“…In order to use realistic numbers for the calculation of the luminosity values of beam parameters for a stored antiproton beam are taken as have been reported in the design report for the planned facility FAIR at GSI [9], [10], Darmstadt, Germany, foreseen for its High Energy Storage Ring (HESR) for the storage of antiprotons. The FAIR facility provides up to n p = 7 • 10 10 /h antiprotons, thereby, the space charge limit N limit p for the number of stored antiprotons for a ring like HESR is N limit A tremendous progress has been made over the past fifteen years by preparing intense polarised electron beams with excellent emittances and high polarisation, see [5]. Several groups are working on a further improvement of the emittance of the beam by using e.g.…”