Minimal inductance for axisymmetric transmission lines with radially dependent anode-cathode gap

Sandia National Laboratories, P.O. Box 5800, Albuquerque, New Mexico 87185-1193, USA(Received 25 July 2009; published 30 September 2009)Weextendthevariational calculustechniqueforinductanceminimizationof constantgapaxisymmetrictransmission lines (TL),introduced byHurricane [J.Appl.Phys. 95,4503(2004)], to the case in which theanode-cathode gap is a linear function of the midgap radius. The full analytic optimal midgap solutioncurve zðrÞ yielding minimum inductance is obtained in terms of a single parameter