  We find that hydromagnetic flux tubes in back-flows in the lobes of radio
galaxies offer a suitable environment for the acceleration of cosmic rays (CR)
to ultra-high energies. We show that CR can reach the Hillas (1984) energy even
if the magnetised turbulence in the flux tube is not sufficiently strong for
Bohm diffusion to apply. First-order Fermi acceleration by successive weak
shocks in a hydromagnetic flux tube is shown to be equivalent to second-order
Fermi acceleration by strong turbulence.
