Magnetic Field Measurement Features With a Miniature B-Dot Probe

For a miniature toroidal single-turn magnetic probe the spatial distribution of a harmonically time-varying uniform external magnetic field, ${B_0} = {B_m}\sin (\omega t)$, is investigated theoretically. Based on the solution obtained, in this article, a method is proposed for increasing the accuracy of measuring pulsed magnetic fields with a miniature probe. The analysis takes into account the effects of skinning of the external field. The magnetic flux $\Phi $ measured by the probe is characterized by a “separation radius” ${R_*}$, which corresponds to the relation $\Phi = {B_0}\pi R_*^2$. The dependence of the separation radius on the governing parameters, namely, the wire radius ${R_w}$, the coil radius ${R_a}$, and the thickness of the skin layer ${\delta _s}$ is found. The problem has an analytical solution for the limiting case of a stationary field ($\omega \to 0$). For arbitrary values of $\omega $, the problem has been solved numerically. The limiting case of high-frequency fields has been analyzed in the approximation of a “surface current.” The numerical solution results are consistent with the analytical solutions. The total set of calculated data on the separation radius is fitted by an analytical function ${R_*}({R_a},{R_w},{\delta _s})$. Using this function, we constructed a level chart that can serve as a convenient tool for quick engineering assessments to accurately determine the amplitude ${B_m}$ of a measured magnetic pulse.