  Recently, HESS and other air Cerenkov telescopes have detected a source of
TeV gamma-rays coincident with the Galactic center. It is not yet clear whether
the gamma-rays are produced via leptonic or hadronic processes, so it is
important to consider possible acceleration sites for the charged particles
which produce the gamma-rays. One exciting possibility for the origin of these
particles is the central black hole, Sgr A*, where the turbulent magnetic
fields close to the event horizon can accelerate protons to TeV energies. Using
a realistic model of the density distribution in a 6 pc x 6 pc x 6pc cube at
the Galactic center, we here calculate the trajectories followed by these TeV
protons as they gyrate through the turbulent medium surrounding Sgr A*.
Diffusing out from the black hole, the protons produce TeV gamma-rays via pi^0
decay following a collision with a proton in the surrounding medium. After
following over 222,000 such trajectories, we find that the circumnuclear ring
around Sgr A* can reproduce the observed 0.1-100 TeV HESS spectrum and flux if
the protons are injected into this medium with an effective power-law index of
0.75, significantly harder than the observed photon index of 2.25. The total
energy in the steady-state 1-40 TeV proton population surrounding Sgr A* is
inferred to be approx 5x10^{45} ergs. Only 31% of the emitted 1-100 TeV protons
encounter the circumnuclear torus, leaving a large flux of protons that diffuse
outward to contribute to the Galactic ridge emission observed by HESS on scales
of >~ 1 degree.
