Physically speaking, the delta function like beam-beam nonlinear forces at interaction points act as a sum of delta function nonlinear multipoles. By applying the general theory established by J. Gao (Nucl. Instr. and Meth. A 451 (2000) 545), in this paper we examine analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between the beam–beam limited beam lifetimes and the beam-beam tune shifts are established, which show clearly why experimentally one has always a maximum beam–beam tune shift, ζy;max, around 0.045 for e+e- circular colliders, and why one can use round beams to double this value approximately. Comparisons with some machine parameters are given.

By considering delta function sextupole, octupole, and decapole perturbations and using di!erence action-angle variable equations, we "nd some useful analytical formulae for the estimation of the dynamic apertures of circular accelerators due to single sextupole, single octupole, single decapole (single 2m pole in general); and their combined e!ects are derived based on the Chirikov criterion of the onset of stochastic motions. Comparisons with numerical simulations are made, and the agreement is quite satisfactory.

nalytical formulae for the coupling coefficient β of a waveguide-traveling wave structure coupling system have been established and compared with experimental results. The dimension of the coupling aperture on the coupler cavity of a traveling wave structure can be determined easily. The relation between the coupling coefficient β and the other parameters. such as aperture dimension, wavelength, group velocity, wall thickness and coupler dimension, is explicitly revealed. These formulae include that for the caes of a waveguide-single cavity coupling system which has been established in ref. [1]

Based on the perturbation method, the resonant frequency changes due to apertures on a cavity wall have been investigated, and analytical formulas have been derived and compared with numerical and experimental resykts, The dispersion relation of a peeriodic disk-loaded slow wave structure, which relates the group velocity explicitly to the shapes and sizes of coupling apertures, is established and verified. These explicitly experssed analytical dispersion relations established in this paper will not only serve as useful tools in the design of forward(electrically coupled) and backward wave(magnetically coupled) linear accelerators, but also show a clear picture of relevant physical processes.

The research works presented in this memoir are oriented not only to the R＆D programs towards future linear colliders, but also to the pedagogic purposes. The first part of this memoir(from Chapter 2 to Chapter9) establishes an analytical framework of the disk-loaded slow wave accelerating structures which can be served as the advanced courses for the students who have got some basic trainings in the linear accelerator theories. The analytical formulae derived in this part describe clearly the properties of the disk-loaded accelerating structures, such as group velocity, shunt impedance, coupling coifficients k and β, loss factors, and wakefields. The second part(from Chapter 11 to Chapter 13) gives the beam dynamics simulations and the final proposal of an S-Band Superconducting Linear Collider(SSLC) which is aimed to avoid the dark current problem i TESLA project. This memoir has not included all the works cunducted since April 1992, such as beam dynamics simulations for CLIC Test Facility(CTF-2) and the design of High Charge Structures (HCS) (11π/12 mode) for CTF-2, in order to make this memoir more harmonious, coherent and continuous