Application of Magneto-Quasi-Static Approximation in the Finite Difference Time Domain Method

Investigations about induction sensors, electromagnetic launchers, shields, transformers, and power line-induced currents address increased number of low-frequency research and industrial applications. In general, a magneto-quasi-static (MQS) approximation is considered for the solutions of low-frequency problems in electromagnetics. This approximation leads to a diffusion process when displacement currents are neglected. However, keeping the displacement currents, Maxwell's equations are valid at low frequencies. In this manner, the finite difference time domain (FDTD) method must be modified by the slowing down propagation velocity at low-frequency regime. In this paper, important and crucial points of the MQS approximation and its application in the FDTD method are clarified in the sense of analytical and numerical aspects. A material scaling technique of dielectric permittivity for the QS FDTD application is analyzed within comprehensive investigations. Furthermore, a criterion for choosing a proper value of scaling parameter will be revealed. Finally, effects of proper and improper values of the scaling parameter are presented with validated analytical and numerical results.