The 2.5‐D analytical model of steady‐state Hall magnetic reconnection

Abstract

[1] An analytical model of steady-state magnetic reconnection in a collisionless incompressible plasma is developed using the electron Hall MHD approximation. It is shown that the initial complicated system of equations may be split into a system of independent equations, and the solution of the problem is based on the solution of the Grad-Shafranov equation for a magnetic potential. This equation is found to be fundamental for the whole problem analysis. An electric field potential jump across the electron diffusion region and the separatrices is proved to be the necessary condition for steady-state reconnection. Besides of this fact, it is found that the protons in-plane motion obeys to Bernoulli law. The solution obtained demonstrates all essential Hall reconnection features, namely proton acceleration up to Alfvén velocities and the formation of Hall current systems and a magnetic field structure as expected.

Three dimensional density cavities in guide field collisionless magnetic reconnection

“…The decoupling of ions and electrons leads to an electron current system surrounding the magnetic separatrices, as suggested by the theory of Hall reconnection [22,23]. The net parallel electric field strongly accelerates the electrons in this region, thus reducing the local density [24].…”

Formation of a quasi-one-dimensional current sheet in the laboratory experiment and in the Earth’s magnetotail

“…This is a classical scenario of the development of cur rent systems in the vicinity of the magnetic field X line. This scenario has been frequently verified by numerical simulations [70][71][72][73] and analytical models [74]. Thus, in the laboratory modeling, we are dealing with CSs the spatial scales of which are comparable with the typical ion scale length and in which the elec tric current is carried by electrons due to the Hall effect.…”

Double power-law spectra of energetic electrons in the Earth magnetotail

“…Corresponding components of the electric field are E z ∼ −z, E x ∼ x (see, e.g., analytical model by Korovinskiy et al, 2008). The amplitude of the scalar potential ϕ is defined by the pressure balance and can reach ∼ B 2 0 /4πn 0 e ∼ 1-10 keV, where n 0 is the plasma density in the X-line (Divin et al, 2012).…”