We present an Inverse Free Electron Laser accelerator proposed for construction at the UCLA Neptune Laboratory. This experiment will use a 1 TW CO2 laser to accelerate through two strongly tapered undulators an electron beam from 16 MeV up to 55 MeV. The scheme proposed is the diffraction dominated IFEL interaction. The Raleigh range of the laser beam is about 2 cm, much shorter than the interaction length (the undulator length is 50 cm). In this regime adiabatic capture is possible in the

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... part of the undulator. In the focus region, we propose a solution to the problem of the dephasing between electrons and photons due to the Guoy phase shift. Ponderomotive effects and implications for tolerances are also studied CP647, Advanced Accelerator Concepts: Tenth Workshop, edited by C. E. Clayton and P. Muggli