  In this Letter, we suggest that the relativistic protons powering the
outflows emanating from radio-loud systems containing black holes are
accelerated at standing, centrifugally-supported shocks in hot,
advection-dominated accretion disks. Such disks are ideal sites for first-order
Fermi acceleration at shocks because the gas is tenuous, and consequently the
mean free path for particle-particle collisions generally exceeds the thickness
of the disk. The accelerated particles are therefore able to avoid
thermalization, and as a result a small fraction of them achieve very high
energies and escape from the disk. In our approach the hydrodynamics and the
particle acceleration are coupled and the solutions are obtained
self-consistently based on a rigorous mathematical treatment. The theoretical
analysis of the particle transport parallels the early studies of cosmic-ray
acceleration in supernova shock waves. We find that particle acceleration in
the vicinity of the shock can extract enough energy to power a relativistic
jet. Using physical parameters appropriate for M87 and Sgr A*, we confirm that
the jet kinetic luminosities predicted by the theory agree with the
observational estimates.
