Crossed undulator polarization control for X-ray FELs in the saturation regime

The crossed-planar undulator is a promising scheme for full and rapid control of X-ray polarization in a high-gain FEL. In this paper, we study the effectiveness of a crossed undulator for SASE FELs in the saturation regime in order to achieve stable operation. Statistical analysis is performed to show that the degree of polarization remains high in the saturation regime, and controllable polarization at the third harmonic of the FEL wavelength is obtained by adjusting the strength of the vertical undulator. We also propose a modified scheme for polarization control using a short pair of crossed undulators tuned to the second harmonic of the main undulator. The scheme is straightforward to implement and can reach high degree of polarization with high stability.