Wave optical description of the Traveling-Wave Thomson-Scattering optical undulator field and its application to the TWTS-FEL

We show that X-ray optical free-electron lasers (OFELs) can be realized using Traveling-Wave Thomson-Scattering (TWTS).
In TWTS pulse front tilted laser pulses are scattered off relativistic electron bunches in a side-scattering geometry.
The pulse-front tilt guarantees overlap between laser and electrons over distances in the meter range while both are traveling in different directions.
An interaction distance of 90 cm is obtained in a setup were 590 MeV electrons scatter off a petawatt class laser incident under an angle of 4.5°.
The amplification of the 1.5 Å radiation saturates at the end of the interaction.
In order to account for spatial and temporal dispersion introduced with the pulse front tilt, we develop an exact three-dimensional analytical description of TWTS pulses that can be used in three-dimensional simulations of the radiation amplification process.
The wave-optical formulation of the TWTS pulse includes dispersion to all orders and provides a general description of laser pulses diffracted at VLS gratings.