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Generating a uniform transverse distributed electron beam along a beam line

It has been reported that transverse distribution shaping can help to further enhance the energy extraction efficiency in a terawatt, tapered X-ray free-electron laser. Thus, methods of creating and keeping an almost uniform transverse distributed (UTD) beam within undulators are required. This study shows that a UTD electron beam can be generated within evenly distributed drift sections where undulators can be placed, by means of octupoles and particular optics. A specific design is presented, and numerical simulations are performed to verify the proposed method.