On the radiative instability.

Abstract

A thin beam of monoenergetic electrons and positrons may be described by a single interface with a surface current and it is shown that wave modes (in particular their growth rates) depend only on the form of this surface current and not explicitly on the geometry, specifically whether it is planar or cylindrical. We give general results for the wave modes which reproduce those previously obtained in the planar and cylindrical geometries and discuss their implications.