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We simulate the evolution of relativistic electrons injected into the mediumof a small galaxy cluster by a central radio galaxy, studying how the initialjet power affects the dispersal and the emission properties of radio plasma. Bycoupling passive tracer particles to adaptive-mesh cosmological MHDsimulations, we study how cosmic-ray electrons are dispersed as a function ofthe input jet power. We also investigate how the latter affects the thermal andnon-thermal properties of the intracluster medium, with differences discernibleup to $\sim$ Gyr after the start of the jet. We evolved the energy spectra ofcosmic-ray electrons, subject to energy losses that are dominated bysynchrotron and inverse Compton emission as well as energy gains viare-acceleration by shock waves and turbulence. We find that in the absence ofmajor mergers the amount of re-acceleration experienced by cosmic-ray electronsis not enough to produce long-lived detectable radio emissions. However, forall simulations the role of re-acceleration processes is crucial to maintain asignificant and volume-filling reservoir of fossil electrons ($\gamma \sim10^3$) for several Gyrs after the first injection by jets. This is important topossibly explain recent discoveries of cluster-wide emission and other radiophenomena in galaxy clusters.

Life cycle of cosmic-ray electrons in the intracluster medium