Runaway Charged Particles and Center Manifolds

We consider the coupled Maxwell{Lorentz equations for a single charge with a rigid charge distribution subject to slowly varying external potentials. In the adiabatic limit, to lowest order, the motion of the charge is governed by an eeective Hamiltonian. In the next order we obtain, as a small correction, the radiation reaction containing q {terms. This equation has a stable center manifold and the true solution stays close to the center manifold. The motion on the center manifold is governed by a novel second order equation which contains \friction" terms whose sign and strength depend on the external potentials.