Wavelength range of the ELBE FELs
The wavelength λn of the produced laser light is nearly identical with the wavelength maxima in the spectrum of the spontaneously emitted radiation which is determined by the electron energy γ (in units of electron rest mass), by the undulator parameter Krms and by the undulator period λu according to
λn= (1+Krms2) / (2n γ2) λu, (2)
where n denotes the harmonic number of the radiation.
The figure shows the wavelength λ1 (first harmonic) of the laser light produced in the FELBE undulators calculated according to eq.(2) as a function of the kinetic electron energy Eekin for the indicated values of the undulator parameter Krms. The upper edges of the colored areas correspond to the maximum value of Krms of either undulator. Above 22 μm (U27) and below 18 μm (U100) the optical cavity losses exceed the gain and lasing does not start.