Maximizing Spectral Flux from Self-Seeding Hard X-ray FELs

Fully coherent x-rays can be generated by self-seeding x-ray free-electron lasers (XFELs). Self-seeding by a forward Bragg diffraction (FBD) monochromator has been recently proposed [1] and demonstrated [2]. Characteristic time To of FBD determines the power, spectral, and time characteristics of the FBD seed [3]. Here we show that for a given electron bunch with duration sigma_e the spectral flux of the self-seeding XFEL can be maximized, and the spectral bandwidth can be respectively minimized by choosing To ~ sigma_e/pi and by optimizing the electron bunch delay tau_e. The choices of To and tau_e are not unique. In all cases, the maximum value of the spectral flux and the minimum bandwidth are primarily determined by sigma_e. Two-color seeding takes place To >> sigma_e/\pi. The studies are performed, for a Gaussian electron bunch distribution with the parameters, close to those used in the short-bunch (sigma_e ~ 5 fs) and long-bunch (sigma_e ~ 20 fs) operation modes of the LCLS XFEL.