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Post-Newtonian dynamics at order 1.5 in the Vlasov-Maxwell system

Sebastian Bauer
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Abstract

We study the dynamics of many charges interacting with the Maxwell field. The particles are modeled by means of non-negative 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, $c$, 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 $|v/c|^2$, 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 Newtonian limit. If all particles have the same charge-to-mass ratio, the dissipation would vanish at that order.

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Sebastian Bauer. 2006-02-13. Post-Newtonian dynamics at order 1.5 in the Vlasov-Maxwell system. https://arxiv.org/abs/math-ph/0602031

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