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).

[1] Generation of electric fields at the scale of the local electron Debye length in collisionless magnetic reconnection is studied through two-dimensional Darwin particle-in-cell simulation. For asymmetric initial temperature and density profile across the Harris current sheet, intense perpendicular electrostatic structure with the local electron Debye-length scaling ($2.9 l De ) is observed near the edge of the magnetic island in the high-temperature/low-density region. It is also found that a weak electron jet with return electron flow on the high-density side results in the formation of an electron current loop. However, in the low density region only a strong electron outflow is detected. Because of a singlelooped electric current on each side of the outflow region, the usual quadrupole structure appearing in the earlier symmetric-profile simulations is replaced by a dipole-like structure of the guiding magnetic field. Possible applications of the present results in the dayside magnetopause are discussed.

An effective resistivity relevant to collisionless magnetic reconnection (MR) in plasma is presented. It is based on the argument that pitch angle scattering of electrons in the small electron diffusion region around the X line can lead to an effective, resistivity in collisionless plasma. The effective resistivity so obtained is in the form of a power law of the local plasma and magnetic field parameters. Its validity is confirmed by direct collisionless particle-in-cell (PIC) simulation. The result agrees very well with the resistivity (obtained from available data) of a large number of environments susceptible to MR: from the intergalactic and interstellar to solar and terrestrial to laboratory fusion plasmas. The scaling law can readily be incorporated into existing collisional magnetohydrodynamic simulation codes to investigate collisionless MR, as well as serve as a guide to ab initio theoretical investigations of the collisionless MR process.

In the framework of two‐dimensional incompressible MHD, we investigate the formation of Alfvénic resonance layers with different super‐Alfvénic shear flows. It is found that Alfvénic resonance layers are formed in the inflow region for the cases with the shear flow thickness larger than the current sheet thickness. The Alfvénic layers exist at where the flow velocity is equal to the local Alfvén speed and slowly drift away from the current sheet region as a magnetic island develops. The ratio (D) between the separation of the Alfvénic resonance layers and the current sheet thickness plays a crucial role on magnetic reconnection. It is found that D ~ 3 is a critical value, which is about the saturated size of a magnetic island in magnetic reconnection without super‐Alfvénic shear flow. For D < 3, the super‐Alfvénic shear flow shows mainly a suppressing effect on magnetic reconnection and the peaked reconnection rate drops below the rate without a super‐Alfvénic shear flow. When D > 3, the boosting effect of Kelvin‐Helmholtz instability surpasses the suppressing effect by Alfvénic resonance and the peaked reconnection rate is larger than that without a super‐Alfvénic shear flow. For D ~ 5, the super‐Alfvénic shear flow gives rise to a strongest boosting effect on magnetic reconnection. Possible applications are briefly discussed.