Models of extragalactic radio sources with a continuous energy supply from a central object

This paper explores the dynamics of radio source models in which energy is carried from a nucleus to the radio components by a relativistic beam. Only a small fraction of the energy supply can be radiated away from tne tip of the beam, and the rest lingers on in a cavity surrounding the beam. For the dynamical development of the source it is not of great importance whether the `beam' consists of strong electromagnetic waves or of fast particles with or without magnetic fields, or even if the energy is supplied from a moving massive object instead of the tip of a beam. if the energy in the cavity contains both fast electrons and magnetic fields, then the cavity rather than the tip of the beam is likely to be the site for the greater part of the radio emission. When the lateral expansion of the cavity becomes subsonic, the outer parts of the cavity swell at the expense of the parts nearest tbe massive nucleus, where the thermal gas pressure is higher.