We perform theoretical study and modeling of enhanced high harmonic generation in X-ray band and low harmonics suppression in single pass free electron lasers (FEL) with a two-frequency undulator. For this purpose a phenomenological model of FEL is applied, which accounts for all main losses. The harmonic radiation in a FEL with a two-frequency undulator and in a FEL with a common planar undulator is compared with each other. The harmonic radiation and FEL induced energy spread are studied in a FEL, where lower than n–th harmonics are suppressed, for example, by the 2π/n phase shift of the electrons respectively to photons between the undulator sections. The advantages of the two-frequency undulators in such phase shifted FEL is elucidated. The possibility of intense X-ray radiation of a harmonic in linear regime, exceeding the power of a fundamental harmonic in a FEL, is demonstrated.
41.60.-m Radiation by moving charges
13.90.+i Other topics in specific reactions and phenomenology of elementary particles
$^1$MSU, Faculty of Physics
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