Impedance of finite length resistive cylinder

We determine the impedance of a cylindrical metal tube (resistor) of radius a, length g, and conductivity σ 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 (k1/a). In the equilibrium regime, ka²g, the impedance per unit length is accurately described by the well-known result for an infinite length tube with conductivity σ. In the transient regime, ka²g, 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.