Electric-Wiggler-Enhanced Three-Quantum Scattering and the Output Power Affected by this Scattering in a Free-Electron Laser

We derive the cross section of scattering through the three-quantum interaction of an electron with the incident laser field, the emitted photon, and an axial electrostatic field produced by the magnetic wiggler in the magnetic wiggler acting as the sole zeroth-order perturbing classical field in the first free-electron laser (FEL). In the derivation, we apply quantum-wiggler electrodynamics (QWD). We find that this scattering predominates the usual two-quantum scattering. The output power of spontaneous free-electron two-quantum Stark emission driven by the above electrostatic field attenuated by the three-quantum scattering agrees within a factor of 10 with the measured power in the case of the first FEL.