  Galaxy clusters are considered to be gigantic reservoirs of cosmic rays
(CRs). Some of the clusters are found with extended radio emission, which
provides evidence for the existence of magnetic fields and CR electrons in the
intra-cluster medium (ICM). The mechanism of radio halo (RH) emission is still
under debate, and it has been believed that turbulent reacceleration plays an
important role. In this paper, we study the reacceleration of CR protons and
electrons in detail by numerically solving the Fokker-Planck equation, and show
how radio and gamma-ray observations can be used to constrain CR distributions
and resulting high-energy emission for the Coma cluster. We take into account
the radial diffusion of CRs and follow the time evolution of their
one-dimensional distribution, by which we investigate the radial profile of the
CR injection that is consistent with the observed RH surface brightness. We
find that the required injection profile is non-trivial, depending on whether
CR electrons have the primary or secondary origin. Although the secondary CR
electron scenario predicts larger gamma-ray and neutrino fluxes, it is in
tension with the observed RH spectrum. In either scenario, we find that galaxy
clusters can make a sizable contribution to the all-sky neutrino intensity if
the CR energy spectrum is nearly flat.
