  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.

Astrophysics