Numerical study of the cascading energy conversion of the reconnection current sheet in solar eruptions

Magnetic reconnection plays an important role in the energy conversion during solar eruptions. In this work, we present a resistive magnetohydrodynamical study (2.5D) of a flux rope eruption based on the Lin and Forbes model regarding cascading reconnection. We use a second-order Godunov scheme code, to better understand the physical mechanisms responsible for high reconnection rates and the internal structure, particularly in chaotic or turbulent regions, of the coronal mass ejection (CME)/flare current sheet (CS). Two sets of simulations with Lundquist numbers of 1.18 x 10(5) and 2.35 x 10(5) in the vicinity of the CS, generating a slow CME and a moderate one, show global dynamic features largely consistent with the flare model. Looking into the fine structure of the CS, magnetic reconnection employs simultaneously the Sweet-Parker mode and time-dependent small-scale Petschek patterns in the early stage. As the flux rope rises, the outflow region becomes turbulent, which further enhances the reconnection rates. Our results show that coalescence and fusion processes of plasmoids provide a large number of small, transient local diffusion regions to dissipate magnetic energy, and confirm that the dissipation starts at macro-MHD scales rather than ion inertial lengths. The two runs have the same range of the local reconnection rates (10(-4)-0.3) relevant to CMEs. The fast rates are closely proportional to the square of the aspect ratio of multiple small-scale CSs. The topology of the magnetic field and the turbulence spectrum of the energy cascade are statistically addressed as well.