Koichi Ishida

Magnetic Field Analysis of an Arbitrary Shaped Coil Using Shape Functions

In eddy-current sensors and eddy-current testing, it is important to analyze the magnetic field of the coil. Toward this end, we analyzed magnetic fields in various coils, such as circular and rectangular coils. We used the double Fourier transformation and applied it to the eddy-current problem of coils facing a sheet conductor. However, only a limited number of coil shapes could be analyzed by this method. We therefore devised a method of magnetic field analysis that could be applied to a variety of coils by double Fourier transformation. We focused attention on the generated magnetic field of the coil, which is a basic characteristic. Our analysis method is made applicable to a much larger variety of coil shapes by defining a completely new type of function, called shape functions. We verified the validity of the analytical results experimentally. Although the Biot-Savart law may be used to analyze magnetic fields of coils, the law is not applicable when the coil faces a sheet conductor.

Self-Inductance of a Racetrack Coil

Superconducting racetrack coils are used for magnetic levitation, magnetic resonance imaging, etc. When using racetrack coils, it is important to determine the coil characteristics (the resistance, self-inductance, mutual inductance, and distributed capacity of the coil). It is difficult to analyze the racetrack coil that has straight and semicircle parts. Therefore, the analytical solution of this coil has not been obtained yet. In this paper, we derive the analytical solution of the magnetic field of a single-layer racetrack coil based on the magnetic field of the one-turn racetrack coil. In addition, the analytical solution of the self-inductance is derived on the basis of this theory. The validity of this theory is confirmed by comparing measured self-inductance values with the calculated values.

Visualization of Eddy Current Distributions for Arbitrarily Shaped Coils Parallel to a Moving Conductor Slab

To visualize eddy current distribution (ECD) of an arbitrarily shaped coil arranged parallel to a moving conductor slab, an exact theoretical solution is derived using an analytical method based on the double Fourier transform method. The arbitrarily shaped coil is regarded as a plane coil of a single turn, and both DC and AC excitation currents can be applied. Furthermore, ECD charts are obtained when the conductor slab is moving. We calculate some examples with respect to a circular coil, rectangular coil, and triangular coil and show the effect of coil excitation frequency and speed of the conductor on ECDs. Results show that the eddy current generated in the moving conductor slab is composed of current induced by the excitation frequency and conductor speed.