Coherent photon beam based diagnostics for a seeded extreme ultraviolet free-electron laser

Independently from electron beam based procedures, photon beam based diagnostics is an alternative way for alignment and commissioning of the numerous undulator cells in a high-gain short-wavelength free-electron laser (FEL). In this paper, using the seed laser modulated electron beam and the undulator fine tuning technique, a coherent photon beam based diagnostic was proposed for seeded FEL, and some preliminary experimental results at Shanghai deep ultraviolet FEL test facility were presented. It demonstrates that the spatial distribution of the coherent harmonic radiation from one individual or two consecutive undulator segments can be used to optimize the electron beam trajectory, to verify the undulator magnetic gap, and to adjust the phase match between two undulator segments.

As well known, the FEL exponential gain requires stringent electron beam trajectory control along 23 the whole undulator system, fine undulator magnetic field setting and well-matched phase between two 24 consecutive undulator segments. For this purpose, the electron beam based alignment [12][13][14] and the 25 photon beam based diagnostics [15][16] have been developed, respectively. While the former has 26 already got great success in x-ray FEL [1], it shows no insight into the magnetic gap or the phase match 27 of adjacent undulator segments. Photon beam based diagnostics serve as an additional tool for the beam 28 alignment and FEL undulator commissioning, independently from the electron beam based procedure.

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Currently, photon beam based diagnostics is routinely used for SACLA Facility [16] and seriously 30 considered by European XFEL project [15], and had been proposed for the LCLS project [17]. The 31 photon beam instruments consisting of a crystal monochromator, a spatial imaging optics and intensity detectors are located downstream of the undulator system, and thus allow to characterize the radiation 1 of selected undulator segment and can be used for photon beam based alignment. The one common 2 diagnostics facilitates a precise alignment and setup of the whole undulator system.

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However, photon beam based diagnostics has only been considered for a self-amplified spontaneous 4 emission (SASE) [18] x-ray FEL. In recent years, several seeded FEL user facilities are proposed from 5 extreme ultraviolet to soft x-ray region [5][6][7] where the monochromic light is directly generated with 6 the help of various laser-beam interactions [19][20][21]. In this paper, using the radiation from spatial 7 density modulated electron beam and the undulator fine tuning technique, a modified, coherent photon 8 beam based diagnostic namely, was proposed for seeded FEL. We first illustrated the principle to 9 optimize the electron beam trajectory, to verify the magnetic gap, and to adjust the phase match

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The schematic of the seeded FEL system layout is shown in Figure 1. The electron beam is spatially 15 modulated after the modulator undulator and the dispersive chicane. It indicates that the electron beam 16 with strong bunching factor emits coherently at the radiator undulator. The intensity analysis of such 17 coherent photon beam will illustrate the temporal structure of the electron beam current, emittance and 18 energy spread [23][24][25], and the spatial profile study will allow optimizing the electron beam trajectory,

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verifying the undulator magnetic gap, and adjusting the phase match between two undulator segments.    According to the undulator radiation physics, the spectral power per unit solid angle due to a single 8 electron in an undulator leads to the following expressions:

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where λ R is the fundamental resonant wavelength of the undulator radiation, N is the undulator period 13 number, λ u is the undulator period length, K is the normalized undulator parameter, γ is the kinetic 14 energy of the electrons measured in units of its rest mass, θ is the observation angle, and B 0 is the peak 15 magnetic field on the undulator axis.

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While the electron beam is spatially bunched at 50nm, Figure    applied to the last 2 radiator segments, i.e., the undulator resonant wavelength become shorter, a ring 16 shape rather than core shape spatial distribution of coherent photon beam will be observed.  to a wavelength of 49.49nm, blue: tuned to a wavelength of 49.84nm, spatial distribution from one 10 undulator segment can be seen in Figure 3) for the best phase difference (the right upper two plots) and 11 the worst phase difference (the right lower two plots).

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It is well known that random quadrupole offset will lead to misalignment of electron beam trajectory 13 along the undulator system, which leads to mismatch of FEL resonance and transverse overlap between 19 Figure 7 gives the spatial profiles of coherent photon beams when the electron beam enters a single 20 radiator segment with a transverse offset or angle, the radiator resonant wavelength is set to be less than   predictions as shown in Figure 3. And this phenomenon is successfully used to optimize the radiator 4 gap to fit the resonant condition. It was found that the composed radiation intensity was on maximum 5 when the spatial distribution of coherent photon beam from two single radiators transferred from a ring 6 to a core profile, and transversely overlapped each other.
7 Figure 9 (left) recorded the spatial distribution of coherent photon beam when changing the entering 8 angle of the electron beam at the entrance of the radiator. The radiator resonant wavelength was set to 9 be a little bit less than the 400nm. Comparing with the spatial distribution in Figure 8 (middle), Figure   10 9 (left) indicates a misalignment of electron beam trajectory in the radiator. The start-to-end simulation

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gives a similar spatial distribution as shown in Figure 9 (right), where a kicker is used to horizontally