Massive conductor impedance and peculiarities of transients in electrical circuits with massive conductors of pulsed power facilities

Abstract

At a small skin depth the electromagnetic field in conductors can be defined by the boundary layer method. The derived asymptotic solution makes it possible to determine the expansion in a series of the voltage drop across massive conductors. In this expansion the first term describes the limiting solution with infinite conductivity and corresponds to self-induction electro-motive force (EMF) of the external magnetic field or voltage drop across external inductance of massive conductors. Asymptotic correction of the first-order approximation corresponds to the fraction of the voltage drop calculated under the impedance boundary conditions on the surface of the conductors. The second-order correction takes into account the curvature of the conductor surface and inhomogeneity of the external magnetic field and varies in time directly as does current in the conductors, i.e. as in the case with voltage drop across a usual resistor. Such approximation establishes the relation between current and voltage drop on massive conductors, which can be included into the Kirchhoff’s equations for analysis and calculation of the transients in the circuits with massive conductors. The purpose of the paper is consideration of the peculiarities of the transients in electrical circuits, the methods of measurement of the massive conductor parameters, as well as the methods of the transients calculations in the time domain, which use the asymptotic representation of the voltage drop on massive conductors.