  Non-thermal radio emission from cosmic ray electrons in the vicinity of
merging galaxy clusters is an important tracer of cluster merger activity, and
is the result of complex physical processes that involve magnetic fields,
particle acceleration, gas dynamics, and radiation. In particular, objects
known as radio relics are thought to be the result of shock-accelerated
electrons that, when embedded in a magnetic field, emit synchrotron radiation
in the radio wavelengths. In order to properly model this emission, we utilize
the adaptive mesh refinement simulation of the magnetohydrodynamic evolution of
a galaxy cluster from cosmological initial conditions. We locate shock fronts
and apply models of cosmic ray electron acceleration that are then input into
radio emission models. We have determined the thermodynamic properties of this
radio-emitting plasma and constructed synthetic radio observations to compare
to observed galaxy clusters. We find a significant dependence of the observed
morphology and radio relic properties on the viewing angle of the cluster,
raising concerns regarding the interpretation of observed radio features in
clusters. We also find that a given shock should not be characterized by a
single Mach number. We find that the bulk of the radio emission comes from gas
with T>5x10^7, \rho~10^(-28)-10^(-27) g/cm^3, with magnetic field strengths of
0.1-1.0 \mu G and shock Mach numbers of M~3-6. We present an analysis of the
radio spectral index which suggests that the spatial variation of the spectral
index can mimic synchrotron aging. Finally, we examine the polarization
fraction and position angle of the simulated radio features, and compare to
observations.
