Force on a moving charge near a metal surface: effect of spatial dispersion

Abstract

The hydrodynamic model is used to investigate the effect of spatial dispersion on the force on a charge which is moving with constant velocity nu parallel to a metal surface. The contributions from both surface and bulk plasmons to the force components F_{perpendicular to} and F/sub /// are readily obtained using a normal-mode decomposition of the non-local dielectric response of the metallic electrons. The conservative F_{perpendicular to} and dissipative F/sub /// forces are analysed in terms of the symmetry properties of the induced density. The velocity dependence of the forces is discussed, with the plasmon contribution to F/sub /// being shown to vanish when nu < beta , which is of the order of the Fermi velocity of the metallic electrons.