Abstract

We present simple analytical formulas describing the evolution from circular to linear polarization of the relativistic deflection of photoelectron trajectories along the direction of laser light propagation, and discuss conditions of applicability of the model used in calculations.

© 1998 Optical Society of America

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  1. C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
    [Crossref] [PubMed]
  2. D. D. Meyerhofer, J. P. Knauer, S. J. McNaught, and C. I. Moore, “Mass shift effects during high-intensity laser-electron interactions,” J. Opt. Soc. Am. B 13, 113–117 (1996).
    [Crossref]
  3. D. D. Meyerhofer, “Laser-electron scattering at relativistic intensities,” in Super - Intense Laser - Atom Physics IV, H. G. Muller and M. V. Fedorov, eds. (Kluwer Academic Publishers, Netherlands, 1996).
    [Crossref]
  4. H. R. Reiss, “Relativistic strong-field ionization,” J. Opt. Soc. Am. B 7, 574–586 (1990).
    [Crossref]
  5. H. R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes,” Prog. Quantum Electron. 161–71 (1992).
    [Crossref]
  6. D. P. Crawford and H. R. Reiss, “Stabilization in relativistic ionization with circularly polarized light;,” Phys. Rev. A 50, 1844–1850 (1994).
    [Crossref] [PubMed]
  7. P. B. Corkum, N. H. Burnett, and F. Brunel, “Multiphoton ionization at large ponderomotive potentials,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic Press, New York, 1992).
  8. S. P. Goreslavskii, M. V. Fedorov, and A. A. Kil’pio, “Relativistic drift of an electron under the influence of a short intense laser pulse,” Laser Phys. 5, 1020–1028 (1995).
  9. Y. I. Salamin and F. H. M. Faisal, “Ponderomotive scattering of electrons in intense laser fields,” Phys. Rev. A 55, 3678–3683 (1997).
    [Crossref]
  10. J. N. Bardsley, B. M. Penetrante, and M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1997).
    [Crossref]
  11. F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
    [Crossref]
  12. S. P. Goreslavskii, N. B. Narozhny, O. V. Shcherbachev, and V. P. Yakovlev, “The dynamics and radiation of a relativistic electron in the field of an intense, focused laser pulse,” Laser Phys. 3, 421–434, (1993).
  13. S. P. Goreslavsky and N. B. Narozhny, “Ponderomotive scattering at relativistic laser intensities,” J. Nonlinear Opt. Phys. Mater. 4, 799–815 (1995).
    [Crossref]
  14. S P. Goreslavskii, “The BSI model and relativistic ponderomotive scattering,” Laser Phys. 6, 74–78 (1996).
  15. S. P. Goreslavskii and S. V. Popruzhenko, “Momentum distribution of photoelectrons in strong low-frequency elliptically polarized laser field,” Laser Phys. 6, 780–784 (1996).
  16. S. P. Goreslavskii and S. V. Popruzhenko, “Differential photoelectron distributions in a strong elliptically polarized low-frequency laser field,” Zh. Eksp. Teor. Fiz. 110, 1200–1215 (1996) (JETP 83, 661–669).
  17. S. P. Goreslavskii and S. V. Popruzhenko, “Photoelectron velocity distribution at the time of ionization by elliptically polarized laser field,” Laser Phys. 7, 700–705 (1997).
  18. S. J. McNaught, J.P. Knauer, and D. D. Meyerhofer, “Measurement of the initial condition of electrons ionized by a linearly polarized high-intensity laser,” Phys. Rev. Lett. 78, 626–629 (1997).
    [Crossref]
  19. S. J. McNaught, J. P. Knauer, and D. D. Meyerhofer, “Photoelectron drift momentum in the long-pulse tunneling limit for an elliptically polarized laser,” Laser Phys. 7, 712–718 (1996).

1997 (4)

Y. I. Salamin and F. H. M. Faisal, “Ponderomotive scattering of electrons in intense laser fields,” Phys. Rev. A 55, 3678–3683 (1997).
[Crossref]

J. N. Bardsley, B. M. Penetrante, and M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1997).
[Crossref]

S. P. Goreslavskii and S. V. Popruzhenko, “Photoelectron velocity distribution at the time of ionization by elliptically polarized laser field,” Laser Phys. 7, 700–705 (1997).

S. J. McNaught, J.P. Knauer, and D. D. Meyerhofer, “Measurement of the initial condition of electrons ionized by a linearly polarized high-intensity laser,” Phys. Rev. Lett. 78, 626–629 (1997).
[Crossref]

1996 (5)

S. J. McNaught, J. P. Knauer, and D. D. Meyerhofer, “Photoelectron drift momentum in the long-pulse tunneling limit for an elliptically polarized laser,” Laser Phys. 7, 712–718 (1996).

S P. Goreslavskii, “The BSI model and relativistic ponderomotive scattering,” Laser Phys. 6, 74–78 (1996).

S. P. Goreslavskii and S. V. Popruzhenko, “Momentum distribution of photoelectrons in strong low-frequency elliptically polarized laser field,” Laser Phys. 6, 780–784 (1996).

S. P. Goreslavskii and S. V. Popruzhenko, “Differential photoelectron distributions in a strong elliptically polarized low-frequency laser field,” Zh. Eksp. Teor. Fiz. 110, 1200–1215 (1996) (JETP 83, 661–669).

D. D. Meyerhofer, J. P. Knauer, S. J. McNaught, and C. I. Moore, “Mass shift effects during high-intensity laser-electron interactions,” J. Opt. Soc. Am. B 13, 113–117 (1996).
[Crossref]

1995 (4)

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

S. P. Goreslavskii, M. V. Fedorov, and A. A. Kil’pio, “Relativistic drift of an electron under the influence of a short intense laser pulse,” Laser Phys. 5, 1020–1028 (1995).

S. P. Goreslavsky and N. B. Narozhny, “Ponderomotive scattering at relativistic laser intensities,” J. Nonlinear Opt. Phys. Mater. 4, 799–815 (1995).
[Crossref]

1994 (1)

D. P. Crawford and H. R. Reiss, “Stabilization in relativistic ionization with circularly polarized light;,” Phys. Rev. A 50, 1844–1850 (1994).
[Crossref] [PubMed]

1993 (1)

S. P. Goreslavskii, N. B. Narozhny, O. V. Shcherbachev, and V. P. Yakovlev, “The dynamics and radiation of a relativistic electron in the field of an intense, focused laser pulse,” Laser Phys. 3, 421–434, (1993).

1992 (1)

H. R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes,” Prog. Quantum Electron. 161–71 (1992).
[Crossref]

1990 (1)

Bardsley, J. N.

J. N. Bardsley, B. M. Penetrante, and M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1997).
[Crossref]

Brunel, F.

P. B. Corkum, N. H. Burnett, and F. Brunel, “Multiphoton ionization at large ponderomotive potentials,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic Press, New York, 1992).

Burnett, N. H.

P. B. Corkum, N. H. Burnett, and F. Brunel, “Multiphoton ionization at large ponderomotive potentials,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic Press, New York, 1992).

Chen, Y. J.

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

Corkum, P. B.

P. B. Corkum, N. H. Burnett, and F. Brunel, “Multiphoton ionization at large ponderomotive potentials,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic Press, New York, 1992).

Crawford, D. P.

D. P. Crawford and H. R. Reiss, “Stabilization in relativistic ionization with circularly polarized light;,” Phys. Rev. A 50, 1844–1850 (1994).
[Crossref] [PubMed]

Faisal, F. H. M.

Y. I. Salamin and F. H. M. Faisal, “Ponderomotive scattering of electrons in intense laser fields,” Phys. Rev. A 55, 3678–3683 (1997).
[Crossref]

Fedorov, M. V.

S. P. Goreslavskii, M. V. Fedorov, and A. A. Kil’pio, “Relativistic drift of an electron under the influence of a short intense laser pulse,” Laser Phys. 5, 1020–1028 (1995).

Fochs, S. N.

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

Goreslavskii, S P.

S P. Goreslavskii, “The BSI model and relativistic ponderomotive scattering,” Laser Phys. 6, 74–78 (1996).

Goreslavskii, S. P.

S. P. Goreslavskii and S. V. Popruzhenko, “Photoelectron velocity distribution at the time of ionization by elliptically polarized laser field,” Laser Phys. 7, 700–705 (1997).

S. P. Goreslavskii and S. V. Popruzhenko, “Momentum distribution of photoelectrons in strong low-frequency elliptically polarized laser field,” Laser Phys. 6, 780–784 (1996).

S. P. Goreslavskii and S. V. Popruzhenko, “Differential photoelectron distributions in a strong elliptically polarized low-frequency laser field,” Zh. Eksp. Teor. Fiz. 110, 1200–1215 (1996) (JETP 83, 661–669).

S. P. Goreslavskii, M. V. Fedorov, and A. A. Kil’pio, “Relativistic drift of an electron under the influence of a short intense laser pulse,” Laser Phys. 5, 1020–1028 (1995).

S. P. Goreslavskii, N. B. Narozhny, O. V. Shcherbachev, and V. P. Yakovlev, “The dynamics and radiation of a relativistic electron in the field of an intense, focused laser pulse,” Laser Phys. 3, 421–434, (1993).

Goreslavsky, S. P.

S. P. Goreslavsky and N. B. Narozhny, “Ponderomotive scattering at relativistic laser intensities,” J. Nonlinear Opt. Phys. Mater. 4, 799–815 (1995).
[Crossref]

Hartemann, F. V.

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

Kerman, A. K.

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

Kil’pio, A. A.

S. P. Goreslavskii, M. V. Fedorov, and A. A. Kil’pio, “Relativistic drift of an electron under the influence of a short intense laser pulse,” Laser Phys. 5, 1020–1028 (1995).

Knauer, J. P.

S. J. McNaught, J. P. Knauer, and D. D. Meyerhofer, “Photoelectron drift momentum in the long-pulse tunneling limit for an elliptically polarized laser,” Laser Phys. 7, 712–718 (1996).

D. D. Meyerhofer, J. P. Knauer, S. J. McNaught, and C. I. Moore, “Mass shift effects during high-intensity laser-electron interactions,” J. Opt. Soc. Am. B 13, 113–117 (1996).
[Crossref]

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

Knauer, J.P.

S. J. McNaught, J.P. Knauer, and D. D. Meyerhofer, “Measurement of the initial condition of electrons ionized by a linearly polarized high-intensity laser,” Phys. Rev. Lett. 78, 626–629 (1997).
[Crossref]

Le Sage, G. P.

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

Luhmann, N. C.

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

McNaught, S. J.

S. J. McNaught, J.P. Knauer, and D. D. Meyerhofer, “Measurement of the initial condition of electrons ionized by a linearly polarized high-intensity laser,” Phys. Rev. Lett. 78, 626–629 (1997).
[Crossref]

S. J. McNaught, J. P. Knauer, and D. D. Meyerhofer, “Photoelectron drift momentum in the long-pulse tunneling limit for an elliptically polarized laser,” Laser Phys. 7, 712–718 (1996).

D. D. Meyerhofer, J. P. Knauer, S. J. McNaught, and C. I. Moore, “Mass shift effects during high-intensity laser-electron interactions,” J. Opt. Soc. Am. B 13, 113–117 (1996).
[Crossref]

Meyerhofer, D. D.

S. J. McNaught, J.P. Knauer, and D. D. Meyerhofer, “Measurement of the initial condition of electrons ionized by a linearly polarized high-intensity laser,” Phys. Rev. Lett. 78, 626–629 (1997).
[Crossref]

S. J. McNaught, J. P. Knauer, and D. D. Meyerhofer, “Photoelectron drift momentum in the long-pulse tunneling limit for an elliptically polarized laser,” Laser Phys. 7, 712–718 (1996).

D. D. Meyerhofer, J. P. Knauer, S. J. McNaught, and C. I. Moore, “Mass shift effects during high-intensity laser-electron interactions,” J. Opt. Soc. Am. B 13, 113–117 (1996).
[Crossref]

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

D. D. Meyerhofer, “Laser-electron scattering at relativistic intensities,” in Super - Intense Laser - Atom Physics IV, H. G. Muller and M. V. Fedorov, eds. (Kluwer Academic Publishers, Netherlands, 1996).
[Crossref]

Mittleman, M. H.

J. N. Bardsley, B. M. Penetrante, and M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1997).
[Crossref]

Moore, C. I.

D. D. Meyerhofer, J. P. Knauer, S. J. McNaught, and C. I. Moore, “Mass shift effects during high-intensity laser-electron interactions,” J. Opt. Soc. Am. B 13, 113–117 (1996).
[Crossref]

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

Narozhny, N. B.

S. P. Goreslavsky and N. B. Narozhny, “Ponderomotive scattering at relativistic laser intensities,” J. Nonlinear Opt. Phys. Mater. 4, 799–815 (1995).
[Crossref]

S. P. Goreslavskii, N. B. Narozhny, O. V. Shcherbachev, and V. P. Yakovlev, “The dynamics and radiation of a relativistic electron in the field of an intense, focused laser pulse,” Laser Phys. 3, 421–434, (1993).

Penetrante, B. M.

J. N. Bardsley, B. M. Penetrante, and M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1997).
[Crossref]

Perry, M. D.

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

Popruzhenko, S. V.

S. P. Goreslavskii and S. V. Popruzhenko, “Photoelectron velocity distribution at the time of ionization by elliptically polarized laser field,” Laser Phys. 7, 700–705 (1997).

S. P. Goreslavskii and S. V. Popruzhenko, “Momentum distribution of photoelectrons in strong low-frequency elliptically polarized laser field,” Laser Phys. 6, 780–784 (1996).

S. P. Goreslavskii and S. V. Popruzhenko, “Differential photoelectron distributions in a strong elliptically polarized low-frequency laser field,” Zh. Eksp. Teor. Fiz. 110, 1200–1215 (1996) (JETP 83, 661–669).

Reiss, H. R.

D. P. Crawford and H. R. Reiss, “Stabilization in relativistic ionization with circularly polarized light;,” Phys. Rev. A 50, 1844–1850 (1994).
[Crossref] [PubMed]

H. R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes,” Prog. Quantum Electron. 161–71 (1992).
[Crossref]

H. R. Reiss, “Relativistic strong-field ionization,” J. Opt. Soc. Am. B 7, 574–586 (1990).
[Crossref]

Salamin, Y. I.

Y. I. Salamin and F. H. M. Faisal, “Ponderomotive scattering of electrons in intense laser fields,” Phys. Rev. A 55, 3678–3683 (1997).
[Crossref]

Shcherbachev, O. V.

S. P. Goreslavskii, N. B. Narozhny, O. V. Shcherbachev, and V. P. Yakovlev, “The dynamics and radiation of a relativistic electron in the field of an intense, focused laser pulse,” Laser Phys. 3, 421–434, (1993).

Woodworth, J. G.

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

Yakovlev, V. P.

S. P. Goreslavskii, N. B. Narozhny, O. V. Shcherbachev, and V. P. Yakovlev, “The dynamics and radiation of a relativistic electron in the field of an intense, focused laser pulse,” Laser Phys. 3, 421–434, (1993).

J. Nonlinear Opt. Phys. Mater. (1)

S. P. Goreslavsky and N. B. Narozhny, “Ponderomotive scattering at relativistic laser intensities,” J. Nonlinear Opt. Phys. Mater. 4, 799–815 (1995).
[Crossref]

J. Opt. Soc. Am. B (2)

Laser Phys. (6)

S. P. Goreslavskii, M. V. Fedorov, and A. A. Kil’pio, “Relativistic drift of an electron under the influence of a short intense laser pulse,” Laser Phys. 5, 1020–1028 (1995).

S P. Goreslavskii, “The BSI model and relativistic ponderomotive scattering,” Laser Phys. 6, 74–78 (1996).

S. P. Goreslavskii and S. V. Popruzhenko, “Momentum distribution of photoelectrons in strong low-frequency elliptically polarized laser field,” Laser Phys. 6, 780–784 (1996).

S. P. Goreslavskii, N. B. Narozhny, O. V. Shcherbachev, and V. P. Yakovlev, “The dynamics and radiation of a relativistic electron in the field of an intense, focused laser pulse,” Laser Phys. 3, 421–434, (1993).

S. P. Goreslavskii and S. V. Popruzhenko, “Photoelectron velocity distribution at the time of ionization by elliptically polarized laser field,” Laser Phys. 7, 700–705 (1997).

S. J. McNaught, J. P. Knauer, and D. D. Meyerhofer, “Photoelectron drift momentum in the long-pulse tunneling limit for an elliptically polarized laser,” Laser Phys. 7, 712–718 (1996).

Phys. Rev. A (3)

D. P. Crawford and H. R. Reiss, “Stabilization in relativistic ionization with circularly polarized light;,” Phys. Rev. A 50, 1844–1850 (1994).
[Crossref] [PubMed]

Y. I. Salamin and F. H. M. Faisal, “Ponderomotive scattering of electrons in intense laser fields,” Phys. Rev. A 55, 3678–3683 (1997).
[Crossref]

J. N. Bardsley, B. M. Penetrante, and M. H. Mittleman, “Relativistic dynamics of electrons in intense laser fields,” Phys. Rev. A 40, 3823–3835 (1997).
[Crossref]

Phys. Rev. E (1)

F. V. Hartemann, S. N. Fochs, G. P. Le Sage, N. C. Luhmann, J. G. Woodworth, M. D. Perry, Y. J. Chen, and A. K. Kerman, “Nonlinear ponderomotive scattering of relativistic electrons by an intense laser field in focus,” Phys. Rev. E 51, 4833–4843 (1995).
[Crossref]

Phys. Rev. Lett. (2)

C. I. Moore, J. P. Knauer, and D. D. Meyerhofer, “Observation of the transition from Thomson to Compton scattering in multiphoton interactions with low-energy electrons,” Phys. Rev. Lett. 74, 2439–2442 (1995).
[Crossref] [PubMed]

S. J. McNaught, J.P. Knauer, and D. D. Meyerhofer, “Measurement of the initial condition of electrons ionized by a linearly polarized high-intensity laser,” Phys. Rev. Lett. 78, 626–629 (1997).
[Crossref]

Prog. Quantum Electron. (1)

H. R. Reiss, “Theoretical methods in quantum optics: S-matrix and Keldysh techniques for strong-field processes,” Prog. Quantum Electron. 161–71 (1992).
[Crossref]

Zh. Eksp. Teor. Fiz. (1)

S. P. Goreslavskii and S. V. Popruzhenko, “Differential photoelectron distributions in a strong elliptically polarized low-frequency laser field,” Zh. Eksp. Teor. Fiz. 110, 1200–1215 (1996) (JETP 83, 661–669).

Other (2)

P. B. Corkum, N. H. Burnett, and F. Brunel, “Multiphoton ionization at large ponderomotive potentials,” in Atoms in Intense Laser Fields, M. Gavrila, ed. (Academic Press, New York, 1992).

D. D. Meyerhofer, “Laser-electron scattering at relativistic intensities,” in Super - Intense Laser - Atom Physics IV, H. G. Muller and M. V. Fedorov, eds. (Kluwer Academic Publishers, Netherlands, 1996).
[Crossref]

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Equations (18)

Equations on this page are rendered with MathJax. Learn more.

A = A ( x , φ ; φ ) = cF x φ ω cos ωφ sin ωφ , 0 ,
π ( φ ) = e c [ A 0 A x 0 φ φ ] ;
c π z ( φ ) = π 2 ( φ ) 2 m ; π 0 ( φ ) = m c 2 + π 2 ( φ ) 2 m .
U = e 2 F 2 4 m ω 2 ( 1 + ξ 2 ) = 2 π e 2 I c ω 2 .
q ( φ ) = e c A 0 ; c q z ( φ ) = ( e A 0 c ) 2 2 m + U x 0 φ ;
q 0 ( φ ) = m c 2 + c q z ( φ ) .
t g 2 θ = q z 2 ( + ) q 2 ( + ) .
( e c A 0 ) 2 = ( e F 0 ω ) 2 ξ 2 + ( e F 0 ω ) 2 F 0 F a ( 1 ξ 2 ) .
t g 2 θ = m c 2 U 0 1 + ξ 2 ξ 2 + ( F 0 F a ) ( 1 ξ 2 ) .
q = q 0 c q z = mc .
q 0 2 c 2 q 2 = m 2 c 2 + 2 mU m * 2 c 2 ,
c q z ( ) = q 0 ( ) m c 2 ; c q z ( ) = q 2 ( ) 2 m .
c q z ( ) = ( e A 0 c ) 2 2 m + U 0 ; q ( ) = ( e c A 0 ) 2 + 2 m U 0 .
t g 2 θ = 2 m c 2 U 0 1 + ξ 2 1 + 3 ξ 2 + ( F 0 F a ) ( 1 ξ 2 ) .
Δ π z = Δ π 0 c
Δ π z = Δ ( π 2 ) 2 mc .
π = π 0 c π z = const .
π ˜ 0 = π 0 ± ω 1 ± ω 2 ± , π ˜ z = π z ± k z 1 ± k z 2 ±

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