Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam

Beginning with a critical examination of the Lorentz-Abraham (LA) classical equation of motion for an extended charge and the closely related Lorentz-Abraham-Dirac (LAD) equation of motion for a mass-renormalized point-charge, the Landau-Lifshitz (LL) approximate solution to the LAD equation of moti...

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Auteur principal:	Arthur D. Yaghjian
Format:	article
Langue:	EN
Publié:	American Physical Society 2021
Sujets:	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Accès en ligne:	https://doaj.org/article/470758aa293543218761d9c2dc9b4aa1
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spelling	oai:doaj.org-article:470758aa293543218761d9c2dc9b4aa12021-11-29T19:33:18ZLorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam10.1103/PhysRevAccelBeams.24.1140022469-9888https://doaj.org/article/470758aa293543218761d9c2dc9b4aa12021-11-01T00:00:00Zhttp://doi.org/10.1103/PhysRevAccelBeams.24.114002http://doi.org/10.1103/PhysRevAccelBeams.24.114002https://doaj.org/toc/2469-9888Beginning with a critical examination of the Lorentz-Abraham (LA) classical equation of motion for an extended charge and the closely related Lorentz-Abraham-Dirac (LAD) equation of motion for a mass-renormalized point-charge, the Landau-Lifshitz (LL) approximate solution to the LAD equation of motion is determined for an electron subject to a counterpropagating linearly or circularly polarized plane-wave pulse with an arbitrarily shaped envelope. A convenient three-vector formulation of the LL equation is used to derive closed-form expressions for the velocities and associated powers of the electron directly in terms of the time in the laboratory frame. The three-vector formulation also reveals definitive criteria for the LL solution to be an accurate approximation to the LAD equation of motion and for the LL solution to reduce to the solution of the Lorentz force equation of motion that ignores radiation reaction. Semiclassical analyses are used to obtain simple conditions for determining the regimes where the quantum effects of either Compton electron scattering by the incident photons or electron recoil produced by the emitted photons is significant. It is proven that the LL approximation becomes an inaccurate solution to the LAD equation of motion only for large enough electron velocities and plane-wave intensities that quantum recoil effects on the electron can greatly alter the classical solution. Comparisons are made with previously published analytical and numerical solutions to the LL equation of motion for the velocity of an electron in a counterpropagating plane wave.Arthur D. YaghjianAmerican Physical SocietyarticleNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENPhysical Review Accelerators and Beams, Vol 24, Iss 11, p 114002 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Arthur D. Yaghjian Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam
description	Beginning with a critical examination of the Lorentz-Abraham (LA) classical equation of motion for an extended charge and the closely related Lorentz-Abraham-Dirac (LAD) equation of motion for a mass-renormalized point-charge, the Landau-Lifshitz (LL) approximate solution to the LAD equation of motion is determined for an electron subject to a counterpropagating linearly or circularly polarized plane-wave pulse with an arbitrarily shaped envelope. A convenient three-vector formulation of the LL equation is used to derive closed-form expressions for the velocities and associated powers of the electron directly in terms of the time in the laboratory frame. The three-vector formulation also reveals definitive criteria for the LL solution to be an accurate approximation to the LAD equation of motion and for the LL solution to reduce to the solution of the Lorentz force equation of motion that ignores radiation reaction. Semiclassical analyses are used to obtain simple conditions for determining the regimes where the quantum effects of either Compton electron scattering by the incident photons or electron recoil produced by the emitted photons is significant. It is proven that the LL approximation becomes an inaccurate solution to the LAD equation of motion only for large enough electron velocities and plane-wave intensities that quantum recoil effects on the electron can greatly alter the classical solution. Comparisons are made with previously published analytical and numerical solutions to the LL equation of motion for the velocity of an electron in a counterpropagating plane wave.
format	article
author	Arthur D. Yaghjian
author_facet	Arthur D. Yaghjian
author_sort	Arthur D. Yaghjian
title	Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam
title_short	Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam
title_full	Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam
title_fullStr	Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam
title_full_unstemmed	Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam
title_sort	lorentz-abraham-dirac and landau-lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam
publisher	American Physical Society
publishDate	2021
url	https://doaj.org/article/470758aa293543218761d9c2dc9b4aa1
work_keys_str_mv	AT arthurdyaghjian lorentzabrahamdiracandlandaulifshitzequationsofmotionandthesolutiontoarelativisticelectroninacounterpropagatinglaserbeam
_version_	1718407102047715328

Lorentz-Abraham-Dirac and Landau-Lifshitz equations of motion and the solution to a relativistic electron in a counterpropagating laser beam

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