The energy gain in laser wakefield accelerators is limited by dephasingbetween the driving laser pulse and the highly relativistic electrons in itswake. Since this phase depends on both the driver and the cavity length, theeffects of dephasing can be mitigated with appropriate tailoring of the plasmadensity along propagation. Preceding studies have discussed the prospects ofcontinuous phase-locking in the linear wakefield regime. However, mostexperiments are performed in the highly non-linear regime and rely onself-guiding of the laser pulse. Due to the complexity of the driver evolutionin this regime it is much more difficult to achieve phase locking. As analternative we study the scenario of rapid rephasing in sharp densitytransitions, as was recently demonstrated experimentally. Starting from aphenomenological model we deduce expressions for the electron energy gain insuch density profiles. The results are in accordance with particle-in-cellsimulations and we present gain estimations for single and multiple stages ofrephasing.
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