The cryogenic storage ring CSR Review of Scientific Instruments 87, 063115 (2016); https://doi

We determine the impedance of a cylindrical metal tube (resistor) of radius a, length g, and conductivity attached at each end to perfect conductors of semi-infinite length. Our main interest is in the asymptotic behavior of the impedance at high frequency k 1=a. In the equilibrium regime, ka 2 g, the impedance per unit length is accurately described by the well-known result for an infinite length tube with conductivity. In the transient regime, ka 2 g, where the contribution of transition radiation arising from the discontinuity in conductivity is important, we derive an analytic expression for the impedance and compute the short-range wakefield. The analytic results are shown to agree with numerical evaluation of the impedance.

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