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

Abstract

A theoretical analysis of the radiation in X-ray free electron lasers (FELs) LCLS, PAL-XFEL, SwissFEL, as well as SACLA, FLASH 2, and European XFEL is presented. Major losses in FELs are analytically accounted for and analyzed, using exact expressions for the Bessel factors in terms of the generalized Bessel functions. This allows distinguishing the contributions of key parameters and accounting for the losses individually for each harmonic, considering higher sensitivity of the electron-photon interaction at higher harmonic wavelengths. The harmonic power evolution along FELs and the spectral width of the radiation lines is studied. The theoretical results are analyzed and are compared with the available experimental data for the FEL experiments. The harmonic generation and amplification in the FELs are modeled and studied with the harmonic lasing self-seed (HLSS) with separate buncher and radiator, and the results are compared with those for SASE. The spectral properties of the radiation are analytically calculated and compared with the measured spectral characteristics. The advantages of HLSS versus SASE FEL are elucidated in the examples of FLASH2, European XFEL, and SwissFEL. The prospected radiation properties of LCLS-II FEL are analyzed and the possibilities of using harmonics in this FEL are proposed.

Second harmonic in FELs: Generation, amplification and suppression

“…We omit the analysis for soft X-rays for conciseness. The power evolution from (3)-( 7) agrees very well with the experimental data as shown earlier in [5][6][7][8], where we accounted for the reported off-axis deviation of the beam in Δ ∼ 10-20 μm on one gain length L gain ≈ 1.5 m and for the effective angle of photon-electron interactions. The emittance and betatron terms alone yield the second harmonic power two-three orders of magnitude lower than the measured one.…”

“…Calibrated formulae (5),( 6) reproduce all measured harmonic powers (red solid line for n = 1, dot-dashed orange line for n = 2 and dashed green line for n = 3) and saturated power oscillations. Interestingly, by assuming the effective angle of photon-electron interactions θ = σ γ /L g ≈ 0.38 mrad for θ in the second line of (8) instead of the divergence ∼ 0.2 mrad supposed in [27], we get from the second line of (8), where θ = θ = σ γ /L g the increased second harmonic power close to the measured values! Thus our approach with the electron-photon interaction angle gives correct results (see fig.…”

“…On-axis radiation from neighboring periods of a planar undulator interferes destructively at the even harmonics wavelength; even harmonics are therefore suppressed in the ideal case. In finite sized beams even harmonics arise mainly due to angular effects [5][6][7][8]; contribution from the betatron oscillations is (a) E-mail: zhukovsk@physics.msu.ru (corresponding author) minor [5,6]. For the even harmonics of the spontaneous UR the divergence and the deflection angles of the beam matter.…”

“…We calibrated saturated powers P n,F and gain length to describe all major FELs [7,8] with one order of magnitude accuracy,…”

“…comes from the preceding undulator sections or is induced by the bunching b n with the calibrated coefficients c n ≈ {1, 1.3, 2, 5, 10}, d n ≈ {1, 3, 8, 40, 120}. Theoretical results for so calibrated saturated harmonic powers (5) and their evolution (7) were carefully matched also with the numerical simulations [25] and describe the available data for all major FELs in [7,8]. Second harmonic oscillations in an optical cavity, such as in [26], are not covered by the proposed formalism.…”