The governing electrodynamic equations of electromagnetic acoustic transducers

Abstract

This paper presents the governing electrodynamic equations of electromagnetic acoustic transducers (EMATs) and extends them to the derivation of the magnetic- and acoustic-field equations in terms of the magnetic vector potential (MVP) and the acoustic wave particle displacement vector (PDV), respectively. It also provides formulations for calculating forces and current densities in the case of two-dimensional (2D) models of EMAT configurations in Cartesian coordinates. Existing methods solve the governing electrodynamic equations for field quantities to analyze EMATs. However, they ignore skin and proximity effects and rely on simple 2D configurations for EMAT coils. Taking into account skin and proximity effects in complex 2D EMAT coil configurations requires the application of the finite element method (FEM). The FEM can be applied to solve the equations stated in terms of the MVP and PDV in the modeling of EMATs. These formulations and expressions facilitate the development and presentation of the FEM for the modeling and analysis of EMATs.