  The spectral evolution of powerful double radio galaxies (FR II's) is thought
to be determined by the acceleration of electrons at the termination shock of
the jet, their transport through the bright head region into the lobes and the
production of the radio emission by synchrotron radiation in the lobes. Models
presented to date incorporate some of these processes in prescribing the
electron distribution which enters the lobes. We have extended these models to
include a description of electron acceleration at the relativistic termination
shock and a selection of transport models for the head region. These are
coupled to the evolution of the electron spectrum in the lobes under the
influence of losses due to adiabatic expansion, by inverse Compton scattering
on the cosmic background radiation and by synchrotron radiation. The
evolutionary tracks predicted by this model are compared to observation using
the power/source-size (P-D) diagram. We find that the simplest scenario, in
which accelerated particles suffer adiabatic losses in the head region which
become more severe as the source expands produces P-D-tracks which conflict
with observation, because the power is predicted to decline too steeply with
increasing size. Agreement with observation can be found by assuming that
adiabatic losses are compensated during transport between the termination shock
and the lobe by a re-acceleration process distributed throughout the head
region.
