An exact expression is given for the orbit of a charged particle accelerated by a non-propagating electrostatic wave. The corresponding current is obtained, for untrapped particles, as an expansion in Bessel functions, and a Lorentz transform allows us to treat the case of a propagating wave. An appropriate form for the absorption coefficient is derived, and an interesting angular and frequency dependence is revealed when the propagating wave is superluminal. Finally, the possible application to pulsars, particularly in explaining the multicomponent pulse profiles, is discussed briefly.