We propose the 3rd harmonic lasing in a new FLASH undulator as a way to
produce intense, narrow-band, and stable SASE radiation down to 1.3 nm with the
present accelerator energy of 1.25 GeV. To provide optimal conditions for
harmonic lasing, we suggest to suppress the fundamental with the help of a
special set of phase shifters. We rely on the standard technology of
gap-tunable planar hybrid undulators, and choose the period of 2.3 cm and the
minimum gap of 0.9 cm; total length of the undulator system is 34.5 m. With the
help of numerical simulations we demonstrate that the 3rd harmonic lasing at
1.3 nm provides peak power at a gigawatt level and the narrow intrinsic
bandwidth, 0.1% (FWHM). Pulse duration can be controlled in the range of a few
tens of femtoseconds, and the peak brilliance reaches the value of 10^31
photons/(s mrad^2 mm^2 0.1%BW). With the given undulator design, a standard
option of lasing at the fundamental wavelength to saturation is possible
through the entire water window and at longer wavelengths. In this paper we
briefly consider additional options such as polarization control, bandwidth
reduction, self-seeding, X-ray pulse compression, and two-color operation. We
also discuss possible technical issues and backup solutions.Comment: arXiv admin note: text overlap with arXiv:1205.250