On skew nonlinear resonance in the SPring-8 storage ring

Recently we accomplish the matrix formulation for the canonical perturbation theory of the linear betatron coupling resonance in circular accelerators. By merging the perturbation theory with the matrix formalism, we manifest the symplectic structure of the former theory, and conversely derive the analytical representation for the latter. The formulation for the coupled betatron motion explicitly implies that the linear coupling causes the excitation of skew resonances through nonlinear fields with mid-plane symmetry. The third order skew coupling resonance is observed in the SPring-8 storage ring, for example, as the blow-up of the vertical beam size. For the purpose of studying the impact of the linear coupling on the skew nonlinear resonance, we investigate the characteristic behavior of the nonlinear resonance deduced from the matrix formulation of the perturbation theory.