  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 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 concrete design is presented, and numerical simulations are done to
verify the proposed method.
