  Cosmological MHD simulations of galaxy cluster formation show a significant
amplification of seed magnetic fields. We developed a novel method to decompose
cluster magnetized turbulence into modes and showed that the fraction of the
fast mode is fairly large, around 1/4 in terms of energy. This is larger than
that was estimated before, which implies that cluster turbulence interacts with
cosmic rays rather efficiently. We propose a framework to deal with electron
and proton reacceleration in galaxy clusters that includes feedback on
turbulence. In particular, we establish a new upper limit on proton and
electron fluxes based on turbulence intensity. These findings, along with
detailed modeling of reacceleration, will help to reconcile the observed giant
radio haloes and the unobserved diffuse gamma-ray emission from these clusters.
