Beam optics modeling at CPS extraction throughout a non-linear fringe field

An accurate optics model of the CPS ring in the extraction region, where the lateral fringe field is highly non-linear, is of importance for transverse emittance preservation of beams for the future LHC. For that reason, the measured field map at 26 GeV/c of the CPS magnets has been converted into a two-dimensional polynomial to get a functional form appropriate for subsequent beam trajectory computations. Effects of magnet shimming, not considered during the magnetic measurements, and changes in the currents of the pole-face windings have been examined, and the field map has been adjusted accordingly by means of calculations with the program Poisson. The equation of the beam trajectory and the transfer matrices through the field map have been derived to yield an accurate knowledge of the optical parameters at ejection, and thus in the transfer channel between the CPS and the SPS machines. Experimental verification of the model has been undertaken with the 26 GeV/c beam for the LHC.