Generating a highly uniform magnetic field inside the magnetically shielded room of the n2EDM experiment

Abstract

We present a coil system designed to generate a highly uniform magnetic field for the n2EDM experiment at the Paul Scherrer Institute. It consists of a main $B_0$ coil and a set of auxiliary coils mounted on a cubic structure with a side length of $273\text{cm}$ , inside a large magnetically shielded room (MSR). We have assembled this system and characterized its performances with a mapping robot. The apparatus is able to generate a $1\mu \text{T}$ vertical field with a relative root mean square deviation $\sigma \left(B_z\right)/B_z=3\times {10}^{-5}$ over the volume of interest, a cylinder of radius $40\text{cm}$ and height $30\text{cm}$ . This level of uniformity overcomes the n2EDM requirements, allowing a measurement of the neutron Electric Dipole Moment with a sensitivity better than $1\times {10}^{-27}e\text{cm}$ .

Fig. 1

Schematic depiction of the n2EDM apparatus inside the magnetic shieding room (MSR), view from a vertical cut (top figure) and a horizontal cut (bottom figure). The coordinate system is defined such that the y axis points from the MSR door to the back of the MSR in the horizontal plane. The MSR together with the coil system (in blue) are designed to generate a uniform vertical field inside the MSR volume, and especially so inside the double precession chamber volume (in pink)

Fig. 2

Design of the $B_0$ coil. The Lamé curves are located at the solenoid extremities in the top and bottom horizontal planes. The red and green frames show a detailed view of the opening bypasses. The inner volume of the coil is accessed through a square door (drawn in blue) with a side length of $200\text{cm}$

Fig. 3

Pictures of the built coil system. Left: inside of the $B_0$ coil. The two openings for the vacuum pipes (UCN guides on the other side) are visible on the left and the $B_0$ door is closed. Middle: the $B_0$ door open. On the door edges, the white custom-made connectors are visible. Right: a typical wire bypass of openings in the $B_0$ coil

Fig. 4

The n2EDM mapper inside the empty vacuum vessel. The fluxgate mounted on the mapper’s arm can travel to any point inside a cylindrical volume of radius $78\text{cm}$ and height $82\text{cm}$, at which it measures the three projections of the magnetic field

Fig. 5

An example of a magnetic field map of the field generated by the n2EDM coil system and recorded by the mapper. Each point corresponds to the vertical projection of the magnetic field inside a cylindrical volume of radius $78\text{cm}$ and height $82\text{cm}$

Fig. 6

Horizontal cut at $z=0$ of the deviations of the vertical $B_0$ magnetic field, in the positive coil polarity. The simulated values from [30] are compared to the 2022 measurements before and after optimization with auxiliary coils. The latter successfully cancels the main contributions of the ${\mathit{\Pi }}_{20}$ and ${\mathit{\Pi }}_{22}$ modes. The dashed black lines show where the walls of the precession chambers are positioned

Fig. 7

Harmonic spectrum of the $B_0$ coil, in the positive polarity, for the simulated field and measured field before and after optimization. The fit is performed up to order $l=7$ but here only modes of indices $l=1,2$ are shown. The considered volume for all spectra is the mapped cylindrical volume. Note that purely transverse harmonic modes with $m=\pm (l+1)$ (in faded colors) do not contribute to the total non-uniformity $\sigma (B_z)$

Fig. 8

The triangle points show measurements of the vertical magnetic field gradient, in both polarities of the coil, at three different vertical positions of the coil center with respect to the magnetic origin of the MSR. The measurements were taken from right to left in chronological order. The slope of the linear fit matches the predicted gradient value

Fig. 9

Normalized gradients responsible for the false EDM through Eq. (2.8), extracted from the magnetic field maps. These maps were recorded in three different magnetic configurations: residual field ($B_0$ coil is turned off), $B_0$ coil turned on in the positive polarity, $B_0$ coil turned on in the positive polarity along with a combination of optimization coils and gradient coils that suppress problematic harmonic gradients. The magnetic field reproducibility with respect to a full demagnetization of the MSR is common to non-optimized and optimized $B_0$ measurements. The $23\text{fT/cm}$ limit imposed on the gradients corresponds to a false EDM of $3\times {10}^{-28}e\text{cm}$. The effect at order $l=7$ is not significant even without optimization, so the harmonic expansion is not carried out beyond that order

Fig. 10

Vertical field component of single harmonic modes in the $z=0$ plane. The field ranges in magnitude from blue to red

Fig. 11

Left: $G_{10}$ gradient coil. The coil is made of four horizontal square loops located at $\text{z}=\pm 1335\text{mm}$ and $\text{z}=\pm 1035\text{mm}$. Middle: $G_{20}$ gradient coil. The $G_{20}$ coil is made of six horizontal square loops located at $\text{z}=\pm 1335\text{mm}$, $\text{z}=\pm 1035\text{mm}$ and $\text{z}=\pm 1005\text{mm}$. Right: $G_{30}$ gradient coil. The $G_{30}$ coil is made of four horizontal square loops located at $\text{z}=\pm 937.5\text{mm}$, $\text{z}=\pm 1035\text{mm}$ and $\text{z}=\pm 892.5\text{mm}$

Fig. 12

Design of the $G_{01}$ (left) and $G_{0-1}$ (right) gradient coils. The $G_{01}$ coil is made of four vertical square loops located at $\text{x}=\pm 1118\text{mm}$ and $\text{x}=\pm 359\text{mm}$. The $G_{0-1}$ coil is made of four vertical square loops located at $\text{y}=\pm 1118\text{mm}$ and $\text{y}=\pm 359\text{mm}$

Fig. 13

Design of the $G_{11}$ gradient coil. The $G_{1-1}$ gradient coil has exactly the same design rotated by 90 degrees i.e. symmetric with respect to (Ox, Oz) instead of (Oy, Oz)