Enhanced betatron radiation by steering a low-energy-spread electron beam in a deflected laser-driven plasma wiggler

Laser wakefield accelerators (LWFA) hold great potential to produce high-quality high-energy electron beams (e beams) and simultaneously bright x-ray sources via betatron radiation, which are very promising for pump-probe study in ultrafast science. However, in order to obtain a high-quality e beam, electron injection and acceleration should be carefully manipulated, where a large oscillation amplitude has to be avoided and thus the emitted x-ray yield is limited. Here, we report a new scheme to experimentally enhance betatron radiation significantly both in photon yield and photon energy by separating electron injection and acceleration from manipulation of the e-beam transverse oscillation in the wake via introducing a slanted thin plasma refraction slab. Particle-in-cell simulations indicate that the e-beam transverse oscillation amplitude can be increased by more than 10 folds, after being steered into the deflected laser-driven wakefield due to refraction at the slab's boundaries. Spectral broadening of the x-rays can be suppressed owing to the small variation in the peak energy of the low-energy-spread e beam in a plasma wiggler regime. We demonstrate that the high-quality e-beam generation, refracting and wiggling can act as a whole to realize the concurrence of monoenergetic e beam and bright x-rays in a compact LWFA.


LWFA.
X-ray synchrotron radiation sources have become immensely useful tools for basic science and broad applications in biology, and material science 1 . State-of-the-art synchrotrons and free-electron lasers 2, 3 based on a radiofrequency accelerator can now produce x-ray sources with unprecedented photon flux and brilliance, but have hitherto been limited to huge facilities which are costly and only accessible to limited users. Over the past decade, a more compact accelerator based on the concept of laser-driven wakefield acceleration 4 has achieved significant progress in generating GeV-class electron beams (e beams) [5][6][7][8][9][10][11] , which holds great potential of becoming a better candidate to produce compact femtosecond x-and γ-ray sources 12 . In such a laser wakefield accelerator (LWFA), electrons in the wakefield would witness an ultrahigh longitudinal acceleration field above 100 GV/m, simultaneously undergo a betatron oscillation as a result of the transverse focusing field of the wake and emit bright high-energy x-rays over a few millimeters through the betatron radiation mechanism [13][14][15] . Attributed to the intrinsic synchronization to the driving laser pulse, both the generated e beam and the x-ray pulse from the same wakefield have an ultrashort duration of several femtoseconds, which are very promising for pump-probe study in ultrafast science.
The properties of betatron radiation are normally characterized by the strength parameter [14][15][16] [ ]  17 . Therefore, an effective way to increase the photon energy and yield of betatron radiation is to increase the oscillation amplitude rβ in additional to increasing the e-beam charge and energy. However, in order to obtain a high-quality high-energy e beam, electron injection and acceleration should be carefully manipulated via a well-performed LWFA, where a large oscillation amplitude rβ has to be avoided. Some ideas of manipulating rβ to enhance betatron radiation have been demonstrated, e.g. by enhancing betatron oscillations resonantly in a plasma wake 18 , applying the driving pulse-front-tilt to induce off-axis electron injection 19 , appropriately tailoring the plasma profile 20 , using a clustering gas jet 21 or via an evolving laser-plasma bubble 22 .
However, the produced x-rays had continuum spectra because the controllability was limited in the e-beam quality. Recently, an idea of a helical plasma undulator has been proposed to produce controllable synchrotron-like radiation by inducing centroid oscillations of the laser pulse 23, 24 in a plasma channel.
In this article, we have experimentally realized a new scheme to enhance the betatron radiation via separating electron injection and acceleration from manipulation of the e-beam transverse oscillation in the wakefield. By producing a 30-μm-thick slanted plasma slab (SPS) with a higher density somewhere in the acceleration stage, the driving laser pulse can be deflected owing to the refraction, but the accelerated monoenergetic e beam can almost keep its initial propagation axis and obtain an increased transverse momentum instantly due to the axes misalignment. By this way, the high-quality e beam can be steered into the deflected laser-driven wakefield with a controllable 3 operation both in the transverse oscillation amplitude and energy of the e beam. Furthermore, by restraining the fluctuation of the e-beam energy in the wakefield, spectral broadening of betatron can be suppressed in a plasma wiggler regime. Brilliant betatron x-rays (~10 23 photons s -1 mm -2 mrad -2 0.1% BW) in tens of keV have been produced with significant enhancement both in photon yield and peak energy.

Results
Electron-beam generation and manipulation. Figure 1 shows the experimental setup. The experiments were carried out at the femtosecond 200TW laser system 25 . The laser pulses with an on-target power of 100 TW were focused to reach a peak intensity of 3.6×10 18 W/cm 2 (see Methods). The laser beam distribution at the focus was also optimized to have a smooth profile to avoid laser filamentation 26,27 . A LWFA consisting of two-segment pure helium gas jets was designed to generate high-quality e beams with low energy spread, sufficient charge, and low divergence 9, 28, 29 . An optical interferometer and a shadowgraphy were set up to measure the plasma density distribution as shown in Fig. 1b   μm. However, while introducing the SPS at z=1.5 mm as shown in Fig. 4a and keeping other parameters the same, the deflection of the laser-driven wakefield in the vertical direction was observed in Fig. 4b. Due to the refraction, the propagation direction of the wakefield is deflected from its initial direction in addition to an absolute offset in the vertical direction. After being steered into the deflected wakfield, the accelerated e-beam transverse radius R b increases rapidly from 0.18 to 1.9 μm, as shown in Fig. 4b and 4d. The e beam is also deflected from the original laser propagation direction with a deviation angle of 0.7 mrad, in good agreement with the aforementioned measurement and analysis.
Besides, the e-beam length remains the same without loss of beam charge and the relative energy spread can even be reduced a little, which might be attributed to energy chirp compensation due to the phase space rotation 37,38 . Some electrons might be injected into the wakefield behind the slab owing to the shock-front injection at the transient downward density ramp 29 , but they can't be efficiently accelerated due to the quick dephasing, because there is a 6 great density difference at the downward density ramp. However, the steered e beam slips forward quickly with respect to the wakefield to the zero-phase region and thus the e-beam energy varies little in the following acceleration stage, which is meant to be operated as a plasma wiggler.
Furthermore, the FWHM energy spread of the e beams in the peak produced in our case is as small as 2.5%. These two effects and periodical oscillation in the wiggler stage are expected to reduce the bandwidth of the betatron radiation spectrum near the peak, which is supported by the simulated radiation distribution from the Lienard-Wiechert potentials according to electrons trajectories. In this scheme, the high-quality e-beam generation, refracting and wiggling can act as a whole to realize the concurrence of monoenergetic e beam and bright x-rays in a compact LWFA by manipulating the transverse oscillation of the e beam .
Enhanced betatron x-ray radiation. Two techniques were employed to measure the betatron radiation spectra in a single-shot (see Methods). Firstly, in the case of no SPS when the yield of betatron radiation was low, an x-ray CCD camera operated in a single-photon-counting (SPC) mode was used to measure the spectra of the betatron radiation, which could also be used to measure the e-beam transverse size and emittance as well [39][40][41] . Secondly, since the x-ray emission would be enhanced both in photon yield and photon energy after introducing the SPS, the SPC technique was not suitable any more for a much higher photon flux and higher photon energies.
Then an x-ray detection system (XRDS) based on the x-ray transmission through an array of filters 28,42,43 was designed to measure the radiation spectra (see Methods). In order to avoid the influence of the driving laser on the detector, a 8-μm-thick Al film or 300-μm-thick Be window was placed in front of the CCD camera or the LSO-crystal scintillator to block the laser.
In the case of no SPS corresponding to the e-beam generation at 465 MeV in Fig. 3a, the 7 recorded betatron radiation pattern via the XRDS, the recorded radiation signal on the x-ray CCD chip, and retrieved radiation spectrum via the SPC were shown respectively in Fig. 5a-c.
According to the retrieved spectral profile (Fig. 5c), the critical photon energy was estimated to be 5.8±0.4 keV, indicating that the betatron oscillation amplitude r β was less than 0.2 μm. This was slightly larger than a matched e-beam size of ~0.1 μm given by the theoretical prediction While introducing a SPS in the acceleration stage to manipulate the e-beam transverse oscillation and betatron radiation, the x-ray spectra were measured via the XRDS. Shown in Fig.   5d and 5e were the recorded radiation patterns without and with inserting filters respectively, when the SPS was introduced at z=1.5 mm. As shown in Fig. 3b, the generated e beam in this case had the peak energy of 259 MeV with a FWHM energy spread of 1.8%. The retrieved radiation spectrum was shown in Fig. 5f. It was found the FWHM bandwidth of betatron radiation spectra in the peak was about 55%, although the higher harmonics could have broadened the spectrum due to the strength parameter (K≈18). In spite of a much lower e-beam energy in this case, the critical energy of the radiated x-ray was increased from 5.5 keV to 26 keV, and the photon number which was estimated to be (2.1±0.8)×10 8 was also enhanced by more than 12 folds, as compared with the radiation spectrum (Fig. 5c) for the case of no SPS. Assuming that the size and duration were around 4 μm and 6 fs, the x-ray source could have a peak brilliance of ~10 23 photons s -1 mm -2 mrad -2 0.1% BW. By varying the SPS position (with z increasing), the e-beam energy was increased from 259 to 351 MeV (Fig. 3b-d) and the corresponding critical photon energy of betatron radiation shifted from 22 to 34 keV (Fig. 5f). For each of the aforementioned cases, both the statistical average x-ray photon energy and yield were increased greatly (Fig. 5g). Besides, the enhanced betatron radiation had a larger divergence angle if compared with the case of no SPS (see Fig. 5a,d) and the central position of the radiation was also shifted upward with a deviation angle of ~ 0.8 mrad, roughly corresponding to the deflection of the generated e beam. These results verified that the high-quality e beam could be steered into the deflected laser-driven wakefield with a controllable operation both in the e-beam energy and transverse oscillation amplitude via introducing a SPS, as demonstrated in the previous section of numerical modeling.

Discussion
We have experimentally realized a new scheme of separating electron injection and acceleration from manipulation of the e-beam transverse oscillation. By introducing a thin SPS with a higher density somewhere in the acceleration stage, both the transverse oscillation amplitude and the e-beam energy could be manipulated successfully in the wakefield, which was supported by the PIC simulations as well. Previous methods reported to enhance betatron radiation by enhancing betatron oscillations resonantly in a plasma wake 18 or applying the driving pulse-front-tilt to induce off-axis electron injection 19 can not maintain a low-energy-spread e beam. However in this 9 scheme, the produced e beam with a low energy spread in a well performed LWFA was steered into the zero-phase region of a deflected wakefield, which was operated as a plasma wiggler. By this way, the e beam acquired a large transverse oscillation amplitude but at the same time the e-beam energy varies little. Therefore the periodical oscillation and radiation in the plasma wiggler with a relatively stable e-beam energy would significantly reduce the bandwidth of the betatron spectrum in the peak. The high-quality e-beam generation, refracting and wiggling can act as a whole to realize the concurrence of monoenergetic e beam and bright x-rays in a compact LWFA by manipulating the transverse oscillation of the e beam. It is anticipated that this compact monoenergetic e beam and brilliant x-ray source will provide practical applications in ultrafast pump-probe study. focused by an f/30 off-axis parabola mirror into the gas jet and the vacuum beam radius w 0 was measured to be 32 um at 1/e 2 , the peak intensity was estimated to be 3.6×10 18 W/cm 2 , corresponding to a normalized amplitude of a 0 = 1.3. The fractional laser energy contained within the laser spot was measured to be ~ 59%.

Methods
Gas jet and density measurement. The gas target consisted of two-segment pure (0.8mm+3mm) helium gas jets, which were used to produce a structured gas flow for realizing cascaded acceleration 28,29 . A probe beam split from the main laser beam was sent perpendicularly across the gas jet, then entered a 4f Michelson-type interferometer and shawdowgraphy using a 4f optical imaging system for measuring the plasma density. The first-segment gas jet was filled with pure He atoms at a pressure of 5bar, once ionized, this pressure corresponded to an electron background density of (1±0.1)×10 19 cm -3 and the second-segment gas flow was operated with an average plasma density of (6±0.5)×10 18 cm -3 as measured. A wedge-shaped face was then fabricated at the top edge of the right wall of the first-segment gas cell, which was placed at the left edge of the second gas jet, to produce an inclined shock front 36, 44 by stopping the supersonic gas flow, and thus a slanted thin gas layer was formed with a higher density than the ambient one. X-ray beam detection and analysis. Firstly, a back-illuminated x-ray charge-coupled device (CCD) camera with 1340×400 pixels of size 20×20 μm 2 operated in a single-photon-counting (SPC) mode [39][40][41] was used to measure the spectra below 20 keV, which was set at 4.7m from the gas jet and protected from the residual laser-light by an 8-μm-thick Al foil in front of the x-ray CCD. The piling events 45 could then be avoided by satisfying the low photon flux requirement.
Secondly, an x-ray detection system (XRDS) based on the x-ray transmission through an array of filters 28,42,43 was also designed to measure the spectrum. The driving laser beam was blocked by a 300-μm-thick Be window. The fluorescence signal of x-ray beams from the   onto the two-segment (0.8+ 3 mm) pure helium gas jets onto the supersonic nozzles. About 5% of the pump laser was split off as a probe pulse, which crossed the interaction region perpendicularly into two CCD cameras to measure the plasma density profile and overview the laser evolution.
The produced e-beams are deflected by a 90-cm-long dipole electromagnet with a maximum magnetic field of 1.1 Tesla, and measured by a Lanex phosphor screen (PS) imaged onto an intensified charge-couple device 16-bit (ICCD) in a single shot. The betatron radiation x-rays was detected by an x-ray CCD or an x-ray spectra analyzer using a transmission filter and a   ) and the measurement uncertainties, respectively. (g) Measured average x-ray peak energy and total photon number from a series shots for each case, plotted versus with the e-beam peak energy.