D.N. Klochkov, K.B. Oganesyan, Y.V. Rostovtsev, G. Kurizki // Threshold characteristics of free electron lasers without inversion, Laser Physics Letters.pdf, 11, 125001 (2014).

Free-electron lasers (FELs)  use the kinetic energy of relativistic electrons moving through a spatially modulated magnetic field (wiggler) to produce coherent radiation. The frequency of radiation is determined by the energy of electrons, the spatial period of magnetic field and the magnetic field strength of the wiggler. This permits tuning a FEL in a wide range unlike atomic or molecular lasers.

More specifically, the idea of FELWI (free-electron laser without inversion) is based on a two wiggler scheme with a specially organized dispersion region between the wigglers. For creation of FELWI, a device between the wigglers must be rather unusual: it must provide the negative-dispersion regime in which the faster electrons spend a longer time in the dispersion region than the slower ones. This goal does not look unachievable but it is not easy to reach it.

Taking into account the finite sizes of the beams, the value of the threshold laser power at the entry of the first undulator of FELWI, above which the selection of electrons via the transverse velocity in the drift region is possible, have been obtained for an FEL without inversion (FELWI). We find, that an FELWI cannot operate under a weak-amplification Thompson regime, for which the spatial amplificationis small. Only a large-amplification regime  should be used to build an FELWI. It can be either the anomalous Thompson or the Raman regime of amplification, using an electron beam with over-dense current density. For an FELWI operation, the optimal angle  between the electron and light beams is shown to depend on the the widthsof the electron  and the laser beams. The mechanism of an FELWI can be realized in the scheme of a ring laser.