6.3 DEEX based LPS manipulation for multi-color X-ray
6.3.2 Experimental demonstration in AWA
After the target bunch passes through the structure, it achieved a sinusoidal energy modulation as shown in the panel (b). This modulation is successfully converted to spectral and density bunchings as shown in panels (c) and (d). The macro-chirp was zero, and the micro-chirp from the modulation was -10.98 m−1. Quadrupole magnets were optimized to generate bunchings, and the DEEX beamline providedR-terms as given in Table 4. Because the macro-chirp is zero, the bunching condition was 11.08 m−1for both cases, which shows good agreement with the micro-chirp calculated from the distribution in Fig. 36(b). Also, we expect that the density and the energy separations would be 2 mm and 100 keV, respectively. These also show good agreements with Figs. 36(c) and (d).
R55 R56 R65 R66 1.33 0.12 1.33 0.12
Table 4: Matrix element used for numerical tracking.R55andR56are matrix elements for density bunch- ing, and the other two elements for the density bunching case are not listed in this table. Similarly,R65 andR66in this table are matrix elements the spectral bunching, and the other two elements are not listed.
at the second beam splitter. The following alpha-BBO crystals also split the laser pulse with time delay of 3.0 ps and 6.2 ps, respectively. So, the multi-splitter generated two pulses and the two alpha-BBO crystals generated four pulses per each incoming pulse.
Because of space charge forces, the micro-bunches in the train was positive chirps (h > 0). The positive chirps were enough to bunching the beam using the DEEX beamline. Figure 38 is measured LPS by the LPS diagnostic section. The bunch train charge is 150 pC, average bunch-to-bunch temporal separation (λ) is 0.39 mm, and micro-bunch’s chirp (micro-chirp,h) is 10.74 m−1. Bunch train’s chirp (macro-chirp,H) is 1.94 m−1.
Figure 38: Longitudinal phase space of bunch train before the DEEX beamline.
The bunch-to-bunch separation and energy deviation depend on the DEEX beamline elementsR55, R56,R65, andR66. These are controllable elements using quadrupoles in the middle of the DEEX beam- line. Density and spectral bunchings occur when RR55
56 =−hand RR65
66 =−h, respectively. In addition the DEEX beamline is able to control both the separation and deviation with density/spectral bunching.
However, completely independent control of the separation and deviation is not feasible due to the con- strain ofR55R66−R56R65=1 .
Figure 39 is comparison between quadrupole grid scan and experimental results. The quadrupole grid scan calculated the final LPS based on Eqs. (6.4) and (6.5). Initial parameters were achieved from LPS measurement before the DEEX beamline. The five quadrupoles in the middle of DEEX beamline were scanned from -4.8 T/m to 4.8 T/m with step size of 0.4 T/m, and used DEEX beamline is identical
(a)
(b)
Figure 39: Comparison between quadrupole grid scan and experiment data of bunch-to-bunch separa- tion and energy deviation. (a) and (b) are density and spectral bunching, respectively. Blue dots are quadrupole grid scan results and red dots are measured data.
with AWA’s DEEX beamline. The grid scan results in Fig. 39 (blue dots) are possible the separation (∆z) and the deviation (∆δ) during the scan. Some combinations might be not feasible in the experiment due to nonlinear effects (e.g., higher order and CSR effect).
In the experiment, we controlled the quadrupoles to generate the different combinations of the sepa- ration and deviation with bunching. Figure 40 shows selected four spectral bunching cases. The energy deviations of Fig. 40(a)-(d) were linearly changed depending on the separations [also see Fig. 39(a)]. As shown in Fig. 39(b), the density bunching also has linearity (see Fig. 41). However, the density bunching could have the diverse the energy deviations at the same separation as shown in Fig. 42. The separations
are fixed at 0.4 mm while the energy deviations are changed from 0.21% to 0.46%. This is an application of chirp control introduced in Sec. 3.2.2.
All measured bunch trains after the DEEX beamline were under-compressed or critical compressed.
Based on the original LPS (positive chirp before the DEEX beamline), the positive macro-chirp is under-compression, and zero macro-chirp is critical compression. Accordingly, both(R55+R56H)and (R65+R66H)should be positive values for under-compression conditions.(R55+R56H) =0 or(R65+ R66H) =0 is critical compression condition. Therefore, measured bunch-to-bunch separations and en- ergy deviations have positive values.
(a) (b)
(c) (d)
Figure 40: Spectral bunching with different bunch-to-bunch separation and spectral deviation. (a) Av- erage bunch-to-bunch separation is 0 mm and spectral deviation is 0.16%. (b) Average bunch-to-bunch separation is 0.21 mm and spectral deviation is 0.35%. (c) Average bunch-to-bunch separation is 0.42 mm and spectral deviation is 0.41%. (d) Average bunch-to-bunch separation is 0.54 mm and spectral deviation is 0.53%.
(a) (b)
(c) (d)
Figure 41: Density bunching with different bunch-to-bunch separation and spectral deviation. (a) Aver- age bunch-to-bunch separation is 0.26 mm and spectral deviation is 0.28%. (b) Average bunch-to-bunch separation is 0.37 mm and spectral deviation is 0.35%. (c) Average bunch-to-bunch separation is 0.42 mm and spectral deviation is 0.41%. (d) Average bunch-to-bunch separation is 0.53 mm and spectral deviation is 0.53%.
(a) (b)
(c) (d)
Figure 42: Density bunching with same bunch-to-bunch separation and different spectral deviation. (a) Average bunch-to-bunch separation is 0.40 mm and spectral deviation is 0.21%. (b) Average bunch-to- bunch separation is 0.40 mm and spectral deviation is 0.30%. (c) Average bunch-to-bunch separation is 0.39 mm and spectral deviation is 0.37%. (d) Average bunch-to-bunch separation is 0.40 mm and spectral deviation is 0.46%.
Chapter 7
Conclusion
In this thesis, we presented theory, preparations and experiment results of multi-functional LPS manip- ulation based on DEEX. In addition, feasible applications were shown via simulations and experiment.
The linear transfer matrix and preliminary simulations show the principle and feasibility of the DEEX beamline’s three functions. These functions might seem like obvious in the experiment. However, there was no dedicated facilities for the DEEX beamline, and the experiment required lots of preparations.
To achieve linear transverse phase space in the middle section, the laser was changed to 300 fs-long Gaussian. Furthermore, we had to design the octupole for the nonlinear LPS manipulation and decided the location in the middle section. In addition, the experiment had to consider the beam diagnostics to provide the exact matching condition to the first and the second EEX beamline, and achieve the final LPS after the DEEX beamline.
The experiment demonstrated tunable chirpless bunch compression via a single quadrupole adjust- ment. Due to the underlying principle (i.e., EEX), the DEEX bunch compressor provided bunch com- pression regardless of the incoming longitudinal chirp. Both full compression and the lengthening of the bunch were achieved by a single quadrupole magnet. This result shows the feasibility of improving power-efficiency by implementing a DEEX bunch compressor. The use of a DEEX bunch compressor ensures that the linear accelerator (linac) does not need to operate at an off-crest phase, thereby intro- ducing a significant energy gain or efficiency improvement. For example, if the linac is operated at -30◦ to generate the chirp, it loses 14% of its energy compared with the on-crest operation. The DEEX bunch compressor can compensate this lost energy or reduce the required RF power to achieve the same beam energy, which can result in significant installation or operation cost saving. Furthermore, the present demonstration only exhibited a maximum compression factor of four; however, this was due to high emittance. The agreement between our estimation and measurement results guarantee that the result is scalable with emittance. If a low-emittance beam is utilized, a DEEX beamline can even generate
atto-second bunches like results in Sec. 6.1, which may open new opportunities [88–90].
Similarly, longitudinal chirp control was demonstrated using two quadrupole magnets. As shown by Eq. (5.9) and the experiment, the DEEX bunch compressor provides a wide range of chirp control while it compresses the bunch. This can also provide a considerable advantage in terms of power effi- ciency because the downstream linac’s off-crest operation is unnecessary. Additionally, the installation of dedicated de-chirpers (e.g., corrugated structure [7, 91]) is not required. The chirp control here can be directly used to compensate for the wakefield effect in the downstream linac [92]. It can intention- ally impart a large longitudinal chirp for broadband radiation generation [93–95] or be used for other radiation schemes, such as fresh-slice injection [73, 96] and two-color radiation [67, 72].
The experiment also demonstrated the correction of the third-order nonlinearity and double-horn feature using a single octupole magnet. This result supports the feasibility of nonlinearity correction by multipole magnets. The nonlinearity correction by a magnet can be a cheap alternative to the expensive harmonic cavity. The result of this study supports the feasibility of a scheme introduced in Sec. 6.2, which implemented a DEEX bunch compressor for the LCLS-II lattice [97] and demonstrated a ∼ 1×10−5energy spread for XFEL oscillator [57,58]. Moreover, the nonlinearity that the harmonic cavity can compensate is limited; however, a series of multipole magnets in the DEEX bunch compressor can impart or eliminate any nonlinear correlation that can be approximated by a polynomial series. Such nonlinearity control is the key to realizing ultrashort bunch generation for suppressed beam-beam effects in future TeV colliders and high-intensity atto-second X-ray pulses.
Application for multi-color X-ray was experimentally demonstrated. The experiment controlled both bunch-to-bunch separations and energy deviation with density or spectral bunching of the micro- bunches. Laser pulse train generated the bunch train with the eight micro-bunches, and the DEEX beam- line manipulated the bunch train. The DEEX beamline compressed the micro-bunches in either density or energy. Their bunch-to-bunch separation and energy deviation were tunable with the compression.
Compressed micro-bunches are feasible to generate each X-ray pulse. If the micro-bunches are com- pressed in energy, the X-ray pulse will have small energy bandwidth. The density bunching enables to provide short pulse duration. Because each micro-bunch radiates the X-ray pulses, the bunch-to-bunch separation and energy deviation determines the X-ray pulses arriving time and photon energy deviation, respectively.
The DEEX beamline has been considered as a candidate longitudinal manipulation method that al- lows for any type of longitudinal manipulation. Such manipulation enables the optimization of all of the beam’s longitudinal properties for specific applications. Several previous studies have demonstrated lon- gitudinal profile shaping capabilities [30, 98]. Now this study demonstrated the control of the remaining longitudinal properties. The results presented in this study indeed serve as evidence of the feasibility of
the DEEX beamline. Owing to its large footprint (∼10 m), the DEEX bunch compressor may not be an attractive option for compact accelerators, such as those used for ultrafast electron diffraction. How- ever, it can provide various interesting new opportunities and performance improvements for current and future large-scale electron accelerator facilities.
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