Nonlinear dynamics in a SPEAR wiggler

BL11, the most recently installed wiggler in the SPEAR storage ring at the Stanford Synchrotron Radiation Laboratory, produces a large nonlinear perturbation of the electron beam dynamics, which was not directly evident in the integrated magnetic field measurements. Measurements of tune shifts with betatron oscillation amplitude and closed orbit shifts were used to characterize the nonlinear fields. Because of the narrow pole width in BL11, the nonlinear fields seen along the wiggling electron trajectory are dramatically different from the magnetic measurements made along a straight line with a stretched wire. This difference explains the tune shift measurements and the observed degradation in dynamic aperture. Because of the relatively large dispersion (1.2 m) at BL11, the nonlinearities particularly reduced the off-energy dynamic aperture. Because of the nature of these nonlinear fields, it is impossible, even theoretically, to cancel them completely with short multipole correctors. Magic finger corrector magnets were built, however, that partially correct the nonlinear perturbation, greatly improving the storage ring performance.