A time-dependent model for magnetic reconnection in the presence of a separator

We present a model for separator reconnection due to an isolated reconnection process. Separator reconnection is a process which occurs in the neighborhood of a distinguished field line (the separator) connecting two null points of a magnetic field. It is, for example, important for the dynamics of magnetic flux at the dayside magnetopause and in the solar corona. We find that, above a certain threshold, such a reconnection process generates new separators, which leads to a complex system of magnetic flux tubes connecting regions of previously separated flux. Our findings are consistent with the findings of large numbers of separators in numerical simulations. We discuss how to measure and interpret the reconnection rate in a configuration with multiple separators.