Several proposals for the production of high brightness X-ray sources by a Free-Electron Laser (FEL) are under development. Self-amplified spontaneous emission (SASE) is the mode of operation of these single pass FELs, although work on High Gain Harmonic Generation also shows promise. An alternative would be to inject X-rays into the FEL and work in a single-pass amplifier mode. As a source of the X-rays, we propose to use Thomson scattering of visible wavelength photons, produced by scattering a high-intensity laser on an intense beam of electrons whose energy is of order 50 MeV. A second beam, of higher energy and small emittance, is then injected into the undulator with the X-rays. By choosing the kinematics properly and using a collimator to select only those X-rays with the desired energy and direction, it appears to be feasible to produce an input signal of order several Watts. According to the standard gain calculations, X-ray output power of several GW could be produced in this way. However, to obtain acceptably narrow bandwidth, the angular divergence and energy spread of the incident photon and electron beams must be very small. The basic mechanism for generating the X-rays, Compton scattering or its low-energy limit, Thomson scattering, has been studied both theoretically and experimentally for many years. Recently very intense short pulse lasers have been used as sources of the visible light, and high yields of short pulses X-rays have been obtained in this process. Given the sophisticated optics techniques available, much development work is devoted to using Thomson scattering of laser light for electron beam diagnostics, in the so-called laser wire-scanners. The laser properties we assume in this note correspond to the state of the art in high power ultra-short Ti:Sapphire laser so that we believe our estimates are not unrealistic. However, since the estimates assume very intense beams, the emittance of the high current electron becomes a significant factor. A conflict arises between yield (which is increased by decreasing the beam width at the interaction point) and narrow bandwidth (which is degraded by the reduction).
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