Feasibility verification of ultrafast FEL generation experimental scheme based on SXFEL

The photon energy in the soft X-ray range corresponds to the fundamental absorption edges of matter. Ultrashort X-ray pulses can be used to observe the breaking of chemical bonds in biochemical reactions and capture the transfer process of electrons in ultrafast physical phenomena. In this paper, the feasibility of ESASE experiments on Shanghai Soft X-ray Free Electron Laser Facility (SXFEL) is theoretically verified. The results show that the ESASE scheme can produce ultrafast light pulses on the order of attosecond, with a peak power of 450 MW. At the same time, the simulation results in this paper verify the feasibility of chirped enhanced SASE schenme based on SXFEL. The results show that compared with the ESASE scheme, the power of the radiation pulse can be greatly improved by this scheme. A relatively low energy electron beam (1.5 GeV) was used to generate about 40 GW of radiation, and the length of the radiation pulse was significantly shortened.


Introduction
The pump-probe technique [1] is often an effective means to study ultrafast time-varying phenomena.The time resolution of the technique is directly related to the pulse duration of the pump and probe lasers.The shorter the pulse duration is, the higher the time resolution is.Attosecond-level optical pulses can even be used to study the dynamics phenomena of electrons, which opens up many new ultrafast scientific fields, such as femtosecond chemistry, ultra-high resolution imaging, etc.
In recent years, the ultrafast science has made great progress.In the extreme ultraviolet range, the pulse duration has been advanced to the order of tens of attoseconds [2], utilizing High-Harmonic Generation (HHG) technique [3,4].However, it is difficult to use HHG technique to produce attosecond X-ray pulses, because the conversion efficiency of HHG decreases dramatically as the laser wavelength decreases.At the same time, X-ray light sources are necessary to study the dynamics of electrons near the nucleus.
In order to study the spatial structure at atomic level, we need light sources with wavelengths up to X-rays, and hopefully isolated attosecond pulses.With this growing demand, the free electron laser (FEL) [5] provides an entirely new method for the generation of attosecond pulses.Various methods have been proposed according to FEL principle to shorten FEL pulses, such as low charge technique [6].One can compress the electron beam to a very short length by reducing the charge of electron beams, and then use such an electron beam to generate ultrafast FELs.Enhanced self-amplified spontaneous emission (ESASE) [7] is a common method to generate ultrashort FELs.It is based on the SASE mode [8,9] and uses a few-cycle laser to produce a large local current.Most of the current methods [10,11,12,13,14,15] are based on SASE.The pulse duration is directly related to the length of electron beams, so the consistent goal is to make the length of the electron beam radiated as short as possible.
In this paper, a theoretical simulation of the ESASE scheme was conducted based on the beam parameters from SXFEL.The results indicate that the ESASE scheme can generate an ultrafast FEL pulse with the peak power of ∼450 MW, and the pulse duration of ∼840 as.However, the radiation pulse produced by ESASE will have two distinct sub-pulses.In order to improve the signal-to-noise ratio of radiation pulses, we used the same parameters to simulate an improved scheme, i.e. chirped-enhanced SASE.This scheme can greatly increase the peak power, and can shorten the radiation pulse length at the same time.

Enhanced self-amplified spontaneous emission
The relativistic electron beam passes through a properly periodic magnetic field, and the kinetic energy of electrons can be converted into the coherent electromagnetic radiation.The radiation wavelength is related to the beam energy and the periodic magnetic field, and the specific relationship between them is given by the following formula: Here, λ s is the radiation wavelength, λ u is the undulator period, γ is the normalized beam energy, and K is the dimensionless undulator parameter.

Theoretical Model of ESASE
SASE mode means that the relativistic electron beam passes through a periodic magnetic field long enough to amplify the initial particle noise to produce coherent radiation.Due to its relatively simple structure, SASE mode is widely used in FEL facilities worldwide.Based on this mode, ESASE applied an optical shaping to the electron beam, namely, by performing an energy modulation with a few-cycle laser, the peak current was significantly enhanced after the subsequent density modulation.Such an electron beam can generate ultrafast FEL pulses after passing through a long undulator.[7], and Fig. 1 is a typical ESASE layout.The electron beam first interacts with the few-cycle lasers in the modulator, exchanging energy between the laser and electrons.Then the electron beam passes through a chicane.Due to the effect of dispersion, electrons with different energy take different paths when passing through the chicane.Finally, a large number of electron beams gather near a certain phase, and the current at this phase will be significantly enhanced.The enhanced current makes the gain length at this phase shorten obviously, so that the spontaneous radiation at this point increases and becomes saturated first in the radiator.In contrast, the radiation at other positions can be ignored, which is the basic principle of ESASE scheme.
In this paper, we will conduct the simulation of ESASE scheme based on the parameters from SXFEL.Fig. 2 shows the energy phase space and current distribution at the exit of linear accelerator in SXFEL.Table 1 shows the main parameters of SXFEL.Among them, the beam energy is 1.5 GeV, the slice energy spread is 0.39 MeV, the normalized emittance is 0.65 mm•mrad, the average current is 800 A, the period length of the planar undulator is 1.6 cm, and each undulator has 250 periods.

Simulation results
Using the above parameters, we carried out a three-dimensional simulation of the FEL gain process, and the main tool used was GENESIS [16].In our scheme, a far-infrared few-cycle laser with a wavelength of 5 µm was adopted as the seed laser.Fig. 3(a) shows the current distribution and the slice energy spread at the entrance of the radiator.The peak current is about 3.6 kA, and the current of the two sub-peaks on both sides of the main peak is about 1.6 kA.Such an electron beam would be sent into the undulator and tuned to be resonant at a wavelength of 2 nm.Fig. 3(b) shows the pulse profile of the radiation pulse at the exit of the undulator.There are three undulators in the radiation section with a total length of 12.64 m.It can be seen that the pulse duration of the main peak is about 840 as (FWHM), the peak power is about 450 MW, and there are two obvious sub-pulses, which leads to the low signal-to-noise ratio (about 70%) of ESASE scheme.

Chirped enhanced SASE
Normally, due to the few-cycle laser itself, the ultrafast pulses generated by the ESASE scheme will have two sub-pulses.If such a radiation pulse is used in the pump-probe experiment, the two sub-pulses will cause a large noise disturbance.In addition, the duration of the FEL pulse produced by ESASE scheme is limited by the slippage effect.The longer the wavelength of radiation, the greater the impact of the slippage effect, which also limits the peak power of the radiation pulse.
Various solutions have been proposed to overcome the defects of the ESASE scheme.In this paper, chirped enhanced SASE [17] scheme will be adopted to enable SXFEL to generate ultrafast X-ray pulses with shorter pulse duration and higher signal-to-noise ratio.Fig. 4 is the schematic diagram of the scheme layout.utilizes a frequency chirped laser to imprint a gradually varied spacing current enhancement on the electron beam.Combined with a suitable set of undulators, an electron beam with such a current distribution can produce a high-power attosecond X-ray pulse.The radiation section consists of an alternating array of undulator-chicane.The function of chicane is to apply a delay to the electron beam, so that the radiation pulse generated by the previous current spike can slip precisely to the next spike.The first undulator section in this scheme is relatively long, for generating a series of pulses with sufficient power, as shown in Fig. 4(b), which can suppress noise interference.Then, a suitable target pulse is selected from the series of pulses.After the electron beam is delayed by chicane, the target pulse is combined with the next current spike and the radiation amplification continues (see Fig. 4(c)).In the process of continuous delay and amplification, the target pulse will soon reach saturation, and then enter the superradiance stage [18].The pulse power will continue to increase, and at the same time, the pulse length will be further shortened under the action of superradiance.In contrast, radiation pulses other than the target pulse cannot interact with current spike due to the difference in the current peak interval, and their radiation will be inhibited due to the lack of accumulation.In this simulation, the beam parameters from SXFEL are still used.The average wavelength of the seed laser is 2500 nm.The energy phase space and current distribution of the electron beam after the dispersion section are shown in Fig. 5.The undulators in the first radiator section are composed of three planar undulators, and the following undulators are all one.The period length of the undulators is 2 cm, and the length of each undulator is 2 m.Fig. 6 shows the evolution process of the FEL radiation structure along the undulator beamline, where the red curve represents the target pulse, and the blue curve represents the noise pulses.The radiation wavelength is 2 nm.It can be seen that all the radiation pulses except the target pulse are suppressed, and the radiation power of the target pulse reaches more than 40 GW under the action of the superradiance.Fig. 7 corresponds to Fig. 6(f), which represents the radiation pulse at the exit of the undulator.It can be seen that the pulse duration is about 560 as, which is about 34% shorter than the pulse length of the ESASE scheme.

Conclusion
In this paper, utilizing the beam parameters of SXFEL, we performed numerical simulations of the ESASE scheme and the chirped-enhanced SASE scheme, respectively.The results show that the ESASE scheme can generate ultrafast pulses of about 450 MW, and the pulse duration is about 840 as.However, there are always two sub-pulses on both sides of the main peak of the radiation pulse generated by the scheme, and these sub-pulses limit the signal-to-noise ratio  of the radiation pulse generated by the scheme.At the same time, due to the corresponding influence of slippage, the power of the X-ray radiation pulses generated by this scheme is also limited.In contrast, chirped enhanced SASE scheme can enable SXFEL to generate ultrafast light source with better performance.The radiation power generated can reach more than 40 GW.Meanwhile, the duration of radiation pulse is shortened to 560 as, which is about 34% shorter than ESASE scheme.

Figure 2 .
Figure 2. Energy phase space of SXFEL electron beam (left) and current profile (right).

Figure 3 .
Figure 3. (a) Current profile (red solid line) and slice energy spread (blue dashed line) at the entrance of the undulator.(b) Radiation pulse at the exit of the undulator.

Figure 4 .
Figure 4. Layout of the chirped enhanced SASE scheme.

Figure 5 .
Figure 5. Energy phase space (top) and current distribution (bottom) of the electron beam.

Figure 6 .
Figure 6.FEL radiation structure evolutions along the undulator beam line at the end of (a) the 1st, (b) the 2nd, (c) the 3rd, (d) the 4th, (e) the 5th, and (f) the 6th undulator section.

Figure 7 .
Figure 7. Radiation pulse at the exit of undulator section.

Table 1 .
Main beam and undulator parameters.