  About 1/3 of X-ray-luminous clusters show smooth, unpolarized radio emission
on ~Mpc scales, known as giant radio halos. One promising model for radio halos
is Fermi-II acceleration of seed relativistic electrons by turbulence of the
intracluster medium (ICM); Coulomb losses prohibit acceleration from the
thermal pool. However, the origin of seed electrons has never been fully
explored. Here, we integrate the Fokker-Planck equation of the cosmic ray (CR)
electron and proton distributions in a cosmological simulations of cluster
formation. For standard assumptions, structure formation shocks lead to a seed
electron population which produces too centrally concentrated radio emission.
Instead, we present three realistic scenarios that each can reproduce the
spatially flat radio emission observed in the Coma cluster: (1) the ratio of
injected turbulent energy density to thermal energy density increase
significantly with radius, as seen in cosmological simulations. This generates
a flat radio profile even if the seed population of CRs is steep with radius.
(2) Self-confinement of energetic CR protons can be inefficient, and CR protons
may stream at the Alfven speed to the cluster outskirts when the ICM is
relatively quiescent. A spatially flat CR proton distribution develops and
produces the required population of secondary seed electrons. (3) The CR proton
to electron acceleration efficiency K_ep ~ 0.1 is assumed to be larger than in
our Galaxy (K_ep ~ 0.01), due to the magnetic geometry at the shock. The
resulting primary electron population dominates. Due to their weaker density
dependence compared to secondary electrons, these primaries can also reproduce
radio observations. These competing non-trivial solutions provide incisive
probes of non thermal processes in the high-beta ICM.
