Exact Solution of the Landau-Lifshitz Equation in a Plane Wave

Piazza, A. Di

doi:10.1007/s11005-008-0228-9

Cited by 179 publications

(217 citation statements)

References 34 publications

(54 reference statements)

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“…The solution (19) differs from that found for LL [56] only by the terms in I a arising from the field derivatives. From (19) and (17) we readily obtain the particle's momentum, u a = Ω u a , and position, x a = x a 0 + Λ a b u b dφ.…”

Section: B Electromagnetic Plane Wavecontrasting

confidence: 61%

“…The Landau-Lifshitz equation in the field (14) has been studied extensively [56][57][58][59][60]. However, a number of conceptual and technical differences arise in the Sokolov theory.…”

Section: B Electromagnetic Plane Wavementioning

confidence: 99%

“…Nevertheless, we can follow the approach in [56], changing the independent variable from proper time s to phase φ. This is possible since the field drops out of the phase derivative:φ…”

Section: B Electromagnetic Plane Wavementioning

confidence: 99%

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Role of momentum and velocity for radiating electrons

et al. 2016

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This version is available at https://strathprints.strath.ac.uk/55486/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. Radiation reaction remains one of the most fascinating open questions in electrodynamics. The development of multi-petawatt laser facilities capable of reaching extreme intensities has leant this topic a new urgency, and it is now more important than ever to properly understand it. Two models of radiation reaction, due to Landau and Lifshitz and to Sokolov, have gained prominence, but there has been little work exploring the relation between the two. We show that in the Sokolov theory electromagnetic fields induce a Lorentz transformation between momentum and velocity, which eliminates some of the counterintuitive results of Landau-Lifshitz. In particular, the Lorentz boost in a constant electric field causes the particle to lose electrostatic potential energy more rapidly than it otherwise would, explaining the long-standing mystery of how an electron can radiate while experience no radiation reaction force. These ideas are illustrated in examples of relevance to astrophysics and laser-particle interactions, where radiation reaction effects are particularly prominent.

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Section: B Electromagnetic Plane Wavecontrasting

confidence: 61%

“…The Landau-Lifshitz equation in the field (14) has been studied extensively [56][57][58][59][60]. However, a number of conceptual and technical differences arise in the Sokolov theory.…”

Section: B Electromagnetic Plane Wavementioning

confidence: 99%

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Role of momentum and velocity for radiating electrons

et al. 2016

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“…to play an important role (Zel'dovich 1975;Zhidkov et al 2002;Bulanov et al 2004b;Di Piazza 2008;Harvey, Heinzl & Marklund 2011;Thomas et al 2012;Heinzl et al 2015). The radiation friction effects change drastically the laser-plasma interaction leading to fast energy losses (see Koga 2004;Koga, Esirkepov & Bulanov 2005 and to phase space contraction, as discussed in Tamburini et al (2011).…”

Section: S V Bulanov and Othersmentioning

confidence: 99%

Charged particle dynamics in multiple colliding electromagnetic waves. Survey of random walk, Lévy flights, limit circles, attractors and structurally determinate patterns

et al. 2017

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The multiple colliding laser pulse concept formulated by Bulanov et al. (Phys. Rev. Lett., vol. 104, 2010b, 220404) is beneficial for achieving an extremely high amplitude of coherent electromagnetic field. Since the topology of electric and magnetic fields of multiple colliding laser pulses oscillating in time is far from trivial and the radiation friction effects are significant in the high field limit, the dynamics of charged particles interacting with the multiple colliding laser pulses demonstrates remarkable features corresponding to random walk trajectories, limit circles, attractors, regular patterns and Lévy flights. Under extremely high intensity conditions the nonlinear dissipation mechanism stabilizes the particle motion resulting in the charged particle trajectory being located within narrow regions and in the occurrence of a new class of regular patterns made by the particle ensembles.

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“…Valuable discussions of this type have appeared recently [10][11][12][13]. In addition, to achieve a realistic and accurate picture of the physics one would like to have (i) a powerful numerical formalism that (ii) respects covariance, and, ideally, exactly so.…”

Section: Introductionmentioning

confidence: 99%