  We describe approximate axisymmetric computations of the dynamical evolution
of material inside radio lobes and X-ray cluster gas cavities in Fanaroff-Riley
II sources such as Cygnus A. All energy is delivered by a jet to the
lobe/cavity via a moving hotspot where jet energy dissipates in a reverse
shock. Our calculations describe the evolution of hot plasma, cosmic rays (CRs)
and toroidal magnetic fields flowing from the hotspot into the cavity. Many
observed features are explained. Gas, CRs and field flow back along the cavity
surface in a "boundary backflow" consistent with detailed FRII observations.
Computed ages of backflowing CRs are consistent with observed radio-synchrotron
age variations only if shear instabilities in the boundary backflow are damped
and we assume this is done with viscosity of unknown origin. Magnetic fields
estimated from synchrotron self-Compton (SSC) X-radiation observed near the
hotspot evolve into radio lobe fields. Computed profiles of radio synchrotron
lobe emission perpendicular to the jet are dramatically limb-brightened in
excellent agreement with FRII observations although computed lobe fields exceed
those observed. Strong winds flowing from hotspots naturally create kpc-sized
spatial offsets between hotspot inverse Compton (IC-CMB) X-ray emission and
radio synchrotron emission that peaks 1-2 kpc ahead where the field increases
due to wind compression. In our computed version of Cygnus A, nonthermal X-ray
emission increases from the hotspot (some IC-CMB, mostly SSC) toward the offset
radio synchrotron peak (mostly SSC). A faint thermal jet along the symmetry
axis may be responsible for redirecting the Cygnus A non-thermal jet.
