Soft X-ray generation in cascade SASE FEL with two-frequency undulator

Abstract

The generation of soft X-ray radiation in cascade self-amplified spontaneous emission free electron laser (SASE FEL) using harmonics of a two-frequency undulator is studied. An advanced phenomenological model of SASE FEL, accounting for the properties of the undulator and of the electron beam, including major losses, is employed. The account for the beam energy spread, divergence and diffraction is harmonic dependent, which is a step forward from the previous models and phenomenological approach, which consider all the losses independent of the harmonic number. The model is validated with the experimental measurements of the FEL harmonic generation and with relevant three-dimensional numerical simulations. The model is adopted for the description of cascading SASE FELs. With its help the dynamics of high-gain harmonic generation (HGHG) SASE FEL cascades is analyzed to obtain the maximum high harmonic power in the X-ray band with the lowest possible seed frequency and the shortest FEL length. The advantages of the two-frequency undulator for SASE FEL in this context are demonstrated and the possibility of its usage in cascading HGHG SASE FEL is shown. Several types of cascade FELs with two-frequency undulators are simulated. Frequency multiplication in two, three and four stage cascades is introduced to obtain soft X-ray radiation. The possibility of the generation of a powerful radiation, 75 MW at λ ∼ 2.5-4.5 nm and a lower intensity 3rd harmonic, 100 kW at λ ∼ 1 nm, is demonstrated in multi-cascade FELs at just 20-35 meters with the seed wavelengths λ seed ∼ 140 nm, ∼40 nm and ∼ 11-13 nm.

Theoretical Analysis of the Radiation Properties of Some Major X‐Ray Free Electron Lasers

“…Experiments on the harmonic generation in HGHG were performed at FERMI facility; [36] it has been using this regime during the last 10 years; the studies showed the possibility to generate harmonic radiation in HGHG with the last undulator. [41] Studies [39][40][41][42][43][44] demonstrate that using HGHG, UV-and X-ray radiation can be produced in more compact devices, as compared with FELs where the fundamental tone is generated at the same wavelength; the typical beam energies in the FELs, where the fundamental wavelengths are 𝜆 < 1 nm are E ≈ 10 GeV. Generation of harmonics was used also in the FLASH FEL, [45,46] whose undulators have variable deflection parameter k. This allowed studies of the harmonic radiation in a FEL with the harmonic lasing self-seed (HLSS), where the first FEL undulators operate in SASE regime and their harmonic is amplified in the last sections.…”

Об Излучении Гармоник В Рентгеновских Лазерах На Свободных Электронах С Изменяемым Параметром Дипольности Ондуляторов

“…Наряду с этим в ЛСЭ также используют эхо нескольких затравочных лазеров, которые последовательно модулируют энергию электронного банча [15]; этот принцип реализован, например, в [16,17]. Возможен случай, когда гармоника в ондуляторе не излучается, но группировка электронов на ее длине волны создает эквивалентную мощность для усиления в следующем ондуляторе, настроенном в резонанс [18,19]; возможно также использование нескольких каскадов для умножения гармоник [20][21][22]. Применение монохроматоров или иная фильтрация излучения между каскадами ЛСЭ, настроенных на гармоники друг друга, позволяет получить от первых ондуляторов в режиме SASE затравочное лазерное излучение для последующих каскадов ЛСЭ (harmonic lasing selfseed, HLSS); этот принцип реализован, например, в ЛСЭ FLASH2 с изменяемым параметром дипольности k ондуляторов [23,24].…”

Synchrotron Radiation in Periodic Magnetic Fields of FEL Undulators—Theoretical Analysis for Experiments

“…The latter is based on the Pierce parameter ρ [45][46][47][48][49][50], and it significantly develops the first approach in [51][52][53], applied with some modifications in [54][55][56][57][58][59][60]. The present formulation in contrast with [51][52][53] describes all losses separately for each FEL harmonic; it also includes the gradual dual-stage saturation and reproduces the oscillations of the saturated power, differently from that in [54][55][56][57][58][59][60]. Moreover, formulae (4)-( 7), ( 22), ( 23) above in Section 2 in the limiting cases of the planar 2-frequency undulator correct the misprinted results in [54][55][56][57][58][59][60].…”