Abstract
A three-step model for calculating the magnetic field generated by coils inside cuboid-shaped shields like magnetically shielded rooms (MSRs) is presented. The shield is modeled as two parallel plates of infinite width and one tube of infinite height. We propose an improved mirror method that considers the effect of the parallel plates of finite thickness. A reaction factor is introduced to describe the influence of the vertical tube, which is obtained from finite element method (FEM) simulations. By applying the improved mirror method and then multiplying the result with the reaction factor, the magnetic flux density within the shielded volume can be determined in a fast computation. The three-step model is verified with both FEM and measurements of the field of a Helmholtz coil inside an MSR with a superconducting quantum interference device. The model allows a fast optimization of shield-coupled coil spacings compared to repetitive, time-consuming FEM calculations. As an example, we optimize the distance between two parallel square coils attached to the MSR walls. Measurements of a coil prototype of 2.75 m side length show a magnetic field change of 18 pT over the central 5 cm at the field strength of 2.7 µT. This obtained relative field change of 6 ppm is a factor of 5.4 smaller than our previously used Helmholtz coil.
Highlights
Uniform magnetic fields with a high temporal stability are essential to various precision measurements, such as electric dipole moment (EDM) measurements1–4 or magnetic field detector calibration.5–7 For the challenging EDM measurements, a nonzero magnetic field gradient enhances vibration noise seen by magnetometers8,9 and shortens the possible measurement time for a single experiment, deteriorating its statistical sensitivity.10–12 The final unavoidable field gradient causes systematic uncertainties like geometric phase shift,13,14 which is the dominant error contribution to the present neutron EDM upper limit.15 More details about the influence of the magnetic field gradient can be found in Refs. 16 and 17.The common method of creating a homogeneous magnetic field is to place a coil set into a multi-layer magnetic shield,18–21 which serves to reduce external field perturbations
We propose a three-step model to calculate the magnetic field generated by coils inside a cuboid-shaped magnetic shield, which is suitable for rapid optimizations of the coil spacings
The proposed three-step model is verified with a complete finite element method (FEM) calculation and a measurement of a 1.6-m-diameter Helmholtz coil placed inside the Berlin Magnetically Shielded Room 2 (BMSR-2)
Summary
Uniform magnetic fields with a high temporal stability are essential to various precision measurements, such as electric dipole moment (EDM) measurements or magnetic field detector calibration. For the challenging EDM measurements, a nonzero magnetic field gradient enhances vibration noise seen by magnetometers and shortens the possible measurement time for a single experiment, deteriorating its statistical sensitivity. The final unavoidable field gradient causes systematic uncertainties like geometric phase shift, which is the dominant error contribution to the present neutron EDM upper limit. More details about the influence of the magnetic field gradient can be found in Refs. 16 and 17. Sweeping the coil parameters in FEM models to find an optimal solution takes even longer For this reason, it is expedient to use a reasonable and sufficiently accurate simplification of the field calculation in order to optimize coil spacings in an efficient way. We propose a three-step model to calculate the magnetic field generated by coils inside a cuboid-shaped magnetic shield, which is suitable for rapid optimizations of the coil spacings. The proposed three-step model is verified with a complete FEM calculation and a measurement of a 1.6-m-diameter Helmholtz coil placed inside the Berlin Magnetically Shielded Room 2 (BMSR-2).. For the newly designed coil pair prototype of 2.75 m side length with the calculated optimal distance, the measured maximal relative magnetic field change in a 5 cm region around the local extremum near the center of the coil is 6 ppm, which is an improvement by a factor of 5.4 compared to the value of our previously used Helmholtz coil
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