Possible instability of the Fermi sea against surface plasma oscillations

We derive a generic formalism for studying the energy conversion processes in bounded metals. Using this formalism we show that in the collision-less limit the Fermi sea of metals should experience an instability against surface plasma oscillations, which opens for the latter an intrinsic self-amplification channel. The origin of the instability is clarified as arising from novel effects resulting from the translation symetry breaking due to the very presence of surface. The amplification rate of this channel is analytically evaluated on the basis of energy conservation and the effects of losses are discussed. In particular, the unique role played by the surface in energy conversion is unveiled. In contrast with common wisdom and in line with observations, Landau damping is shown as always overcompensated and therefore poses no serious issues in sub-wavelength plasmonics.