Abstract
Keywords
1 Introduction
Highbrightness, highly stable and fully coherent pulses from high repetition rate freeelectron lasers (FELs) in the extreme ultraviolet (EUV) and Xray spectral regimes are capable of driving scientific applications^{[}1^{,}2^{]} such as timeresolved coherent spectroscopy^{[}3^{]}, photon scattering^{[}4^{]} and coherent control^{[}5^{,}6^{]}. Currently available megahertz repetition rate shortwavelength FEL user facilities, the European XFEL^{[}7^{]} and FLASH^{[}8^{]}, both operate in burst mode. Several continuous wave (CW) facilities are under construction, including the LCLSII^{[}9^{]} and SHINE^{[}10^{]}. One of the main operation modes for these FEL facilities is selfamplified spontaneous emission (SASE)^{[}11^{,}12^{]}. Originating from electron shot noise, SASE FELs have poor temporal coherence and large shottoshot fluctuations^{[}13^{]}.
For the current FEL facilities worldwide^{[}12^{,}14^{]}, one effective method to improve the temporal coherence is adopting seeded schemes, which can be classified as selfseeding and external seeding. Compared with selfseeding schemes, external seeding schemes, including highgain harmonic generation (HGHG)^{[}15^{–}17^{]} and echoenabled harmonic generation (EEHG)^{[}18^{–}21^{]}, can generate FEL pulses with lower energy fluctuation. They also provide extra capabilities to be highly synchronized with the external laser and to control the coherence in multicolor, multipulse implementations^{[}6^{,}22^{]}. These fulfill the requirements of the aforementioned scientific applications.
In HGHG FELs^{[}15^{]}, a sinusoidal energy modulation is first introduced to the electrons via the interaction between the electron beam and an external seed laser within a modulation undulator (called a modulator). After a magnetic chicane, the energy modulation is converted to density modulation, creating microbunching at the harmonic of the seed laser wavelength. The bunched beam is then delivered to a radiation undulator (called a radiator) resonant at the harmonic wavelength. To obtain sufficient bunching at a higher harmonic, the amplitude of the energy modulation imprinted by the seed laser needs to be large enough. However, for efficient FEL amplification in the radiator, the induced electron beam energy spread should be kept at a low level. This, in turn, places a restriction on the highest achievable harmonic for an HGHG FEL. For example, for the FERMI FEL1, the highest harmonic for FEL emission was the 13th harmonic, although coherent emission could be observed at a higher (15th) harmonic^{[}17^{]}. Recently, the operation range of the FERMI FEL1 was extended to the 25th harmonic by employing an electron beam with a low slice energy spread^{[}23^{]}.
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For high repetition rate HGHG FELs, the external laser becomes a determinant at the megahertz repetition rate. The stateoftheart laser system capable of delivering the hundredmegawatt pulses required by an HGHG scheme is limited to the kilohertz repetition rate. Several methods have been proposed to relax the peak power or repetition rate requirements for the seed laser^{[}24^{]}, including using an optical cavity for seed laser recirculation and/or amplification^{[}25^{,}26^{]} and employing a long modulator for both seed laser amplification and electron beam modulation^{[}27^{–}29^{]}. To enhance the energy modulation efficiency, a selfmodulation HGHG scheme was also proposed^{[}27^{,}30^{]}, which was demonstrated at the Shanghai Soft Xray Freeelectron Laser facility (SXFEL) recently^{[}31^{,}32^{]}. With a singlestage HGHG setup, the seventh harmonic emission has been obtained, while with a twostage cascaded HGHG setup and the ‘fresh bunch’ technique, the 30th harmonic emission has been obtained. It is worth noting that the selfmodulator was also proposed to resonate at the second harmonic of the seed laser wavelength in Refs. [27,31], in which case the 10th harmonic emission could be obtained according to simulation.
In this paper, we study a compact harmonicenhanced HGHG scheme to further extend the highest harmonic for FEL emission in a high repetition rate, singlestage HGHG scheme. Compared to a regular HGHG scheme, an additional modulation undulator resonant at a highharmonic wavelength is introduced, which essentially causes efficient electron density modulation up to the 20th harmonic wavelength, but with a relaxed peak power requirement for the seed laser and reduced electron energy spread growth. Moreover, since the electrons are bunched at a high harmonic of the seed laser wavelength, the density modulation can be achieved via a short dispersion section. This ensures the compactness of the proposed scheme.
The remainder of this paper is organized as follows. In Section 2, we give a detailed description of the scheme. In Section 3, the performance of the scheme is illustrated with simulations. Section 4 gives a summary and some discussions.
2 The scheme
A layout of the proposed scheme is sketched in Figure 1, which mainly comprises a short modulation undulator
Figure 1.Schematic layout of the harmonicenhanced HGHG FEL. Here, is a short modulation undulator, where an external seed laser with a wavelength of and a peak power at the megawatt level is used to modulate the electron beam; is a harmonicenhanced modulation undulator resonant at and is a radiation undulator resonant at ; and are two dispersion chicanes. (a)–(e) Sketches of electron beam distribution in the longitudinal phase space.
A similar layout can be found in the scheme of selfmodulation HGHG^{[}31^{]}, where the first stage of the HGHG radiator is resonant at the fundamental or the second harmonic wavelength. Our work can be distinguished by the highorder harmonic modulator and the significant bunching factor up to the 20th harmonic of the seed laser wavelength. Another scheme with a similar layout is the doublestage harmonic cascade HGHG demonstrated at the FERMI FEL to extend the wavelength coverage of the HGHG scheme^{[}33^{]}. However, the firststage radiator resonates at a much higher harmonic (13th) wavelength, which then requires a higher seed laser power for the high repetition rate operation.
For sufficient FEL emission at harmonic wavelength, it is essential to induce effective electron bunching at the target wavelength while keeping the energy spread growth as low as possible. In this scheme, the electron beam undergoes twostage modulation, one in the fundamental modulator
The setup of the scheme can be very compact. Since the optimal dispersion of
3 FEL simulations of harmonicenhanced HGHG
To demonstrate the feasibility of the proposed scheme, timedependent FEL simulations using GENESIS code^{[}37^{]} have been carried out, with the representative parameters summarized in Table 1. The electron beam was assumed to have a central energy of 1 GeV, a slice energy spread (

Table 1. Main parameters used in the simulations.
For the proposed scheme, a proper choice of the harmonic number
Similarly, the length of the harmonicenhanced modulator should also be chosen properly. On one hand,
In this case, the interaction between the seed laser and the electron beam in
Figure 2.Electron distribution in the longitudinal phase space and the corresponding bunching factor at different harmonics of the seed laser wavelength after (a), (b) , (c), (d) and (e), (f) .
The longitudinal phase space after
To fully convert the electron energy modulation after
Fifty GENESIS runs were then performed with different random shot noise initializations and with the radiator resonant at the wavelength of 13.5 nm (
Figure 3.(a) The evolution of radiation pulse energy along and averaged over 50 GENESIS runs and (b) the FEL spectra for the 50 runs for the case with . The averaged spectrum is plotted as a dark line in (b).
To facilitate the estimation of repetition rate improvement of the proposed scheme compared to a regular HGHG scheme, we simulated a regular HGHG scheme using the same parameters for the modulator
We also investigated the case without
Figure 4.Bunching factor evolution at the fifth and 20th harmonics of seed laser wavelength along the radiation undulator for the case without .
The evolutions of the radiation spectrum, electron phase space and beam current profile along
Figure 5.Evolution of the radiation spectra (upper) and the longitudinal phase space of the electron beam (lower) along : (a) and (e) at the entrance of , (b) and (f) after the first undulator segment, (c) and (g) after the third segment and (d) and (h) after the fifth segment. The longitudinal coordinates are scaled to . The electron current profiles are plotted as red curves in (e)–(h).
Fifty GENESIS runs have been performed as well, and the results are plotted in Figure 6. As shown in Figure 6(a), the FEL saturates at 21.6 m of
Figure 6.(a) The evolution of radiation pulse energy along and averaged over 50 GENESIS runs and (b) the FEL spectra for the 50 runs for the case without . The averaged spectrum is plotted as a dark line in (b).
We finally investigated the robustness of the scheme against machine errors. For the simulation, we used the configuration without
Figure 7.FEL pulse energy for 200 GENESIS runs with random machine errors.
The radiation bandwidth of the proposed scheme is also sensitive to the nonlinear energy chirp, as is a normal HGHG scheme. Some methods have been developed to control the nonlinear energy chirp at a low level^{[}42^{]}. With an assumed 0.3 MeV/
4 Summary and discussion
In summary, we have studied a robust harmonicenhanced HGHG scheme to generate high repetition rate coherent FEL using a low peak power seed laser. The performance for two possible configurations has been investigated using GENESIS simulations, one with a short dispersion chicane after the harmonicenhanced modulator and the other without the chicane. Both configurations can generate coherent FEL output at 13.5 nm with a 270 nm, 1 MW (peak power) seed laser. For the case with the dispersion chicane, a bunching factor of 0.13 can be achieved at the 20th harmonic of the seed laser wavelength before the electron beam enters the radiator, and the FEL saturates at about 13.6 m in the radiator with a pulse energy of 193 μJ. The case without the dispersion chicane has a longer saturation length of 21.6 m and a lower pulse energy of 176 μJ. However, it is only necessary to tune a few radiation undulator segments in a regular HGHG scheme for it to be resonant at a higher harmonic (e.g., fifth harmonic in our simulation) of the fundamental wavelength. The length of these undulator segments (i.e., the harmonicenhanced modulator) can be varied easily, providing the flexibility of optimizing the harmonicenhanced modulator for different harmonics. In particular, with a longer modulator, even higher harmonics for soft Xray emission might be reached. Besides, a few methods can be used to further improve the FEL performance. For example, the first undulator segment of
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