Amplification and Compression of Radiation Emitted by a Dense Relativistic Cold Electron Beam

Starting from a three-wave interaction system of equations for free-electron lasers in the framework of a quantum fluid model, the full spatio-temporal solution of this set of equations is numerically obtained. Although this quantum fluid model does not take into account the electron recoil, it is accurate enough to model free-electron lasers down to soft X-ray range using a counter propagating optical wiggler and a moderately relativistic electron beam for a table-top compact device. We have shown that the scattered radiation is amplified and divided into sub-pulses while it absorbs energy from the optical wiggler through the negative energy beam plasma mode. Furthermore, the leading pulse gets more energy than the others while the longitudinal waist is reduced and has a shape similar to a “ π -pulse” solution from the sine-Gordon equation.