Impedance minimization by nonlinear tapering

There exist analytical approximations that express the transverse geometric impedance of tapered transitions in the inductive regime as a functional of the transition boundary and its derivatives. Assuming the initial and final cross-sections and the transition length are fixed, one can minimize these functionals by appropriate choice of the boundary variation with the longitudinal coordinate. In this paper we numerically investigate how well this works for the cases of optimized tapered transitions in circular, elliptical and rectangular geometry by running ABCI, ECHO, and GdfidL EM field solvers. We show that a substantial reduction of impedance for optimized boundary compared to that of a linear taper is indeed possible in some cases, and then we compare this reduction to analytical predictions.