  We extend de concept of Compton scattering to the case of plasmons. This
concept was originally applied to electrons in vacuum. Here, we consider
electrons in a plasma, and study the scattering properties of photon-plasmon
interactions. We show that a number $n$ of plasmons with frequency $ \omega
\simeq \omega_p$ is scattered by an electron, for an incident photon with
frequency $\omega' \geq \omega_p$, where $\omega_p$ is the plasma frequency. We
describe the general case of arbitrary $n$ and assume that Compton scattering
of plasmons is intrinsically a nonlinear process. Our theoretical model is
based on Volkov solutions of the Klein-Gordon equation describing the state of
relativistic electrons, when the spin is ignored. We derive the corresponding
scattering probability, as well as the recoil formula associated with arbitrary
the final electron states. This process can be relevant to intense laser plasma
interactions.
