Abstract
We study the dynamics of many charges interacting with the Maxwell field. The particles are modeled by means of nonnegative distribution functions \(f^+\) and \(f^-\) representing two species of charged matter with positive and negative charge, respectively. If their initial velocities are small compared to the speed of light, \(\mathrm{c}\), 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 \(|\bar{\mathrm{v}}/\mathrm{c}|^2\), has been proved previously. In this contribution, we obtain the dissipative corrections due to radiation damping, which are of order \(|\bar{\mathrm{v}}/\mathrm{c}|^3\) relative to the Newtonian limit. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.
Published Version
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