  Stochastic acceleration of electrons interacting resonantly with a turbulent
magnetic field in a small accretion torus appears to be the likely mechanism
responsible for much of Sagittarius A*'s millimeter and shorter wavelength
spectrum. The longer wavelength radiation is produced at larger radii by
electrons either diffusing from smaller scales or accelerated in situ. An
important prediction of this model is the ejection of a significant flux of
relativistic protons from a magnetic-field-dominated acceleration site into the
wind-shocked medium surrounding the black hole. Recently, several air Cerenkov
telescopes, notably HESS, have detected TeV emission from the Galactic center,
with characteristics hinting at a p-p-induced pion decay process for the
\gamma-ray emission. Given (1) the size of this acceleration region measured in
the radio band and (2) the wind-injected ISM mapped with Chandra using the
diffuse X-rays, it is feasible to test the idea that protons accelerated within
\~20 Schwarzschild radii of the black hole produce the TeV emission farther
out. We show a fraction of TeV protons scattering about once within ~3 pc of
Sagittarius A* and the proton power (~10^37 erg s^-1) produced in concert with
the 7 mm radio emission matches the TeV luminosity well. This model explains
why the TeV source does not vary on a timescale of a year or less. The particle
cascade generated by the p-p scatterings also produces bremsstrahlung, inverse
Compton, and synchrotron emission at longer wavelengths from secondary
particles. We compare these with current measurements and demonstrate that
GLAST will detect this source during its one-year all-sky survey.
