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.