Three-Dimensional Pulsed Electromagnetic Field of Current Flowing Near Conducting Half-Space

In this chapter the study of pulsed three-dimensional electromagnetic fields is based on the obtained accurate analytical solution to the problem of the field of arbitrary alternating initial sources near conducting half-space with account to eddy current in conducting body. For the pulse current, the obtained solution is a frequency spectrum of the electromagnetic field created by a current with a set frequency spectrum. Time dependencies can be obtained by performing the inverse Fourier transform. In this case, the solution is represented by triple improper integrals, that, despite of the analytical form of the expressions, has some calculation difficulties. To simplify the computational procedures under the condition of strong skin effect asymptotic calculation method is developed, which takes into account the features of the pulsed process. For the calculation of three-dimensional pulsed electromagnetic fields the integrands are represented by bounded asymptotic series, in each term of which the dependences on coordinates and time are calculated separately using well-known simple expressions. Since the applied expansion into the asymptotic series is valid in the high-frequency interval of the spectrum, then for the terms of the series, the lower boundaries of the frequency spectrum and, accordingly, the maximum values of the time intervals from the pulse start are determined. Based on comparison of the results of exact and approximate calculations for non-uniform field at the interface between the media the proposed choice of the limited time interval for calculating electromagnetic field using the asymptotic method is justified. As an example, some results of the application of the developed calculation methods in the field of high-density pulsed current technology to change the mechanical properties and control the stress–strain state of metal products are given.