Improvements of a staggered-array undulator by tapered iron disks

A staggered-array undulator consists of two rows of simply stacked iron and aluminum disks alternately set in a solenoid coil. Its performance characteristics studied by the 2-D code show insufficient beam transverse focusing. Also, the original arrangement of iron disks at the entrance of the undulator is found not adequate for electron beam walk-off. Reduction of the beam walk-off effects is provided successfully by an addition of an auxiliary iron disk at the entrance, but the deviation of electrons in the transverse x-direction is found crucial even in this improved undulator. A tapered iron disk is qualitatively found to provide focusing effects in the x-direction, and optimization is made by a newly developed 3-D numerical code for magnetic fields using FEM and the reduced scalar potential. The focusing forces due to these methods will play an important role, in particular, in the ultra-long staggered-array undulator for shorter wavelength FELs.