Transverse Modes in Periodic Cylindrical Cavities

Transverse forces acting on charged particles passing off-axis through resonant structures can lead to instabilities and beam break-up in high-energy particle accelerators or storage rings. These forces can be calculated from the resonant transverse modes, which are calculated here for a structure consisting of periodically repeating circular-cylindrical cavities connected by concentric side tubes. Results for the dipole mode are presented graphically for a wide variety of geometries, as well as Brillouin diagrams for m=1 and m=2.