Symplectic Expression for Chromatic Aberrations

Chromatic aberrations characterize how linear optics parameters, including tunes, beta functions, and x-y coupling parameters, depend on momentum deviation. The definition of chromatic aberration is based on static or slowly varying momentum deviations. Linear optics parameters are expanded in terms of momentum deviation; their coefficients are called chromatic aberrations in this paper. The Hamiltonian and a six-dimensional symplectic map, which are taken into account in both betatron a nd synchrotron motions, are reconstructed using the measured chromatic aberrations. This map can be used to study the effects of chromatic aberrations in beam-beam, space charge, and electron cloud phenomena. Subject Index: 600, 630