In this paper we give analytical expressions for the maximum beam-beam parameter and related beam-beam limited beam lifetime in e+e- storgae ring colliders. The performances of some existing or existed machines are analyzed

In this paper we consider the wakefields induced in periodic disk-loaded cavities by charged particles of velocities less than that of light. In frequency domain the particle velocity-dependent wakefields can be calculated by generalizing the analytical formulae given in J. Gao (Nucl. Instr. and Meth. A 381 (1996) 174; or LAL/RT 95-01, April 1995). The physical picture of this effect can be drawn so that the frequencies of the excited modes in cavities felt by the particles are increased by a factor of 1/b (b is the normalized particle's velocity). Some examples are given to demonstrate the utility of these formulae in obtaining the quantities, such as loss factors, short-range and long-range wakefields as functions of cavity dimension, bunch length and particle velocity.

Starting from June 1986 a single cavity RF gun with thermionic cathode(LaB6) was studied and constructed at the Institute of High Eneergy Physics, Academia Sinica, Beijing Free Electron Laser Project. In the experiments the electron back-bombardment effect and another phenomenon connected with cathode temperature were obseerved. After carefuly choosing the opeeration parameters, this RF gun injector could stably provide clectron beams suitable for doing preliminary FEL experiments. Based on the theoretical analysis a computer code(including space charge forces) was written to simulate the dynamics of electrons in this injector. Since May 1986, at LAL, Orsay, France, the photocathode RF gun was investigated theoretically and new design criteria were established. Based on these criteria a two decoupled cavities RF gun, using a laser triggered photocathode, has been designed for the "LAL/Orsay RF gun project"(CANDELA), and model cavities have been fabricated. Based on the model cavity measurement results, the final cavities have been fabricated and measured. Aiming at reducing further the emittance of electron bunches coming out of the second cavity, Linear and nonlinear emittance compensating techniques have been proposed. As a new kind of electron injector suitable for FEL and future e+e- linear colliders, a travelling wave RF gun has been investigated theoretically and compared with the standing wave RF gun. Some preliminary numeerical calculations have been made also. Stimulated by the experimental results on the model cavities, several useful analytical formulae have been derived and verified by the experimental results: (1) Analytical formulae for the coupling coefficient β of a cavity-waveguide coupling system (2) Analytical formulae for the resonant frequency changes due to opening apertures on cavity walls (3) Analytical formulae for the coupling coefficient k(or group velocity vg) of forward and backward travelling wave linear accelerators

Starting from a single resonant rf cavity, disk-loaded travelling(forward or backward) wave accelerating structures'properties, such as the coupling coefficient K in the dispersion relation, group velocity vg, shunt impedance R, wake potential W (longitudinal and transverse), the coupling coefficient β of the coupler cavity and the coupler cavity axis shift δr which is introduced to compensate the asymmetry caused by the coupling apeerture, can be determined by rather simple analytical formulae

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.