Abstract
Undulator radiation (UR) was studied taking the broadening of spectral lines via homogeneous and nonhomogeneous contributions into account. Exact analytical expressions for the UR spectrum and intensity in the case of relativistic high-energy electrons were obtained. Analytical expressions that characterize the interrelation between the constant components of the magnetic field in undulators and the electron beam divergence within them were derived. These expressions suggest that this divergence may be partially compensated. The radiation of a double-frequency undulator and the higher harmonic radiation in an ordinary planar undulator were investigated taking the broadening of spectral lines into account. We discuss examples of UR in actual devices and demonstrate that the developed method and the results may be used in the calculation of induced UR.
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References
V. L. Ginzburg, Izv. Akad. Nauk SSSR, Ser. Fiz. 11, 1651 (1946).
H. Motz, W. Thon, and R. N. J. Whitehurst, Appl. Phys. 24, 826 (1953).
A. A. Sokolov and I. M. Ternov, Relativistic Electron (Nauka, Moscow, 1983) [in Russian].
J. Feldhaus and B. Sonntag, in Strong Field Laser Physics, Ed. by T. Brabec (Springer, 2009), p. 91.
A. A. Zholents, Laser Phys. 115, 855 (2005).
E. N. Rogozin and I. I. Sobel’man, Phys.-Usp. 47, 195 (2004).
V. V. Mikhailin, Synchrotron Radiation in Spectroscopy (Inst. Yad. Fiz., Moscow, 2011) [in Russian].
I. M. Ternov, V. V. Mikhailin, and V. R. Khalilov, Synchrotron Radiation and Its Applications (Mosk. Gos. Univ., Moscow, 1980) [in Russian].
A. L. Artsimovich and I. J. Pomeranchuk, J. Phys. USSR 9, 267 (1945).
D. F. Alferov, Yu. A. Bashmakov, and E. G. Bessonov, Sov. Phys. Tech. Phys. 17, 1540 (1973).
Synchrotron Radiation Theory and Its Development: In the Memory of I. Ternov, Ed. by V. A. Bordovitsyn (World Scientific, Singapore, 1999).
A. A. Sokolov, A. V. Borisov, and V. Ch. Zhukovskii, Sov. Phys. J. 18, 1400 (1975).
A. A. Sokolov, A. V. Borisov, D. V. Gal’tsov, and V. Ch. Zhukovskii, Sov. Phys. J. 17, 1835 (1974).
V. G. Bagrov, G. S. Bisnovaty–Kogan, V. A. Bordovitsyn, A.V. Borisov, O. F. Dorofeev, V. Ya. Epp, Yu. L. Pivovarov, O. V. Shorokhov, and V. Ch. Zhukovsky, Radiation Theory of Relativistic Particles, Ed. by V. A. Bordovitsyn (Fizmatlit, Moscow, 2002) [In Russian].
A. V. Borisov, V. A. Vshivtsev, and A. I. Ternov, Moscow Univ. Phys. Bull. 53, 8 (1998).
A. V. Borisov and I. A. Kelekhsaeva, Vestn. Mosk. Univ., Fiz., Astron. 28, 20 (1987).
A. V. Borisov and K. V. Zhukovsky, Phys. At. Nucl. 58, 1218 (1995).
A. V. Borisov and V. Yu. Grishina, J. Exp. Theor. Phys. 79, 837 (1994).
E. G. Bessonov, Proc. SPIE 6634, 66340X (2007).
K. V. Zhukovsky and V. V. Mikhailin, Moscow Univ. Phys. Bull. 60, 50 (2005).
G. Dattoli, V. V. Mikhailin, P. L. Ottaviani, and K. Zhukovsky, J. Appl. Phys. 100, 084507 (2006).
K. Zhukovsky, in Synchrotron: Design, Properties and Applications, Ed. by Dao Ming Chua and Huang Fu Toh (Nova Science, USA, 2012), p. 39.
G. Dattoli, N. S. Mirian, E. DiPalma, and V. Petrillo, Phys. Rev. Spec. Top. Accel. Beams 17, 050702 (2014).
D. F. Alferov, U. A. Bashmakov, and P. A. Cherenkov, Phys.-Usp. 32, 200 (1989).
R. P. Walker, Nucl. Instrum. Methods Phys. Res., Sect. A 335, 328 (1993).
H. Onuki and P. Elleaume, Undulators, Wigglers and their Applications (Taylor and Francis, New York, 2003).
H. R. Reiss, Phys. Rev. A 22, 1786 (1980).
K. V. Zhukovsky, Prog. Electromagn. Res. B 59, 245 (2014).
K. V. Zhukovsky, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 8, 1068 (2014).
K. Zhukovsky, J. Electromagn. Waves Appl. 28, 1869 (2014).
D. Dattoli, V. V. Mikhailin, and K. V. Zhukovsky, Moscow Univ. Phys. Bull. 64, 507 (2009).
V. V. Mikhailin, K. V. Zhukovsky, and A. I. Kudiukova, J. Surf. Invest.: X-ray, Synchrotron Neutron Tech. 8, 422 (2014).
G. Dattoli, V. V. Mikhailin, and K. V. Zhukovsky, J. Appl. Phys. 104, 124507 (2008).
G. Dattoli, Lectures on the Free Electron Laser Theory and Related Topics (World Scientific, Singapore, 1993).
K. V. Zhukovsky, J. Electromagn. Waves Appl. 29, 132 (2015).
L. D. Landau and E. M. Lifshits, The Classical Theory of Fields, 4th ed. (Pergamon, New York, 1975).
J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).
W. B. Colson, C. Pellegrini, and A. Renieri, Laser Handbook (North Holland, Amsterdam, 1993), Vol. VI.
G. Dattoli, P.-L. Ottaviani, and S. Pagnutti, Booklet for FEL Design: A Collection of Practical Formulae, (ENEA, Rome, 2007).
K. V. Zhukovsky, Moscow Univ. Phys. Bull. 70, 93 (2015).
K. Zhukovsky, Sci. World J. 2014, 454865 (2014).
G. Mishra, M. Gehlot, and J.-K. Hussain, Nucl. Instrum. Methods Phys. Res., Sect. A 603, 495 (2009).
J. Hussain, V. Gupta, and G. Mishra, Nucl. Instrum. Methods Phys. Res., Sect. A 608, 344 (2009).
N. S. Mirian, G. Dattoli, E. di Palma, and V. Petrillo, Nucl. Instrum. Methods Phys. Res., Sect. A 767, 227 (2014).
H. Jeevakhan and G. Mishra, Nucl. Instrum. Methods Phys. Res., Sect. A 656, 101 (2011)
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Original Russian Text © K.V. Zhukovsky, 2015, published in Vestnik Moskovskogo Universiteta. Fizika, 2015, No. 4, pp. 18–25.
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Zhukovsky, K.V. Harmonic radiation in a double-frequency undulator with account for broadening. Moscow Univ. Phys. 70, 232–239 (2015). https://doi.org/10.3103/S0027134915040177
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DOI: https://doi.org/10.3103/S0027134915040177