Gamma-ray emission from galaxy cluster outskirts versus radio relics
  Galaxy cluster peripheries provide important information on the nature of
ICM/IGM linkage. In this paper we consider potential future observations in the
gamma-ray domain at cluster edges involving the radio relic phenomenon.
  We focus on the spectral signature of gamma radiation that should be evident
in the energy range of Fermi--LAT, i.e. $\gtrsim 10^{-1}$ GeV and the CTA
energy range $\sim$ $ 10^{2}$ GeV. The spectral signature results from a
comparable gamma-ray flux due to the IC and $ \pi ^{0} $ decay on the edge of
the cluster, and its spectral position is a function of the magnetic field and
relative efficiency of the acceleration of protons and electrons. We aim to
draw attention to the dependence of the gamma-ray structure on the magnetic
field value.
  As an example, we carried out analyses of two types of non-thermal diffuse
radio emission: the radio relic of A 2256 and the radio halo of Coma cluster.
We suggest that in both cases the expected spatially correlated gamma-ray
spectrum should have a characteristic structure that depends on the strength of
the local magnetic field. In both of the clusters we calculated the combined
flux of gamma radiation from the actual observational values of the used
observables.
  The revealed spectral dependence on the magnetic field would allow us to
relate the future spectral observations, in particular the position of the
gamma-ray signature, to the value of the magnetic field in the border area
between galaxy clusters and their connecting filaments, possibly constraining
the estimated relative efficiency of particle acceleration at the edge of the
cluster.
