Scaling of Optical Free-Electron Lasers in Traveling-Wave Geometries

Optical free electron lasers in the X-ray range using high power lasers are difficult to realize in the standard head-on Thomson-scattering geometry. Problems arise from the nonlinear Thomson intensity threshold and the Rayleigh-length limiting the interaction distance which prevent the SASE process to occur.

These limits can be circumvented in a Travelling-wave Thomson-scattering (TWTS) geometry, in which ultrashort and narrow-band light pulses in the X-Ray region of the spectrum are created by scattering high intensity laser pulses from relativistic electron bunches. TWTS uses lasers with a pulse front tilt in a sidescattering geometry to scale the interaction length into the centimeter to meter range with undulator periods in the region of one hundred to a few hundred micrometer.

Starting from a fully 3D, wave-optical representation of the TWTS pulse, including its dispersion properties, we present a self-consistent 1.5D FEL-theory which accounts for the coupling of the obliquely incident laser pulse to the electron dynamics. Furthermore, we give scaling laws on the interaction geometry and FEL-amplification with respect to incidence angle and electron beam parameters. Using these findings we discuss possible experimental scenarios and its requirements on laser pulses and electron beams.