Computation of Resistive Wakefields
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We evaluate longitudinal resistive wakefields for cylindrical beam pipes numerically and compare the results with existing approximate formulæ. We consider an ultra-relativistic bunch traversing a cylindrical, metallic tube for a model in which the wall conductivity is taken to be first independent and second dependent on frequency, and we show how these can be included simply and efficiently in particle tracking simulations. We also extend this to higher order modes, and to the transverse wakes. This full treatment can be necessary in the design of modern nano-beam accelerators.