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Analytical formulae for the wakefields produced by the nonrelativistic charged particles in periodic disk-loaded structures

In this paper we consider the wakefields induced in periodic disk-loaded cavities by charged particles. In the frequency domain the particle velocity dependent wakefields can be calculated by generalizing the analytical formulae. The physical picture of this effect can be drawn such that the frequencies of the excited modes in the cavities felt by the particles are increased by a factor of 1//spl beta/ (/spl beta/ is the normalized particle 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.