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Magnetic reconnection is believed to be the driver of many explosivephenomena in Astrophysics, from solar to gamma-ray flares in magnetars and inthe Crab nebula. However, reconnection rates from classic MHD models are fartoo slow to explain such observations. Recently, it was realized that when acurrent sheet gets sufficiently thin, the reconnection rate of the tearinginstability becomes "ideal", in the sense that the current sheet destabilizeson the "macroscopic" Alfv\'enic timescales, regardless of the Lundquist numberof the plasma. Here we present 2D compressible MHD simulations in theclassical, Hall, and relativistic regimes. In particular, the onset ofsecondary tearing instabilities is investigated within Hall-MHD for the firsttime. In the frame of relativistic MHD, we summarize the main results from DelZanna et al. [1]: the relativistic tearing instability is found to be extremelyfast, with reconnection rates of the order of the inverse of the light crossingtime, as required to explain the high-energy explosive phenomena.

Fast magnetic reconnection: The "ideal" tearing instability in classic, Hall, and relativistic plasmas