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Second-order equation of motion for electromagnetic radiation back-reaction

Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Pázmány P. stny. 1/C, H-1117 Budapest, Hungary

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T. Fülöp

Department of Energy Engineering, Budapest University of Technology and Economics, Bertalan L. u. 4-6, H-1111 Budapest, Hungary

E-mail Address: fulop@energia.bme.hu

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, and

M. Weiner

Department of Analysis, Budapest University of Technology and Economics, Egry J. u. 1, H-1111 Budapest, Hungary

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https://doi.org/10.1142/S0217732317501474Cited by:1 (Source: Crossref)

Abstract

We take the viewpoint that the physically acceptable solutions of the Lorentz–Dirac equation for radiation back-reaction are actually determined by a second-order equation of motion, the self-force being given as a function of spacetime location and velocity. We propose three different methods to obtain this self-force function. For two example systems, we determine the second-order equation of motion exactly in the non-relativistic regime via each of these three methods, leading to the same result. We reveal that, for both systems considered, back-reaction induces a damping proportional to velocity and, in addition, it decreases the effect of the external force.

Keywords:

PACS: 03.50.De, 41.60.-m, 45.20.D-, 11.10.Gh

References

1. J. D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, 1998). Google Scholar
2. S. R. de Groot and L. G. Suttorp, Foundations of Electrodynamics (North-Holland, 1972). Google Scholar
3. J. G. Taylor, Math. Proc. Camb. Philos. Soc. 52, 119 (1956). Crossref, ADS, Google Scholar
4. T. Matolcsi, Classical Electrodynamics, extracts from the Scientific Works of the Department of Applied Analysis, Eötvös University, 1977. Google Scholar
5. E. G. P. Rowe, Phys. Rev. D 18, 3639 (1978). Crossref, Web of Science, ADS, Google Scholar
6. A. Gsponer, arXiv:0812.3493v2. Google Scholar
7. P. A. M. Dirac, Proc. R. Soc. Lond. A 167, 148 (1938). Crossref, ADS, Google Scholar
8. R. Haag, Z. Naturforsch. A 10, 752 (1955). Crossref, ADS, Google Scholar
9. M. M. de Souza, Braz. J. Phys. 28, 250 (1998). Crossref, Web of Science, ADS, Google Scholar
10. H. Spohn, EPL 50, 287 (2000). Crossref, Web of Science, ADS, Google Scholar
11. R. F. O’Connell, Phys. Lett. A 313, 491 (2003). Crossref, Web of Science, ADS, Google Scholar
12. H. Spohn, Dynamics of Charged Particles and Their Radiation Field (Cambridge Univ. Press, 2004). Crossref, Google Scholar
13. A. D. Yaghjian, Relativistic Dynamics of a Charged Sphere, 2nd edn., Lecture Notes Physics, Vol. 686 (Springer, 2006). Crossref, Google Scholar
14. F. Rohrlich, Classical Charged Particles, 3rd edn. (World Scientific, 2007). Link, Google Scholar
15. R. Mares, P. I. Ramírez-Baca and G. Ares de Parga, J. Vector. Relativ. 5, 1 (2010). Google Scholar
16. G. Ares de Parga, R. Mares and M. Ortiz-Domínguez, J. Vector. Relativ. 5, 26 (2010). Google Scholar
17. A. Kar and S. G. Rajeev, Ann. Phys. 326, 958 (2011). Crossref, Web of Science, ADS, Google Scholar
18. P. Forgács, T. Herpay and P. Kovács, Phys. Rev. Lett. 109, 029501 (2012). Crossref, Web of Science, ADS, Google Scholar
19. L. D. Landau and E. M. Lifshitz, Classical Theory of Fields (Butterworth-Heinemann, 1982). Google Scholar
20. J. Polonyi, Ann. Phys. 342, 239 (2014). Crossref, Web of Science, ADS, Google Scholar