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Radio relics are giant sources of diffuse synchrotron radio emission in theoutskirts of galaxy clusters that are associated with shocks in theintracluster medium. Still, the origin of relativistic particles that make uprelics is not fully understood. For most relics, diffusive shock acceleration(DSA) of thermal electrons is not efficient enough to explain observed radiofluxes. In this paper, we use a magneto-hydrodynamic simulation of galaxyclusters in combination with Lagrangian tracers to simulate the formation ofradio relics. Using a Fokker-Planck solver to compute the energy spectra ofrelativistic electrons, we determine the synchrotron emission of the relic. Wefind that re-acceleration of fossil electrons plays a major role in explainingthe synchrotron emission of radio relics. Particles that pass through multipleshocks contribute significantly to the overall luminosity of a radio relic andgreatly boosts the effective acceleration efficiency. Furthermore, we find thatthe assumption that the luminosity of a radio relic can be explained with DSAof thermal electrons leads to an overestimate of the acceleration efficiency bya factor of more than $10^3$.

A multishock scenario for the formation of radio relics