Beam tracking of SXLS with realistic magnetic field

In early 1977, while working for NSLS at Brookhaven National Lab., Dr. Ohnuma noticed that tunes of NSLS calculated with code SYNCH were significantly different from those obtained with code PATRICIA. This problem surfaced again in 1991 when people at BNL discovered discrepancies in their compact ring SXLS chromaticities calculated with different code. One potential source of the ambiguities is the different treatment of the edge field and the combined function field of dipole magnet. There are two dipoles each of which with the bending angle of 180{degrees} instead of at most a few degrees which is common in high energy synchrotrons. The calculation of a three-dimensional field using TOSCA indicates that the fringe field extends to cover the whole region between the dipole and the quadrupole, having a vertical field strength of 250 gauss at the edge of the quadrupole. In this case, the fringe multiple field will undoubtedly play a nontrival role in determining basic machine parameters. Therefore, the classical treatment for simulating particle motion in synchrotron, which uses the isomagnetic approximation plus then lens kicks, no longer accurately models the closed orbit of the machine. In order to correctly calculate tunes, chromaticities as well as the dynamicmore » aperture in such kind of machine with a large magnetic bending angle, it is necessary to integrate the exact equations of motion in a realistic representation of the magnetic field.« less