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In Cygnus A and other classical FR II double radio sources, powerful opposingjets from the cores of halo-centered galaxies drive out into the surroundingcluster gas, forming hotspots of shocked and compressed cluster gas at the jetextremities. The moving hotspots are sandwiched between two shocks. Aninner-facing shock receives momentum and cosmic rays from the jet and createsadditional cosmic rays that form a radio lobe elongated along the jet axis. Anouter-facing bow shock moves directly into the undisturbed group or clustergas, creating a cocoon of shocked gas enclosing the radio lobe. We describecomputations that follow the self-consistent dynamical evolution of the shockedcluster gas and the relativistic synchrotron-emitting gas inside the lobes.Relativistic and non-relativistic components exchange momentum by interactingwith small magnetic fields having dynamically negligible energy densities. Theevolution of Cygnus A is governed almost entirely by cosmic ray energy flowingfrom the hotspots. Mass flowing into hotspots from the jets is assumed to besmall, greatly reducing the mass of gas flowing back along the jet, common inprevious calculations, that would disrupt the spatial segregation ofsynchrotron-loss ages observed inside FR II radio lobes. We compute theevolution of the cocoon when the velocity and cosmic ray luminosity of thehotspots are constant and when they vary with time. If cosmic rays mix withcluster gas in hotspots before flowing into the radio lobe, the thermal gas isheated to mildly relativistic temperatures, producing an unobserved pressureinside the lobe.

Self-consistent evolution of gas and cosmic rays in Cygnus A and similar FR II classic double radio sources