Comparison of analytical and computational estimates of reduction in linear aperture in the presence of sextupole field

For an easy comparison of the expected improvement in the linear aperture when magnets are sorted according to various schemes, it is desirable to have a figure of merit which can be evaluated without time-consuming tracking calculations. Such a figure of merits is proposed in terms of the sextupole distortion functions introduced by T. Collins (9184). A test lattice composed of 512 dipoles with a random sextupole field component is used to calculate the figure of merit, and the indicated improvement in the linear aperture is compared with the results from numerical tracking. Two definitions for the linear aperture are used, one by the SSC-CDG (smear=6.4%) and the other by CERN SPS (Super Proton Synchrotron) (smear=1.75%)