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
[
High Power Laser Science and Engineering, Volume. 6, Issue 4, 04000e64(2018)
Dispersion effects on performance of free-electron laser based on laser wakefield accelerator
In this study, we investigate a new simple scheme using a planar undulator (PU) together with a properly dispersed electron beam ( beam) with a large energy spread ( ) to enhance the free-electron laser (FEL) gain. For a dispersed beam in a PU, the resonant condition is satisfied for the center electrons, while the frequency detuning increases for the off-center electrons, inhibiting the growth of the radiation. The PU can act 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 significantly owing to the high-peak current of the beam. Theoretical analysis and simulation results indicate that this method can be used for the improvement of the radiation performance, which has great significance for short-wavelength FEL applications.
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
[
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.
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
[
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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
[
We attempt to perform the EUV FEL operation by employing the attainable LWFA beam parameters from Shanghai Institute of Optics and Fine Mechanics (SIOM)
[
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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
[
We now consider an FEL operating at the ‘water window’ radiation wavelength. The parameters of the
beam and the undulator considered in Ref. [
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
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
[
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. [
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 :
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.
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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
Category: Research Articles
Received: Jun. 5, 2018
Accepted: Oct. 15, 2018
Posted: Oct. 16, 2018
Published Online: Dec. 27, 2018
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