Betatron coupling and related impact of radiation

Linear coupling of vertical and horizontal oscillations in a circular accelerator or collider is analyzed in the presence of solenoidal and tilted-quadrupole fields. An analytical treatment of the coupled motions based on a Hamiltonian formalism is proposed. Solutions are first given explicitly in the absence of synchrotron radiation and then extended to the case of loss of energy and photon emission by the particles. Applications of the derived formulas to a generic accelerator are presented. Finally, pertinent information related to the large electron-positron collider of CERN is conveyed, in which strategies for dealing with a very large, low harmonic, tilted quadrupole are detailed and a particular scheme for the local compensation of solenoids is discussed.