  The energy gain in laser wakefield accelerators is limited by dephasing
between the driving laser pulse and the highly relativistic electrons in its
wake. Since this phase depends on both the driver and the cavity length, the
effects of dephasing can be mitigated with appropriate tailoring of the plasma
density along propagation. Preceding studies have discussed the prospects of
continuous phase-locking in the linear wakefield regime. However, most
experiments are performed in the highly non-linear regime and rely on
self-guiding of the laser pulse. Due to the complexity of the driver evolution
in this regime it is much more difficult to achieve phase locking. As an
alternative we study the scenario of rapid rephasing in sharp density
transitions, as was recently demonstrated experimentally. Starting from a
phenomenological model we deduce expressions for the electron energy gain in
such density profiles. The results are in accordance with particle-in-cell
simulations and we present gain estimations for single and multiple stages of
rephasing.
