Analytical solutions of transient pulsed eddy current problem due to elliptical electromagnetic concentrative coils

The electromagnetic concentrative coils are indispensable in the functional magnetic stimulation and have potential applications in nondestructive testing. In this paper, we propose a figure-8-shaped coil being composed of two arbitrary oblique elliptical coils, which can change the electromagnetic concentrative region and the magnitude of eddy current density by changing the elliptical shape and/or spread angle between two elliptical coils. Pulsed current is usually the excitation source in the functional magnetic stimulation, so in this paper we derive the analytical solutions of transient pulsed eddy current field in the time domain due to the elliptical concentrative coil placed in an arbitrary position over a half-infinite plane conductor by making use of the scale-transformation, the Laplace transform and the Fourier transform are used in our derivation. Calculation results of field distributions produced by the figure-8-shaped elliptical coil show some behaviours as follows: 1) the eddy currents are focused on the conductor under the geometric symmetric centre of figure-8-shaped coil; 2) the greater the scale factor of ellipse is, the higher the eddy current density is and the wider the concentrative area of eddy current along y axis is; 3) the maximum magnitude of eddy current density increases with the increase of spread angle. When spread angle is 180°, there are two additional reverse concentrative areas on both sides of x axis.