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Recent radio observations have identified a class of structures, so-calledradio relics, in clusters of galaxies. The radio emission from these sources isinterpreted as synchrotron radiation from GeV electrons gyrating inmicroG-level magnetic fields. Radio relics, located mostly in the outskirts ofclusters, seem to associate with shock waves, especially those developed duringmergers. In fact, they seem to be good structures to identify and probe suchshocks in intracluster media (ICMs), provided we understand the electronacceleration and re-acceleration at those shocks. In this paper, we describetime-dependent simulations for diffusive shock acceleration at weak shocks thatare expected to be found in ICMs. Freshly injected as well as pre-existingpopulations of cosmic-ray (CR) electrons are considered, and energy losses viasynchrotron and inverse Compton are included. We then compare the synchrotronflux and spectral distributions estimated from the simulations with those intwo well-observed radio relics in CIZA J2242.8+5301 and ZwCl0008.8+5215.Considering that the CR electron injection is rather inefficient at weak shockswith Mach number M <~ a few, the existence of radio relics could indicate thepre-existing population of low-energy CR electrons in ICMs. The implication ofour results on the merger shock scenario of radio relics is discussed.

Diffusive Shock Acceleration Simulations of Radio Relics