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As part of a project to calibrate the polarization of the RHIC proton beams we designed a polarized atomic hydrogen beam source for use as a jet target at RHIC. The model we developed agrees well with measured outputs from two working sources and for the system we designed predicts 9×1016 atoms/s into a 9 mm diameter aperture 285 mm from the last focussing magnet and a target thickness of 9×1011 atoms/cm2, 316 mm from the last magnet. © 2003 American Institute of Physics [ABSTRACT FROM AUTHOR]