▎ 摘　　要

We derive a dielectric response model for dynamic polarization of freestanding multilayer graphene induced by an external charged particle moving at an arbitrary angle of incidence. Using a two-dimensional, two-fluid hydrodynamic model for the single-layer polarizability, we evaluate the probability density for energy loss and the total energy loss of fast electrons traversing graphene under normal incidence for a broad range of the incident electron kinetic energies. Numerical results are obtained in the cases of one, two, and three layers of graphene. When the incident electron kinetic energy T increases, both the probability density and the total energy loss strongly decrease. It is also found that when the kinetic energy T decreases, the pi and sigma + pi plasmon peak positions move to higher energies omega. In addition, the total energy loss approximately scales with the number of graphene layers N for all observed incident electron kinetic energies. (C) 2015 Elsevier B.V. All rights reserved.