  Relativistic outflows (jets) of matter are commonly observed from systems
containing black holes. The strongest outflows occur in the radio-loud systems,
in which the accretion disk is likely to have an advection-dominated structure.
In these systems, it is clear that the binding energy of the accreting gas is
emitted primarily in the form of particles rather than radiation. However, no
comprehensive model for the disk structure and the associated outflows has yet
been produced. In particular, none of the existing models establishes a direct
physical connection between the presence of the outflows and the action of a
microphysical acceleration mechanism operating in the disk. In this paper we
explore the possibility that the relativistic protons powering the jet are
accelerated at a standing, centrifugally-supported shock in the underlying
accretion disk via the first-order Fermi mechanism. The theoretical analysis
employed here parallels the early studies of cosmic-ray acceleration in
supernova shock waves, and the particle acceleration and disk structure are
treated in a coupled, self-consistent manner based on a rigorous mathematical
approach. We find that first-order Fermi acceleration at standing shocks in
advection-dominated disks proves to be a very efficient means for accelerating
the jet particles. Using physical parameters appropriate for M87 and SgrA*, we
verify that the jet kinetic luminosities computed using our model agree with
estimates based on observations of the sources.
