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]

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.

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.