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We consider the radiative acceleration to relativistic bulk velocities of acold, optically thin plasma which is exposed to an external source ofgamma-rays. The flow is driven by radiative momentum input to the gas, theaccelerating force being due to Compton scattering in the relativisticKlein-Nishina limit. The bulk Lorentz factor of the plasma, Gamma, derived as afunction of distance from the radiating source, is compared with thecorresponding result in the Thomson limit. Depending on the geometry andspectrum of the radiation field, we find that particles are accelerated to theasymptotic Lorentz factor at infinity much more rapidly in the relativisticregime; and the radiation drag is reduced as blueshifted, aberrated photonsexperience a decreased relativistic cross section and scatter preferentially inthe forward direction. The random energy imparted to the plasma by gamma-rayscan be converted into bulk motion if the hot particles execute many Larmororbits before cooling. This `Compton afterburn' may be a supplementary sourceof momentum if energetic leptons are injected by pair creation, but can beneglected in the case of pure Klein-Nishina scattering. Compton drag byside-scattered radiation is shown to be more important in limiting the bulkLorentz factor than the finite inertia of the accelerating medium. Theprocesses discussed here may be relevant to a variety of astrophysicalsituations where luminous compact sources of hard X- and gamma-ray photons areobserved, including active galactic nuclei, galactic black hole candidates, andgamma-ray bursts.Comment: LateX, 20 pages, 5 figures, revised version accepted for publication  in the Ap

Relativistic Winds from Compact Gamma‐Ray Sources. I. Radiative Acceleration in the Klein‐Nishina Regime