Massive conductor impedance and peculiarities of transients in electrical circuits with massive conductors of pulsed power facilities
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.
Skin effect in massive conductors used in pulsed electrical devices: I. Electromagnetic field of massive conductors
The diffusion of a pulsed electromagnetic field into massive conductors with an arbitrary smooth surface is considered for the case where the field penetration depth is small. By using the boundary layer method, an asymptotic solution for the electromagnetic field is constructed. First-and second-order corrections to the limiting solution, which corresponds to the field distribution at an indefinitely high conductivity of the conductors, are found. Time dependences of the first-and second-order approximations to the electric field on the surface of the conductor are determined.
Skin effect in massive conductors used in pulsed electrical devices: II. Massive conductors in electric circuits
Approximate relationships between the current and voltage drop across a set of massive conductors are established. They include two constant parameters: external inductance L of the conductors and skin parameter S. Specific shapes of the voltage across the massive conductors are illustrated with oscillograms. Mathematical processing of current and voltage oscillograms to estimate L and S is developed.