Analytic models for the broad band impedance

In order to overcome the limitations of the broadband resonator impedance model, two different models are proposed which have more realistic properties at both very high and very low frequencies. For each model two types are specified which are proportional to either ω^-1/2 or ω^-3/2 at high frequencies. At low frequencies, the real part of the first impedance model rises quadratically or-for a special choice of the parameters-with the fourth power of frequency. In the second model it is identically zero up to a chosen cutoff frequency, and thereby yields the very fast decrease of the loss factor with bunch length which is always found by direct solution of Maxwell´s equations for lossless structures. Although not quite as simple as the broadband resonator, both models have impedances and Green functions which can be expressed by analytic functions and depend only on a few parameters. Thus, they should lead to improved estimates of beam stability limitations in particle accelerators and storage rings