The effect of NEG coating on resistive wall wake field

The procedure for calculating the resistive wall impedance is simplified using Gaussian elimination with a sufficiently large floating point precision. This procedure generalises readily to the multilayer beam pipe wall. We apply this to investigate the effect of NEG coating on the transverse wake field coupling between electron bunches in the ILC damping ring. For a 5 GeV electron beam and 3 cm radius aluminium beam pipe, a 1 μm thick NEG coating is found to increase the impedance around 10 GHz. The wake field over a distance of 300 km around the ring is required for the study of the multi-bunch instabilities. This has to be obtained by Fourier transforming over a very wide range of frequencies. To overcome the computation problem, we developed a way of splitting up the frequencies into three overlapping ranges, and then joining the transforms together to obtain the overall wake field. The results for a few NEG coating thicknesses are presented.