Design and modeling of shaped-field magnetoquasistatic sensors

The depth of penetration of periodic-field magnetoquasistatic sensors depends on two factors: the skin depth into the material under test and the spatial wavelength of the imposed periodic magnetic field. In applications where high depth of penetration is desirable, the second factor may result in the need for sensors with impractically large dimensions. We describe a way to overcome this problem by generating a field whose effective spatial wavelength is on the order of the sensor length. The magnetic field is shaped by a distributed primary winding that consists of multiple winding segments, with the total current amplitude in each segment following a sinusoidal envelope function. The effective spatial wavelength of the imposed magnetic field may be changed dynamically by changing the excitation current pattern in the primary windings. From a modeling perspective, an advantage of this kind of magnetic field excitation is that the drive current distribution is known from the beginning, since the width of the individual windings is small compared to the wavelength and may be approximated as being infinitely narrow. This greatly simplifies numerical computation, since it makes it possible to apply fast discrete Fourier transform methods directly. We discuss first sensors with Cartesian geometry. We then discuss cylindrical geometry sensors whose models use fast Hankel transforms.