Extending the Photon Energy Coverage of a Seeded Free-Electron Laser via Reverse Taper Enhanced Harmonic Cascade

External seeded free-electron lasers (FELs) hold promising prospects for producing intense coherent radiation at high harmonics of a conventional laser. The practical harmonic up-conversion efficiencies of current seeding techniques are limited by various three-dimensional effects on the electron beam. In this paper, a novel method is proposed to extend the wavelength coverage of a seeded FEL by combining the reverse taper undulator with the echo-enabled harmonic generation. The proposed technique can significantly enhance the bunching at ultra-high harmonics and preserve the electron beam qualities from degradation by deleterious effects. Theoretical analysis and numerical simulation are performed, and the results demonstrate that stable, intense, nearly fully coherent FEL pulses with photon energy up to 1 keV can be generated. The proposed technique may open up new opportunities to obtain laser-like pulses at sub-nanometer wavelength.