A simple analytical estimate of the loss parameter of a large tapered chamber

In the case of a cylindrical chamber that is very large compared with the bunch length, and tapers on each end, an estimate for the loss parameter may be made by first making some assumptions about the distribution of electromagnetic fields, and then calculating the electromagnetic energy left behind when the bunch leaves the chamber. The result is an analytic formula for the loss parameter, with no free or empirical parameters, that agrees well with TBCI calculations of a 20 degrees tapered chamber. This formula has intuitive appeal and is especially useful in providing design assistance as to the best taper angle, diameter, and chamber lengths.<>