Dispersion effects on performance of free-electron laser based on laser wakefield accelerator Download: 577次
1 Introduction
Free-electron lasers (FELs), which serve as tunable coherent sources of short-wavelength radiation, have attracted considerable attention owing to their widespread application in spectroscopy [ 1 ] , materials science [ 2 ] , biology [ 3 ] and other fields [ 4 , 5 ] . Several FEL facilities based on state-of-the-art linear accelerators have been operated successfully at X-ray wavelengths [ 6 – 9 ] but have hitherto been limited to these large facilities, which are costly and only accessible to limited users. It is highly desirable to develop a compact and affordable laboratory-scale electron accelerator. In recent years, remarkable progress has been made in generating high-energy ( GeV), high-peak current ( kA), and low-emittance ( ) electron beams ( beams) using laser wakefield accelerators (LWFAs) [ 10 – 18 ] . Such accelerators can be used for driving next-generation advanced light sources. However, these beams usually have a large energy spread of a few percent [ 19 , 20 ] , which degrades the FEL gain [ 21 ] . Various efforts have been directed toward energy-spread compression in LWFAs via energy chirp control [ 17 , 22 ] . Researchers have also focused on compensating the large energy-spread effects in high-gain FELs by using a transverse gradient undulator (TGU) together with a properly dispersed beam [ 23 – 25 ] . The dispersion of the beam must be matched with the transverse gradient field of the TGU to satisfy the resonant condition [ 24 ] . However, the transversely tapered TGUs require a special design and manufacturing process, and the transverse gradient cannot be tuned arbitrarily. A similar scheme using the natural transverse gradient of a normal planar undulator (PU) doubling as a TGU was recently proposed [ 26 ] , where the vertical dispersion of the beam is introduced.
In this study, we investigate a simple scheme to improve the performance of the radiation using a PU together with a properly dispersed beam from the LWFA. Our scheme has no need of extra field for correcting the orbit deflection induced by the field gradient and is easy to implement. In the proposed scheme, the energy of the beam is dispersed with its horizontal position so that only the center electrons satisfy the resonant condition, but the frequency detuning increases when the electrons deviate from the beam center, which inhibits the radiation growth. This mechanism can be regarded as a selection process, in which the PU acts as a filter for selecting the electrons near the beam center to achieve the radiation. Although only the center electrons contribute, the radiation can be enhanced owing to the high-peak current of the beam. Theoretical analysis and numerical simulations demonstrate the feasibility of a self-amplified spontaneous emission (SASE) FEL with sub-gigawatt power, a narrow bandwidth ( ) and good transverse coherence in the proposed scheme with typical parameters of the beam from the LWFA.
Fig. 1. SASE FEL scheme using the PU with the beam from the LWFA. The transverse distribution of the beam (a) without and (c) with the transverse dispersion. (b), (d) Corresponding angular profiles of the radiation power.
2 Dispersion effects on FEL radiation
Assuming a highly relativistic beam with normalized energy propagating through an undulator with the period and strength parameter , the on-axis radiation wavelength is . To obtain a high-gain FEL, the beam energy spread should satisfy [ 21 ]
Considering an
beam with horizontal dispersion
, the horizontal position of the electrons depends on the energy:
, as shown in Figure
Once the horizontal dispersion is introduced, the horizontal size of the beam increases to , and the density of the beam decreases. Using the method of perturbation analysis and integration along the unperturbed trajectories [ 25 ] , the effective energy spread can be reduced as follows:
Fig. 2. (a) Radiation power along the PU around 30 nm; (b) single-shot spectra of an SASE FEL; (c), (d) corresponding transverse angular profiles of the radiation power obtained by beam without and with the horizontal dispersion.
We attempt to perform the EUV FEL operation by employing the attainable LWFA beam parameters from Shanghai Institute of Optics and Fine Mechanics (SIOM)
[
17
,
28
,
29
]
and the compact beam transport system considered in Ref. [
30
]. The parameters for the
beam at the entrance of the undulator are shown in Table
Table 1. beam and undulator parameters used in our study for EUV and soft X-ray FELs.
|
The FEL radiation was simulated in the time-dependent mode of GENESIS, which includes three-dimensional (3D) effects, such as the diffraction and transverse modes
[
31
]
. Figure
We now consider an FEL operating at the ‘water window’ radiation wavelength. The parameters of the
beam and the undulator considered in Ref. [
24
] are used. The transverse dispersion is
cm. Reasonably assuming a beta function of
m, we obtain an initial beam size of
. After dispersion, the horizontal beam size increases to
. The radiation power is improved by two orders of magnitude and reaches saturation with a properly dispersed
beam, as shown in Figure
Fig. 3. (a) Radiation power along the PU around 3.9 nm; (b) single-shot spectra of the SASE FEL; (c), (d) corresponding transverse angular profiles of the radiation power obtained by beam without and with the horizontal dispersion.
3 Analysis of radiation properties
According to the aforementioned discussion, the radiation properties can be significantly improved by utilizing a properly dispersed
beam in the PU scheme. Taking the 30 nm radiation as an example, we now study the properties of the radiation with different dispersions of the
beam. Figure
Fig. 4. SASE FEL (a) radiation power, (b) bandwidth and (c) transverse mode parameter at 30 nm at the exit of the undulator with different dispersions of the beam in the PU (blue) and TGU (red) schemes.
Figure
Because of the stronger diffraction and smaller spatial overlap with the beam, the higher-order modes can be suppressed. Thus, the SASE FEL can reach almost full transverse coherence before saturation, and the radiation emittance is almost given by the diffraction-limited radiation emittance , where is the resonant wavelength of the radiation. However, the large transverse beam size due to the dispersion provides enough transverse space for the high-order modes to couple with the beam, reducing the transverse coherence. The transverse mode parameter can be defined as [ 21 ]
4 Physical mechanism of proposed scheme
Consider an
beam having a horizontal dispersion, whose phase-space distribution is schematically illustrated in Figure
We now give a theoretical description of the radiation with a dispersed beam and compare between the PU and TGU schemes. A 3D theoretical model based on the analysis of the eigenmode was established in Ref. [ 33 ] to explain the properties of the FEL radiation. Each growth mode of the radiation, characterized by the transverse profile and the complex growth rate , has a solution of the form . The growth rate with a negative imaginary part represents the growth mode. An analytical solution is obtained for the case where the transverse emittance and focusing are negligible (which is suitable for beams from an LWFA owing to the small emittance), and the scaled growth rate of a growing mode is obtained using the relation [ 33 ]
Fig. 5. Negative imaginary part of the FEL growth rate (in units of ) as a function of the horizontal position (in units of ) for both the PU and TGU schemes in the fundamental mode ( cm).
The above theoretical analysis is based on the TGU scheme and cannot be directly applied to the PU scheme. From a local viewpoint, the wavelength of a photon emitted by an electron is determined by the energy of the electron, which follows the relation . We make the simple assumption that , which means that all the electrons satisfy the resonant condition under the large-dispersion approximation in both the PU and TGU schemes. However, the radiation wavelength shifts in the PU scheme when the energy of the electron deviates from , which can be described by the frequency-detuning parameter . The difference between the TGU and PU schemes is that the frequency detuning is independent upon the transverse position in the TGU when the matching condition is fulfilled (here, we set under the large-dispersion approximation). In the PU scheme, the detuning increases when the electron deviates from the horizontal beam center. We define a detuning parameter in the PU scheme that depends on the horizontal position :
Fig. 6. (a) SASE FEL power with different halfwidths of the slit at the entrance of the undulator in the PU scheme. (b)–(e) Horizontal distribution of the radiation with different halfwidths of the slit in the PU scheme. The halfwidths of the slit are , , and , respectively. The horizontal dispersion is 2.5 cm.
The simulation results and theoretical analysis demonstrate that the significant fraction of the off-center electrons makes no contribution to the lasing in our proposed scheme. This mechanism is similar to the collimation of the energy tail. Next, we conduct simulations by adding a horizontal collimator with different widths of the slit at the entrance of the undulator to perform a comparison. The horizontal dispersion of the
beam is
cm. Figure
5 Conclusions
Simulations demonstrate that the FEL performance can be significantly improved with a PU by introducing the horizontal dispersion of the beam from the LWFA. Although only part of the electrons near the beam center contribute to the radiation, intense FEL radiation can be obtained owing to the high-peak current of the beam. The radiation pulses can be sub-gigawatt level in power with a narrow bandwidth below 1% and good transverse coherence without seeding. The proposed scheme is easy to implement, which is significant for the experimental realization of the LWFA-based FEL. Further investigations on driving short-wavelength LWFA-based FELs are ongoing.
[5] 5.K.Tono ,High Power Laser Sci. Eng.5 , e7 ( 2017 ). 10.1017/hpl.2017.6
[10] 10.T.Tajima and J. M.Dawson ,Phys. Rev. Lett.43 , 267 ( 1979 ). 10.1103/PhysRevLett.43.267
[14] 14.J. S.Liu ,C. Q.Xia ,W. T.Wang ,H. Y.Lu ,C.Wang ,A. H.Deng ,W. T.Li ,H.Zhang ,X. Y.Liang ,Y. X.Leng ,X. M.Lu ,C.Wang ,J. Z.Wang ,K.Nakajima ,R. X.Li , and Z. Z.Xu ,Phys. Rev. Lett.107 , 035001 ( 2011 ).
[17] 17.W. T.Wang ,W. T.Li ,J. S.Liu ,Z. J.Zhang ,R.Qi ,C. H.Yu ,J. Q.Liu ,M.Fang ,Z. Y.Qin ,C.Wang ,Y.Xu ,F. X.Wu ,Y. X.Leng ,R. X.Li , and Z. Z.Xu ,Phys. Rev. Lett.117 , 124801 ( 2016 ).
[21] 21.Z.Huang and K.- J.Kim ,Phys. Rev. Accel. Beams10 , 034801 ( 2007 ).
[22] 22.Z. J.Zhang ,J. S.Liu ,W. T.Wang ,W. T.Li ,C. H.Yu ,Y.Tian ,R.Qi ,C.Wang ,Z. Y.Qin ,M.Fang ,J. Q.Liu ,K.Nakajima ,R. X.Li , and Z. Z.Xu ,New J. Phys.17 , 103011 ( 2015 ).
[24] 24.Z.Huang ,Y.Ding , and C. B.Schroeder ,Phys. Rev. Lett.109 , 204801 ( 2012 ).
[25] 25.P.Baxevanis ,Y.Ding ,Z.Huang , and R.Ruth ,Phys. Rev. Accel. Beams17 , 020701 ( 2014 ).
[26] 26.Q.Jia and H.Li ,Phys. Rev. Accel. Beams20 , 020707 ( 2017 ).
[28] 28.Z.Qin ,C.Yu ,W.Wang ,J.Liu ,W.Li ,R.Qi ,Z.Zhang ,J.Liu ,M.Fang ,K.Feng ,Y.Wu ,L.Ke ,Y.Chen ,Y.Xu ,Y.Leng ,C.Wang ,R.Li , and Z.Xu ,Phys. Plasmas25 , 023106 ( 2018 ).
[29] 29.M.Fang ,W.Wang ,Z.Zhang ,J.Liu ,C.Yu ,R.Qi ,Z.Qin ,J.Liu ,K.Feng ,Y.Wu ,C.Wang ,T.Liu ,D.Wang ,Y.Xu ,F.Wu ,Y.Leng ,R.Li , and Z.Xu ,Chin. Opt. Lett.16 , 040201 ( 2018 ).
[30] 30.T.Liu ,T.Zhang ,D.Wang , and Z.Huang ,Phys. Rev. Accel. Beams20 , 020701 ( 2017 ).
[33] 33.P.Baxevanis ,Z.Huang ,R.Ruth , and C. B.Schroeder ,Phys. Rev. Accel. Beams18 , 010701 ( 2015 ).
Article Outline
Ke Feng, Changhai Yu, Jiansheng Liu, Wentao Wang, Zhijun Zhang, Rong Qi, Ming Fang, Jiaqi Liu, Zhiyong Qin, Ying Wu, Yu Chen, Lintong Ke, Cheng Wang, Ruxin Li. Dispersion effects on performance of free-electron laser based on laser wakefield accelerator[J]. High Power Laser Science and Engineering, 2018, 6(4): 04000e64.