Nonlinear dependence of anomalous resistivity on the reconnecting electric field in the Earth’s magnetotail

Abstract

Based upon the observational data of the fast magnetic reconnection in the nearly collisionless magnetotail and the particle in cell (PIC) simulations on the electron acceleration in the reconnecting current sheet with guide magnetic field, we self consistently solved one dimension Vlasov equation with the magnetotail parameters and realistic mass ratio to explore the relationship between the anomalous resistivity and the induced electric field. As compared with theoretic formula for the current driven ion-acoustic and Buneman anomalous resistivity, the anomalous resistivity may result from the ion acoustic instability for small reconnecting electric field and the Buneman instability for large reconnecting electric field. The discrepancy between the theoretic results and numerical simulations may be caused by the high frequency instability that results from the deviation of electron distribution from Maxwellian one. These results are consistent with the early experimental results and favorable for the fast reconnection to take place. In a collissioness coronal and the Earth's magnetotail plasma, anomalous resistivity caused by kinetic-scale wave-particle interactions is usually assumed to trigger fast magnetic reconnection, which was widely accepted as the main mechanism that converts free magnetic energy into heating and accelerating electrons and produces magnetospheric substorms [1][2][3][4]. The energetic electrons up to ∼300 keV were measured in a rare crossing of the diffusion region of reconnecting current sheet (RCS) by the Wind spacecraft [5]. Egedal et al.[6], after analyzing in-situ measurements of electron distribution functions inside the magnetotail RCS respectively from Wind and Cluster, found that the relative energy gain of the superthermal electrons is the same and nearly independent of their initial energy, while the electrons with the thermal energy are less accelerated. Hence, they concluded that the super thermal electrons are accelerated by reconnecting parallel electric field in vicinity of the reconnection region. For other acceleration mechanisms, such as Fermi acceleration of electrons in contracting magnetic islands and stochastic acceleration, the *Corresponding author (email: wuguiping@seu.edu.cn) relative energy gain of the electrons is a function of their initial energy. Therefore, these direct observational signatures suggest that the electrons are accelerated to relativistic energy by reconnecting electric field inside the diffusion region. On the other hand, the role of the electron dynamics inside the diffusive region of RCS is very important to understand the collissionless magnetic reconnection [7]. The 2D and 3D particle-in-cell (PIC) simulations was widely used to trace the typical electron trajectories [8,9]. It is found that, with the guiding magnetic field or external driven reconnection in RCS, the electrons can only be accelerated by the electric field in the X-type region and then spread out along the separatrices. In the O-type region, no obvious electron accelerati...

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