A Post-Newtonian Expansion Including Radiation Damping for a Collisionless Plasma

摘要

We study the dynamics of many charges interacting with the Maxwell field. The particles are modeled by means of nonnegative distribution functions f+ representing two species of charged matter with positive and negative charge, respectively. If their initial velocities are small compared to the speed of light, c, then in lowest order, the Newtonian or classical limit, their motion is governed by the Vlasov-Poisson system. We investigate higher-order corrections with an explicit control on the error terms. The Darwin order correction, order |v over bar /c|3 relative to the Newtonian limit. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.