Comparison of tracking results with Ziemann's conjecture for the LHC dynamic aperture

In the design study for the LHC an important task is to evaluate the dynamic aperture for the error tables of the magnetic elements and propose an improvement of these tables so as to achieve a sufficiently large dynamic aperture. A proper study which requires the variation of many parameters is very time-comsuming. A method to speed-up this process without sacrificing too much precision would therefore be very welcome. To this end a simple conjecture to predict the dynamic aperture has been proposed some time ago by Ziemann [1]: partial dynamic apertures are determined for single multipoles of some strength; the partial dynamic apertures at any other strength of these single multipoles are given by an exact scaling law: these partical dynamic apertures are then combined via the approximate Ziemann conjecture to derive a total dynamic aperture. This procedure has been used to build up the target error table of the LHC. This report compares extended tracking results with the predictions of the Ziemann conjecture for different combinations of multipoles. The conjecture predicts the average dynamic aperture resulting from a complete errortable with reasonable accuracy, but fails to reproduce the effect of the reduction of specific combinations of multipoles.