Second harmonic in FELs: Generation, amplification and suppression

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. 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.

The Influence of Increased Electron Energy Spread on the Radiation of the Second Harmonic in Free Electron Lasers

“…Note that formula (11) describes the saturated FEL harmonic powers in their nonlinear growth induced by the fundamental, and thus, it involves the Pierce parameter for the fundamental tone ρ 1 and not the Pierce parameter ρ n for the harmonics n > 1. The results of such a phenomenological account for the main FEL parameters agree with the data for major operating FELs in the range from visible to X-rays, and also with the results of an accurate formula by M.Xie [79,80], where seventeen independent parameters correct the gain length accordingly (see [45,[81][82][83] for details). The finite beam section is accounted for in the Bessel coefficients, and it is also important in the calculation of electron beam current density.…”

“…where Θ is a numerical coefficient of the order of ~0.1. The values from ( 16) exceed the measurements for most FELs by an order of magnitude, so we suggested in [82] a correction factor of Θ ~0.01, which restored the agreement with most measured FEL data. Huang also estimated the second harmonic saturated power [69], which reasonably agreed with reported experimental data; we reformulated the result of Huang in terms of the Fresnel number Γ = 4πσ 2 x,y /Nλ u λ 1 in [58].…”