A New Method for Determining the Penetration Depth in Superconductors

Abstract

IT is a well-known property of high-frequency electrical transmission lines¹ operating in the normal mode that the velocity of propagation of a wave along the line is given by the equation v = 1šLC, where L and C are the inductance and capacitance per unit length. But whereas for all frequencies used in practice the value of C is simply the electrostatic capacity between the conductors, the inductance must be considered as the sum of the two quantities, usually referred to as the internal and external inductances. The latter, L_ext., is the value that would be assumed by the inductance if all the current were to flow on the surface, and the internal inductance, L_int., represents a correction, very small at high frequencies, due to the finite penetration of the current into the body of the conductors. If the internal inductance be neglected, as indeed is common, the velocity is found to be in general the velocity of propagation of a plane unbounded wave in the dielectric medium surrounding the transmission line. The effect of the internal inductance is to alter the velocity by a factor (1 — L_int./2L_ext.)