  Radio relics are arc-like synchrotron sources at the periphery of galaxy
clusters, produced by cosmic-ray electrons in a $\mu$G magnetic field which are
believed to have been (re-)accelerated by merger shock fronts. However, not all
relics appear at the same location as shocks as seen in the X-ray. In a
previous work, we suggested that the shape of some relics may result from the
pre-existing spatial distribution of cosmic-ray electrons, and tested this
hypothesis using simulations by launching AGN jets into a cluster atmosphere
with sloshing gas motions generated by a previous merger event. We showed that
these motions could transport the cosmic ray-enriched material of the AGN
bubbles to large radii and stretch it in a tangential direction, producing a
filamentary shape resembling a radio relic. In this work, we improve our
physical description for the cosmic rays by modeling them as a separate fluid
which undergoes diffusion and Alfv\'en losses. We find that including this
additional cosmic ray physics significantly diminishes the appearance of these
filamentary features, showing that our original hypothesis is sensitive to the
modeling of cosmic ray physics in the intracluster medium.
