Application of the modified Cagniard technique to transient electromagnetic diffusion problems

Abstract

SUMMARY A version of Cagniard’s technique for inverting integral transforms is adapted to diffusion problems and illustrated with the 2-D example of two semi-infinite media of different electrical conductivity excited by a transient line-source of electric current at their interface. The field equations are first solved in the transform domain, i.e. following a Laplace transformation with respect to time (with real, positive transform parameter) and a Fourier transformation with respect to the spatial coordinate parallel to the interface. Deformation of the path of integration for the inverse Fourier transformation allows the inverse Laplace transformation to be obtained by inspection. The electromagnetic field at any point in the configuration can then be obtained by numerical evaluation of well-behaved integrals. In the more diffusive half-space, there is a single integral to be evaluated, whereas in the less diffusive domain, there are two: one corresponding to the direct ‘wave’, the other to a diffusive ‘head wave’ which develops along the interface and influences certain regions of space-time.