Non-linear effects in the forces acting on fast charged particles passing over two-dimensional electron gas

We study the interactions of fast charged particles with a two-dimensional electron gas describing its collective or plasmon excitations by a hydrodynamic model with the parameters characteristic of graphene. We solve the sets of first and second order equations in a perturbational treatment of the hydrodynamic model, and obtain numerical results for the stopping force and the image force on a particle moving parallel to the electron gas. Although the second order effects in these forces are relatively small, they could be observed in experiments on grazing scattering of, e.g., fast protons and antiprotons from the surface of graphene.