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

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 $\pm 50$ $\mu$T (homogeneous components) and $\pm 5$ $\mu$T/m (first-order gradients), suppressing them to a few $\mu$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.