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Magnetic reconnection plays a critical role in many astrophysical processeswhere high energy emission is observed, e.g. particle acceleration,relativistic accretion powered outflows, pulsar winds and probably indissipation of Poynting flux in GRBs. The magnetic field acts as a reservoir ofenergy and can dissipate its energy to thermal and kinetic energy via thetearing mode instability. We have performed 3d nonlinear MHD simulations of thetearing mode instability in a current sheet. Results from a temporal stabilityanalysis in both the linear regime and weakly nonlinear (Rutherford) regime arecompared to the numerical simulations. We observe magnetic island formation,island merging and oscillation once the instability has saturated. The growthin the linear regime is exponential in agreement with linear theory. In thesecond, Rutherford regime the island width grows linearly with time. We findthat thermal energy produced in the current sheet strongly dominates thekinetic energy. Finally preliminary analysis indicates a P(k) 4.8 power law forthe power spectral density which suggests that the tearing mode vortices play arole in setting up an energy cascade.

3-d resistive MHD simulations of magnetic reconnection and the tearing mode instability in current sheets