Hamiltonian formulation for the classical EM radiationreaction problem: Application to the kinetic theory for relativistic collisionless plasmas
 C. Cremaschini,
 M. Tessarotto
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
A notorious difficulty in the covariant dynamics of classical charged particles subject to nonlocal electromagnetic (EM) interactions arising in the EM radiationreaction (RR) phenomena is due to the definition of the related nonlocal Lagrangian and Hamiltonian systems. As a basic consequence, the lack of a standard Lagrangian/Hamiltonian formulation in the customary asymptotic approximation for the RR equation may inhibit the construction of consistent kinetic and fluid theories. In this paper the issue is investigated in the framework of Special Relativity. It is shown that, for finitesize sphericallysymmetric classical charged particles, nonperturbative Lagrangian and Hamiltonian formulations in standard form can be obtained, which describe particle dynamics in the presence of the exact EM RR selfforce. As a remarkable consequence, based on axiomatic formulation of classical statistical mechanics, the covariant kinetic theory for systems of charged particles subject to the EM RR selfforce is formulated in Hamiltonian form. A fundamental feature is that the nonlocal effects enter the kinetic equation only through the retarded particle 4position. This permits, in turn, the construction of the related fluid equations, in which the nonlocal contributions carried by the RR effects are explicitly displayed. In particular, it is shown that the moment equations obtained in this way do not contain higherorder moments, allowing as a consequence the adoption of standard closure conditions. A remarkable aspect of the theory is related to the short delaytime asymptotic expansions. Here it is shown that two possible expansions are permitted. Both can be implemented for the singleparticle dynamics as well as for the corresponding kinetic and fluid treatments. In the last case, they are performed a posteriori, namely on the relevant moment equations obtained after integration of the kinetic equation over the velocity space. Comparisons with the literature are pointed out.
 R.P. Feynman, Feynman’s Thesis: A New Approach to Quantum Theory, edited by L.M. Brown (World Scientific, 2005).
 Llosa, J., Vives, J. (1994) J. Math. Phys. 35: pp. 2856 CrossRef
 Kerner, E.J. (1962) J. Math. Phys. 3: pp. 35 CrossRef
 Marnelius, R. (1974) Phys. Rev. D 10: pp. 2335
 P Gaida, R., Tretyak, V.I. (1980) Acta Phys. Pol. B 11: pp. 509
 Jaen, X., Llosa, J., Molina, A. (1986) Phys. Rev. D 34: pp. 2302 CrossRef
 Dorigo, M., Tessarotto, M., Nicolini, P., Beklemishev, A. (2008) AIP Conf. Proc. 1084: pp. 152 CrossRef
 Lorentz, H.A. (1892) Arch. Néerl. Sci. Exactes Nat. 25: pp. 363
 M. Abraham, Theorie der Elektrizität: Elektromagnetische Strahlung, Vol. II (Teubner, Leiptzig, 1905).
 Dirac, P.A.M. (1938) Proc. Roy. Soc. London, Ser. A 167: pp. 148 CrossRef
 L.D. Landau, E.M. Lifschitz, Field theory, Theoretical Physics, Vol. 2 (AddisonWesley, N.Y., 1957).
 H. Goldstein, Classical Mechanics, 2nd edition (AddisonWesley, 1980).
 V. Arnold, Les Méthodes Mathématiques de la Méchanique Classique (MIR, Moscow, 1976).
 Hakim, R. (1967) J. Math. Phys. 8: pp. 1315 CrossRef
 Hakim, R. (1968) J. Math. Phys. 9: pp. 116 CrossRef
 Tamburini, M., Pegoraro, F., Piazza, A., Keitel, C.H., Macchi, A. (2010) New J. Phys. 12: pp. 123005 CrossRef
 Berezhiani, V.I., Hazeltine, R.D., Mahajan, S.M. (2004) Phys. Rev. E 69: pp. 056406 CrossRef
 Tessarotto, M., Dorigo, M., Cremaschini, C., Nicolini, P., Beklemishev, A. (2008) AIP Conf. Proc. 1084: pp. 158 CrossRef
 Cremaschini, C., Tessarotto, M. (2011) Eur. Phys. J. Plus 126: pp. 42 CrossRef
 Nodvik, J.S. (1964) Ann. Phys. 28: pp. 225 CrossRef
 S.R. De Groot, W.A. Van Leeuwen, Ch.G. Van Weert, Relativistic Kinetic Theory (NorthHolland, 1980).
 J.D. Jackson, Classical Electrodynamics (John Wiley and Sons, New York, 1975).
 Title
 Hamiltonian formulation for the classical EM radiationreaction problem: Application to the kinetic theory for relativistic collisionless plasmas
 Journal

The European Physical Journal Plus
126:63
 Online Date
 July 2011
 DOI
 10.1140/epjp/i2011110633
 Online ISSN
 21905444
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Authors

 C. Cremaschini ^{(1)} ^{(2)}
 M. Tessarotto ^{(2)} ^{(3)}
 Author Affiliations

 1. International School for Advanced Studies (SISSA), Trieste, Italy
 2. Consortium for Magnetofluid Dynamics, University of Trieste, Trieste, Italy
 3. Department of Mathematics and Informatics, University of Trieste, Trieste, Italy