A Classical Electron Model with Synchrotron Radiation

Günter Poelz

doi:doi:10.11648/j.wjap.20210601.12

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A Classical Electron Model with Synchrotron Radiation

Günter Poelz

Published in World Journal of Applied Physics (Volume 6, Issue 1)

Received: 26 April 2020 Accepted: 13 January 2021 Published: 30 March 2021

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Abstract

A classical model of the electron based on Maxwell’s equations is presented in which the wave character is described by classical physics. Most properties follow from the description of a classical massless charge circulating with v=c. The magnetic moment of the electron yields the radius of this circulation and the generated synchrotron radiation removes the singularity of the Coulomb field. The residual field equals then to the mass of the electron. Quantum mechanics yields its spin and the fine structure constant α compares this dynamic structure of the electron with the classical point-like static view. This configuration is not stable. It will decay by the emission of synchrotron radiation. The stability of this description is therefor investigated by extending this model to 3 dimensions. The field lines within the free electromagnetic fields of the creation process, solved in polar coordinates, yield possible tracks for a massless charge. Many possible circulating tracks are found but only a combination of background fields yield environments in which stable tracks for β = 1 - charges may be created. Knotted toroidal tracks yield the stability. A knotted field line e.g. with T(3,2)-symmetry may describe a spin-1/3-particle and a field line with T(2,3)-symmetry in form of a knotted trefoil may belong to an electron as a stable spin-1/2-particle. With its fixed internal revolution frequency this electron appears to the external world as a standing wave with an amplitude propagating like the de Broglie wave.

Published in	World Journal of Applied Physics (Volume 6, Issue 1)
DOI	10.11648/j.wjap.20210601.12
Page(s)	9-23
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Electron, Classical Wave Model, Spherical Wave Field, Elementary Charge, α, Mass, Knotted Structure, Wave Character

References

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[2]	L. de Broglie, Nonlinear Wave Mechanics (Elsevier, Amsterdam 1960) p. 6.
[3]	P. A. M. Dirac, Proc. Roy. Soc. London A268, (1962) 57.
[4]	J. D. Jackson Classical Electrodynamics (Wiley, New York 1975) §17.4.
[5]	F. Rohrlich, Am. J. Phys. 65, (1997) 1051.
[6]	J. L. Jimenez and I. Campos, Found. Phys. Lett.. 12, (1999) 127.
[7]	J. Orear, Jay Orear Physics (Macmillan, New York 1979)) Chp. 18-4.
[8]	M. Alonso, E.J. Finn, Fundamental University Physics II (Addison-Wesley, Amsterdam 1974) 515.
[9]	M. H. McGregor, The Enigmatic Electron (Kluwer Academic, Dortrecht 1992).
[10]	A. Sommerfeld, Electrodynamics: Lectures on Theoretical Physics (Academic Pr., New York 1952) §33.
[11]	H. Jehle, Phys. Rev. D15, (1977) p. 3727 and citations there.
[12]	J. G. Williamson and M.B. van der Mark, Ann. de la Foundation Louis de Broglie 22, (1997) 133.
[13]	Qiu-Hong Hu, Physics Essays, 17, (2004) 442.
[14]	A. O. Barut and N. Zanghi, Phys. Rev. Lett. 52, (1984) 2009.
[15]	D. Hestenes, Found. Phys. 20, (1990) 1213.
[16]	L. D. Landau and E. M. Lifshitz The Classical Theory of Fields (Butterworth-Heinemann, Oxford 2000) 2, Chp. 8.
[17]	http://chip-architect.com/news/2004 10 04 The Electro Magnetic coupling constant.html
[18]	2017 L. K. C. Leighton An Explanation of the de Vries Formula for the Fine Structure Constant; http://vixra.org/abs/1701.0006; viXra:1701.0006
[19]	D. Iwanenko and A. Sokolov Klassische Feldtheorie (Akademie-Verlag, Berlin 1953) §39ff.
[20]	J. D. Jackson Classical Electrodynamics (Wiley, New York 1975) Chp. 16.
[21]	Handbook of Mathematical Functions (editors: M. Abramowitz and I.A. Stegun; National Bureau Std., Appl. Math. Series 55, Washington 1966) Chp. 8, Chp. 10.
[22]	P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York 1953) Chp. 10, Chp. 11.

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APA Style

Günter Poelz. (2021). A Classical Electron Model with Synchrotron Radiation. World Journal of Applied Physics, 6(1), 9-23. https://doi.org/10.11648/j.wjap.20210601.12

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ACS Style

Günter Poelz. A Classical Electron Model with Synchrotron Radiation. World J. Appl. Phys. 2021, 6(1), 9-23. doi: 10.11648/j.wjap.20210601.12

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AMA Style

Günter Poelz. A Classical Electron Model with Synchrotron Radiation. World J Appl Phys. 2021;6(1):9-23. doi: 10.11648/j.wjap.20210601.12

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@article{10.11648/j.wjap.20210601.12,
  author = {Günter Poelz},
  title = {A Classical Electron Model with Synchrotron Radiation},
  journal = {World Journal of Applied Physics},
  volume = {6},
  number = {1},
  pages = {9-23},
  doi = {10.11648/j.wjap.20210601.12},
  url = {https://doi.org/10.11648/j.wjap.20210601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20210601.12},
  abstract = {A classical model of the electron based on Maxwell’s equations is presented in which the wave character is described by classical physics. Most properties follow from the description of a classical massless charge circulating with v=c. The magnetic moment of the electron yields the radius of this circulation and the generated synchrotron radiation removes the singularity of the Coulomb field. The residual field equals then to the mass of the electron. Quantum mechanics yields its spin and the fine structure constant α compares this dynamic structure of the electron with the classical point-like static view. This configuration is not stable. It will decay by the emission of synchrotron radiation. The stability of this description is therefor investigated by extending this model to 3 dimensions. The field lines within the free electromagnetic fields of the creation process, solved in polar coordinates, yield possible tracks for a massless charge. Many possible circulating tracks are found but only a combination of background fields yield environments in which stable tracks for β = 1 - charges may be created. Knotted toroidal tracks yield the stability. A knotted field line e.g. with T(3,2)-symmetry may describe a spin-1/3-particle and a field line with T(2,3)-symmetry in form of a knotted trefoil may belong to an electron as a stable spin-1/2-particle. With its fixed internal revolution frequency this electron appears to the external world as a standing wave with an amplitude propagating like the de Broglie wave.},
 year = {2021}
}

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TY - JOUR
T1 - A Classical Electron Model with Synchrotron Radiation
AU - Günter Poelz
Y1 - 2021/03/30
PY - 2021
N1 - https://doi.org/10.11648/j.wjap.20210601.12
DO - 10.11648/j.wjap.20210601.12
T2 - World Journal of Applied Physics
JF - World Journal of Applied Physics
JO - World Journal of Applied Physics
SP - 9
EP - 23
PB - Science Publishing Group
SN - 2637-6008
UR - https://doi.org/10.11648/j.wjap.20210601.12
AB - A classical model of the electron based on Maxwell’s equations is presented in which the wave character is described by classical physics. Most properties follow from the description of a classical massless charge circulating with v=c. The magnetic moment of the electron yields the radius of this circulation and the generated synchrotron radiation removes the singularity of the Coulomb field. The residual field equals then to the mass of the electron. Quantum mechanics yields its spin and the fine structure constant α compares this dynamic structure of the electron with the classical point-like static view. This configuration is not stable. It will decay by the emission of synchrotron radiation. The stability of this description is therefor investigated by extending this model to 3 dimensions. The field lines within the free electromagnetic fields of the creation process, solved in polar coordinates, yield possible tracks for a massless charge. Many possible circulating tracks are found but only a combination of background fields yield environments in which stable tracks for β = 1 - charges may be created. Knotted toroidal tracks yield the stability. A knotted field line e.g. with T(3,2)-symmetry may describe a spin-1/3-particle and a field line with T(2,3)-symmetry in form of a knotted trefoil may belong to an electron as a stable spin-1/2-particle. With its fixed internal revolution frequency this electron appears to the external world as a standing wave with an amplitude propagating like the de Broglie wave.
VL - 6
IS - 1
ER -

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Author Information

Günter Poelz

Hamburg University, Institute of Experimental Physics, Hamburg, Germany

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APA Style

Günter Poelz. (2021). A Classical Electron Model with Synchrotron Radiation. World Journal of Applied Physics, 6(1), 9-23. https://doi.org/10.11648/j.wjap.20210601.12

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ACS Style

Günter Poelz. A Classical Electron Model with Synchrotron Radiation. World J. Appl. Phys. 2021, 6(1), 9-23. doi: 10.11648/j.wjap.20210601.12

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AMA Style

Günter Poelz. A Classical Electron Model with Synchrotron Radiation. World J Appl Phys. 2021;6(1):9-23. doi: 10.11648/j.wjap.20210601.12

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@article{10.11648/j.wjap.20210601.12,
  author = {Günter Poelz},
  title = {A Classical Electron Model with Synchrotron Radiation},
  journal = {World Journal of Applied Physics},
  volume = {6},
  number = {1},
  pages = {9-23},
  doi = {10.11648/j.wjap.20210601.12},
  url = {https://doi.org/10.11648/j.wjap.20210601.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.wjap.20210601.12},
  abstract = {A classical model of the electron based on Maxwell’s equations is presented in which the wave character is described by classical physics. Most properties follow from the description of a classical massless charge circulating with v=c. The magnetic moment of the electron yields the radius of this circulation and the generated synchrotron radiation removes the singularity of the Coulomb field. The residual field equals then to the mass of the electron. Quantum mechanics yields its spin and the fine structure constant α compares this dynamic structure of the electron with the classical point-like static view. This configuration is not stable. It will decay by the emission of synchrotron radiation. The stability of this description is therefor investigated by extending this model to 3 dimensions. The field lines within the free electromagnetic fields of the creation process, solved in polar coordinates, yield possible tracks for a massless charge. Many possible circulating tracks are found but only a combination of background fields yield environments in which stable tracks for β = 1 - charges may be created. Knotted toroidal tracks yield the stability. A knotted field line e.g. with T(3,2)-symmetry may describe a spin-1/3-particle and a field line with T(2,3)-symmetry in form of a knotted trefoil may belong to an electron as a stable spin-1/2-particle. With its fixed internal revolution frequency this electron appears to the external world as a standing wave with an amplitude propagating like the de Broglie wave.},
 year = {2021}
}

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