Adiabatic limit for the Maxwell-Lorentz equations

Authors
Citation
M. Kunze et H. Spohn, Adiabatic limit for the Maxwell-Lorentz equations, ANN HENRI P, 1(4), 2000, pp. 625-653
Citations number
15
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
ANNALES HENRI POINCARE
ISSN journal
1424-0637 → ACNP
Volume
1
Issue
4
Year of publication
2000
Pages
625 - 653
Database
ISI
SICI code
1424-0637(2000)1:4<625:ALFTME>2.0.ZU;2-0
Abstract
We consider the Abraham model of a rigid charge distribution coupled to the electromagnetic field and subject to, on the scale of the charge diameter, slowly Varying external potentials. We prove that in the adiabatic limit t he motion of the charged particle is governed by a effective Hamiltonian. T o next order one has to add as a small correction the relativistically cova riant radiation reaction. This third order equation has a repulsive center manifold and the true solution is well approximated by a trajectory on the center manifold. We also prove that in the adiabatic limit the fields are d erived from the Lienard-Wiechert potentials of a moving point charge and th at the radiated energy is given by Larmor's formula.