title: Circular modes, beam adapters, and their applications in beam optics.
abstract: In the optics of charged particle beams, circular transverse modes can be introduced; they provide an adequate basis for rotation-invariant transformations. A group of these transformations is shown to be identical to a group of the canonical angular momentum preserving mappings. These mappings and the circular modes are parametrized similar to the Courant-Snyder forms for the conventional uncoupled, or planar, case. The planar-to-circular and reverse transformers (beam adapters) are introduced in terms of the circular and planar modes; their implementation on the basis of skew quadrupole blocks is described. Various kinds of matching for beams, adapters and solenoids are considered. Applications of the planar-to-circular, circular-to-planar and circular-to-circular transformers are discussed. A range of applications includes round beams at the interaction region of circular colliders, flat beams for linear colliders, relativistic electron cooling, and ionization cooling.
authors.affiliation: Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA. burov@fnal.gov
authors.forename: Alexey
authors.initials: A
authors.lastname: Burov
authors.forename: Sergei
authors.initials: S
authors.lastname: Nagaitsev
authors.forename: Yaroslav
authors.initials: Y
authors.lastname: Derbenev