Beam Performance_RF2009_Beam Performance

The vertical beam spread is one of the most important parameters for the high brilliance storage ring, which is represented by the coupling ratio of the horizontal and vertical beam emittances. The coupling between the horizontal and vertical betatron oscillations and the vertical dispersion with the energy spread generate the vertical beam spread, so that they should be corrected. The latter has been corrected since 1999, and the former since 2007, both of which are controlled using skew quadrupole magnets [1-3]. The betatron coupling has an effect on the beam through the resonance of the beam motion. The coupling has sum and difference resonances that form the lattice on the tune map, as shown in Fig. 1. In the early stage of the coupling correction, only the nearest neighbor resonance (νx – νy = 22) to the operation point (40.15, 18.35) was corrected. At present, to improve the correction, four resonances surrounding the operation point are corrected. From the perturbation theory of the betatron motion with the single resonance approximation [4,5], it is implied that the vertical beam size is proportional to the strength of the coupling resonance. Hence, the strengths of the skew quadrupole magnets for the coupling correction are determined so as to give the minimum vertical beam size. Resonance modes are orthogonal to each other, so that they are corrected independently by the appropriate combination of skew quadrupole magnets. Moreover, although the strength of the coupling resonance is a complex value and has two degrees of freedom, it is corrected independently with a sufficient number of skew quadrupole magnets. The tuning process of the coupling correction is shown in Fig. 2. The fitting curves obtained with the quadratic approximations represent the changes in the vertical beam size with respect to the strengths of the coupling resonances in terms of the skew quadrupole magnets. The light blue crossing symbols joined by the straight lines represent the minimum vertical beam size in each tuning process of the coupling resonances. The more the modes of the coupling resonances are corrected, the smaller the vertical beam size becomes. In tuning of the emittance coupling, the vertical dispersion correction is performed after the betatron coupling resonance correction. This is because the former correction can be performed without exciting the coupling resonances. As a result of these corrections, we achieve the emittance coupling ratio of 0.2%.