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Stochastic acceleration of electrons interacting resonantly with a turbulentmagnetic field in a small accretion torus appears to be the likely mechanismresponsible for much of Sagittarius A*'s millimeter and shorter wavelengthspectrum. The longer wavelength radiation is produced at larger radii byelectrons either diffusing from smaller scales or accelerated in situ. Animportant prediction of this model is the ejection of a significant flux ofrelativistic protons from a magnetic-field-dominated acceleration site into thewind-shocked medium surrounding the black hole. Recently, several air Cerenkovtelescopes, 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 inthe radio band and (2) the wind-injected ISM mapped with Chandra using thediffuse X-rays, it is feasible to test the idea that protons accelerated within\~20 Schwarzschild radii of the black hole produce the TeV emission fartherout. We show a fraction of TeV protons scattering about once within ~3 pc ofSagittarius A* and the proton power (~10^37 erg s^-1) produced in concert withthe 7 mm radio emission matches the TeV luminosity well. This model explainswhy the TeV source does not vary on a timescale of a year or less. The particlecascade generated by the p-p scatterings also produces bremsstrahlung, inverseCompton, and synchrotron emission at longer wavelengths from secondaryparticles. We compare these with current measurements and demonstrate thatGLAST will detect this source during its one-year all-sky survey.Comment: 19 pages, 3 figure

Stochastic Acceleration in the Galactic Center HESS Source