  We have developed an economical, effective numerical scheme for cosmic-ray
transport suitable for treatment of electrons up to a few hundreds of GeV in
multidimensional simulations of radio galaxies. The method follows the electron
population in sufficient detail to allow computation of synthetic radio and
X-ray observations of the simulated sources, including spectral properties (see
the companion paper by Tregillis et al. 1999). The cosmic-ray particle
simulations can follow the effects of shock acceleration, second-order Fermi
acceleration as well as radiative and adiabatic energy losses. We have applied
this scheme to 2-D and 3-D MHD simulations of jet-driven flows and have begun
to explore links between dynamics and the properties of high energy electron
populations in radio lobes. The key initial discovery is the great importance
to the high energy particle population of the very unsteady and inhomogeneous
flows, especially near the end of the jet. Because of this, in particular, our
simulations show that a large fraction of the particle population flowing from
the jet into the cocoon never passes through strong shocks. The shock strengths
encountered are not simply predicted by 1-D models, and are quite varied.
Consequently, the emergent electron spectra are highly heterogeneous. Rates of
synchrotron aging in "hot-spots" seem similarly to be very uneven, enhancing
complexity in the spectral properties of electrons as they emerge into the
lobes and making more difficult the task of comparing dynamical and radiative
ages.
