New method for calculation of low-frequency coupling impedance

摘要

In high-energy proton accelerators and storage rings the bunch length is typically at least a few times larger than the radius of the vacuum chamber. For example, the SSC will have an rms bunch length above 6 cm and a beam-pipe radius below 2 cm. The main concern for beam stability in such a machine is the low-frequency impedance, i.e., the coupling impedance at frequencies wen below the cut-off frequency of the vacuum chamber. In the present paper we develop a new analytical approach for calculation of the low-frequency impedance of axisymmetric structures that allows us to give quick and reliable estimates of contributions to the impedance from various chamber discontinuities. Simple formulae for the longitudinal impedance of some typical discontinuities are obtained.