Polarization buildup by spin ltering in storage rings

There has been much recent research into polarizing an antiproton beam, in-stigated by the recent proposal from the PAX (Polarized Antiproton eXperiment) project at GSI Darmstadt [1]. It plans to polarize an antiproton beam by repeated interaction with a polarized internal target in a storage ring. The method of po-larization by spin ltering requires many of the beam particles to remain within the ring after scattering o the polarized internal target via electromagnetic and hadronic interactions. Sets of dierential equations which describe the buildup of polarization by spin ltering in many dierent scenarios have recently been pre-sented and solved [2 { 8]. In this paper we add to this literature by investigating a scenario where unpolarized particles are input into the beam at a linearly increasing rate, i.e. the input rate is ramped up. The spin ltering method of polarization buildup [9, 10, 11] consists of a circulating beam repeatedly interacting with a polarized internal target in a storage ring. Many particles are scattered at small angles but remain in the beam. This introduces a charac