  We study the generation and distribution of high energy electrons in cosmic
environment and their observational consequences by carrying out the first
cosmological simulation that includes directly cosmic ray (CR) particles.
Starting from cosmological initial conditions we follow the evolution of
primary and secondary electrons (CRE), CR ions (CRI) and a passive magnetic
field. CRIs and primary CREs are injected and accelerated at large scale
structure shocks. Secondary CREs are continuously generated through inelastic
p-p collisions. We include spatial transport, adiabatic expansion/compression,
Coulomb collisions, bremsstrahlung, synchrotron (SE)and inverse Compton (IC)
emission. We find that, from the perspective of cosmic shock energy and
acceleration efficiency, the few detections of hard X-ray radiation excess
could be explained in the framework of IC emission of primary CREs in clusters
undergoing high accretion/merger phase. Instead, IC emission from both primary
and secondary CREs accounts at most for a small fraction of the radiation
excesses detected in the extreme-UV (except for the Coma cluster as reported by
Bowyer et al.1999). Next, we calculate the SE after normalizing the magnetic
field so that for a Coma-like cluster <B^2>^1/2~3 \muG. Our results indicate
that the SE from secondary CREs reproduces several general properties of radio
halos, including the recently found P_1.4GHz vs T relation, the morphology and
polarization of the emitting region and, to some extent, the spectral index.
Moreover, SE from primary CREs turns out sufficient to power extended regions
resembling radio relics observed at the outskirts of clusters. Again we find
striking resemblance between morphology, polarization and spectral index of our
synthetic maps and those reported in the literature.
