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.

By applying the perturbation method, we show in a general way how to determine the coupling coefficient of a waveguide cavity coupling system and as a special example we derive the analytical expressions ofthe coupling coefficient for a waveguide cavity coupling system. The term "cavity" in this paper stands for the cavity in both standing and travelling wave structures.

In this paper, we investigate the dynamical behaviours of a continuous intense charged particle beam in a transport system. It is assumed that fermion particles, such as electron and proton, in the beam follow Fermi-Dirac statistics in the equilibrium state. The halo particles executing stochastic motions due to the envelope oscillation induced nonlinear resonances are investigated. Analytical formulae for the halo current and halo current loss rate on the beam pipe wall are established.

In this paper the single bunch emittance growth in the main linac of a linear collider is analytically treated in analogy to the Brownian motion of a molecule, and the analytical formulae for the emittance growth due to accelerating structure misalignment errors are obtained by solving Langevin equation. The same set of formulae are derived also by solving directly Fokker-Planck equation. Comparison with numerical simulation result is made and the agreement is quite well. The problem of the single bunch emittance growth in an electron storage ring is also discussed.

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.