Abstract
In this paper, we will report on the basic concepts of ultra-relativistic wake-fields and their effects on particles while focusing; in this context, particularly on particle accelerators. We will introduce the commonly used terminology, and will derive and explain important quantities, such as the wake potential and wake function, the impedance as the Fourier transform of the wake potential, and loss parameters. To deepen knowledge on wake functions and potentials further, we will illustrate the derived quantities using, as examples, the cylindrical cavity and a rectangular waveguide lined with dielectrics.
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