Operation of higher harmonic oscillations in free-electron lasers

N. Sei; H. Ogawa; K. Yamada

doi:10.1364/OE.20.000308

Optics Express
Vol. 20,
Issue 1,
pp. 308-316
(2012)
•https://doi.org/10.1364/OE.20.000308

Operation of higher harmonic oscillations in free-electron lasers

N. Sei, H. Ogawa, and K. Yamada

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N. Sei, H. Ogawa, and K. Yamada, "Operation of higher harmonic oscillations in free-electron lasers," Opt. Express 20, 308-316 (2012)

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Related Topics
Table of Contents Category
- Lasers and Laser Optics
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Free-electron lasers (FELs) (140.2600)
- Infrared and far-infrared lasers (140.3070)
- UV, EUV, and X-ray lasers (140.7240)

About this Article
History
- Original Manuscript: October 17, 2011
- Revised Manuscript: November 27, 2011
- Manuscript Accepted: November 27, 2011
- Published: December 20, 2011

Abstract

We report for the first time the experimental achievement of a seventh-harmonic free-electron laser (FEL) oscillation. The measured FEL gains and average FEL powers for higher harmonics were identical to those calculated by a one-dimensional FEL theory. The measured linewidths of the higher-harmonic FELs were narrower than that of the fundamental FEL owing to the narrower spectral widths of the spontaneous emissions. By applying the higher-harmonic FEL oscillation to a resonator-type FEL with an advanced accelerator, an x-ray FEL oscillator can be realized at lower electron-beam energy.

1. Introduction

Free-electron lasers (FELs) generated by a relativistic electron beam in a periodic electromagnetic filed are capable of, in principle, achieving laser amplification in the entire wavelength region [1]. Worldwide, the wavelength tunability has been used to promote x-ray projects in which a concept of a self-amplified spontaneous emission (SASE) FEL is adopted [2–5]. The FEL wavelength has been reduced to 1 Ǻ by the Linac Coherent Light Source (LCLS) [4] and the SPring-8 Angstrom Compact free electron Laser (SACLA) [5]. Since the FEL wavelength is inversely proportional to the square of the electron-beam energy [1], a higher-energy electron beam is necessary for realization of a shorter-wavelength FEL. Thus, techniques to decrease the required electron-beam energy, such as coherent harmonic generation [6], high gain harmonic generation [7] and echo-enabled harmonic generation [8], have been investigated. These techniques generate high-intensity spontaneous emissions with an energy modulation caused by an external laser in an insertion device. Higher-harmonic spontaneous emissions generated by these techniques are expected to be promising light sources in the extreme-ultraviolet (EUV) and x-ray regions, where it is difficult to obtain high-reflectivity mirrors, because they do not need an optical cavity.

Higher-harmonic FEL oscillation has been also studied for obtaining shorter-wavelength coherent light [1, 9]. It is superior to the above techniques to generate higher-harmonic spontaneous emissions in terms of an average power and stability of the wavelength. Limitation of the FEL wavelength due to the cavity mirrors is regarded as a restriction on the higher-harmonic FEL oscillation. Recently, however, an x-ray FEL oscillator (X-FELO), based on an advanced energy-recovery linac and a high-reflectivity crystal for the x-ray cavity, was proposed [10]. The X-FELO is expected to have a much higher brilliance than the SASE FEL. Applying the higher-harmonic FEL oscillation to the X-FELO, the electron-beam energy necessary for oscillation in the x-ray region can be decreased and the accelerator facility for the x-ray source can be compacted. Decrease of the electron-beam energy causes an enhancement of electron-beam emittance in an X-FELO, so that it reduces the FEL gain. When the higher-harmonic FEL oscillation is used, it is necessary to decrease the electron-beam energy with considering the FEL gain.

Theoretical studies of higher-harmonic FELs have been reported [11, 12], and several groups have already achieved FEL oscillations on the fifth or lower harmonics [13, 14]. However, most of the higher-harmonic FEL oscillations were developed for demonstrating the high performance of FEL devices. Differences between the higher-harmonic FEL and fundamental FEL have not been discussed sufficiently. Thus, an optical klystron ETLOK-III [15] was developed for investigating characteristics of the higher-harmonic FEL oscillations with the storage ring NIJI-IV, which contributed to shortening the FEL wavelength with a UV optical cavity [16]. New optical-cavity mirror chambers were installed at the ends of another IR optical cavity [17], and a mid-IR FEL and the third-harmonic FEL oscillated with the ETLOK-III [18, 19]. Moreover, high-reflectivity dielectric multilayer mirrors were used to achieve the fifth- and seventh-harmonic FEL oscillations at wavelengths of approximately 890 nm. This seventh-harmonic FEL is the highest achieved order in higher-harmonic FEL oscillations. In this study, the experimental results of the higher-harmonic FELs are shown and the differences between the higher-harmonic FELs and the fundamental FEL are clarified in detail.

2. FEL gain and oscillation for higher harmonics

The two methods for oscillating some higher-harmonic FELs at the same wavelength are adjusting the electron-beam energy and adjusting the gap of an undulator [1]. The method of adjusting the electron-beam energy results in an energy-saving effect of the higher-harmonic FELs. However, comparing the differences between the higher-harmonic FELs is difficult because the electron-beam qualities change depending on the energy. Then, the method of the adjusting the undulator gap was selected to realize the higher-harmonic FEL oscillations in this study. When the characteristics of the electron-beam qualities are fixed, an FEL gain on the nth harmonic (G_n) is given by an FEL gain on the fundamental harmonic (G₁) as

G_{n} = \frac{F_{n} (K_{n}) f_{n}}{F_{1} (K_{1}) f_{1}} n G_{1},

F_{n} = \frac{4 n^{2} K_{n}^{2}}{{(2 + K_{n}^{2})}^{2}} {[J_{\frac{n + 1}{2}} (\frac{n K_{n}^{2}}{4 + 2 K_{n}^{2}}) - J_{\frac{n - 1}{2}} (\frac{n K_{n}^{2}}{4 + 2 K_{n}^{2}})]}^{2},

where n is a positive odd number [19]. All the higher-harmonic FELs are assumed to oscillate at the same wavelength. The deflection parameter of the optical klystron for the nth harmonic is

K_{n}^{} = \sqrt{2 (\frac{2 + K_{1}^{2}}{2} n - 1)} .

The wavelength of the higher-harmonic FEL oscillation in $K_{n} < \sqrt{2 (n - 1)}$ is shorter than that of the fundamental FEL oscillation for any K₁ value. Therefore, the higher-harmonic FEL is effective for developing a shorter-wavelength coherent light source. The modulation rate for the nth harmonic (f_n) is an additional factor for the optical klystron [20]. Although f_n consists of some factors which represent effects of the gain reduction, it is approximated to f_γn, which represents a contribution of the energy spread of the electron bunch without an FEL oscillation (σ_γ0/γ), namely,

f_{n} ≅ f_{γ n} = \exp [- 8 π^{2} n^{2} {(N_{u} + N_{d})}^{2} {(\frac{σ_{γ 0}}{γ})}^{2}],

where N_u is the number of periods in one undulator section and N_d is the number of periods of the fundamental wavelength passing over an electron in the dispersive section.

In the case of the NIJI-IV FEL system, the energy spread is 4.0×10⁻⁴ at the electron-beam energy of 310 MeV in a low-current region (< 15mA) [17]. The optimum value of n(N_u + N_d) for the FEL gain is approximately 200. As shown in Table 1 , however, the values of n(N_u + N_d) for higher-harmonic FEL oscillations are above 200 at a wavelength of 890 nm because the available gap of the dispersive section of the ETLOK-III (g_d) is limited. The ratio of the FEL gain for the higher harmonic to that for the fundamental harmonic becomes small in the shorter-wavelength region owing to the larger n(N_u +N_d) and smaller K_n. Nevertheless, the FEL gain for the seventh harmonic is approximately 0.2 times that for the fundamental harmonic in the near-IR region as shown in Fig. 1 . We used a low-loss optical cavity to realize the higher-harmonic FEL oscillations satisfactorily with the ETLOK-III.

Table 1. Performance of the ETLOK-III for higher-harmonic FEL oscillations at a wavelength of approximately 890 nm. See text for explanation of symbols. Lasing wavelength of FELs can be changed by slightly adjusting g_u and g_d from the values in this table. Values in parentheses of the column of the threshold current express in peak current.

View Table

Fig. 1 Calculated FEL gains in the case of g_d = g_u + 17 for the fundamental harmonic and g_d = g_u + 37 for the higher (third, fifth and seventh) harmonics. The electron-beam current and energy are set to 5 mA and 310 MeV, respectively.

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Experiments for higher-harmonic FEL oscillations were conducted with the storage ring NIJI-IV and the optical klystron ETLOK-III at wavelengths of approximately 890 nm, where high-reflectivity dielectric multilayer mirrors were available for the optical cavity [18]. The electron-beam energy was set to 310 MeV and the bunch length was approximately 90 ps. The fundamental FEL oscillation continued for more than 1 h and stopped when the storage-ring electron-beam current decreased to 0.55 mA in a single electron-bunch operation. The charge in a bunch was 0.1 nC for the storage-ring electron-beam current of 1 mA. The cavity loss was estimated to be 0.045% from the threshold current of the fundamental FEL oscillation. The threshold currents of the higher-harmonic FEL oscillations were estimated to be 0.82 mA for the third harmonic, 1.5 mA for the fifth harmonic and 3.6 mA for the seventh harmonic using Eqs. (1)-(4) based on a one-dimensional FEL theory [20]. As shown in reference 18, the cavity mirrors were designed for a wavelength of 2560 nm and had narrow high-reflectivity regions (> 99%) at wavelengths of around 550, 890 and 2560 nm owing to multilayer mirrors. The high-reflectivity regions shifted to a longer wavelength, as compared with the accurate wavelength of the higher harmonic. The cavity loss at a wavelength of 2670 nm was more than 0.3%, so that it was much higher than the cavity loss at the wavelength of 890 nm. Then, an order harmonic FEL up to the seventh harmonic at the wavelength of 890 nm did not oscillate simultaneously with other order harmonic FELs. Figure 2 shows the energy spectra of backscattered FEL-Compton x rays [21] with respect to the undulator gap (g_u) ranging from 86.5 to 88.0 mm. These spectra were measured by a 25ϕ×51 mm LaBr₃(Ce) scintillation detector, which was located behind the downstream mirror chamber with a lead collimator of 10 mm in bore and 100 mm in thickness. As shown in Fig. 2, the fundamental FEL at 2560 nm and the third-harmonic FEL at 890 nm can be interchanged by adjusting K_n. The third-harmonic FEL oscillated until the electron-beam current decreased to 0.90 mA in a single electron-bunch operation. The measured threshold current (I_th) showed good agreement with the calculated value. By increasing K_n to 5.52 and 6.62, the FEL oscillations for the fifth and seventh harmonics were achieved at the wavelengths of approximately 890 nm. Figure 3 shows the spectrum of the seventh-harmonic FEL oscillation, which is the highest achieved order in the higher-harmonic FEL oscillations. The measured threshold currents for the fifth and seventh harmonics were 1.5 and 3.8 mA, respectively, and they showed good agreement with the calculated values. It is an important fact that an FEL for any higher harmonic can oscillate at a gain beyond the cavity loss. Although the K_n value was relatively high in the present experiments, a higher-harmonic FEL was shown to oscillate with an optical cavity at an FEL gain of only 0.045%.

Fig. 2 Energy spectra of the FEL-Compton x ray measured in a two-electron-bunch operation. With changing g_u from 86.5 to 88.0 mm at the electron-beam current of 7.3-6.5 mA, the Compton edge shifted from 0.71 to 2.03 MeV.

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Fig. 3 Measured spectrum of the seventh-harmonic FEL oscillation at the electron-beam current of 4.3 mA.

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3. FEL power for higher harmonics

In the case of a storage ring, a saturated FEL caused an increase in the electron-bunch energy spread due to a ‘heating’ process [22]. The average power of a saturated FEL for the nth harmonic has the following relationship [23] with σ_γ0/γ and the energy spread with an FEL oscillation (σ_γ/γ):

P_{n} \propto η_{c} [{(\frac{σ_{γ}}{γ})}^{2} - {(\frac{σ_{γ 0}}{γ})}^{2}] P_{S},

where η_c is the optical cavity effect, which is an output transmission over the cavity loss (l_c), and P_s is the total synchrotron radiation power emitted in the whole storage ring and is proportional to the electron-beam current (I_n). Bunch length is proportional to the energy spread, so it increases with the FEL oscillation. Bunch length without FEL oscillation was almost constant at a beam current of less than 15 mA in the single electron-bunch operation of the storage ring NIJI-IV. When no anomalous bunch lengthening in the electron bunch occurs, the following equation for FEL gain and energy spread is valid for I_th < I_n:

\frac{G_{n}}{l_{c}} = \frac{(\frac{σ_{γ}}{γ})}{(\frac{σ_{γ 0}}{γ})} \frac{f_{γ n} (\frac{σ_{γ 0}}{γ})}{f_{γ n} (\frac{σ_{γ}}{γ})} .

In the case of the NIJI-IV FEL experiments, the parameter nN_d was set in order to maximize the FEL gain. According to Eq. (4), the contribution of the energy spread to the FEL gain is superior to that of the bunch length to the FEL gain. Ignoring the contribution of the bunch length in Eq. (6), one can rewrite the relationship (5) with Eq. (4) as

P_{n} \propto η_{c} \frac{ln (G_{n} / l_{c})}{n (N_{u} + N_{d})} P_{S} .

This relationship is particularly effective for the higher harmonic owing to the larger value of nN_d.

The average FEL power transmitted through a vacuum window was measured using a calibrated power detector [17]. Figure 4 shows the FEL power for the fundamental and higher harmonics with respect to the electron-beam current. The measured FEL power was roughly in accord with fitting curves calculated using relationship (7). The FEL power per electron-beam current for the higher harmonic was compared to that for the fundamental harmonic at G_n/l_c = 2. The measured values of (P₃/I₃)/(P₁/I₁) and (P₅/I₅)/(P₁/I₁) were 0.76 and 0.45, respectively. According to the relationship (7), P_n/I_n is proportional to the factor 1/ n(N_u +N_d). The ratios of 1/ n(N_u +N_d) for the third- and fifth-harmonic FELs to 1/ n(N_u +N_d) for the fundamental FEL were 0.72 and 0.55, respectively, as shown in Table 1. These values were similar to the measured values of (P_n/I_n)/(P₁/I₁). The dependence of the average power of the higher-harmonic FEL on the FEL gain was determined, and the average power of the higher-harmonic FEL per electron-beam current was experimentally demonstrated to be proportional to the factor 1/ n(N_u +N_d).

Fig. 4 Dependence of the average FEL power for the fundamental and higher (third, fifth and seventh) harmonics on the electron-beam current in the single electron-bunch operation.

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4. Linewidth for higher harmonics

For a conventional undulator, the relative spectral width of a higher-harmonic spontaneous emission narrows as the order of harmonics increases [1]. Even for an optical klystron, peak intervals in a higher-harmonic spontaneous emission spectrum decrease because of a higher value of nN_d. Then, the relative linewidth of the higher-harmonic FEL is expected to be narrower than that of the fundamental FEL. In our previous study, the linewidth of the third-harmonic FEL was shown to be narrower than that of the fundamental FEL at wavelengths of approximately 870 nm [19]. In this study, the spectroscopic system was improved and the FEL spectra were measured with a resolution of 0.162 nm at wavelengths of approximately 890 nm. As shown in Fig. 5 , the linewidths considered with the resolution of the measurement system in the case where G_n/l_c ≅ 2 were 0.154, 0.119 and 0.098 nm for the fundamental harmonic, third harmonic and fifth harmonic, respectively.

Fig. 5 Measured spectra of the FEL oscillations for the fundamental, third and fifth harmonics. The electron-beam currents were 1.3 mA for the fundamental harmonic, 2.1 mA for the third harmonic and 2.8 mA for the fifth harmonic. The linewidths considered with the resolution of the measurement system were 0.154 nm for the fundamental harmonic, 0.119 nm for the third harmonic and 0.098 nm for the fifth harmonic in full width at half maximum.

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Pulse widths of the FEL for the higher harmonic were not measured, owing to insufficient sensitivity of the streak camera for measurement at the 890 nm wavelength. However, the pulse width of the fundamental FEL at the 870 nm wavelength was 9.9 ps as previously reported [19], so that the higher-harmonic FEL oscillations would reach to the Fourier transfer limit. The ratios of the relative linewidths for the third- and fifth-harmonic FELs to that for the fundamental FEL were 0.77 and 0.64, respectively. The linewidths of the higher-harmonic FELs are roughly proportional to the factor 1/ n(N_u +N_d). This suggests that the linewidth and pulse width can be controlled by changing characteristics of the seed light for the FEL.

5. Discussion

In conclusion, FEL oscillations were achieved up to the seventh harmonic with the storage ring NIJI-IV and the optical klystron ETLOK-III. The seventh-harmonic FEL oscillation was the highest achieved order in the higher-harmonic FEL oscillations. The measured FEL gains for higher harmonics agreed well with those calculated by the FEL theory. The FEL power with respect to the FEL gain was also measured for the higher harmonics, and the average power of the higher-harmonic FEL per electron-beam current was shown to be proportional to the factor 1/ n(N_u +N_d). Moreover, the linewidths of the FEL oscillations for the higher harmonics at an FEL gain were measured with a high-resolution spectroscopic system. The ratios of the relative linewidths for the higher-harmonic FELs to that for the fundamental FEL were proportional to the factor 1/ n(N_u +N_d). The higher-harmonic FEL was demonstrated to be useful for controlling characteristics of the FEL.

As advanced accelerator technology helps SASE-FELs to be realized in the x-ray region, an FEL oscillation with an optical resonator can be developed in the EUV and x-ray regions by using advanced accelerator and optical material technologies. Multilayer mirrors and crystals with reflectivity of approximately 70% [24] and 96% [10] are available in the EUV and x-ray regions, respectively. When the FEL gain for the higher harmonic is over 100% in the EUV region and 10% in the x-ray region, a resonator-type FEL oscillation, which is superior to the SASE and coherent harmonic generation in terms of the average power and stability of the wavelength, is capable of oscillating in those regions. Using an advanced energy-recovery linac, it is possible to obtain such an FEL gain with an undulator which is much shorter than that of the SASE. The high-power resonator-type EUV-FEL can even be applied to the photolithography in a semiconductor manufacturing process. The X-FELO is promising technology that may lead to applications for imaging the structure and dynamics of matter at an atomic size and timescales. The higher-harmonic FEL oscillation technique is useful for realizing a resonator-type FEL with lower electron-beam energy in the EUV and x-ray regions. For saving energy and advancing science, higher-harmonic FEL oscillation should be developed for the EUV-FEL and X-FELO.

Acknowledgments

This study was financially supported by the Budget for Nuclear Research of the Ministry of Education, Culture, Sports, Science and Technology, based on the screening and counseling by the Atomic Energy Commission.

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Publication

C. A. Brau, Free-Electron Lasers (Academic Press, Inc., 1990), Chapt. 2.
V. Ayvazyan, N. Baboi, I. Bohnet, R. Brinkmann, M. Castellano, P. Castro, L. Catani, S. Choroba, A. Cianchi, M. Dohlus, H. T. Edwards, B. Faatz, A. A. Fateev, J. Feldhaus, K. Flöttmann, A. Gamp, T. Garvey, H. Genz, Ch. Gerth, V. Gretchko, B. Grigoryan, U. Hahn, C. Hessler, K. Honkavaara, M. Hüning, R. Ischebeck, M. Jablonka, T. Kamps, M. Körfer, M. Krassilnikov, J. Krzywinski, M. Liepe, A. Liero, T. Limberg, H. Loos, M. Luong, C. Magne, J. Menzel, P. Michelato, M. Minty, U.-C. Müller, D. Nölle, A. Novokhatski, C. Pagani, F. Peters, J. Pflüger, P. Piot, L. Plucinski, K. Rehlich, I. Reyzl, A. Richter, J. Rossbach, E. L. Saldin, W. Sandner, H. Schlarb, G. Schmidt, P. Schmüser, J. R. Schneider, E. A. Schneidmiller, H.-J. Schreiber, S. Schreiber, D. Sertore, S. Setzer, S. Simrock, R. Sobierajski, B. Sonntag, B. Steeg, F. Stephan, K. P. Sytchev, K. Tiedtke, M. Tonutti, R. Treusch, D. Trines, D. Türke, V. Verzilov, R. Wanzenberg, T. Weiland, H. Weise, M. Wendt, I. Will, S. Wolff, K. Wittenburg, M. V. Yurkov, and K. Zapfe, “Generation of GW radiation pulses from a VUV free-electron laser operating in the femtosecond regime,” Phys. Rev. Lett. 88(10), 104802 (2002).
[Crossref] [PubMed]
T. Shintake, H. Tanaka, T. Hara, T. Tanaka, K. Togawa, M. Yabashi, Y. Otake, Y. Asano, T. Bizen, T. Fukui, S. Goto, A. Higashiya, T. Hirono, N. Hosoda, T. Inagaki, S. Inoue, M. Ishii, Y. Kim, H. Kimura, M. Kitamura, T. Kobayashi, H. Maesaka, T. Masuda, S. Matsui, T. Matsushita, X. Maréchal, M. Nagasono, H. Ohashi, T. Ohata, T. Ohshima, K. Onoe, K. Shirasawa, T. Takagi, S. Takahashi, M. Takeuchi, K. Tamasaku, R. Tanaka, Y. Tanaka, T. Tanikawa, T. Togashi, S. Wu, A. Yamashita, K. Yanagida, C. Zhang, H. Kitamura, and T. Ishikawa, “A compact free-electron laser for generating coherent radiation in the extreme ultraviolet region,” Nat. Photonics 2(9), 555–559 (2008).
[Crossref]
P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, Ph. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]
D. Pile, “X-rays: First light from SACLA,” Nat. Photonics 5(8), 456–457 (2011).
[Crossref]
J. M. Ortega, Y. Lapierre, B. Girard, M. Billardon, P. Elleaume, C. Bazin, M. Bergher, M. Velghe, and Y. Petroff, “Ultraviolet coherent generation from an optical klystron,” IEEE J. Quantum Electron. 21(7), 909–919 (1985).
[Crossref]
L.-H. Yu, M. Babzien, I. Ben-Zvi, L. F. DiMauro, A. Doyuran, W. Graves, E. Johnson, S. Krinsky, R. Malone, I. Pogorelsky, J. Skaritka, G. Rakowsky, L. Solomon, X. J. Wang, M. Woodle, V. Yakimenko, S. G. Biedron, J. N. Galayda, E. Gluskin, J. Jagger, V. Sajaev, and I. Vasserman, “High-gain harmonic-generation free-electron laser,” Science 289(5481), 932–934 (2000).
[Crossref] [PubMed]
G. Stupakov, “Using the beam-echo effect for generation of short-wavelength radiation,” Phys. Rev. Lett. 102(7), 074801 (2009).
[Crossref] [PubMed]
S. V. Benson and J. M. J. Madey, “Demonstration of harmonic lasing in a free-electron laser,” Phys. Rev. A 39(3), 1579–1581 (1989).
[Crossref] [PubMed]
K. J. Kim, Y. Shvyd’ko, and S. Reiche, “A proposal for an X-ray free-electron laser oscillator with an energy-recovery linac,” Phys. Rev. Lett. 100(24), 244802 (2008).
[Crossref] [PubMed]
W. B. Colson, “The nonlinear wave equation for higher harmonics in free-electron lasers,” IEEE J. Quantum Electron. 17(8), 1417–1427 (1981).
[Crossref]
E. Jerby and A. Gover, “A kinetic small signal gain analysis of a planar wiggler FEL, operating in the high harmonic (strong wiggler) regime,” Nucl. Instrum. Methods Phys. Res A 250, 192 (1986).
S. Benson, M. Shinn, G. R. Neil, and T. Siggins, “First demonstration of 5th harmonic Lasing in a FEL,” Proceedings of the 22nd International Free Electron Laser Conference, 23–26 August 1999, Hamburg, FRG, edited by J. Feldhaus and H. Weise (Elsevier Science, Amsterdam, 2000), II 1–2.
G. R. Neil, S. V. Benson, G. Biallas, J. Gubeli, K. Jordan, S. Myers, and M. D. Shinn, “Second harmonic FEL oscillation,” Phys. Rev. Lett. 87(8), 084801 (2001).
[Crossref] [PubMed]
N. Sei, K. Yamada, H. Ohgaki, T. Mikado, M. Yasumoto, and H. Ogawa, “Study of expected performance of the hard X-ray beam for the FEL-X project,” Nucl. Instrum. Methods Phys. Res A 483, 429 (2002).
K. Yamada, N. Sei, H. Ohgaki, T. Mikado, S. Sugiyama, and T. Yamazaki, “Lasing towards the VUV in the NIJI-IV FEL,” Nucl. Instrum. Methods Phys. Res A 445, 173 (2000).
N. Sei, H. Ogawa, and K. Yamada, “Lasing of infrared free-election lasers using the storage ring NIJI-IV,” Opt. Lett. 34(12), 1843–1845 (2009).
[Crossref] [PubMed]
N. Sei, H. Ogawa, and K. Yamada, “Lasing of middle-infrared free-election lasers using the storage ring NIJI-IV,” Opt. Lett. 36(18), 3645–3647 (2011).
[Crossref] [PubMed]
N. Sei, H. Ogawa, and K. Yamada, “Third harmonic lasing in a storage ring free-electron laser,” J. Phys. Soc. Jpn. 79(9), 093501 (2010).
[Crossref]
P. Elleaume, “Optical klystrons,” J. Phys. (Paris) 44(C1), C1-333–C352 (1983).
[Crossref]
V. N. Litvinenko, B. Burnham, M. Emamian, N. Hower, J. M. J. Madey, P. Morcombe, P. G. O'Shea, S. H. Park, R. Sachtschale, K. D. Straub, G. Swift, P. Wang, Y. Wu, R. S. Canon, C. R. Howell, N. R. Roberson, E. C. Schreiber, M. Spraker, W. Tornow, H. R. Weller, I. V. Pinayev, N. G. Gavrilov, M. G. Fedotov, G. N. Kulipanov, G. Y. Kurkin, S. F. Mikhailov, V. M. Popik, A. N. Skrinsky, N. A. Vinokurov, B. E. Norum, A. Lumpkin, and B. Yang, “Gamma-ray production in a storage ring free-electron laser,” Phys. Rev. Lett. 78(24), 4569–4572 (1997).
[Crossref]
P. Elleaume, “Macro-temporal structure of storage ring free electron lasers,” J. Phys. (Paris) 45(6), 997–1001 (1984).
[Crossref]
P. Elleaume, “Storage ring FEL theory,” Nucl. Instrum. Methods Phys. Res A 237, 28 (1985).
S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “EUV reflectance and scattering of Mo/Si multilayers on differently polished substrates,” Opt. Express 15(21), 13997–14012 (2007).
[Crossref] [PubMed]

2011 (2)

D. Pile, “X-rays: First light from SACLA,” Nat. Photonics 5(8), 456–457 (2011).
[Crossref]

N. Sei, H. Ogawa, and K. Yamada, “Lasing of middle-infrared free-election lasers using the storage ring NIJI-IV,” Opt. Lett. 36(18), 3645–3647 (2011).
[Crossref] [PubMed]

2010 (2)

N. Sei, H. Ogawa, and K. Yamada, “Third harmonic lasing in a storage ring free-electron laser,” J. Phys. Soc. Jpn. 79(9), 093501 (2010).
[Crossref]

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, Ph. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

2009 (2)

G. Stupakov, “Using the beam-echo effect for generation of short-wavelength radiation,” Phys. Rev. Lett. 102(7), 074801 (2009).
[Crossref] [PubMed]

N. Sei, H. Ogawa, and K. Yamada, “Lasing of infrared free-election lasers using the storage ring NIJI-IV,” Opt. Lett. 34(12), 1843–1845 (2009).
[Crossref] [PubMed]

2008 (2)

T. Shintake, H. Tanaka, T. Hara, T. Tanaka, K. Togawa, M. Yabashi, Y. Otake, Y. Asano, T. Bizen, T. Fukui, S. Goto, A. Higashiya, T. Hirono, N. Hosoda, T. Inagaki, S. Inoue, M. Ishii, Y. Kim, H. Kimura, M. Kitamura, T. Kobayashi, H. Maesaka, T. Masuda, S. Matsui, T. Matsushita, X. Maréchal, M. Nagasono, H. Ohashi, T. Ohata, T. Ohshima, K. Onoe, K. Shirasawa, T. Takagi, S. Takahashi, M. Takeuchi, K. Tamasaku, R. Tanaka, Y. Tanaka, T. Tanikawa, T. Togashi, S. Wu, A. Yamashita, K. Yanagida, C. Zhang, H. Kitamura, and T. Ishikawa, “A compact free-electron laser for generating coherent radiation in the extreme ultraviolet region,” Nat. Photonics 2(9), 555–559 (2008).
[Crossref]

K. J. Kim, Y. Shvyd’ko, and S. Reiche, “A proposal for an X-ray free-electron laser oscillator with an energy-recovery linac,” Phys. Rev. Lett. 100(24), 244802 (2008).
[Crossref] [PubMed]

2007 (1)

S. Schröder, T. Feigl, A. Duparré, and A. Tünnermann, “EUV reflectance and scattering of Mo/Si multilayers on differently polished substrates,” Opt. Express 15(21), 13997–14012 (2007).
[Crossref] [PubMed]

2002 (2)

N. Sei, K. Yamada, H. Ohgaki, T. Mikado, M. Yasumoto, and H. Ogawa, “Study of expected performance of the hard X-ray beam for the FEL-X project,” Nucl. Instrum. Methods Phys. Res A 483, 429 (2002).

V. Ayvazyan, N. Baboi, I. Bohnet, R. Brinkmann, M. Castellano, P. Castro, L. Catani, S. Choroba, A. Cianchi, M. Dohlus, H. T. Edwards, B. Faatz, A. A. Fateev, J. Feldhaus, K. Flöttmann, A. Gamp, T. Garvey, H. Genz, Ch. Gerth, V. Gretchko, B. Grigoryan, U. Hahn, C. Hessler, K. Honkavaara, M. Hüning, R. Ischebeck, M. Jablonka, T. Kamps, M. Körfer, M. Krassilnikov, J. Krzywinski, M. Liepe, A. Liero, T. Limberg, H. Loos, M. Luong, C. Magne, J. Menzel, P. Michelato, M. Minty, U.-C. Müller, D. Nölle, A. Novokhatski, C. Pagani, F. Peters, J. Pflüger, P. Piot, L. Plucinski, K. Rehlich, I. Reyzl, A. Richter, J. Rossbach, E. L. Saldin, W. Sandner, H. Schlarb, G. Schmidt, P. Schmüser, J. R. Schneider, E. A. Schneidmiller, H.-J. Schreiber, S. Schreiber, D. Sertore, S. Setzer, S. Simrock, R. Sobierajski, B. Sonntag, B. Steeg, F. Stephan, K. P. Sytchev, K. Tiedtke, M. Tonutti, R. Treusch, D. Trines, D. Türke, V. Verzilov, R. Wanzenberg, T. Weiland, H. Weise, M. Wendt, I. Will, S. Wolff, K. Wittenburg, M. V. Yurkov, and K. Zapfe, “Generation of GW radiation pulses from a VUV free-electron laser operating in the femtosecond regime,” Phys. Rev. Lett. 88(10), 104802 (2002).
[Crossref] [PubMed]

2001 (1)

G. R. Neil, S. V. Benson, G. Biallas, J. Gubeli, K. Jordan, S. Myers, and M. D. Shinn, “Second harmonic FEL oscillation,” Phys. Rev. Lett. 87(8), 084801 (2001).
[Crossref] [PubMed]

2000 (2)

K. Yamada, N. Sei, H. Ohgaki, T. Mikado, S. Sugiyama, and T. Yamazaki, “Lasing towards the VUV in the NIJI-IV FEL,” Nucl. Instrum. Methods Phys. Res A 445, 173 (2000).

L.-H. Yu, M. Babzien, I. Ben-Zvi, L. F. DiMauro, A. Doyuran, W. Graves, E. Johnson, S. Krinsky, R. Malone, I. Pogorelsky, J. Skaritka, G. Rakowsky, L. Solomon, X. J. Wang, M. Woodle, V. Yakimenko, S. G. Biedron, J. N. Galayda, E. Gluskin, J. Jagger, V. Sajaev, and I. Vasserman, “High-gain harmonic-generation free-electron laser,” Science 289(5481), 932–934 (2000).
[Crossref] [PubMed]

1997 (1)

V. N. Litvinenko, B. Burnham, M. Emamian, N. Hower, J. M. J. Madey, P. Morcombe, P. G. O'Shea, S. H. Park, R. Sachtschale, K. D. Straub, G. Swift, P. Wang, Y. Wu, R. S. Canon, C. R. Howell, N. R. Roberson, E. C. Schreiber, M. Spraker, W. Tornow, H. R. Weller, I. V. Pinayev, N. G. Gavrilov, M. G. Fedotov, G. N. Kulipanov, G. Y. Kurkin, S. F. Mikhailov, V. M. Popik, A. N. Skrinsky, N. A. Vinokurov, B. E. Norum, A. Lumpkin, and B. Yang, “Gamma-ray production in a storage ring free-electron laser,” Phys. Rev. Lett. 78(24), 4569–4572 (1997).
[Crossref]

1989 (1)

S. V. Benson and J. M. J. Madey, “Demonstration of harmonic lasing in a free-electron laser,” Phys. Rev. A 39(3), 1579–1581 (1989).
[Crossref] [PubMed]

1986 (1)

E. Jerby and A. Gover, “A kinetic small signal gain analysis of a planar wiggler FEL, operating in the high harmonic (strong wiggler) regime,” Nucl. Instrum. Methods Phys. Res A 250, 192 (1986).

1985 (2)

J. M. Ortega, Y. Lapierre, B. Girard, M. Billardon, P. Elleaume, C. Bazin, M. Bergher, M. Velghe, and Y. Petroff, “Ultraviolet coherent generation from an optical klystron,” IEEE J. Quantum Electron. 21(7), 909–919 (1985).
[Crossref]

P. Elleaume, “Storage ring FEL theory,” Nucl. Instrum. Methods Phys. Res A 237, 28 (1985).

1984 (1)

P. Elleaume, “Macro-temporal structure of storage ring free electron lasers,” J. Phys. (Paris) 45(6), 997–1001 (1984).
[Crossref]

1983 (1)

P. Elleaume, “Optical klystrons,” J. Phys. (Paris) 44(C1), C1-333–C352 (1983).
[Crossref]

1981 (1)

W. B. Colson, “The nonlinear wave equation for higher harmonics in free-electron lasers,” IEEE J. Quantum Electron. 17(8), 1417–1427 (1981).
[Crossref]

Akre, R.

Arthur, J.

Asano, Y.

Ayvazyan, V.

Baboi, N.

Babzien, M.

Bazin, C.

Benson, S. V.

G. R. Neil, S. V. Benson, G. Biallas, J. Gubeli, K. Jordan, S. Myers, and M. D. Shinn, “Second harmonic FEL oscillation,” Phys. Rev. Lett. 87(8), 084801 (2001).
[Crossref] [PubMed]

S. V. Benson and J. M. J. Madey, “Demonstration of harmonic lasing in a free-electron laser,” Phys. Rev. A 39(3), 1579–1581 (1989).
[Crossref] [PubMed]

Ben-Zvi, I.

Bergher, M.

Biallas, G.

G. R. Neil, S. V. Benson, G. Biallas, J. Gubeli, K. Jordan, S. Myers, and M. D. Shinn, “Second harmonic FEL oscillation,” Phys. Rev. Lett. 87(8), 084801 (2001).
[Crossref] [PubMed]

Biedron, S. G.

Billardon, M.

Bionta, R.

Bizen, T.

Bohnet, I.

Bostedt, C.

Bozek, J.

Brachmann, A.

Brinkmann, R.

Bucksbaum, P.

Burnham, B.

Canon, R. S.

Castellano, M.

Castro, P.

Catani, L.

Choroba, S.

Cianchi, A.

Coffee, R.

Colson, W. B.

W. B. Colson, “The nonlinear wave equation for higher harmonics in free-electron lasers,” IEEE J. Quantum Electron. 17(8), 1417–1427 (1981).
[Crossref]

Decker, F.-J.

DiMauro, L. F.

Ding, Y.

Dohlus, M.

Dowell, D.

Doyuran, A.

Duparré, A.

Edstrom, S.

Edwards, H. T.

Elleaume, P.

P. Elleaume, “Storage ring FEL theory,” Nucl. Instrum. Methods Phys. Res A 237, 28 (1985).

P. Elleaume, “Macro-temporal structure of storage ring free electron lasers,” J. Phys. (Paris) 45(6), 997–1001 (1984).
[Crossref]

P. Elleaume, “Optical klystrons,” J. Phys. (Paris) 44(C1), C1-333–C352 (1983).
[Crossref]

Emamian, M.

Emma, P.

Faatz, B.

Fateev, A. A.

Fedotov, M. G.

Feigl, T.

Feldhaus, J.

Fisher, A.

Flöttmann, K.

Frisch, J.

Fukui, T.

Galayda, J.

Galayda, J. N.

Gamp, A.

Garvey, T.

Gavrilov, N. G.

Genz, H.

Gerth, Ch.

Gilevich, S.

Girard, B.

Gluskin, E.

Goto, S.

Gover, A.

E. Jerby and A. Gover, “A kinetic small signal gain analysis of a planar wiggler FEL, operating in the high harmonic (strong wiggler) regime,” Nucl. Instrum. Methods Phys. Res A 250, 192 (1986).

Graves, W.

Gretchko, V.

Grigoryan, B.

Gubeli, J.

G. R. Neil, S. V. Benson, G. Biallas, J. Gubeli, K. Jordan, S. Myers, and M. D. Shinn, “Second harmonic FEL oscillation,” Phys. Rev. Lett. 87(8), 084801 (2001).
[Crossref] [PubMed]

Hahn, U.

Hara, T.

Hastings, J.

Hays, G.

Hering, Ph.

Hessler, C.

Higashiya, A.

Hirono, T.

Honkavaara, K.

Hosoda, N.

Howell, C. R.

Hower, N.

Huang, Z.

Hüning, M.

Inagaki, T.

Inoue, S.

Ischebeck, R.

Ishii, M.

Ishikawa, T.

Iverson, R.

Jablonka, M.

Jagger, J.

Jerby, E.

E. Jerby and A. Gover, “A kinetic small signal gain analysis of a planar wiggler FEL, operating in the high harmonic (strong wiggler) regime,” Nucl. Instrum. Methods Phys. Res A 250, 192 (1986).

Johnson, E.

Jordan, K.

G. R. Neil, S. V. Benson, G. Biallas, J. Gubeli, K. Jordan, S. Myers, and M. D. Shinn, “Second harmonic FEL oscillation,” Phys. Rev. Lett. 87(8), 084801 (2001).
[Crossref] [PubMed]

Kamps, T.

Kim, K. J.

K. J. Kim, Y. Shvyd’ko, and S. Reiche, “A proposal for an X-ray free-electron laser oscillator with an energy-recovery linac,” Phys. Rev. Lett. 100(24), 244802 (2008).
[Crossref] [PubMed]

Kim, Y.

Kimura, H.

Kitamura, H.

Kitamura, M.

Kobayashi, T.

Körfer, M.

Krassilnikov, M.

Krinsky, S.

Krzywinski, J.

Kulipanov, G. N.

Kurkin, G. Y.

Lapierre, Y.

Liepe, M.

Liero, A.

Limberg, T.

Litvinenko, V. N.

Loos, H.

Lumpkin, A.

Luong, M.

Madey, J. M. J.

S. V. Benson and J. M. J. Madey, “Demonstration of harmonic lasing in a free-electron laser,” Phys. Rev. A 39(3), 1579–1581 (1989).
[Crossref] [PubMed]

Maesaka, H.

Magne, C.

Malone, R.

Maréchal, X.

Masuda, T.

Matsui, S.

Matsushita, T.

Menzel, J.

Messerschmidt, M.

Miahnahri, A.

Michelato, P.

Mikado, T.

K. Yamada, N. Sei, H. Ohgaki, T. Mikado, S. Sugiyama, and T. Yamazaki, “Lasing towards the VUV in the NIJI-IV FEL,” Nucl. Instrum. Methods Phys. Res A 445, 173 (2000).

Mikhailov, S. F.

Minty, M.

Moeller, S.

Morcombe, P.

Müller, U.-C.

Myers, S.

G. R. Neil, S. V. Benson, G. Biallas, J. Gubeli, K. Jordan, S. Myers, and M. D. Shinn, “Second harmonic FEL oscillation,” Phys. Rev. Lett. 87(8), 084801 (2001).
[Crossref] [PubMed]

Nagasono, M.

Neil, G. R.

G. R. Neil, S. V. Benson, G. Biallas, J. Gubeli, K. Jordan, S. Myers, and M. D. Shinn, “Second harmonic FEL oscillation,” Phys. Rev. Lett. 87(8), 084801 (2001).
[Crossref] [PubMed]

Nölle, D.

Norum, B. E.

Novokhatski, A.

Nuhn, H.-D.

Ogawa, H.

N. Sei, H. Ogawa, and K. Yamada, “Lasing of middle-infrared free-election lasers using the storage ring NIJI-IV,” Opt. Lett. 36(18), 3645–3647 (2011).
[Crossref] [PubMed]

N. Sei, H. Ogawa, and K. Yamada, “Third harmonic lasing in a storage ring free-electron laser,” J. Phys. Soc. Jpn. 79(9), 093501 (2010).
[Crossref]

N. Sei, H. Ogawa, and K. Yamada, “Lasing of infrared free-election lasers using the storage ring NIJI-IV,” Opt. Lett. 34(12), 1843–1845 (2009).
[Crossref] [PubMed]

Ohashi, H.

Ohata, T.

Ohgaki, H.

K. Yamada, N. Sei, H. Ohgaki, T. Mikado, S. Sugiyama, and T. Yamazaki, “Lasing towards the VUV in the NIJI-IV FEL,” Nucl. Instrum. Methods Phys. Res A 445, 173 (2000).

Ohshima, T.

Onoe, K.

Ortega, J. M.

O'Shea, P. G.

Otake, Y.

Pagani, C.

Park, S. H.

Peters, F.

Petroff, Y.

Pflüger, J.

Pile, D.

D. Pile, “X-rays: First light from SACLA,” Nat. Photonics 5(8), 456–457 (2011).
[Crossref]

Pile, G.

Pinayev, I. V.

Piot, P.

Plucinski, L.

Pogorelsky, I.

Popik, V. M.

Rakowsky, G.

Ratner, D.

Rehlich, K.

Reiche, S.

K. J. Kim, Y. Shvyd’ko, and S. Reiche, “A proposal for an X-ray free-electron laser oscillator with an energy-recovery linac,” Phys. Rev. Lett. 100(24), 244802 (2008).
[Crossref] [PubMed]

Reyzl, I.

Richter, A.

Roberson, N. R.

Rossbach, J.

Rzepiela, J.

Sachtschale, R.

Sajaev, V.

Saldin, E. L.

Sandner, W.

Schlarb, H.

Schmidt, G.

Schmüser, P.

Schneider, J. R.

Schneidmiller, E. A.

Schreiber, E. C.

Schreiber, H.-J.

Schreiber, S.

Schröder, S.

Schultz, D.

Sei, N.

N. Sei, H. Ogawa, and K. Yamada, “Lasing of middle-infrared free-election lasers using the storage ring NIJI-IV,” Opt. Lett. 36(18), 3645–3647 (2011).
[Crossref] [PubMed]

N. Sei, H. Ogawa, and K. Yamada, “Third harmonic lasing in a storage ring free-electron laser,” J. Phys. Soc. Jpn. 79(9), 093501 (2010).
[Crossref]

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Fig. 3 Measured spectrum of the seventh-harmonic FEL oscillation at the electron-beam current of 4.3 mA.

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Fig. 4 Dependence of the average FEL power for the fundamental and higher (third, fifth and seventh) harmonics on the electron-beam current in the single electron-bunch operation.

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Tables (1)

Table 1 Performance of the ETLOK-III for higher-harmonic FEL oscillations at a wavelength of approximately 890 nm. See text for explanation of symbols. Lasing wavelength of FELs can be changed by slightly adjusting g_u and g_d from the values in this table. Values in parentheses of the column of the threshold current express in peak current.

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Equations (7)

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G_{n} = \frac{F_{n} (K_{n}) f_{n}}{F_{1} (K_{1}) f_{1}} n G_{1},

F_{n} = \frac{4 n^{2} K_{n}^{2}}{{(2 + K_{n}^{2})}^{2}} {[J_{\frac{n + 1}{2}} (\frac{n K_{n}^{2}}{4 + 2 K_{n}^{2}}) - J_{\frac{n - 1}{2}} (\frac{n K_{n}^{2}}{4 + 2 K_{n}^{2}})]}^{2},

K_{n}^{} = \sqrt{2 (\frac{2 + K_{1}^{2}}{2} n - 1)} .

f_{n} ≅ f_{γ n} = \exp [- 8 π^{2} n^{2} {(N_{u} + N_{d})}^{2} {(\frac{σ_{γ 0}}{γ})}^{2}],

P_{n} \propto η_{c} [{(\frac{σ_{γ}}{γ})}^{2} - {(\frac{σ_{γ 0}}{γ})}^{2}] P_{S},

\frac{G_{n}}{l_{c}} = \frac{(\frac{σ_{γ}}{γ})}{(\frac{σ_{γ 0}}{γ})} \frac{f_{γ n} (\frac{σ_{γ 0}}{γ})}{f_{γ n} (\frac{σ_{γ}}{γ})} .

P_{n} \propto η_{c} \frac{ln (G_{n} / l_{c})}{n (N_{u} + N_{d})} P_{S} .

	g_u [mm]	g_d [mm]	K value	n(N_u+N_d)	I_th (measurement) [mA (A)]
Fundamental	122.5	140	2.13	195	0.55 (0.24)
Third harmonic	86.5	123	4.19	269	0.90 (0.40)
Fifth harmonic	72.0	109	5.52	357	1.5 (0.66)
Seventh harmonic	62.7	100	6.62	434	3.8 (1.67)