research papers
Electronbunch lengthening on higherharmonic oscillations in storagering freeelectron lasers
^{a}Research Institute for Measurement and Analytical Instrumentation, National Institute of Advanced Industrial Science and Technology, 111 Umezono, Tsukuba, Ibaraki 3058568, Japan, and ^{b}Quantum and Radiation Engineering, Osaka Prefecture University, 11 Gakuencho, Sakai, Osaka 5998531, Japan
^{*}Correspondence email: sei.n@aist.go.jp
The influence of higherharmonic freeelectron laser (FEL) oscillations on an electron beam have been studied by measuring its bunch length at the NIJIIV storage ring. The bunch length and the lifetime of the electron beam were measured, and were observed to have become longer owing to harmonic lasing, which is in accord with the increase of the FEL gain. It was demonstrated that the saturated FEL power could be described by the theory of bunch heating, even for the harmonic lasing. Cavitylength detuning curves were measured for the harmonic lasing, and it was found that the width of the detuning curve was proportional to a parameter that depended on the bunch length. These experimental results will be useful for developing compact resonatortype FELs by using higher harmonics in the extremeultraviolet and the Xray regions.
1. Introduction
The generation of higherharmonic oscillation is an effective technique for shortening the wavelength of a freeelectron laser (FEL) oscillation. Because this technique requires an optical cavity, the working region of the wavelength of the higherharmonic oscillation is limited by the performance of the optical cavity. However, pioneering studies on higherharmonic FEL oscillations have made significant advances since the dawn of the development of FEL devices (Colson, 1981; Jerby & Gover, 1986). A thirdharmonic FEL oscillation was achieved for the first time with a linear accelerator during the 1980s (Benson & Madey, 1989), and over the years several groups have achieved FEL oscillations on seventh or lower harmonics (Warren et al., 1990; Kato et al., 1998; Neil et al., 2001; Hajima et al., 2001; Wu et al., 2008; Sei et al., 2012a). Recently, the technique of higherharmonic oscillation has been examined for its application in an Xray FEL oscillator (Dai et al., 2012), which is based on an advanced energyrecovery linear accelerator and is equipped with a highreflectivity crystal in the Xray cavity (Kim et al., 2008). By utilizing this technique, the FEL oscillation in the Xray region can be realised using an electron beam with a relatively low energy of 3.5 GeV (Deng & Dai, 2013).
Previously, we have carried out advanced studies to determine the characteristics of higherharmonic FEL oscillations using the infrared FEL system of the NIJIIV storage ring (Yamazaki et al., 1998; Sei et al., 2009). We demonstrated the generation of FEL oscillations using up to the seventh harmonic (Sei et al., 2012b), which is the highest harmonic order ever achieved in the field of higherharmonic FEL oscillations. In addition, it was demonstrated that the higher harmonic was useful for shortening the FEL wavelength using the higher interference of the dielectric multilayer mirrors in the optical cavity (Sei et al., 2012c). Several aspects of the FEL gain for the higherharmonic FEL oscillations were clarified in detail by the experiments performed with the NIJIIV infrared FEL system (Sei et al., 2010, 2014b).
However, systematic studies on the influence of higherharmonic FEL oscillations on the electron beam have not been reported. It is important for the development of the beam physics to investigate the behaviour of the electron beam on the higherharmonic FEL oscillation. The storagering FEL oscillation causes bunch lengthening of the electron beam via energy spreading (Renieri, 1979). Thus, we observed the bunch length of the electron beam on higherharmonic FEL oscillations by direct and indirect methods. It was clarified that the behaviour of the electron beam on higherharmonic FEL oscillation could be described using the theory of bunch heating in the storage ring (Elleaume, 1984a). In this article we report on a variety of such observational results of the electron beam on the higherharmonic FEL oscillation using the NIJIIV infrared FEL system.
2. Observation of bunch lengthening with a dual streak camera
The FEL receives energy from the electron beam while interacting with it and causes a spread in the energy of the electron beam. In the case of a storagering FEL, the relative energy spread σ_{γ}/γ has the following relationship with the bunch length of the electron beam σ_{l} (Wiedemann, 1995),
where c is the speed of light, α is the momentum compaction factor, and Ω_{s} is the angular synchrotron frequency. As is evident from equation (1), an increase in the energy spread due to the FEL oscillation leads to an increase in the bunch length (Roux et al., 1997). Because the FEL gain is inversely proportional to the bunch length, the bunch lengthening suppresses the amount of FEL oscillation. Furthermore, an increase in the energy spread causes an increase in the electronbeam size at positions in the storage ring that have a large dispersion function. However, the dispersion function is almost zero along the two long straight sections, where each optical klystron is installed in the NIJIIV (Sei et al., 2003). For these two regions, the FEL gain is not affected by an increase in the beam size on the FEL oscillation. Therefore, the saturation of the FEL power is caused by an increase of the energy spread and the bunch length of the FEL systems in the NIJIIV. When the power of the storagering FEL saturates, the FEL gain on the nth harmonic G_{n} is equal to the loss of the optical cavity l_{c}. According to the onedimensional FEL theory on the bunch heating process using the optical klystron (Elleaume, 1984a), the following approximation for the bunch length holds true (Sei et al., 2003),
where the suffixes `ON' and `OFF' denote the state of the FEL oscillation (Billardon et al., 1985); namely, [σ_{l}]_{ON} and [σ_{l}]_{OFF} are the laseron and laseroff bunch lengths, respectively. The modulation factor for the nth harmonic f_{γn} is given by
where N_{u} is the number of periods in one undulator section of the optical klystron and N_{d} is the number of periods of the fundamental wavelength passing over an electron in the dispersive section (Elleaume, 1984b). By using equation (1), equation (3) can be described using the bunch length in substitution for the energy spread. It is possible to quantitatively evaluate the influence of the FEL oscillation on the electron beam by observing the influence of the bunch length on the FEL oscillation.
Then, we observed the synchrotron radiation from a bending magnet with a dualsweep et al., 2008). The electron energy in the infrared FEL experiments operated in single electronbunch mode was 310 MeV. The relative energy spread of the electron bunch was 4.0 × 10^{−4} in the singlebunch mode, and the bunch length, which was independent of the electronbeam current below 5 mA, was approximately 90 ps (Sei et al., 2009). Dielectric multilayer mirrors having target wavelengths of 870 nm were used in the experiments (Sei et al., 2010). As shown in Fig. 1, the higherharmonic FEL whose profile was almost a perfect TEM_{00} mode was obtained in the NIJIIV infrared FEL system. Table 1 shows the parameters of the optical klystron ETLOKIII and the values of the saturated FEL power derived from the higherharmonic FEL experiments. The deflection parameter of the ETLOKIII (Sei et al., 2002), K, was 2.09 and 4.14 for the fundamental and the thirdharmonic FELs, respectively, and their corresponding values of threshold current were 2.3 and 3.5 mA. As shown in Fig. 2, the bunch lengths on the fundamental and thirdharmonic FEL oscillations were different for the same value of singlebunch current. Because the FEL gain for the fundamental FEL is higher compared with that for the thirdharmonic FEL, the difference in bunch length with respect to the order of the higher harmonic should be based on investigations of the dependence of the bunch length on the ratio G_{n}/l_{c}, as opposed to the beam current. Fig. 3 shows the measured dependence of the relative bunch length on the ratio in the fundamental and thirdharmonic FEL oscillations. The solid curves in Fig. 3, which are the calculated dependence using equation (2), are roughly in accord with the measured data. Thus, the bunch lengthening on the higherharmonic FEL oscillation can be also described by equation (2), which is based on the theory of bunch heating for the fundamental FEL oscillation. We demonstrate that the theory of bunch heating is applicable to the higherharmonic FEL oscillations.
of 2 ps resolution and measured the bunch lengths on the fundamental and thirdharmonic FEL oscillations (Sei

3. Saturated power of the storagering FEL
An electron beam serves as the laser medium for the FEL interaction, and a FEL oscillation reaches saturation when more energy cannot be extracted from the electron beam. According to the theory of bunch heating extended for the higherharmonic FEL oscillations, the saturated output power of the storagering FEL, P_{T}, has the following relationship with the ratio G_{n}/l_{c} (Elleaume et al., 1984; Sei et al., 2014a),
where η_{c} is the optical cavity efficiency, which is defined as the quotient of the output mirror transmission divided by the cavity loss. The symbol P_{s} is the total synchrotron radiation power emitted in the entire storage ring, and it is proportional to the electronbeam current I_{b}. This equation indicates that P_{T} is a function of the ratio G_{n}/l_{c}, and, subsequently, also of the bunch length on the FEL oscillation. To experimentally confirm that equation (4) holds for any arbitrary order of higher harmonic, we measured the ratio R_{a} as follows,
The saturated output power was measured using a calibrated power meter (Coherent Inc., OP2 IR) with the fundamental and the thirdharmonic FEL oscillations at a wavelength of ∼1530 nm (Sei et al., 2017). Fig. 4 depicts a plot of the relationship between the measured values of R_{a} and the G_{n}/l_{c} ratio. It is noted that the measured values of R_{a} were roughly constant for both the harmonics in the large area of G_{n}/l_{c}. The mean values of the measured R_{a} were 5.4 ± 0.52 for the fundamental FEL oscillation and 5.1 ± 0.32 for the thirdharmonic FEL oscillation, and it was confirmed that they were almost equal. Therefore, the theory of bunch heating is valid for the higherharmonic oscillation in the storagering FEL, and the saturated power of the storagering FEL can be described using the effect of bunch lengthening on the higherharmonic oscillation.
4. Increase of electronbeam lifetime in higherharmonic FEL oscillations
Generally, the bunch lengthening increases the lifetime of the electron beam in the storage ring. It has been previously reported that the lifetime was increased by the bunch lengthening on the FEL oscillation. For a lowenergy storage ring such as the NIJIIV, the Touschek effect mainly influences the lifetime. The Touschek lifetime τ_{T} can be represented using the momentum acceptance (Δp/p)_{c} by the following equation (Wallén, 2003),
where γ, r_{e}, N_{b} and are the energy of the electron expressed in units of its rest energy, the classical electron radius, the number of electrons in a bunch, and the angular divergence of the electron beam in the horizontal plane, respectively. The symbol V_{b} denotes the volume of the bunch, and it is inversely proportional to the bunch length. The parameter ∊_{A} is given by
In the case of ∊_{A} << 1, the function F(∊_{A}) is approximately given by the following equation,
In the infrared experiments, the horizontal and vertical betatron tunes of the storagering NIJIIV were 2.29 and 1.38, respectively. The horizontal and vertical beam sizes at the centre of the long straight section were measured to be 0.9 and 0.2 mm at a beam current of 3 mA, respectively. The beam sizes were almost constant in the 2–5 mA current region. Although the dispersive function was almost zero in the two long straight sections, it increased in the sections containing the bending magnets (Sei et al., 2003). Subsequently, the horizontal beam size and the horizontal angular divergence increased due to energy spreading on the FEL oscillation. The lifetime was also increased owing to other factors besides the bunch lengthening.
To investigate the influence of the order of the higherharmonic FEL oscillation on the lifetime, we measured the electron beam current on the fifthharmonic FEL oscillation at the wavelength 890 nm and on the thirdharmonic FEL oscillation at the wavelength 1530 nm. As shown in Table 1, the two FEL oscillations could be operated under almost the same conditions as for the K and N_{d} values. In other words, the electron beam orbit in the thirdharmonic FEL experiment was the same as that in the fifthharmonic FEL experiment. The threshold current in the NIJIIV infrared FEL system for the thirdharmonic FEL oscillation was almost equal to that of its fifthharmonic. Furthermore, it was possible to observe the influence of the order of the higherharmonic FEL oscillation on the electron beam at a certain G_{n}/l_{c} ratio. Fig. 5 shows the decay curves of the electronbeam currents in the presence or absence of the higherharmonic FEL oscillations. Because the electron beam orbit was set on the central axis of the ETLOKIII, the closed orbit distortion of the electron beam in NIJIIV increased in the infrared FEL experiments. When the K value was 5.6, the momentum acceptance was approximately 1.5 × 10^{−3}. As shown in Fig. 5, the Touschek lifetime was only 9 min at a electronbeam current of 3.0 mA in the singlebunch operation. It can be deduced that the lifetime of the electron beam increased by oscillating the FEL and its length increased for decreasing order of the higher harmonics. Table 2 shows the values of the products of the current and lifetime in the presence and absence of the higherharmonic FEL oscillations for a current region of 3.6–3.0 mA. Generally, the product at a storage ring was constant despite the differences in the values of current (Bernardini et al., 1963). The products for the third and the fifth harmonics were, respectively, 1.53 ± 0.22 times and 1.34 ± 0.11 times higher than that for the case where the FEL oscillation was absent. Table 2 also shows the products calculated with the electronbeam parameters evaluated by the bunch lengthening on the higherharmonic FEL oscillations at a current of 3.6 mA. According to the estimation, the calculated products for the third and the fifth harmonics were, respectively, 1.52 times and 1.25 times higher than the case where the FEL oscillation was absent. These are in accord with the measured values. These experimental results suggest that the theory of bunch heating can describe the properties of the electron beam on the higherharmonic FEL oscillations.

5. Detuning of the cavity length
It is known that a macrotemporal structure appears in the storagering FEL due to a detuning of the optical cavity (Elleaume et al., 1984; Couprie et al., 1993; Roux et al., 1997; Litvinenko et al., 2001; Sei et al., 2004). The minute detuning causes period oscillations in the FEL output power and the bunch length, whose typical time scales are from 1 ms to 100 ms. Such period structures were observed on the higherharmonic FEL oscillations in the NIJIIV infrared FEL system. However, we are interested in the longerterm behaviour of the FEL output power and the bunch length on the higherharmonic FEL oscillations. In this paper, we consider timeaveraged physical quantities of millisecond order.
Since the FEL gain is proportional to the electron density in the electron bunch, the FEL gain has a Gaussian distribution with a standard deviation equal to the bunch length in the direction of the electron orbit. When the cavitylength detuning is much smaller than the bunch length, the FEL can reach an oscillation even for a low G_{n}/l_{c} ratio. The bunch length is an essential parameter for the cavitylength detuning curve, which describes a relationship between the detuning length and the FEL intensity. When the maximum FEL gain is fixed, it is anticipated that the FEL intensity at a certain detuning length should be higher as the bunch length is longer. To confirm this estimate, we measured the cavitylength detuning curves on the fifthharmonic FEL oscillation at 890 nm and the thirdharmonic FEL oscillation at 1530 nm. As mentioned in the last section, these higherharmonic FELs could oscillate under the same conditions of magnetic field as the ETLOKIII, and the threshold electronbeam currents of these higherharmonic FELs were approximately equal. Fig. 6 shows the cavitylength detuning curves on two higherharmonic FEL oscillations at a G_{n}/l_{c} ratio of 2.2. The bunch lengths calculated using equation (2) for the thirdharmonic FEL oscillation and the fifthharmonic FEL oscillation are 122 and 107 ps, respectively, at a G_{n}/l_{c} ratio of 2.2. On the other hand, the full width at halfmaximums of the detuning curves, ΔD, were measured to be 1.89 µm on the thirdharmonic FEL oscillation and 1.28 µm on the fifthharmonic FEL oscillation. These experimental results demonstrated for the first time that the values of ΔD were different due the difference in the bunch lengths on the FEL oscillations, despite the conditions of the insertion device and the G_{n}/l_{c} ratio being the same. We could realise such comparisons using the higherharmonic FEL oscillations.
We experimentally investigate a relationship between the width of the detuning curve and the bunch length on the higherharmonic FEL oscillation. The detuning can be understood as a gap between the electron bunch and the resonated light pulse in the direction of the electronbeam orbit. When a gap exists in the optical cavity, the number of FEL interactions for the light pulse is proportional to the bunch length. The electron bunch has a delay with respect to the light pulse due to its undulating motion in the optical klystron, which is proportional to n(N_{u} + N_{d}) (Deacon et al., 1984). This delay increases the region of the FEL interaction linearly, and is considered to have a positive correlation with ΔD. Moreover, the detuning curve represents the amplification factor of the light pulse caused by the FEL interaction, such that ΔD would be proportional to the FEL intensity normalized by the electronbeam current, P_{T}/I_{b}. When ΔD is much smaller than the bunch length, it is expected that ΔD is approximately proportional to the product of these parameters [σ_{l}, n(N_{u} + N_{d}) and P_{T}/I_{b}], despite the FEL interaction being a nonlinear phenomenon between the electron bunch and the light pulse. Fig. 7 plots the correlation between the product of n(N_{u} + N_{d})σ_{l}P_{OUT}/I_{b} and ΔD in the higherharmonic FEL experiments. The Pearson between these parameters was evaluated to be 0.9996 for all the higher harmonics. It is noted that the width of the detuning curve was perfectly proportional to the product n(N_{u} + N_{d})σ_{l}P_{OUT}/I_{b}. Because the FEL intensity is a function of the bunch length given by equations (2) and (4), ΔD can be directly described in terms of the bunch length. An expression for the width of the detuning curve was determined experimentally, which could be applied to higherharmonic FEL oscillations.
6. Conclusion
We developed higherharmonic FELs using the infrared FEL system in the NIJIIV storage ring and observed various phenomena caused by the electron bunch on the higherharmonic FEL oscillations. The temporal structure of the electronbeam micropulse was measured by a dualsweep G_{n}/l_{c} ratio. The measured lifetimes of the electron beam on the higherharmonic FELs were affected by the phenomenom of energy spreading. Moreover, we demonstrated that the full width at halfmaximum of the detuning curve was proportional to the product depending on the bunch length in the higherharmonic FEL oscillation.
and it was confirmed that bunch lengthening occurred on the higherharmonic FEL oscillations. The saturated power of the storagering FEL was also measured on the higherharmonic FEL oscillation, and it was demonstrated that the power could be described by the theory of bunch heating. It was observed that the third and the fifthharmonic FELs could oscillate for the same conditions of the electron beam and optical klystron by changing the optical cavity mirrors. By adjusting the threshold currents for two higherharmonic FELs to the same value, we could set a condition of the bunch lengths being different for the higherharmonic FELs despite having the sameThe generation of the higherharmonic oscillation is a technique that allows systems of an extremeultraviolet (EUV) FEL and Xray FEL oscillators (XFELO) to have compact designs. It would be possible to develop a compact EUV FEL system using a higherharmonic resonator in an optical cavity as a seed light. There are few papers that report on the experimental results of the characteristics of the higherharmonic FEL; however, there are hardly any reports on the influence of the higherharmonic FEL oscillation on the electron beam. We clarified this aspect by measuring the bunch length on the harmonic lasing in the NIJIIV infrared FEL system. We believe that these experimental results will be useful for developing compact EUV FEL and XFELO systems.
Funding information
The following funding is acknowledged: JSPS KAKENHI (award No. JP16H03912).
References
Benson, S. V. & Madey, J. M. J. (1989). Phys. Rev. A, 39, 1579–1581. CrossRef CAS PubMed Web of Science Google Scholar
Bernardini, C., Corazza, G. F., Di Giugno, G., Ghigo, G., Haissinski, J., Marin, P., Querzoli, R. & Touschek, B. (1963). Phys. Rev. Lett. 10, 407–409. CrossRef CAS Web of Science Google Scholar
Billardon, M., Elleaume, P., Ortega, J. M., Bazin, C., Bergher, M., Velghe, M., Deacon, D. A. & Petroff, Y. (1985). IEEE J. Quantum Electron. 21, 805–823. CrossRef Web of Science Google Scholar
Colson, W. B. (1981). IEEE J. Quantum Electron. 17, 1417–1427. CrossRef Web of Science Google Scholar
Couprie, M. E., Litvinienko, V., Garzella, D., Delboulbé, A., Velghe, M. & Billardon, M. (1993). Nucl. Instrum. Methods Phys. Res. A, 331, 37–41. CrossRef Web of Science Google Scholar
Dai, J., Deng, H. & Dai, Z. (2012). Phys. Rev. Lett. 108, 034502. Web of Science PubMed Google Scholar
Deacon, D. A. G., Billardon, M., Elleaume, P., Ortega, J. M., Robinson, K. E., Bazin, C., Bergher, M., Velghe, M., Madey, J. M. J. & Petroff, Y. (1984). Appl. Phys. B, 34, 207–219. CrossRef Web of Science Google Scholar
Deng, H. X. & Dai, Z. M. (2013). Chin. Phys. C. 37, 102001. Web of Science CrossRef Google Scholar
Elleaume, P. (1984a). J. Phys. Fr. 45, 997–1001. CrossRef CAS Web of Science Google Scholar
Elleaume, P. (1984b). J. Phys. (Paris), 44(C1), 333–352. Google Scholar
Elleaume, P., Ortéga, J. M., Billardon, M., Bazin, C., Bergher, M., Velghe, M., Petroff, Y., Deacon, D. A. G., Robinson, K. E. & Madey, J. M. J. (1984). J. Phys. Fr. 45, 989–996. CrossRef CAS Web of Science Google Scholar
Hajima, R., Nagai, R., Nishimori, N., Kikuzawa, N. & Minehara, E. J. (2001). Nucl. Instrum. Methods Phys. Res. A, 475, 43–46. Web of Science CrossRef CAS Google Scholar
Jerby, E. & Gover, A. (1986). Nucl. Instrum. Methods Phys. Res. A, 250, 192–202. CrossRef Web of Science Google Scholar
Kato, R., Okuda, S., Nakajima, Y., Kondo, G., Iwase, Y., Kobayashi, H., Suemine, S. & Isoyama, G. (1998). Nucl. Instrum. Methods Phys. Res. A, 407, 157–160. Web of Science CrossRef CAS Google Scholar
Kim, K. J., Shvyd'ko, Y. & Reiche, S. (2008). Phys. Rev. Lett. 100, 244802. Web of Science CrossRef PubMed Google Scholar
Litvinenko, V. N., Park, S. H., Pinayev, I. V. & Wu, Y. (2001). Nucl. Instrum. Methods Phys. Res. A, 475, 240–246. Web of Science CrossRef CAS Google Scholar
Neil, G. R., Benson, S. V., Biallas, G., Gubeli, J., Jordan, K., Myers, S. & Shinn, M. D. (2001). Phys. Rev. Lett. 87, 084801. Web of Science CrossRef PubMed Google Scholar
Renieri, A. (1979). Nuov. Cim. B, 53, 160–178. CrossRef Web of Science Google Scholar
Roux, R., Couprie, M. E., Hara, T., Bakker, R. J., Visentin, B., Billardon, M. & Roux, J. (1997). Nucl. Instrum. Methods Phys. Res. A, 393, 33–37. CrossRef CAS Web of Science Google Scholar
Sei, N., Ogawa, H. & Okuda, S. (2017). J. Appl. Phys. 121, 023103. Web of Science CrossRef Google Scholar
Sei, N., Ogawa, H. & Yamada, K. (2009). Opt. Lett. 34, 1843–1845. CrossRef PubMed CAS Google Scholar
Sei, N., Ogawa, H. & Yamada, K. (2010). J. Phys. Soc. Jpn, 79, 093501. Web of Science CrossRef Google Scholar
Sei, N., Ogawa, H. & Yamada, K. (2012a). Appl. Phys. Lett. 101, 144101. Web of Science CrossRef Google Scholar
Sei, N., Ogawa, H. & Yamada, K. (2012b). Opt. Express, 20, 308–316. Web of Science CrossRef CAS PubMed Google Scholar
Sei, N., Ogawa, H. & Yamada, K. (2012c). J. Phys. Soc. Jpn, 81, 093501. Web of Science CrossRef Google Scholar
Sei, N., Ogawa, H. & Yamada, K. (2014a). JPS Conf. Proc. 1, 014005. Google Scholar
Sei, N., Ogawa, H., Yamada, K., Koike, M. & Ohgaki, H. (2014b). J. Synchrotron Rad. 21, 654–661. Web of Science CrossRef IUCr Journals Google Scholar
Sei, N., Ohgaki, H., Mikado, T. & Yamada, K. (2002). Jpn. J. Appl. Phys. 41, 1595–1601. Web of Science CrossRef CAS Google Scholar
Sei, N., Yamada, K. & Mikado, T. (2004). Jpn. J. Appl. Phys. 43, 577–584. Web of Science CrossRef CAS Google Scholar
Sei, N., Yamada, K. & Ogawa, H. (2008). J. Phys. Soc. Jpn, 77, 074501. Web of Science CrossRef Google Scholar
Sei, N., Yamada, K., Ogawa, H., Yasumoto, M. & Mikado, T. (2003). Jpn. J. Appl. Phys. 42, 5848–5858. Web of Science CrossRef CAS Google Scholar
Wallén, E. (2003). Nucl. Instrum. Methods Phys. Res. A, 508, 487–495. Google Scholar
Warren, R. W., Haynes, L. C., Feldman, D. W., Stein, W. E. & Gitomer, S. J. (1990). Nucl. Instrum. Methods Phys. Res. A, 296, 84–88. CrossRef Web of Science Google Scholar
Wiedemann, H. (1995). Particle Accelerator Physics II, ch. 10, p. 350. New York: SpringerVerlag. Google Scholar
Wu, Y. K., Benson, S. V., Li, J., Mikhailov, S. F., Neil, G. & Popov, V. (2008). Proceedings of the 30th International Free Electron Laser Conference, Gyeongju, Korea. Google Scholar
Yamazaki, T., Yamada, K., Sei, N., Ohgaki, H., Sugiyama, S., Suzuki, R., Mikado, T., Noguchi, T., Chiwaki, M., Ohdaira, T. & Toyokawa, H. (1998). Nucl. Instrum. Methods Phys. Res. B, 144, 83–89. Web of Science CrossRef CAS Google Scholar
This is an openaccess article distributed under the terms of the Creative Commons Attribution (CCBY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.