Feasibility study of a single stage echo-seeded FEL at nm wavelength at SLAC Motivation: FELs can provide tunable high-power coherent radiation which has wide applications in biology, chemistry, physics and material science, etc. In x-ray wavelength range, most of the FELs operate in the self-amplified spontaneous emission (SASE). One FEL (LCLS) working in the SASE mode has been successfully operated at hard x-ray wavelengths, which marks the beginning of a new era of x-ray sciences. While the radiation from a SASE FEL has excellent transverse coherence, it typically has rather limited temporal coherence and relatively large statistical fluctuations because a SASE FEL starts from electron beam shot noise. There are many applications that require, or could benefit from, improved temporal coherence. Seeding the FELs with external coherent laser pulse not only improves the temporal coherence of the radiation, but also provides an FEL signal with well-defined timing with respect to the seed laser, thus allowing pump-probe experiment to be performed with high temporal resolution. The leading candidate for seeding x-ray FELs with external laser pulse is the recently proposed echo-enabled harmonic generation technique. Previous studies have shown that with echo seeding technique one can reach soft x-rays in the range 4~5 nm from UV seed lasers at ~200 nm in a single stage. In order to meet the scientific needs for spectroscopic studies of transition metal materials, it is highly desirable to extend the FEL wavelength to 1 nm. It is known that the success of echo-seeded FELs relies on the preservation of the long-term memory of phase space correlations. In this ultrahigh harmonic regime (n~200) many effects, such as quantum diffusion, coulomb collision, second order transport effects etc. may potentially wash out the correlations. To address the feasibility of ECHO-200, we propose to study echo seeding technique in a realistic scenario (~2 GeV energy, ~1 kA peak current) with all the smearing effects taken into account. The proposed work will address the feasibility of ECHO-200 in a single stage and will provide guidance in design of future user machine based on echo seeding. Topic: Study the feasibility of ECHO-200 in a single stage; Identify the main effects that limit echo technique to reach ultrahigh harmonic number; Find ways to mitigate these effects; Provide guidance in design of future user machine based on echo seeding. Time table of milestones: 07-2011, number; 10-2011, 12-2011, scenario; 02-2012. Identify the main effects that limit echo technique to reach ultrahigh harmonic Feasibility study of ECHO-50, ECHO-100, ECHO-200; Determine the highest harmonic number reasonably achievable in the realistic Document the findings for future guidance. Deliverables: A report should be documented for SLAC-PUB.