IMPEDANCES OF TWO DIMENSIONAL MULTILAYER CYLINDRICAL AND FLAT CHAMBERS IN THE NON-ULTRARELATIVISTIC CASE

Two dimensional electromagnetic models (i.e. assuming an infinite length) for the vacuum chamber elements in a synchrotron are often quite useful to give a first estimate of the total beam-coupling impedance. In these models, classical approximations can fail under certain conditions of frequency or material properties. We present here two formalisms for flat and cylindrical geometries, enabling the computation of fields and impedances in the multilayer case without any assumption on the frequency, beam ve-locity or material properties (except linearity, isotropy and homogeneity)