TL;DR
This paper derives a model for magnetic reconnection rates in Hall MHD, showing that when ion inertial length exceeds the reconnection layer thickness, the rate is independent of resistivity and proportional to the ion inertial length.
Contribution
It provides an analytical calculation of the reconnection rate in Hall MHD, highlighting the role of ion inertial length and electron layer structure.
Findings
Reconnection rate is independent of resistivity when d_i > layer thickness.
Reconnection rate equals d_i / L, with L being the external magnetic field scale.
The model applies to quasi-stationary, two-dimensional magnetic reconnection.
Abstract
The rate of quasi-stationary, two-dimensional magnetic reconnection is calculated in the framework of incompressible Hall magnetohydrodynamics (MHD). The calculation is based on the solution of Hall-MHD equations that include Hall and electron pressure terms for electric current. These equations are solved in a local region across the reconnection electron layer, including only the upstream region and the layer center. In the case when the ion inertial length d_i is larger than the Sweet-Parker reconnection layer thickness, the dimensionless reconnection rate is found to be independent of the electrical resistivity and equal to d_i/L, where L is the scale length of the external magnetic field in the upstream region outside the electron layer.
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