  We introduce a simple and economical but effective method for including
relativistic electron transport in multi-dimensional simulations of radio
galaxies. The method is designed to follow explicitly diffusive acceleration at
shocks, and, in smooth flows 2nd order Fermi acceleration plus adiabatic and
synchrotron cooling. We are able to follow both the spatial and energy
distributions of the electrons, so that direct synchrotron emission properties
can be modeled in time-dependent flows for the first time.
  Here we present first results in the form of some axis-symmetric MHD
simulations of Mach 20 light jet flows. These show clearly the importance of
nonsteady terminal shocks that develop in such flows even when the jet inflow
is steady. As a result of this and other consequences of the fundamentally
driven character of jets, we find complex patterns of emissivities and
synchrotron spectra, including steep spectral gradients in hot spots, islands
of distinct spectra electrons within the lobes and spectral gradients coming
from the dynamical histories of a given flow element rather than from
synchrotron aging of the embedded electrons. In addition, spectral aging in the
lobes tends to proceed more slowly than one would estimate from regions of high
emissivity.
