Abstract

Synchrotron radiation has been used as a source for spectroscopic experiments in many countries. In this paper, the statistical properties of a light pulse emitted by an electron pulse in a storage ring or a synchrotron are studied in a classical formalism. The field is shown to be gaussian for every wavelength. The coherence time of the filtered synchrotron radiation is calculated.

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  1. R. P. Godwin, Springer Tracts Mod. Phys. 51, 1 (1969); K. Codling, Rep. Prog. Phys. 36, 541 (1973).
  2. Proceedings of the International Symposium on Synchrotron Radiation Uses, edited by I. Munro and G. Marr (Publ. Daresbury Nuclear Phys. Lab., Daresbury, 1973), Rapport 26.
  3. R. J. Glauber, in Quantum Optics and Electronics edited by C. de Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965); L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).
  4. M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), Ch. X. See also the first of Ref. 3, p. 69.
  5. For simplification, this function is assumed to be scalar and not vectorial. This can be understood by supposing that one polarization only is considered.
  6. By chaotic field, we mean a stationary gaussian field. See, for instance, B. Picinbono and M. Rousseau, Phys. Rev. A 1, 635 (1970).
  7. A. A. Sokolov and I. M. Ternov, Synchrotron Radiation (Pergamon, New York, 1968), and references therein.
  8. J. Schwinger, Phys. Rev. 75, 1912 (1949); Phys. Rev. D 7, 1696 (1973).
  9. R. J. Glauber, Phys. Rev. 84, 395 (1951).
  10. M. Sands, Phys. Rev. 97, 470 (1956).
  11. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).
  12. H. Bruck, A ccéleérateurs circulaires de particules (Presses Universitaires de France, Paris, 1966).
  13. A. A. Kolomenskii and A. N. Lebedev, Zh. Tekh, Fiz. 32, 1237 (1962) [Sov. Phys.-Tech. Phys. 7, 913 (1963)].
  14. L. V. logansen and M. S. Rabinovitch, Zh. Eksp. Teor. Fiz. 35, 1013 (1958); 37, 118 (1959) [Sov. Phys.–JETP 35, 708 (1958); 37, 83 (1960)]. I. L. Zel'Manov, A. S. Kompaneets, and Yu S. Sayasov, Dokl. Akad. Nauk. SSSR 143, 72 (1962) [Sov. Phys.-Doklady 7, 201 (1962)].
  15. P. Goldreich and D. A. Keeley, Astrophys. J. 170, 463 (1971).
  16. M. S. Livingstone and J. P. Blewett, Particle Accelerators (McGraw-Hill, New York, 1962).
  17. See Eqs. (14–62) and (14–68) of Ref. 13, Sec. 14.5, [equation] The complex amplitude of the field for the given frequency ω can be written as a time Fourier transform of a function [equation] where Ri(t) is the distance from 0 of the ith electron at the same time t, for every i.
  18. Synchronous electron located in the middle of the bunch.
  19. The authors are grateful to Dr. H. Zyngier for having pointed this out.
  20. The authors are grateful to Dr. H. Zyngier for having pointed this out.

Blewett, J. P.

M. S. Livingstone and J. P. Blewett, Particle Accelerators (McGraw-Hill, New York, 1962).

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), Ch. X. See also the first of Ref. 3, p. 69.

Bruck, H.

H. Bruck, A ccéleérateurs circulaires de particules (Presses Universitaires de France, Paris, 1966).

Glauber, R. J.

R. J. Glauber, Phys. Rev. 84, 395 (1951).

R. J. Glauber, in Quantum Optics and Electronics edited by C. de Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965); L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

Godwin, R. P.

R. P. Godwin, Springer Tracts Mod. Phys. 51, 1 (1969); K. Codling, Rep. Prog. Phys. 36, 541 (1973).

Goldreich, P.

P. Goldreich and D. A. Keeley, Astrophys. J. 170, 463 (1971).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

Keeley, D. A.

P. Goldreich and D. A. Keeley, Astrophys. J. 170, 463 (1971).

Kolomenskii, A. A.

A. A. Kolomenskii and A. N. Lebedev, Zh. Tekh, Fiz. 32, 1237 (1962) [Sov. Phys.-Tech. Phys. 7, 913 (1963)].

Lebedev, A. N.

A. A. Kolomenskii and A. N. Lebedev, Zh. Tekh, Fiz. 32, 1237 (1962) [Sov. Phys.-Tech. Phys. 7, 913 (1963)].

Livingstone, M. S.

M. S. Livingstone and J. P. Blewett, Particle Accelerators (McGraw-Hill, New York, 1962).

logansen, L. V.

L. V. logansen and M. S. Rabinovitch, Zh. Eksp. Teor. Fiz. 35, 1013 (1958); 37, 118 (1959) [Sov. Phys.–JETP 35, 708 (1958); 37, 83 (1960)]. I. L. Zel'Manov, A. S. Kompaneets, and Yu S. Sayasov, Dokl. Akad. Nauk. SSSR 143, 72 (1962) [Sov. Phys.-Doklady 7, 201 (1962)].

Picinbono, B.

By chaotic field, we mean a stationary gaussian field. See, for instance, B. Picinbono and M. Rousseau, Phys. Rev. A 1, 635 (1970).

Rabinovitch, M. S.

L. V. logansen and M. S. Rabinovitch, Zh. Eksp. Teor. Fiz. 35, 1013 (1958); 37, 118 (1959) [Sov. Phys.–JETP 35, 708 (1958); 37, 83 (1960)]. I. L. Zel'Manov, A. S. Kompaneets, and Yu S. Sayasov, Dokl. Akad. Nauk. SSSR 143, 72 (1962) [Sov. Phys.-Doklady 7, 201 (1962)].

Rousseau, M.

By chaotic field, we mean a stationary gaussian field. See, for instance, B. Picinbono and M. Rousseau, Phys. Rev. A 1, 635 (1970).

Sands, M.

M. Sands, Phys. Rev. 97, 470 (1956).

Schwinger, J.

J. Schwinger, Phys. Rev. 75, 1912 (1949); Phys. Rev. D 7, 1696 (1973).

Sokolov, A. A.

A. A. Sokolov and I. M. Ternov, Synchrotron Radiation (Pergamon, New York, 1968), and references therein.

Ternov, I. M.

A. A. Sokolov and I. M. Ternov, Synchrotron Radiation (Pergamon, New York, 1968), and references therein.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), Ch. X. See also the first of Ref. 3, p. 69.

Other (20)

R. P. Godwin, Springer Tracts Mod. Phys. 51, 1 (1969); K. Codling, Rep. Prog. Phys. 36, 541 (1973).

Proceedings of the International Symposium on Synchrotron Radiation Uses, edited by I. Munro and G. Marr (Publ. Daresbury Nuclear Phys. Lab., Daresbury, 1973), Rapport 26.

R. J. Glauber, in Quantum Optics and Electronics edited by C. de Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1965); L. Mandel and E. Wolf, Rev. Mod. Phys. 37, 231 (1965).

M. Born and E. Wolf, Principles of Optics (Pergamon, New York, 1964), Ch. X. See also the first of Ref. 3, p. 69.

For simplification, this function is assumed to be scalar and not vectorial. This can be understood by supposing that one polarization only is considered.

By chaotic field, we mean a stationary gaussian field. See, for instance, B. Picinbono and M. Rousseau, Phys. Rev. A 1, 635 (1970).

A. A. Sokolov and I. M. Ternov, Synchrotron Radiation (Pergamon, New York, 1968), and references therein.

J. Schwinger, Phys. Rev. 75, 1912 (1949); Phys. Rev. D 7, 1696 (1973).

R. J. Glauber, Phys. Rev. 84, 395 (1951).

M. Sands, Phys. Rev. 97, 470 (1956).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962).

H. Bruck, A ccéleérateurs circulaires de particules (Presses Universitaires de France, Paris, 1966).

A. A. Kolomenskii and A. N. Lebedev, Zh. Tekh, Fiz. 32, 1237 (1962) [Sov. Phys.-Tech. Phys. 7, 913 (1963)].

L. V. logansen and M. S. Rabinovitch, Zh. Eksp. Teor. Fiz. 35, 1013 (1958); 37, 118 (1959) [Sov. Phys.–JETP 35, 708 (1958); 37, 83 (1960)]. I. L. Zel'Manov, A. S. Kompaneets, and Yu S. Sayasov, Dokl. Akad. Nauk. SSSR 143, 72 (1962) [Sov. Phys.-Doklady 7, 201 (1962)].

P. Goldreich and D. A. Keeley, Astrophys. J. 170, 463 (1971).

M. S. Livingstone and J. P. Blewett, Particle Accelerators (McGraw-Hill, New York, 1962).

See Eqs. (14–62) and (14–68) of Ref. 13, Sec. 14.5, [equation] The complex amplitude of the field for the given frequency ω can be written as a time Fourier transform of a function [equation] where Ri(t) is the distance from 0 of the ith electron at the same time t, for every i.

Synchronous electron located in the middle of the bunch.

The authors are grateful to Dr. H. Zyngier for having pointed this out.

The authors are grateful to Dr. H. Zyngier for having pointed this out.

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