  Context. The recent discovery of so-called mega radio halos as a new class of
diffuse, steep-spectrum radio sources in clusters of galaxies has raised
questions about the origin and the evolution of cluster-wide radio emission.
Aims. We investigate whether the formation mechanisms of radio halos and mega
radio halos differ, or whether they can be produced by different modalities of
the same (re)acceleration mechanism. Here we present results of a cosmological
simulation of a disturbed galaxy cluster, with the aim to study the origin of
mega radio halos. Methods. We analysed the evolution of cosmic-ray electrons,
subject to gains and losses using a Fokker-Planck solver. In particular, we
included the effects of Adiabatic Stochastic Acceleration (ASA) which is caused
by the stochastic interaction of cosmic rays with diffusing magnetic field
lines in super-Alfvenic turbulence. Moreover, we included shock acceleration
and the seeding of cosmic-ray electrons by galaxies. Results. Our simulations
generate cluster-scale radio sources during mergers, with properties that are
in agreement with those observed for real radio halos. Furthermore, we find
evidence of additional emission on larger scales. This emission resembles the
radial distribution and the spectrum of a mega radio halo, but only when viewed
close to the merger axis. Conclusions. In our simulation, the mechanism
responsible for the formation of diffuse radio emission, both in the form of
classical and mega radio halos, is cosmic-ray re-acceleration by turbulence.
This turbulence is more solenoidal and more subsonic in the classical radio
halo region, than in the mega radio halo region.
