High-Energy Wave Packets. ‘Half-Bare’ Electron

  • Nikolai Shul’ga Akhiezer Institute for Theoretical Physics of NSC KIPT, Kharkov, Ukraine
  • Sergii Trofymenko National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine
Keywords: electromagnetic wave packets, ionization energy losses, transition radiation, density effect


The evolution in space and time of localized high-energy electromagnetic wave packets, which take place in processes of radiation by ultra relativistic electrons is considered. It is shown that high energies make stabilizing influence on the motion of such packets and that the lengths, within which their dispersion and reconstruction into the packets of diverging waves occurs, can be macroscopic. The electromagnetic field evolution in the process of ultra relativistic electron emission from substance into vacuum is considered. It is demonstrated, that in this case the electron can be in ‘half-bare’ state with considerably suppressed low frequency Fourier-components of the field around it during long period of time after the emission. It is shown that such state of electron can manifest itself in significant dependence of further ionization energy losses of the electron in thin plate situated in the direction of the particle motion on the distance between the plate and the scattering point.


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Ter-Mikaelyan M.L. High-Energy Electromagnetic Processes in media. – Yerevan: Publ. of Acad. of Sc. of Arm. SSR, 1969. – 457 p.

Akhiezer A.I., Shul’ga N.F. High Energy Electrodynamics in Matter. – Moscow: Nauka, 1993. – 344 p.

Dokshitzer Yu. L., Khoze V.A., Mueller A.H. and Troyan S.I. Basics of Perturbative QCD. – Gif sur Yvette Cedex: Editions Frontiers, 1991. – 274p.

Garibyan G.M., Shi Y. X-Ray transition radiation. – Yerevan: Publ. of Acad. of Sc. of Arm. SSR, 1983. – 320p.

Ginzburg V.L., Tsytovich V.N. Transition Radiation and Transition Scattering. – Moscow: Nauka, 1984, 360 p.

Rullhusen P., Artru X., Dhez P. Novel radiation sources using relativistic electrons. – Singapore: World Scientific Publ., 1998. – 202p.

Shibata Y., Hasebe S., Ishiki K., et al. Observation of coherent diffraction radiation from bunched electrons passing through a circular aperture in the millimeter- and submillimeter- wave length regions // Phys. Rev. E. – 1995. – Vol. 52. – P. 6737.

Dobrovolsky S.N., Shul’ga N.F. Transversal spatial distribution of transition radiation by relativistic electron in formation zone by the dotted detector // Nucl. Instrum. Methods B. – 2003. – Vol. 201. – P. 123-132.

Gorham P. et al. Radio-frequency measurements of coherent transition and Cherenkov radiation: implication for high energy neutrino detection // Phys. Rev. E. – 2000. – Vol. 62. – P. 8590-8605.

Verzilov V. A. Transition radiation in the pre-wave zone // Phys. Lett. A. – 2000. – Vol. 273. – P. 135-140.

Akhiezer A.I., Shul’ga N.F., Fomin S.P. Landau-Pomeranchuk-Migdal Effect . – Physics Reviews. – 2005. – Vol. 22. – P. 1-215 (Edited by I. M. Khalatnikov), Cambridge Sci. Publ., Printed in UK.

Potylitsyn A.P. Electromagnetic Radiation of Electrons in Periodic Structures. – Berlin: Springer, 2011. – 213 p.

Naumenko G.N., Potylitsyn A.P., Sukhih L. G. et. al. Macroscopic effect of shadow of electromagnetic field of relativistic electrons // Pis’ma v Zh. Eksp. Teor. Fiz. – 2009. – Vol. 90, Iss. 2. – P. 105-110.

Shul’ga N.F., Trofymenko S.V., Syshchenko V.V. On transition radiation and bremsstrahlung by relativistic electron with nonequilibrium field // Pis’ma v Zh. Eksp. Teor. Fiz. – 2011. – Vol. 93, Iss. 1. – P. 3-7.

Shul’ga N.F., Trofymenko S.V., Syshchenko V.V. The Space-Time Evolution of the Process of Transition Radiation by Relativistic Electron // Visnyk of Kharkiv National University. – 2010. – № 916, phys. series “Nuclei, Particles, Fields” Iss. 3(47). – P. 23-41.

Shul’ga N.F., Trofymenko S.V., Syshchenko V.V. The prewave zone effect in transition radiation and bremsstrahlung by relativistic electron // Problems of atomic science and technology. – 2012. – №1 series: Nuclear Physics Investigations. Vol. 57. – P. 134-138.

Feinberg E.L. Consecutive interaction at high energies // Zh. Eksp. Teor. Fiz. – 1966. – Vol. 50. – P. 202.

Akhiezer A.I., Shul’ga N.F. Radiation by relativistic particles in single crystals // UFN. – 1982. – Vol. 137. – P. 561-604.

Miller W. Classical Limit Quantum Mechanics and the Theory of Molecular Collisions. – New York: Wiley, 1974. – P. 69-177.

Blokhintsev D.I. In the book: High-Energy Physics and Elementary Particles Theory. – Kiev: Nauk. Dumka, 1967. – P. 778.

Shul’ga N.F., Syshchenko V.V., Shul’ga S.N. On the motion of high-energy wave packets and transition radiation by ‘half-bare’ electron // Phys. Lett. A. – 2009. – Vol. 374. – P. 331-334.

Landau L.D., Lifshitz E.M. The Classical Theory of Fields. – Moscow: Nauka, 1967. – 460 p.

Landau L.D., Pomeranchuk I.Ya. Electron-cascade processes at ultra-high energies // Dokl. Acad. Nauk. SSSR. – 1953. – Vol. 92. – P. 735.

Migdal A.B. Bremsstrahlung and pair production in condensed media at high energies // Phys. Rev. – 1956. – Vol. 103. – P. 1811.

Ternovsky F.F. On the theory of radiative processes in piece wise homogeneous media // Zh. Eksp. Teor. Fiz. – 1960. – Vol. 39. – P. 171.

Shul’ga N.F., Fomin S.P. Suppression of radiation in an amorphous medium and a crystal // Pis’ma v Zh. Eksp. Teor. Fiz. – 1978. – Vol. 27. – P. 126.

Landau L.D., Lifshitz E.M. Electrodynamics of Continuous Media. – Moscow: Nauka, 1982. – 621 p.

Bethe H.A. Theory of the passage of rapid corpuscular rays through matter // Ann. de Phys. – 1930. – Vol. 5. – P. 325.

Bloch F. Bremsvermögen von Atomen mit mehreren Electronen // Zs. Phys. – 1933. – Vol. 81. – P. 363.

Fermi E. The ionization loss of energy in gases and in condensed materials // Phys. Rev. – 1940. – Vol. 57. – P. 485-493.

Garibian G.M. On the theory of transition radiation and ionization energy losses of a particle // Zh. Eksp. Teor. Fiz. – 1959. – Vol. 37. – P. 527-533.

Alikhanian A.I., Garibian G.M., Lorikian M.P., Walter A.K., Grishaiev I.A., Petrenko V.A., Fursov G.L. Ionization energy losses of fast electrons in thin films // Zh. Eksp. Teor. Fiz. – 1963. – Vol. 44. – P. 1122-1124.

Alikhanian A.I., Garibian G.M., Lorikian M.P. et al. Ionization energy losses of fast electrons in thin layers of polystyrene // Zh. Eksp. Teor. Fiz. – 1964. – Vol. 46. – P. 1212-1215.

Andersen K.K., Esberg J., Hansen K.R. et. al. Restricted energy loss of ultrarelativistic particles in thin targets – a search for deviations from constancy // Nucl. Instrum. Methods B. – 2010. – Vol. 268. – P. 1412-1415.

Bohr N. On the theory of the decrease of velocity of moving electrified particles on passing through matter // Phil. Mag. – 1913. – Vol. 25. – P. 10.

Bohr N. On the decrease of velocity of swiftly moving electrified particles in passing through matter // Phil. Mag. – 1915. – Vol. 30. – P. 581.

Fermi E. Nuclear Physics. – Moskow: Publ. of foreign lit., transl. from English, 1950. – 346 p.

Jackson J. D., Classical Electrodynamics. – Moscow: Mir, first ed., 1965. – 702 p.

Shul’ga N.F., Syshchenko V.V. On ionization energy losses of relativistic particles created in matter // Nucl. Instrum. Methods B. – 2000. – Vol. 164-165. – P. 180-185.

How to Cite
Shul’ga, N., & Trofymenko, S. (2013). High-Energy Wave Packets. ‘Half-Bare’ Electron. East European Journal of Physics, (1040(1), 59-69. Retrieved from https://periodicals.karazin.ua/eejp/article/view/13563