Suppression of injection bump leakage caused by sextupole magnets within a bump orbit

We propose a scheme to suppress leakage of an injection bump orbit caused by sextupole magnets within the bump orbit. Since the bump leakage excites a stored beam oscillation synchronized with beam injection, its suppression is one of the most crucial issues for achieving top-up operation at third generation synchrotron radiation (SR) sources. In the common case where sextupole magnets are located within the bump orbit, the condition for closing the bump depends on the amplitude of the bump orbit due to the nonlinear kicks by the sextupole magnets. Accordingly the bump orbit never closes for all amplitudes even under ideal condition. To solve this problem, we use a minimal condition for emittance increase due to the bump leakage caused by sextupole magnets in the lowest order of the nonlinear perturbation. The condition is obtained by optimizing linear optics and satisfying specific relation among integrated strengths of the sextupole magnets within the bump orbit. Furthermore, the condition does not depend on the bump amplitude. Calculations using the perfectly similar field patterns reveal that the proposed scheme can reduce the rms of the stored beam oscillation down to a few tens of microns for all bump amplitudes. The residual oscillation is negligibly small compared to the horizontal beam sizes presently achieved in the SR sources. The suppression effect of the scheme was also confirmed experimentally by the results obtained at the SPring-8 storage ring.