  While a fully relativistic collisionless plasma is modeled by the
Vlasov-Maxwell system a good approximation in the non-relativistic limit is
given by the Vlasov-Poisson system. We modify the Vlasov-Poisson system so that
damping due to the relativistic effect of radiation reaction is included. We
prove the existence and uniqueness as well as the higher regularity of local
classical solutions. These theorems also include the higher regularity of
classical solutions of the Vlasov-Poisson system depending on the regularity of
the initial datum.
