Evolutionary models for radio sources from compact sources to classical doubles

An analytical model is presented for the evolution of powerful double radio sources on small physical scales less than about 100 kpc when radiative losses can be neglected. The selfsimilar model of Kaiser & Alexander is extended to allow for expansion in an atmosphere with a King profile. Distribution functions for the number of sources in a logarithmic interval of linear size within a flux-limited sample are calculated and compared with observation. The observational data can be reproduced if it is assumed that there exists a population of sources that evolve and survive to sizes greater than the core radius, together with a population that suffer disruption of their jets before escaping the core radius. The latter population, while they may be regarded as frustrated sources, are not old sources, but just short-lived.