  We simulate the evolution of relativistic electrons injected into the medium
of a small galaxy cluster by a central radio galaxy, studying how the initial
jet power affects the dispersal and the emission properties of radio plasma. By
coupling passive tracer particles to adaptive-mesh cosmological MHD
simulations, we study how cosmic-ray electrons are dispersed as a function of
the input jet power. We also investigate how the latter affects the thermal and
non-thermal properties of the intracluster medium, with differences discernible
up to $\sim$ Gyr after the start of the jet. We evolved the energy spectra of
cosmic-ray electrons, subject to energy losses that are dominated by
synchrotron and inverse Compton emission as well as energy gains via
re-acceleration by shock waves and turbulence. We find that in the absence of
major mergers the amount of re-acceleration experienced by cosmic-ray electrons
is not enough to produce long-lived detectable radio emissions. However, for
all simulations the role of re-acceleration processes is crucial to maintain a
significant and volume-filling reservoir of fossil electrons ($\gamma \sim
10^3$) for several Gyrs after the first injection by jets. This is important to
possibly explain recent discoveries of cluster-wide emission and other radio
phenomena in galaxy clusters.
