Simulation and optimization of the Active Magnetic Shield of the n2EDM experiment

TL;DR

This work develops and validates a finite-element, COMSOL-based simulation of the Active Magnetic Shield (AMS) operating with the magnetically shielded room (MSR) in the n2EDM neutron EDM experiment. By confirming linear AMS behavior against measurements, it enables a genetic-algorithm–driven optimization of fluxgate sensor placement to minimize the conditioning number of the coil–sensor mapping, while considering practical spatial constraints. The resulting workflow yields an optimized eight-sensor configuration with good agreement between simulated and experimental conditioning ($\sigma$) and residual-field suppression, demonstrating a scalable approach for designing active magnetic shields in precision experiments. The methodology and optimization framework are transferable to other experiments requiring ultra-stable magnetic environments and dynamic field compensation.

Abstract

The n2EDM experiment at the Paul Scherrer Institute aims to conduct a high-sensitivity search for the electric dipole moment of the neutron. Magnetic stability and control are achieved through a combination of passive shielding, provided by a magnetically shielded room (MSR), and a surrounding active field compensation system by an Active Magnetic Shield (AMS). The AMS is a feedback-controlled system of eight coils spanned on an irregular grid, designed to provide magnetic stability to the enclosed volume by actively suppressing external magnetic disturbances. It can compensate static and variable magnetic fields up to $\pm 50$ $μ$T (homogeneous components) and $\pm 5$ $μ$T/m (first-order gradients), suppressing them to a few $μ$T in the sub-Hertz frequency range. We present a full finite element simulation of magnetic fields generated by the AMS in the presence of the MSR. This simulation is of sufficient accuracy to approach our measurements. We demonstrate how the simulation can be used with an example, obtaining an optimal number and placement of feedback sensors using genetic algorithms.

Figures (12)

• Figure 1: Magnetic field suppression performance of the AMS after commissioning. FG1 to FG8 are used as acronyms for the respective fluxgates. The lines show the magnitude of the field picked up by fluxgate sensors when the AMS is off (\ref{['ams_old:top']}) and when the AMS is actively compensating the external field (\ref{['ams_old:bot']}), demonstrating the ability of the AMS to compensate large external field disturbances down to the level of a few $µT$. In both cases, the magnetic field change is caused by a full SULTAN ramp. Small (sub-$µT$) spikes are caused by short-term, local disturbances the AMS is not primarily designed to compensate. The placement of the sensors is discussed in section \ref{['sec:Optimization']}.
• Figure 2: Image of fluxgate FG8 mounted close to a corner of the MSR.
• Figure 3: AMS grid structure (yellow). Parts of the grid have been cut out to allow a clear view onto the MSR. The directions of the coordinate system are indicated in the figure. The origin is located at the center of the MSR (figure adapted from n2EDM).
• Figure 4: Simulation of the X-coil's magnetic field at maximum current, showing a top-view of an AMS cross-section at $z=0$ (plane through the middle of MSR). The simulation is performed without the MSR. The X-coil is designed to produce a homogeneous field in $x$-direction of up to $\pm 50µT$. The color map indicates the magnetic field strength, gray lines represent the magnetic field lines. The wires of the X-coil are projected onto the plane of the cross-section.
• Figure 5: $\langle\|\vec{B}\|\rangle$ and $\langle C(\vec{B})\rangle$ of magnetic field lines across the AMS volume as a function of permeability of the simulated MSR. In this simulation, a $50µT$ magnetic field was applied in the $x$-direction, compare Figs. \ref{['fig:COMSOL_NoMSR']} and \ref{['fig:COMSOL_MSR']}. A vertical red line indicates where $\mu_r=2000~\rm cm^{-1}$.