Rapid Stochastic Acceleration of Protons to Energies Above 100~TeV in the Accretion Column Of Hercules X-1

An investigation into the acceleration of protons by scattering off relativistic Alfv'{e}n waves in the accretion column of Hercules X-1 is presented. The mechanism is shown to achieve mean particle energies of 30~TeV under very reasonable assumptions about the environment, and 250~TeV is available under some circumstances. The highest individual energy attained is almost 1~PeV. The protons emerge in the form of a narrow beam directed at the inner edge of the accretion disk, which is favourable because of the reduced power requirement and presence of target material for gamma-ray production.