Analytical account for off-axis effects in X-ray radiation of free electron lasers
We give analytical description of generation of harmonics of the undulator radiation (UR) with account for the finite electron beam size, emittance, off-axis beam deviation and electron energy spread, as well as for the constant magnetic components and field harmonics effects. We give exact analytical expressions for the generalized Bessel and Airy functions, which describe the spectrum line shape and intensities in the two-frequency bi-harmonic undulator with account for the above factors. The obtained analytical formulae distinguish contributions of each field component and every undulator and beam parameter on the harmonic radiation in free electron lasers (FEL). The effect of the field on the harmonic radiation is analyzed with account for the beam finite size and its off-axis deviation. The phenomenological model is employed for the FEL modeling; with its help we study the harmonic generation, including even ones, in the experiments LCLS and LEUTL. We demonstrate analytically that strong second FEL harmonic in X-ray FEL at the wavelengths λ = 0.75nm in the LCLS experiment is caused by the deviation of the electron trajectories off the axis in 15 μm on the gain length 1.6 m, which is comparable with the beam size; the strong second FEL harmonic in the LEUTL experiment at the wavelength λ = 192nm can be attributed to interaction of the electrons in wide, ~ 0.2 mm, beam with the photon radiation at the gain length 0.87 m. The modeling results fully agree with the measurements. The developed formalism allows the analysis of projected and built FELs and their radiation, helps minimizing losses and correcting magnetic fields; it also shows physical background and reasons for each harmonic radiated power in the FEL.
Keywords
undulator radiation,
harmonic generation,
multi-period undulator,
free-electron laserAuthors
| Zhukovsky K.V. | Moscow State University Lomonosov | zhukovsk@physics.msu.ru |
Всего: 1
References
Гинзбург В.Л. // Изв. АН СССР, сер. физич. - 1947. - Т. 11. - С. 1651.
Motz H., Thon W., and Whitehurst R.N.J. // Appl. Phys. - 1953. - V. 24. - P. 826.
McNeil B. W. J. and Thompson N. R. // Nature Photonics. - 2010. - V. 4. - P. 814.
Pellegrini C., Marinelli A., and Reiche S. // Rev. Mod. Phys. - 2016. - V. 88. - P. 015006.
Schmüser P., Dohlus M., Rossbach J., and Behrens C. Free-Electron Lasers in the Ultraviolet and X-Ray Regime. Springer Tracts in Modern Physics, 258, Cham (ZG). - Springer International Publishing, 2014.
Huang Z. and Kim K.J. // Phys. Rev. ST-AB. - 2007. - V. 10. - P. 034801.
Margaritondo G. and Ribic P.R. // J. Synchrotron Rad. - 2011. - V. 18. - P. 101.
Saldin E.L., Schneidmiller E.A., and Yurkov M.V. The Physics of Free Electron Lasers. - Berlin; Heidelberg: Springer Verlag, 2000.
Bonifacio R., Pellegrini C., and Narducci L. // Opt. Commun. - 1984. - V. 50. - P. 373.
Margaritondo G. // Rivista del Nuovo Cimento. - 2017. - V. 40. - No. 9. - P. 411.
Багров В.Г., Бисноватый-Коган Г.С., Бордовицын В.А. и др. Теория излучения релятивистских частиц. - М.: Физматлит, 2002. - 575 с.
Тернов И.М., Михайлин В.В., Халилов В.Р. Синхротронное излучение и его применения. - М.: Изд-во МГУ, 1980.
Margaritondo G. // Synchrotron Radiation / eds. S. Mobilio, F. Boscherini, and C. Meneghini. - Berlin; Heidelberg: Springer, 2015.
Lee K., Mun J., Park S. Hee, et al. // Nucl. Instrum. Methods Phys. Res. A. - 2015. - V. 776. - P. 27.
Zhukovsky K. and Kalitenko A. // J. Synchrotron Rad. - 2019. - V. 26. - P. 605.
Zhukovsky K. // J. Optics. - 2018. - V. 20. - No. 9. - P. 095003.
Zhukovsky K. // Results Phys. - 2019. - V. 13. - P. 102248.
Zhukovsky K.V. // J. Synchrotron Rad. - 2019. - V. 26. - P. 1481.
Жуковский К.В. // Изв. вузов. Физика. - 2019. - T. 62. - № 6. - С. 109.
Alexeev V.I. and Bessonov E.G. // Nucl. Instrum. Methods. A. - 1991. - V. 308. - P. 140.
Emma P., Akre R., Arthur J., et al. // Nature Photonics. - 2010. - V. 4. - P. 641.
Ratner D., Brachmann A., Decker F.J., et al. // Phys. Rev. ST-AB. - 2011. - V. 14. - P. 060701.
Milton S.V., Gluskin E., Arnold N.D., et al. // Science. - 2001. - V. 292. - P. 2037.
Henderson J.R., Campbell L.T., Freund H.P., and McNeil B.W.J. // New J. Phys. - 2016. - V. 18. - P. 062003.
Freund H.P., van der Slot P.J.M., Grimminck D.L.A.G., et al. // New J. Phys. - 2017. - V. 19. - P. 023020.
Freund H.P. and van der Slot P.J.M. // New J. Phys. - 2018. - V. 20. - P. 073017.
Heung-Sik Kang et al. // Nature Photonics. - 2017. - V. 11. - P. 708.
Zhukovsky K. and Kalitenko A. // J. Synchrotron Rad. - 2019. - V. 26. - P. 159.
Жуковский К.В., Калитенко А.М. // Изв. вузов. Физика. - 2019. - T. 62. - № 2. - P. 153.
Zhukovsky K. // J. Electromagn. Waves Appl. - 2014. - V. 28. - No. 15. - P. 1869.
Zhukovsky K.V. // J. Electromagn. Waves Appl. - 2015. - V. 29. - No. 1. - P. 132.
Dattoli G., Mikhailin V.V., and Zhukovsky K. // J. Appl. Phys. - 2008. - V. 104. - P. 124507.
Dattoli G., Mikhailin V.V., and Zhukovsky K.V. // Mosc. Univ. Phys. Bull. - 2009. - V. 64. - No. 5. - P. 507.
Zhukovsky K.V. // Mosc. Univ. Phys. Bull. - 2018. - V. 73. - No. 4. - P. 364.
Zhukovsky K. // Opt. Commun. - 2018. - V. 418. - P. 57.
Zhukovsky K. // J. Appl. Phys. - 2017. - V. 122. - P. 233103.
Zhukovsky К. // J. Phys. D. - 2017. - V. 50. - P. 505601.
Zhukovsky K. and Potapov I. // Laser Part. Beams. - 2017. - V. 35. - P. 326.
Zhukovsky K.V. // J. Math. Anal. Appl. - 2017. - V. 446. - P. 628.
Алферов Д.Ф., Башмаков Ю.А., Бессонов Е.Г. // ЖТФ. - 1973. - T. 43. - Вып. 10. - С. 2126.
Алферов Д.Ф., Башмаков Ю.А., Черенков П.А. // УФН. - 1989. - T. 157. - Вып. 3. - С. 389.
Багров В.Г., Тернов И.М., Холомай Б.В. Излучение релятивистских электронов в продольном периодическом электрическом поле кристалла. - Томск: ТФ СО АН СССР, 1987. - 13 с.
Винокуров Н.А., Левичев Е.Б. // УФН. - 2015. - Т. 185. - С. 917.
Бессонов Е.Г. К теории источников ондуляторного излучения. - Препринт ФИАН № 18, 1982.
Prakash B., Huse V., Gehlot M., et al. // Optik. - 2016. - V. 127. - P. 1639.
Zhukovsky K.V. // Mosc. Univ. Phys. Bull. - 2019. - V. 74. - No. 5. - P. 480.
