure tensor, with (j × B)/ne term being dominant. This large Hall electric field is due to the large out-of-plane current density j_y inside the island, which consists mainly of accelerated electrons forming a strong bulk flow in the -y direction. The electric field E_y shows a bipolar structure across the island, with negative E_y corresponding to negative B_z and positive E_y corresponding to positive B_z. It is balanced by (j × B)/ne and the convective electric field. There are significant parallel electric fields, forming a quadrupolar structure inside the island, with maximum amplitude of about 0.3B₀V_A.