Reconnection dynamics with secondary tearing instability in compressible Hall plasmas

Abstract

The dynamics of a secondary tearing instability is systematically investigated based on compressible Hall magnetohydrodynamic. It is found that in the early nonlinear phase of magnetic reconnection before onset of the secondary tearing instability, the geometry of the magnetic field in the reconnection region tends to form a Y-type structure in a weak Hall regime, instead of an X-type structure in a strong Hall regime. A new scaling law is found that the maximum reconnection rate in the early nonlinear stage is proportional to the square of the ion inertial length (γ∝di2) in the weak Hall regime. In the late nonlinear phase, the thin elongated current sheet associated with the Y-type geometry of the magnetic field breaks up to form a magnetic island due to a secondary tearing instability. After the onset of the secondary tearing mode, the reconnection rate is substantially boosted by the formation of the X-type geometries of magnetic field in the reconnection regions. With a strong Hall effect, the maximum reconnection rate linearly increases with the increase of the ion inertial length (γ∝di).