Three-dimensional analyses of magnetic fields in a staggered-array undulator

A staggered-array undulator set inside the superconducting solenoid coils is shown to provide high undulator fields together with original longitudinal magnetic fields, a small undulator period of a few centimeters, easy tunability through the solenoid coil current, as well as compact, less expensive and easy fabrication. These performance characteristics seems very favorable for the single path X-ray FEL generation, since a great number of the undulator period is essential, in general. The previous two-dimensional analyses of electron beam trajectories have shown the necessity of the transverse stabilizing effect, which led to the three-dimensional analyses with successful stabilizing effects for the staggered-array undulator of about one meter for IR FEL. For X-ray FEL generation, electron trajectories with least deviation from the z-axis is rather mandatory for the light to grow over the undulator. Three-dimensional analyses are made to show the effect of parameters on the electron trajectories