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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
38/1999

Adiabatic limit for the Maxwell-Lorentz equations

Markus Kunze and Herbert Spohn

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 the motion of the charged particle is governed by a effective Hamiltonian. To next order one has to add as a small correction the relativistically covariant 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 derived from the Liénard-Wiechert potentials of a moving point charge and that the radiated energy is given by Lamor's formula.

Received:
09.06.99
Published:
09.06.99

Related publications

inJournal
2000 Repository Open Access
Markus Kunze and Herbert Spohn

Adiabatic limit for the Maxwell-Lorentz equations

In: Annales Henri Poincaré, 1 (2000) 4, pp. 625-653