Suppression of Even Harmonics in Free-Electron Lasers by Modifying the Energy Spread of the Beam

Using an analytical description of the evolution of harmonic power in free-electron laser (FEL) undulators, the influence of electron beam parameters on the fundamental characteristics of FEL radiation is investigated: gain length, spectrum, and harmonic power. The possibility of suppressing even harmonics in the FEL as a light source for material and surface studies using second harmonic generation (SHG) nonlinear response analysis is explored. The main factors affecting the emission of even harmonics in FELs are identified; the influence of the beam cross-section and the spread of electron energies on their radiation is analyzed. The example of the FEL LEUTL with visible light emission, which is used in the studies of optical properties of materials and the chemical state of molecules on surfaces and at interfaces, is considered. In this context, the possibility of suppressing the second harmonic in FELs is analyzed.