A new born-approximation approach to compute the effects of motion on the solution of electromagnetic problems involving moving materials with stationary boundaries

Abstract

The non-relativistic motion of media induces very weak effects on electromagnetic fields. For this reason, it is extremely difficult to compute such effects with traditional techniques. To overcome this difficulty, a novel approach is introduced in this work. It is based on the Born approximation of the solution of electromagnetic problems involving media in motion. The formulation of these problems makes use of equivalent field sources and is specifically tailored to find the effects of motion on the electromagnetic field. The new methodology exploits traditional simulators able to deal with media at rest. The motion of the materials has to be managed by specific programs performing simple algebraic calculations. The simplest of the methods proposed does not present any additional complexity with respect to more traditional approaches to the same problems. All methods deal with time-harmonic electromagnetic fields and, for this reason, they can manage materials in motion with stationary boundaries. A complete set of simulations for cylinders moving in the axial direction show that the new methods outperform traditional numerical approaches and, in some significant cases, traditional approaches based on semi-analytical techniques. The good features of the new methodology are shown to hold true for a range of velocity values spanning 11 decades; such a range covers most of the applications of practical interest.