volume | PIER Journals

Abstract

We construct an analytical model for the description of emission of undulator radiation (UR) harmonics with account for several sources of line broadening, including the effect of a constant magnetic constituent. We compare it with that of the beam energy spread, emittance and focusing components. The analytical expressions obtained for the UR intensity and spectrum allow for profound analysis of homogeneous and inhomogeneous losses in their explicit form. We analyse the contributions to the fundamental frequency as well as to higher harmonics in long undulators. We study a possibility to compensate for the off-axis effects in undulators by a properly imposed constant magnetic field and obtain an expression for the intensity of such compensating effect. The results obtained are discussed in the context of their possible applications to free electron lasers (FEL). Recommendations for improvement of an UR harmonic line quality, profitable for FEL, are also proposed.

1. Ivanenko, D. D. and I. A. Pomeranchuk, "On the maximal energy, obtainable in a betatron," Phys. Rev., Vol. 65, 343, 1944.
doi:10.1103/PhysRev.65.343 Google Scholar

2. Elder, F. R., A. M. Gurewitsch, R. V. Langmuir, and H. C. Pollock, "Radiation from electrons in a synchrotron," Phys. Rev., Vol. 71, 829, 1947.
doi:10.1103/PhysRev.71.829.5 Google Scholar

3. Ivanenko, D. D. and A. A. Sokolov, "On the theory of the `luminous' electron," Doklady Akademii Nauk SSSR, Vol. 59, 1551, 1948. Google Scholar

4. Schwinger, J., "On the classical radiation of accelerated electrons," Phys. Rev., Vol. 75, 1912, 1949.
doi:10.1103/PhysRev.75.1912 Google Scholar

5. Schott, G. A., Electromagnetic Radiation and the Mechanical Reactions Arising from It, Cambridge University Press, New York, 1912.

6. Milton, , K. A. and J. Schwinger, Electromagnetic Radiation: Variational Methods, Wave-guides and Accelerators, 360p, Springer, 2006.

7. Schwinger, J., W.-Y. Tsai, and T. Erber, "On the classical radiation of accelerated electrons," Annals of Physics, Vol. 96, 303, 1976.
doi:10.1016/0003-4916(76)90194-9 Google Scholar

8. Sokolov, A. A. and I. M. Ternov, Synchrotron Radiation, Academie Verlag, Berlin, 1968.

9. Ginzburg, V. L., "On the radiation of microradiowaves and their absorbtion in the air," Isvestia Akademii Nauk SSSR, Vol. 11, No. 2, 165, Fizika, 1947. Google Scholar

10. Motz, H., W. Thon, and . N. J. Whitehurst, "Experiments on radiation by fast electron beams," Appl. Phys., Vol. 24, 826, 1953.
doi:10.1063/1.1721389 Google Scholar

11. Artcimovich, A. L. and I. J. Pomeranchuk, "Radiation from fast electrons in a magnetic field," JETP, Vol. 16, 1, 1946. Google Scholar

12. Ternov, I. M., V. V. Mikhailin, and V. R. Khalilov, Synchrotron Radiation and Its Applications, Moscow, 1980.

13. Bordovitsyn, V. A., "Synchrotron Radiation Theory and Its Development: In the Memory of I. M. Ternov," Series on Synchrotron Radiation Technique and Applications, Vol. 5, World Scientific Publishing, Singapore, 1999.
doi:10.1142/9789812816993_0001 Google Scholar

14. Sokolov, A. A., D. V. Gal'tsov, and V. C. Zhukovsky, "Radiation from electrons, moving along spiral orbits with relativistic longitudinal velocity," Zh. Tekhn. Fiz., Vol. 43, 682, 1973 (in Russian). Google Scholar

15. Koch, E. E., Handbook of Synchrotron Radiation, North Holland, Amsterdam, 1983.

16. Tripathi, S. and G. Mishra, "Three frequency undulator radiation and free electron laser gain," Rom. Journ. Phys., Vol. 56, No. 3-4, 411, 2011. Google Scholar

17. Alferov, D. F., U. A. Bashmakov, and P. A. Cherenkov, "Radiation from relativistic electrons in a magnetic undulator," Uspehi Fis. Nauk, Vol. 157, No. 3, 389, 1989.
doi:10.3367/UFNr.0157.198903b.0389 Google Scholar

18. Iracane, D. and P. Bamas, "Two-frequency wiggler for better control of free-electronlaser dynamics," Phys. Rev. Lett., Vol. 67, 3086, 1991.
doi:10.1103/PhysRevLett.67.3086 Google Scholar

19. Feldhaus, J. and B. Sonntag, Strong Field Laser Physics, Vol. 134, 91, Springer Series in Optical Sciences, 2009.
doi:10.1007/978-0-387-34755-4_5

20. Zholents, A. A., "Attosecond X-ray pulses from free-electron lasers," Laser Physics, Vol. 15, No. 6, 855, 2005. Google Scholar

21. Zhukovsky, K. V. and V. V. Mikhailin, "Two-frequency undulator and harmonic generation by an ultrarelativistic electron," Moscow University Physics Bulletin c/c of Vestnik-Moscovskii Universitet Fizika I Astronomiia, Vol. 60, No. 2, 50, 2005. Google Scholar

22. Dattoli, G., V. Mikhailin, P.-L. Ottaviani, and K. Zhukovsky, "Two-frequency undulator and harmonic generation by an ultrarelativistic electron," J. Appl. Phys., Vol. 100, 084507, 2006.
doi:10.1063/1.2357841 Google Scholar

23. Zhukovsky, K., "Undulator radiation in multiple magnetic fields," Synchrotron: Design, Properties and Applications, 39, Nova Science Publishers, Inc., USA, 2012. Google Scholar

24. Reiss, H. R., "Effect of an intense electromagnetic field on a weakly bound system," Phys. Rev., Vol. A22, 1786, 1980. Google Scholar

25. Walker, R. P., "Interference effects in undulator and wiggler radiation sources," Nucl. Instrum. Methods, Vol. A335, No. 328, 1993. Google Scholar

26. Onuki, H. and P. Elleaume, Undulators, Wigglers and Their Applications, Taylor & Francis, New York, 2003.
doi:10.4324/9780203218235

27. Dattoli, G., V. V. Mikhailin, and K. Zhukovsky, "Undulator radiation in a periodic magnetic fieldwith a constant component," Journal of Applied Physics, Vol. 104, 124507, 2008.
doi:10.1063/1.3039094 Google Scholar

28. Dattoli, G., V. V. Mikhailin, and K. V. Zhukovsky, "In°uence of a constant magnetic field on the radiation of a planar undulator," Moscow University Physics Bulletin, Vol. 64, No. 5, 507, 2009.
doi:10.3103/S0027134909050087 Google Scholar

29. Landau, L. D. and E. M. Lifshits, The Classical Theory of Fields, 4th Ed., Pergamon, New York, 1975.

30. Jackson, J. D., Classical Electrodynamics, 2rd Ed., Wiley, New York, 1975.

31. Mikhailin, V. V., K. V. Zhukovskii, and A. I. Kudyukova, "On the radiation of a planar undulator with constant magnetic field on its axis taken into account," J. Surf. Invest.: X-Ray, Synchrotron Neutron Tech., Vol. 8, No. 3, 422, 2014. Google Scholar

32. Dattoli, G., Lectures on Free Electron Lasers, World Scientific, 1993.

33. Korchuganov, V. N., N. Yu. Sveshnikov, N. V. Smolyakov, and S. I. Tomin, "Special-purpose radiation sources based on the Siberia-2 storage ring," J. Surf. Invest.: X-Ray, Synchrotron Neutron Tech., Vol. 4, No. 6, 891, 2010.
doi:10.1134/S1027451010060030 Google Scholar

Professor Konstantin V. Zhukovsky