Optics effects of splitting dipole magnets into several thin lenses

The evaluation of the dynamic aperture and the calculation of non linear optics parameters have been made so far with the simplest model of dipole, i.e. a single thin lens positioned at the centre of each thick dipole. It was shown recently that the non-linear chromaticity decreases significantly when the thick lens is represented by two thin lenses or more instead of one. In this note the study is extended to amplitude detuning and dynamic aperture. Unlike the observation reported on non-linear chromatic detuning we find no significant changes for the dynamic aperture and amplitude d etuning when the dipole magnets are split in more than one thin lens. Furthermore, non-uniform azimuthal distribution of the multipoles inside the dipole is shown not to change the above-mentio ned results. In both cases, the influence of the beta-funtions is expected to give large effect for a given dipole. However, integrated over one cell this effect is shown to compensate to a large extent. erture reported on non-linear chromatic