Many-fluxon kinetics in an inhomogeneous damped dc driven Josephson junction

Radiative effects accompanying a fluxon-antifluxon collision on the background of a localized inhomogeneity (microshort or microresistance) or in a randomly inhomogeneous long Josephson junction are studied. The total emitted energy and the corresponding threshold value of the bias current density for radiative annihilation of a fluxon-antifluxon pair into a breather are found. The obtained results are applied to a qualitative description of neutral fluxon-antifluxon "rarefied gas" in a junction with periodic or random inhomogeneities. In particular, we obtain an estimate for the maximum possible equilibrium density of the "gas" at given density of bias current. Some kinetic characteristics of the "gas" in a non-equilibrium state, e.g. mean lifetime and free path length of a fluxon in the case when the density exceeds the equilibrium value, are estimated too.