title: Generalized Courant-Snyder theory for charged-particle dynamics in general focusing lattices.
abstract: The Courant-Snyder (CS) theory for one degree of freedom is generalized to the case of coupled transverse dynamics in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D sympletic rotation. The envelope equation, the transfer matrix, and the CS invariant of the original CS theory all have their counterparts, with remarkably similar expressions, in the generalized theory.
authors.affiliation: Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
authors.forename: Hong
authors.initials: H
authors.lastname: Qin
authors.affiliation: Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA.
authors.forename: Ronald C
authors.initials: RC
authors.lastname: Davidson
authors.affiliation: Accelerator Physics Center, Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA.
authors.forename: Moses
authors.initials: M
authors.lastname: Chung
authors.affiliation: Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA.
authors.forename: Joshua W
authors.initials: JW
authors.lastname: Burby