  In this work the explicit solution of the electronic plasma diffusion with
radiation reaction force, under the action of an exponential decay external
electric field is given. The electron dynamics is described by a classical
generalized Langevin equation characterized by an Ornstein-Uhlenbeck-type
friction memory kernel, with an effective memory time which accounts for the
effective thermal interaction between the electron and its surroundings
(thermal collisions between electrons + radiation reaction force). The incident
electric field exerts an electric force on the electron, which in turn can
induce an additional damping to the braking radiation force, allowing a delay
in the electron characteristic time. This fact allows that the effective memory
time be finite and positive, and as a consequence, obtaining physically
admissible solutions of the stochastic Abraham-Lorentz-like equation. It is
shown that the diffusion process is quasi-Markovian which includes the
radiation effects.
