Abstract
The generation of undulator X-ray radiation harmonics in free-electron lasers (FELs), which has been observed in different experiments, has been given an analytical explanation. Expressions for spectrum lines and radiation intensity are written in explicit form in terms of generalized Bessel and Airy functions with regard to the spreads of electron energy, electron beam size, emittance, spectrum line splitting, and magnetic field constant components. The theory proposed here adequately explains the spectrum and intensity of radiation harmonics in all experiments with a SACLA FEL, a Linac coherent light source (LCLS) based on an FEL, PAL-XFEL, SwissFEL, and other equipment conducted under different conditions in a wide wavelength range, including hard X-ray radiation.
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REFERENCES
B. W. J. McNeil and N. R. Thompson, Nat. Photonics 4, 814 (2010).
C. Pellegrini, A. Marinelli, and S. Reiche, Rev. Mod. Phys. 88, 015006 (2016).
G. Margaritondo, Riv. Nuovo Cimento 40 (9), 411 (2017).
V. G. Bagrov, G. S. Bisnovaty-Kogan, V. A. Bordovitsyn, A. V. Borisov, O. F. Dorofeev, V. Ya. Epp, Y. L. Pivovarov, O. V. Shorokhov, and V. C. Zhukovsky, Synchrotron Radiation Theory and Its Development, Ed. by V. A. Bordovitsyn (Word Sci., Singapore, 1999), p. 447.
K. Zhukovsky, J. Phys. D: Appl. Phys. 50 (50), 505601 (2017). https://doi.org/10.1088/1361-6463/aa97b1
K. Zhukovsky, J. Opt. 20 (9), 095003 (2018).
K. Zhukovsky, Results Phys. 13, 102248 (2019).
K. Zhukovsky and A. Kalitenko, J. Synchrotron Radiat. 26, 159 (2019).
K. Zhukovsky, J. Synchrotron Radiat. 26, 1481 (2019).
K. V. Zhukovsky and A. M. Kalitenko, Russ. Phys. J. 62 (2), 354 (2019). https://doi.org/10.1007/s11182-019-01719-7
K. V. Zhukovsky, Russ. Phys. J. 62 (6), 1043 (2019). https://doi.org/10.1007/s11182-019-01812-x
K. V. Zhukovskii, Tech. Phys. 64 (3), 389 (2019). https://doi.org/10.1134/S1063784219030289
K. V. Zhukovskii and A. M. Kalitenko, Tech. Phys. 65 (8), 1285 (2020). https://doi.org/10.1134/S1063784220080241
K. V. Zhukovsky, Moscow Univ. Phys. Bull. 74 (5), 480 (2019). https://doi.org/10.3103/S0027134919050187
N. Nakao, M. Kokubo, K. Imasaki, M. Fujita, K. Ohkubo, A. Moon, P. K. Roy, H. Tanaka, N. Ohigashi, Y. Sunawaki, K. Mima, S. Nakai, and C. Yamanaka, Nucl. Instrum. Methods Phys. Res., Sect. A 407, 374 (1998).
G. Sharma, G. Mishra, and M. Gehlot, J. Instrum. 9, T01002 (2014).
F. Bazouband and B. Maraghechi, J. Plasma Phys. 81 (3), 905810305 (2015).
M. Asakawa, K. Mima, S. Nakai, K. Masaki, and C. Yamanaka, Nucl. Instrum. Methods Phys. Res., Sect. A 318, 538 (1992).
M. Asakawa, N. Inoue, K. Mima, S. Nakai, K. Imasaki, M. Fujita, J. Chen, C. Yamanaka, N. Nakao, T. Agari, T. Asakuma, A. Moon, N. Ohigashi, T. Minamiguchi, and Y. Tsunawaki, Nucl. Instrum. Methods Phys. Res., Sect. A 358, 399 (1995).
M. Asakawa, N. Nakao, H. Ohkubob, T. Ishida, T. Watanabec, E. Yasuda, Y. Okudad, M. Fujita, J. Chen, A. Moon, P. K. Royb, S. Kuruma, K. Imasaki, K. Mimah, N. Ohigashi, et al., Nucl. Instrum. Methods Phys. Res., Sect. A 375, 416 (1996).
D. Iracane and P. Bamas, Phys. Rev. Lett. 67, 3086 (1991).
K. Lee, J. Mun, S. H. Park, K.-H. Jang, Y. U. Jeong, and N. A. Vinokurov, Nucl. Instrum. Methods Phys. Res., Sect. A 776, 27 (2015).
K. Halbach, J. Phys. Colloq. 44, C1 (1983).
K. Halbach, J. Appl. Phys. 57 (8), 3605 (1985).
B. Prakash, V. Huse, M. Gehlot, G. Mishra, and S. Mishra, Optik 127, 1639 (2016).
V. Huse, G. Sharma, S. Mishra, and G. Mishra, Chin. Phys. Lett. 31 (3), 034101 (2014).
H. Jeevakhan and G. Mishra, Nucl. Instrum. Methods Phys. Res., Sect. A 656, 101 (2011).
V. Gupta and G. Mishra, Nucl. Instrum. Methods Phys. Res., Sect. A 574, 150 (2007).
V. Gupta and G. Mishra, Nucl. Instrum. Methods Phys. Res., Sect. A 556 (1), 350 (2006).
Y. Yang and W. Ding, Phys. Plasmas 5 (3), 782 (1998).
G. Mishra and A. Sharma, Nucl. Instrum. Methods Phys. Res., Sect. A 976, 164287 (2020).
Th. Schmidt, A. Anghel, P. Böhler, M. Brügger, M. Calvi, S. Danner, P. Huber, A. Keller, and M. Locher, “Magnetic design of an APPLE III undulator for SwissFEL,” in Proc. FEL2014 (Basel, Switzerland, 2014), p. 116 (MOP043). http://accelconf.web.cern.ch/AccelConf/FEL2014/ papers/mop043.pdf.
A. B. Temnykh, Phys. Rev. Spec. Top.–Accel. Beams 11, 120702 (2008).
H.-D. Nuhn, S. D. Anderson, R. N. Coffee, Y. Ding, Z. Huang, M. Ilchen, Yu. I. Levashov, A. A. Lutman, J. P. MacArthur, A. Marinelli, S. P. Moeller, F. Peters, Z.R. Wolf, J. Buck, G. Hartmann, et al., “Commissioning of the Delta polarizing undulator at LCLS,” in Proc. FEL2015 (Daejeon, Korea, 2015), p. 757 (WED01). https://accelconf.web.cern.ch/FEL2015/papers/wed01.pdf
J. R. Henderson, L. T. Campbell, H. P. Freund, and B.W.J. McNeil, New J. Phys. 18, 062003 (2016).
K. Zhukovsky, J. Electromagn. Waves Appl. 28 (15), 1869 (2014).
K. V. Zhukovsky, Phys.-Usp. (2021) (in press). https://doi.org/10.3367/UFNe.2020.06.038803
K. Zhukovsky, Opt. Laser Technol. 131, 106311 (2020).
H. Jeevakhan and G. Mishra, Opt. Commun. 335, 126 (2015).
K. V. Zhukovsky, J. Math. Anal. Appl. 446, 628 (2017).
H.-S. Kang, C.-K. Min, H. Heo, C. Kim, H. Yang, G. Kim, I. Nam, S. Y. Baek, H.-J. Choi, G. Mun, B. R. Park, Y. J. Suh, D. C. Shin, J. Hu, J. Hong, et al., Nat. Photonics 11, 708 (2017).
P. Emma, “First lasing of the LCLS X-ray FEL at 1.5 Å,” in Proc. PAC09 (Vancouver, BC, Canada, 2009), p. TH3PBI01.
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, et al., Nat. Photonics 4, 641 (2010).
N. A. Vinokurov and E. B. Levichev, Phys.-Usp. 58 (9), 850 (2015). https://doi.org/10.3367/UFNe.0185.201509b.0917
G. Geloni, E. Saldin, E. Schneidmiller, and M. Yukov, Opt. Commun. 271, 207 (2007).
D. F. Alferov, Yu. A. Bashmakov, and P.A. Cherenkov, Sov. Phys.-Usp. 32, 200 (1989). https://doi.org/10.1070/PU1989v032n03ABEH002688
V. G. Bagrov, G. S. Bisnovatyi-Kogan, and V. A. Bordovitsyn, Theory of Radiation of Relativistic Particles (Fizmatlit, Moscow, 2002) [in Russian].
V. G. Bagrov, I. M. Ternov, and B. V. Kholomai, Radiation of Relativistic Electrons in a Longitudinal Periodic Electric Field of a Crystal (TFSO Akad. Nauk SSSR, Tomsk, 1987) [in Russian].
D. F. Alferov, Yu. A. Bashmakov, and E. G. Bessonov, Sov. Phys.-Tech. Phys. 18, 1336 (1973).
E. G. Bessonov, Preprint FIAN No. 18 (Lebedev Phys. Inst. Acad. Sci. USSR, Moscow, 1982).
D. Ratner, A. Brachmann, F. J. Decker, Y. Ding, D. Dowell, P. Emma, A. Fisher, J. Frisch, S. Gilevich, Z. Huang, P. Hering, R. Iverson, J. Krzywinski, H. Loos, M. Messerschmidt, et al., Phys. Rev. Spec. Top.–Accel. Beams 14, 060701 (2011).
S. Owada, K. Togawa, T. Inagaki, T. Hara, T. Tanaka, Y. Joti, T. Koyama, K. Nakajima, H. Ohashi, Y. Senba, T. Togashi, K. Tono, M. Yamaga, H. Yumoto, M. Yabashi, et al., J. Synchrotron Radiat. 25, 282 (2018).
I. Inoue, Nat. Photonics 13, 319 (2019).
http://xfel.riken.jp/eng/users/bml02-11.html
H. Ego, “RF system of the SPring-8 upgrade project,” in Proc. IPAC2016 (Busan, Korea, 2016), MOPMW009.
K. Tono, T. Hara, M. Yabashi, and H. Tanaka. J. Synchrotron Radiat. 26, 595 (2019).
T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano1, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa, S. Goto, H. Hanaki, T. Hara, T. Hasegawa, T. Hatsui, et al., Nat. Photonics 6, 540 (2012).
K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Katayama, K. Ogawa, H. Ohashi, H. Kimura, S. Takahashi, K. Takeshita, H. Tomizawa, S. Goto, T. Ishikawa, and M. Yabashi, New J. Phys. 15, 083035 (2013).
C. J. Milne, T. Schietinger, M. Aiba, A. Alarcon, J. Alex, A. Anghel, V. Arsov, C. Beard, P. Beaud, S. Bettoni, M. Bopp, H. Brands, M. Brönnimann, I. Brunnenkant, M. Calvi, et al., Appl. Sci. 7, 720 (2017).
R. Abela, P. Beaud, J. A. van Bokhoven, M. Chergui, T. Feurer, J. Haase, G. Ingold, S. L. Johnson, G. Knopp, H. Lemke, C. J. Milne, B. Pedrini, P. Radi, G. Schertler, J. Standfuss, et al., Struct. Dyn. 4, 061602 (2017).
P. Juranić, J. Rehanek, C. A. Arrell, C. Pradervand, A. Cassar, M. Calvi, R. Ischebeck, C. Erny, P. Heimgartner, I. Gorgisyan, V. Thominet, K. Tiedtke, A. Sorokin, R. Follath, M. Makita, et al., J. Synchrotron Radiat. 26, 906 (2019).
R. Abela, A. Alarcon, J. Alex, C. Arrell, V. Arsov, S. Bettoni, M. Bopp, C. Bostedt, H.-H. Braun, M. Calvi, T. Celcer, P. Craievich, A. Dax, P. Dijkstal, S. Dordevic, et al., J. Synchrotron Radiat. 26, 1073 (2019).
S. V. Milton1, E. Gluskin, N. D. Arnold, C. Benson, W. Berg, S. G. Biedron, M. Borland, Y.-C. Chae, R. J. Dejus, P. K. Den Hartog, B. Deriy, M. Erdmann, Y. I. Eidelman, M. W. Hahne, Z. Huang, et al., Science 292 (5524) 2037 (2001).
S. G. Biedron, R. J. Dejus, Z. Huang, S. V. Milton, V. Sajaev, W. Berg, M. Borland, P. K. Den Hartog, M. Erdmann, W. M. Fawley, H. P. Freund, E. Gluskin, K. J. Kim, J. W. Lewellen, Y. Li, et al., Nucl. Instrum. Methods Phys. Res., Sect. A 483, 94 (2002).
T. Tschentscher, C. Bressler, J. Grünert, A. Madsen, A. P. Mancuso, M. Meyer, A. Scherz, H. Sinn, and U. Zastrau, Appl. Sci. 7 (6), 592 (2017). https://doi.org/10.3390/app7060592
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Zhukovskii, K.V. Harmonics Generation in Experiments with Free-Electron Lasers in the X-Ray Wavelength Range: a Theoretical Analysis. Tech. Phys. 66, 481–490 (2021). https://doi.org/10.1134/S1063784221030245
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DOI: https://doi.org/10.1134/S1063784221030245