An analytical expression for the energy loss of fast electrons travelling parallel to the axis of a cylindrical interface

Abstract

Abstract An expression for the probability of energy loss of electrons travelling at relativistic speeds parallel to the axis of an infinite cylindrical interface is obtained by solving Maxwell's eauations to find the electric field acting on the electron. This expression is evaluated for the case of an electron travelling through a hole in aluminium and through a hole in amorphous aluminium fiuoride and a comparison is made with the equivalent non-relativistic expression obtained from Poisson's eauation. The non-relativistic solution is shown to underestimate the magnitude and overestimate the energy of the surface plasmon modes. Some calculations are also made to demonstrate the effect of a spatially distributed electron probe on the spectra.