Para depositar en Docta Complutense, identifícate con tu correo @ucm.es en el SSO institucional: Haz clic en el desplegable de INICIO DE SESIÓN situado en la parte superior derecha de la pantalla. Introduce tu correo electrónico y tu contraseña de la UCM y haz clic en el botón MI CUENTA UCM, no autenticación con contraseña.
 

Radiation reaction on a classical charged particle: a modified form of the equation of motion

Simple item page
dc.contributor.authorLlanes Estrada, Felipe José
dc.contributor.authorGarcía Alcaine, Guillermo
dc.date.accessioned2023-06-19T13:22:35Z
dc.date.available2023-06-19T13:22:35Z
dc.date.issued2013-09-19
dc.description© 2013 American Physical Society. The authors would like to thank Norbert M. Nemes and Juan Ramirez Mittelbrunn for reading the manuscript.We also thank the constructive comments and additional references provided by the anonymous referees. This work was supported by Spanish Grants FPA2011-27853-01, FIS2008-01323 and UCM-BS GICC 910758.
dc.description.abstractWe present and numerically solve a modified form of the equation of motion for a charged particle under the influence of an external force, taking into account the radiation reaction. This covariant equation is integro differential, as Dirac-Rohrlich's, but has several technical improvements. First, the equation has the form of Newton's second law, with acceleration isolated on the left hand side and the force depending only on positions and velocities: Thus, the equation is linear in the highest derivative. Second, the total four-force is by construction perpendicular to the four-velocity. Third, if the external force vanishes for all future times, the total force and the acceleration automatically vanish at the present time. We show the advantages of this equation by solving it numerically for several examples of external force.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipUCM
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/23900
dc.identifier.doi10.1103/PhysRevE.88.033203
dc.identifier.issn1539-3755
dc.identifier.officialurlhttp://dx.doi.org/10.1103/PhysRevE.88.033203
dc.identifier.relatedurlhttp://pre.aps.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/33411
dc.issue.number3
dc.journal.titlePhysical Review E
dc.language.isoeng
dc.publisherPhysical Review E
dc.relation.projectIDFPA2011-27853-01
dc.relation.projectIDFIS2008-01323
dc.relation.projectIDUCM-BS GICC 910758
dc.rights.accessRightsopen access
dc.subject.cdu53
dc.subject.keywordCausality Violation
dc.subject.keywordResolution
dc.subject.keywordLorentz
dc.subject.ucmFísica (Física)
dc.subject.unesco22 Física
dc.titleRadiation reaction on a classical charged particle: a modified form of the equation of motion
dc.typejournal article
dc.volume.number88
dcterms.references[1] J. D. Jackson, Classical Electrodynamics, 3d ed. (Wiley & Sons, Hoboken, NJ, 1998), p. 745. [2] V. Krivitskii and V. Tsytovich, Sov. Phys. Usp. 34, 250 (1991). [3] Phillip R. Johnson andB. L.Hu,Phys. Rev.D65, 065015 (2002). [4] C. Harvey, T. Heinzl, N. Iji, and K. Langfeld, Phys. Rev. D 83, 076013 (2011). [5] G. D. R. Martin, arXiv:0805.0666; Y. Yaremko and V. Tretyak, Radiation Reaction in Classical Field Theory (LAP LAMBERT Academic Publishing, Saarbr¨ucken, Germany, 2009). [6] H. Spohn, Europhys. Lett. 49, 287 (2000). [7] T. Matolcsi, T. F¨ul¨op, and M. Weiner, arXiv:1207.0428. [8] J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley & Sons, New York, 1975). [9] Dots indicate laboratory time derivatives when acting on a (boldfaced) three-dimensional vector, but derivatives with respect to invariant interval s (with dimension of proper time multiplied by c) of the moving particle when acting on a four-vector. [10] D. J. Griffiths, T. C. Proctor, and D. F. Schroeter, Am. J. Phys. 78, 391 (2010). [11] A. O. Barut, Electrodynamics and Classical Theory of Fields and Particles (Dover, New York, 1980). [12] F. Rohrlich, Classical Charged Particles (Addison Wesley, Redwood City, CA, 1990). [13] F. Rohrlich, Ann. Phys. (NY) 13, 93 (1961). [14] G. N. Plass, Rev. Mod. Phys. 33, 37 (1961). [15] N. P. Klepikov, Sov. Phys. Ups. 28, 506 (1985). [16] This can be checked by noting that the left-hand side of Eq. (3), the four-acceleration, is a spacelike four vector, while the righthand side in the absence of the external force must be timelike, so that the equality can be satisfied only by ¨xμ = 0. [17] P. O. Kazinski and M. A. Shipulya, Phys. Rev. E 83, 066606 (2011). [18] This in itself is an interesting equation among two exterior products. The right-hand side is similar to the familiar mechanical torque by substituting position by velocity, and it may be called “velocity torque.” Likewise, the tensor in the left-hand side is a sort of angular momentum with higher derivatives. [19] A. Gr¨unbaum and A. I. Janis, Am. J. Phys. 46, 337 (1978). [20] This is a soft version of infinite-time asymptotic freedom that in particular excludes the motion under a constant force extending to t =∞. [21] The first objection could be lifted by integrating once Eq. (30) by parts to obtain ˙x μ(s) = − _ ∞ S ds _e(s−s _ )/L _ f μ(s _) m − xμ(s _) L2 _ . This is a bit closer to our equation (4) in that the highest derivative can be isolated on the left-hand side, and it simplifies the numerical solution some. [22] See the consortium’s extensive information at www.cells.es. [23] A. Valentini, Phys. Rev. Lett. 61, 1903 (1988). [24] C. J. Goebel, Phys. Rev. Lett. 62, 3010 (1989). [25] P. O. Kazinski and A. A. Sharapov, Classical Quantum Gravity 20, 2715 (2003). [26] C.-H. Park, L. Yang, Y. W. Son, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 101, 126804 (2008). [27] We thank an anonymous referee for pointing this out to us. [28] R. L. Burden and J. D. Faires, Numerical Analysis, 8th ed. (Thomson Brooks/Cole, Belmont, CA, 2005). [29] A. A. Vlasov, arXiv:hep-th/9703001. [30] Note that f i = γFi , f 0 = γ F・v, and therefore at each step of the iteration the external force depends on the velocity ˙x μ obtained in the previous step, until convergence is attained. [31] Since we have an explicit exact solution, it will satisfy the integral equation identically, except for round off errors. If we begin with an initial ansatz that is not close to the actual solution, convergence is attained in a few tens of iterations. [32] It is well known that the Lorentz-Dirac differential equation has analytical solutions with constant acceleration under a constant force in the proper reference system (hyperbolic motion), for which the last two terms in Eq. (2) cancel mutually in an exact way. Here, in the iterative solution of our Eq. (4), this constancy of the acceleration in the laboratory frame at the beginning of the action of the force is only approximate, and it stays so only as long as the dilatation factor γ remains near one, and the motion under a constant force in the laboratory almost coincides with an exact hyperbolic motion in the proper system. [33] S. Bellucci, V. M. Biryukov, G. I. Britvich, Yu. A. Chesnokov, C. Balasubramanian, G. Giannini, V. Guidi, Yu. M. Ivanov, V. I. Kotov, V. A. Maisheev, C. Malagu, G. Martinelli, A. A. Petrunin, V. A. Pikalov, A. Raco, L. Silvi, V. V. Skorobogatov, M. Stefancich, F. Tombolini, and D. Vincenzi, Conf. Proc. C 030512, 917 (2003) [Phys. Rev. ST Accel. Beams 7, 023501 (2004)]. [34] A. Kostyuk, A. Korol, A. Solov’yov, andW. Greiner, Eur. Phys. J. D 67, 108 (2013). [35] N. F. Shulga, V. V. Syshchenko, and A. I. Tarnovsky, J. Phys. Conf. Series 357, 012026 (2012). [36] K. G. Batrakov, P. P. Kuzhir, and S. A. Maksimenio, Physica E 40, 1065 (2008). [37] A. di Piazza et al. Rev. Mod. Phys. 84, 1177 (2012). [38] K. Seto, H. Nagatomo, J. Koga, and K. Mima, Communication to the 39th EPS Conference and 16th International Congress on Plasma Physics (European Physical Society, http://ocs.ciemat.es/EPSICPP2012ABS/pdf/P4.096.pdf, 2012), P4.096 [Phys. Plasmas 18, 123101 (2011)]. [39] F. Denef, J. Raeymaekers, U. M. Studer, and W. Troost, Phys. Rev. E 56, 3624 (1997); see also the preprint by A. Vlasov, arXiv:physics/9911059 that studies the phenomenon for a charged, finite sphere, that, due to retardation, passes through the barrier before it can fully realize that it should not.
dspace.entity.typePublication
relation.isAuthorOfPublication6290fe55-04e6-4532-91e6-1df735bdbdca
relation.isAuthorOfPublication0dff92db-2dae-4f1f-9405-9d6d21586e09
relation.isAuthorOfPublication.latestForDiscovery6290fe55-04e6-4532-91e6-1df735bdbdca

Download

Original bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
Llanes-Estrada_FJ79libre.pdf
Size:
1.54 MB
Format:
Adobe Portable Document Format
downoload Download

Collections

Artículos