Post-Coulombian Dynamics at Order 1.5

We study the dynamics of N charges interacting with the Maxwell field. If their initial velocities are small compared to the velocity of light, c, then in lowest order their motion is governed by the static Coulomb Lagrangian. We investigate higher order corrections with an explicit control on the error terms. The Darwin correction, order (v/c)^2, has been proved previously. In this contribution we obtain the dissipative corrections due to radiation damping, which are of order (v/c)^3 relative to the Coulomb dynamics. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.