Abstract
Theoretical analysis of the second harmonic generation in undulators shows physical reasons for their radiation in free electron lasers (FELs). The harmonic powers, the second in particular, are calculated with several different analytical approaches and compared with each other and with well documented experimental data for LEUTL and LCLS FELs. Various contributions to the harmonic powers are distinguished, their influence is explored. The possibility to suppress the second harmonic radiation by the second harmonic of the undulator magnetic field is shown in the example of LCLS FEL. The amplification and radiation of the second FEL harmonic in a FEL, using harmonic lasing self-seed (HLSS), is shown in the example of SwissFEL with separate harmonic buncher and amplifier.
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