Impedance of finite length resistive cylinder

We determine the impedance of a cylindrical metal tube ( resistor) of radius a, length g, and conductivity sigma 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 much greater than 1/a). In the equilibrium regime, ka(2) much less than g, the impedance per unit length is accurately described by the well-known result for an infinite length tube with conductivity sigma. In the transient regime, ka(2) much greater than 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.