Spatial dimensions of the electron diffusion region in anti-parallel magnetic reconnection

Spatial dimensions of the detailed structures of the electron diffusion region in anti-parallel magnetic reconnection were analyzed based on two-dimensional fully kinetic particle-in-cell simulations. The electron diffusion region in this study is defined as the region where the positive reconnection electric field is sustained by the electron inertial and non-gyrotropic pressure components. Past kinetic studies demonstrated that the dimensions of the whole electron diffusion region and the inner non-gyrotropic region are scaled by the electron inertial length <i>d</i>_e and the width of the electron meandering motion, respectively. In this study, we successfully obtained more precise scalings of the dimensions of these two regions than the previous studies by performing simulations with sufficiently small grid spacing (1∕16–1∕8 <i>d</i>_e) and a sufficient number of particles (800 particles cell⁻¹ on average) under different conditions changing the ion-to-electron mass ratio, the background density and the electron <i>β</i>_e (temperature). The obtained scalings are adequately supported by some theories considering spatial variations of field and plasma parameters within the diffusion region. In the reconnection inflow direction, the dimensions of both regions are proportional to <i>d</i>_e based on the background density. Both dimensions also depend on <i>β</i>_e based on the background values, but the dependence in the inner region ( ∼ 0.375th power) is larger than the whole region (0.125th power) reflecting the orbits of meandering and accelerated electrons within the inner region. In the outflow direction, almost only the non-gyrotropic component sustains the positive reconnection electric field. The dimension of this single-scale diffusion region is proportional to the ion-electron hybrid inertial length (<i>d</i>_i<i>d</i>_e)^1∕2 based on the background density and weakly depends on the background <i>β</i>_e with the 0.25th power. These firm scalings allow us to predict observable dimensions in real space which are indeed in reasonable agreement with past in situ spacecraft observations in the Earth's magnetotail and have important implications for future observations with higher resolutions such as the NASA Magnetospheric Multiscale (MMS) mission