A model of a free electron laser (FEL) amplifier operating simultaneously with two electron beams of different energy is presented. The electron beam energies are chosen so that the fundamental resonance of the higher energy beam is at a harmonic of the lower energy beam. By seeding the lower energy FEL interaction with its fundamental radiation wavelength, an improved coherence of the unseeded higher energy FEL emission is predicted. This method may offer an important alternative to those seeding proposals for FELs currently under development in the xuv and x-ray regions of the spectrum.
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