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In high gain Free Electron Lasers (FELs), it is possible to use undulator tapering to increase power and energy extraction beyond saturation. For some applications, however, tapering is not sufficient or results in excessively long structures. Here we the study use of tapered undulators interrupted by short accelerator sections to increase the power extracted per unit length. Re-acceleration restores nominal energy to the beam with minimal disruption to bunching, and allows repeated use of a single taper profile. We show that for suitable parameter sets this approach can perform better than ideal tapering alone, and may serve to greatly improve and simplify high peak and average power FELs. Based on these findings, we propose a first experiment to test the re-acceleration with tapering concept.
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