Feedback processes by active galactic nuclei in the centres of galaxy clusters appear to prevent large-scale cooling flows and impede star formation. However, the detailed heating mechanism remains uncertain. One promising heating scenario invokes the dissipation of Alfven waves that are generated by streaming cosmic rays (CRs). In order to study this idea, we use three-dimensional magneto-hydrodynamical simulations with the AREPO code that follow the evolution of jet-inflated bubbles that are filled with CRs in a turbulent cluster atmosphere. We find that a single injection event produces the CR distribution and heating rate required for a successful CR heating model. As a bubble rises buoyantly, cluster magnetic fields drape around the leading interface and are amplified to strengths that balance the ram pressure. Together with helical magnetic fields in the bubble, this initially confines the CRs and suppresses the formation of interface instabilities. But as the bubble continues to rise, bubble-scale eddies significantly amplify radial magnetic filaments in its wake and enable CR transport from the bubble to the cooling intracluster medium. By varying the jet parameters, we obtain a rich and diverse set of jet and bubble morphologies ranging from Fanaroff-Riley type I-like (FRI) to FRII-like jets. We identify jet energy as the leading order parameter (keeping the ambient density profiles fixed), whereas jet luminosity is primarily responsible for setting the Mach numbers of shocks around FRII-like sources. Our simulations also produce FRI-like jets that inflate bubbles without detectable shocks and show morphologies consistent with cluster observations.
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