Optical free-electron lasers with Traveling-Wave Thomson-Scattering

We present a fully analytic model of an all-optical free electron laser (OFEL) undulator based on the Traveling-Wave Thomson-Scattering (TWTS) scheme. The TWTS undulator provides for sub-mm undulator wavelengths, does not require any material or plasma to generate or contain the undulator field and allows for sub-meter saturation lengths. Starting from a fully analytic description of the three-dimensional TWTS field we derive the OFEL pendulum equation for electrons in the TWTS field and discuss the constraints on laser and electron pulse parameters that have to be fulfilled for OFEL operation. We conclude in applying the TWTS OFEL to the realization of compact free electron laser sources at 13.5 nm and 0.2 nm using laser and electron sources in reach of present day technologies.