Dynamics of rising magnetized cavities and UHECR acceleration in
  clusters of galaxies
  We study the expansion of low density cavities produced by Active Galactic
Nuclei jets in clusters of galaxies. The long term stability of these cavities
requires the presence of linked magnetic fields. We find solutions describing
the self-similar expansion of structures containing large-scale electromagnetic
fields. Unlike the force-free spheromak-like configurations, these solutions
have no surface currents and, thus, are less susceptible to resistive decay.
The cavities are internally confined by external pressure, with zero gradient
at the surface. If the adiabatic index of the plasma within the cavity is
$\Gamma>4/3$, the expansion ultimately leads to the formation of large-scale
current sheets. The resulting dissipation of the magnetic field can only
partially offset the adiabatic and radiative losses of radio emitting
electrons. We demonstrate that if the formation of large-scale current sheets
is accompanied by explosive reconnection of the magnetic field, the resulting
reconnection layer can accelerate cosmic rays to ultra high energies. We
speculate that the enhanced flux of UHECRs towards Centaurus A originates at
the cavities due to magnetic reconnection.
