Compton Scattering of Plasmons

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.