In the current ''conceptual'' model of magnetospheric substorms, the growth phase terminates and the expansion phase commences with the onset of rapid reconnection at a new, near-earth X-type neutral line. Physical concepts developed in the analysis of the collisionless tearing mode and the flow of collisionless plasma in weakly magnetized, thin current sheets are combined to construct a model of purely collisionless, time-dependent, ion-dominated reconnection. Formulated in the context of time-dependent magnetospheric convection, the model describes the reconnection collapse of the initially thick plasma sheet. In the nonlinear phase the reconnection rate grows explosively in time and saturates into a steady collisionless reconnection flow when the initial magnetic flux in the current sheet has reconnected; at saturation the reconnection rate is comparable to the maximum Petschek rate. The time scale and dynamics of the explosive reconnection model are broadly consistent with observations of substorm growth phase and expansion phase onset. For typical plasma sheet parameters the explosive reconnection electromotive force across the tail approaches 1 MV at saturation.