  We report a stochastic mechanism of particle acceleration from first
principles in an environment having properties like those of Radio Lobes in
AGNs. We show that energies $\sim 10^{20}$ eV are reached in $\sim 10^6$ years
for protons. Our results reopen the question regarding the nature of the
high-energy cutoff in the observed spectrum: whether it is due solely to
propagation effects, or whether it is also affected by the maximum energy
permitted by the acceleration process itself.
