Reconnection via the Tearing Instability

We discuss the role of tearing instabilities in magnetic reconnection. In three dimensions this instability leads to the formation of strong Alfvenic waves that remove plasma efficiently from the reconnection layer. As a result the instability proceeds at high rates while staying close to the linear regime. Our calculations show that for a resistive fluid the reconnection speed scales as the product of the Alfven speed V_A over the magnetic Reynolds number to the power -0.3. In the limit of vanishing resistivity, tearing modes proceed at a non-zero rate, driven by the electron inertia term, giving rise to a reconnection speed V_A (c/ω_p L_x)^{3/5}, where ω_p is the plasma frequency and L_x is the transverse scale of the reconnection layer. Formally this solves the problem of fast reconnection, but in practice this reconnection speed is small.