There has been much recent research into polarizing an antiproton beam, instigated by the recent proposal from the PAX (Polarized Antiproton eXperiment) project at GSI Darmstadt. It plans to polarize an antiproton beam by repeated interaction with a polarized internal target in a storage ring. The method of polarization by spin filtering requires many of the beam particles to remain within the ring after scattering off the polarized internal target via electromagnetic and hadronic interactions. We present and solve sets of differential equations which describe the buildup of polarization by spin filtering in many different scenarios of interest to projects planning to produce high intensity polarized beams. These scenarios are: 1) spin filtering of a fully stored beam, 2) spin filtering while the beam is being accumulated, i.e. unpolarized particles are continuously being fed into the beam, 3) the particle input rate is equal to the rate at which particles are being lost due to scattering beyond ring acceptance angle, the beam intensity remaining constant, 4) increasing the initial polarization of a stored beam by spin filtering, 5) the input of particles into the beam is stopped after a certain amount of time, but spin filtering continues. The rate of depolarization of a stored polarized beam on passing through an electron cooler is also shown to be negligible. PACS: 13.88.+e Polarization in interactions and scattering -24.70.+s Polarization phenomena in reactions -25.43.+t Antiproton-induced reactions -29.27.Hj Polarized beams * donie@maths.tcd.ie

Abstract. The PAX project at GSI Darmstadt plans to polarize an antiproton beam by repeated interaction with a hydrogen target in a storage ring. Many of the beam particles are required to remain within the ring after interaction with the target, so small scattering angles are important. Hence we concentrate on low momentum transfer (small t), a region where electromagnetic effects dominate the hadronic effects. A colliding beam of polarized electrons with energy sufficient to provide scattering of antiprotons beyond ring acceptance may polarize an antiproton beam by spin filtering. Expressions for spin observables are provided and are used to estimate the rate of buildup of polarization of an antiproton beam.

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Many sets of polarization evolution equations have been suggested to describe the method of polarization buildup by spin filtering in storage rings. In this paper a generic system of polarization evolution equations describing spin filtering is derived and solved, then we compare and contrast this system to other descriptions of spin filtering appearing in the literature. This is of interest to projects planning to produce a polarized antiproton beam by spin filtering, and to any project utilizing spin filtering in storage rings. The physical processes responsible for spin filtering are analysed and their contributions to the dynamics of polarization buildup are highlighted. It is hoped that this will shed light on some of the confusion in the literature.Comment: 10 pages, 2 figures, presented at the Polarized Antiproton Beams - How? workshop, Cockcroft Institute, UK. August 200