Magnetic Omniconversion: Source-Independent Molding of Magnetostatic Fields

Abstract

Magnetic fields are constrained by the geometry and location of their sources, limiting the ability to freely tailor their spatial distribution. We introduce a general framework to passively convert the magnetic field generated by arbitrary sources into any prescribed desired field within a finite source-free region. Our method relies on field shaping using linear magnetic materials, enabling source-independent magnetic-field molding. We provide the general recipe, analytical and numerical demonstrations for some paradigmatic examples, and a proof-of-concept experiment that validates the idea and materials implementation. This approach enables novel possibilities in magnetic shielding, targeted field delivery, advanced imaging technologies, and a broad range of field-control applications.

Figures (3)

• Figure 1: Magnetic omniconversion. Formation of the volume $\mathcal{V}_0$ with the desired field. $S_0$ is an equipotential surface and $\Gamma_0$ any closed line belonging to this surface. Black lines are field lines, and those that thread $S_0$ through $\Gamma_0$ generate a lateral surface, $S_L$. Another equipotential surface, $S_1$, bounds the volume. The white arrow represents a $\text{d}\textbf{l}$ vector of Eq. \ref{['eq:Hparalleldl']}.
• Figure 2: Magnetic omniconversion examples. (a) and (b) A uniform magnetic field is generated within region $\mathcal{V}_0$, regardless of the external source (a dipole in (a), a coil in (b)). (c) The external source is a horizontal dipole, but the desired and generated field is that of a vertical dipole. (d) An external dipole source generates a monopolar field inside $\mathcal{V}_0$. (e) A quadrupolar field with a central singular point is generated. (f) The external source is a dipole, but the generated field lines inside $\mathcal{V}_0$ have a parabolic shape. In the 3D sketches at the bottom left of each case, the IMP surfaces are shown in red and the ZMP surfaces in blue. Green indicates the applied field sources: dipoles in (a, c-f) and a current loop in (b). Note that the magnetic moments of the dipoles are not necessarily equal in magnitude across the different cases, and that the color scale is saturated in some regions for visualization purposes.
• Figure 3: Proof-of-concept magnetic omniconversion demonstrator. Experimental system configurations (a)-(d), corresponding simulation results (e)-(h), and experimental measurements (i)-(l). The induced magnetic fields from the same flat circular coil are compared under four configurations: (a), (e), and (i) coil and PCB with sensors only; (b), (f), and (j) with added soft ferromagnetic caps; (c), (g), and (k) with the superconducting aluminum tube added but without the caps; and (d), (h), and (l) with the full assembly-tube and caps. Color scales represent the axial magnetic field component, $B_z$, normalized to the respective maximum values in simulation and experiment, $B_{z,\text{max}}^\text{sim}$ and $B_{z,\text{max}}^\text{exp}$. In the simulations (e)-(h), black lines indicate magnetic field lines, and white rectangles mark the actual sensor positions. The same rectangles are used in the experimental plots (i)-(l), uniformly colored according to the $B_z$ value measured by each sensor, and framed by a larger rectangle of the same color with reduced opacity to enhance visibility.