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.
The detection of the free precession of co‐located 3He/129Xe nuclear spins (clock comparison) is used as ultra‐sensitive probe for non‐magnetic spin interactions, since the magnetic dipole ...interaction (Zeeman‐term) drops out in the weighted frequency difference, i.e., Δω = ωHe‐ γHe/γXe·ωXe of the respective Larmor frequencies. Recent results are reported on searches for (i) short‐range P‐ and T‐violating interactions between nucleons, and (ii) Lorentz violating signatures by monitoring the Larmor frequencies as the laboratory reference frame rotates with respect to distant stars (sidereal modulation). Finally, a new experimental initiative to search for an electric dipole moment of 129Xe (CP‐violation) is discussed, which strongly benefits from the long spin‐coherence times obtained, reaching T2,He*> 100 h and T2,Xe*> 8 h in case of 3He and 129Xe, respectively.
The detection of the free precession of co‐located 3He/129Xe nuclear spins (clock comparison) is used as ultra‐sensitive probe for non‐magnetic spin interactions, since the magnetic dipole interaction (Zeeman‐term) drops out in the weighted frequency difference, i.e., Δω = ωHe‐ γHe/γXe·ωXe of the respective Larmor frequencies. Recent results are reported on searches for (i) short‐range P‐ and T‐violating interactions between nucleons, and (ii) Lorentz violating signatures by monitoring the Larmor frequencies as the laboratory reference frame rotates with respect to distant stars (sidereal modulation). Finally, a new experimental initiative to search for an electric dipole moment of 129Xe (CP‐violation) is discussed, which strongly benefits from the long spin‐coherence times obtained, reaching T*2,He> 100 h and T*2,Xe> 8 h in case of 3He and 129Xe, respectively.
By measuring the spin precession frequencies of polarized 129Xe and 3He, a new upper limit on the 129Xe atomic electric dipole moment (EDM) \({d}_{\text{A}}\left({}^{129}\mathrm{X}\mathrm{e}\right)\) ...was reported in Sachdev et al (2019 Phys. Rev. Lett. 123, 143003). Here, we propose a new evaluation method based on global phase fitting (GPF) for analyzing the continuous phase development of the 3He–129Xe comagnetometer signal. The Cramer–Rao lower bound on the 129Xe EDM for the GPF method is theoretically derived and shows the potential benefit of our new approach. The robustness of the GPF method is verified with Monte-Carlo studies. By optimizing the analysis parameters and adding data that could not be analyzed with the former method, we obtain a result of \({d}_{\text{A}}\left({}^{129}\mathrm{X}\mathrm{e}\right)=\left1.1{\pm}3.6\enspace \left(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\right){\pm}2.0\enspace \left(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}\right)\right{\times}1{0}^{-28}\enspace \text{e}\enspace \mathrm{c}\mathrm{m}\) in an unblinded analysis. For the systematic uncertainty analyses, we adopted all methods from the aforementioned PRL publication except the comagnetometer phase drift, which can be omitted using the GPF method. The updated null result can be interpreted as a new upper limit of \(\vert {d}_{\text{A}}\left({}^{129}\mathrm{X}\mathrm{e}\right)\vert {< }8.3\enspace {\times}1{0}^{-28}\enspace \text{e}\enspace \mathrm{c}\mathrm{m}\) at the 95% C.L.
•An expression for coils in finite-thickness finite-μ cylindrical shields is given.•A comparison with FEM and the known expression for infinite permeability is made.•We present a graph for selecting ...optimal spacing of a coil pair to match shields.•We extend the classic image method to the case involving finite-thickness plates.
The common approach to create a uniform magnetic field in the μT range is placing a coil set inside a magnetic shield. One of the main obstacles to achieving the requested uniformity can be a field distortion caused by the shield. We derive an approximate expression for the magnetic field generated by circular coils enclosed in ferromagnetic cylinders, the most used shield geometry. The main advantage of the expression over the known approximation is considering the finite permeability and the finite thickness of the cylindrical shield. To model the cylinder end caps, we propose the finite thickness mirror method, which extends the method of mirror image to the case of finite thickness. The cylinder barrel is modeled as an infinite tube and its effect on the field is analytically solved. The error of the expression and its dependency on the observation point and the shield geometry are discussed. Compared with finite-element simulations our analytic method is consistent within a relative error of less than 0.3% for practical shielding setups. The expression enables the rapid optimization of shield-coupled coil sets with a custom-designed objective function. To show the applicability of our method, we present simulations for the direct selection of the optimum spacing of a coil pair to match the given dimensions of a cylindrical shield.
During the last decades, the development of increasingly sensitive magnetic sensors led to numerous applications of magnetic field measurements in neuro-science, medical diagnostics, brain-computer ...interfaces, metrology or for experiments testing the fundamental laws of nature. Especially the development of small, lightweight, rather mobile and easy to handle optically pumped magnetometers allows for more advanced and dynamic studies of, for e.g., the brain. The limitation for the quality of such magnetic signals are gradients and drifts in the measuring environment. This article combines the result of many years of work, resulting in calculations to quantitatively predict the areas with ultra-low magnetic fields inside passive magnetic shields, as well as the experimental confirmation. The calculation shows that a conventional three-layer chamber with an improved degaussing system will already provide environmental conditions never reached before. In the most recent implementation an unprecedented residual field of <inline-formula><tex-math notation="LaTeX">< </tex-math></inline-formula> 130 pT was repeatedly achieved over 0.5 x 0.5 x 0.5 m inside an easily accessible space, consistent with the numerical modeling.
Abstract
By measuring the spin precession frequencies of polarized
129
Xe and
3
He, a new upper limit on the
129
Xe atomic electric dipole moment (EDM)
d
A
X
e
129
was reported in Sachdev
et al
(2019
...Phys. Rev. Lett.
123
, 143003). Here, we propose a new evaluation method based on global phase fitting (GPF) for analyzing the continuous phase development of the
3
He–
129
Xe comagnetometer signal. The Cramer–Rao lower bound on the
129
Xe EDM for the GPF method is theoretically derived and shows the potential benefit of our new approach. The robustness of the GPF method is verified with Monte-Carlo studies. By optimizing the analysis parameters and adding data that could not be analyzed with the former method, we obtain a result of
d
A
X
e
129
=
1.1
±
3.6
(
s
t
a
t
)
±
2.0
(
s
y
s
t
)
×
1
0
−
28
e
c
m
in an unblinded analysis. For the systematic uncertainty analyses, we adopted all methods from the aforementioned PRL publication except the comagnetometer phase drift, which can be omitted using the GPF method. The updated null result can be interpreted as a new upper limit of
|
d
A
X
e
129
|
<
8.3
×
1
0
−
28
e
c
m
at the 95% C.L.
The magnetic field inside a spherical magnetic shield with infinite permeability and a circular aperture in a homogeneous magnetic field of arbitrary direction is analytically derived. The ...closed-form formulas for the static shielding factors are theoretical upper limits for real shields. We discuss the magnetic field gradient inside the shield caused by a single aperture, implying that using symmetric aperture pairs is more favorable. Based on the theoretical results for ideal shields, an approximate solution to calculate the shielding factor for shields with finite permeability and/or multiple apertures is developed. The calculations for one aperture pair are compared to finite-element analysis. The basic effects could be guidance for the design of apertures in shields of various shapes.
Magnetic shields are specified by the shielding factor (SF) determined with an external ac magnetic field that is uniform in the absence of the shield. External excitation coils (EECs) close to the ...shield are widely used as the field source. An analytic solution for the SF measured with an EEC is presented for the case of a spherical magnetic shield, which is a common approximation for magnetic shields. At the sphere center, the SF is independent of the EEC dimensions and its value is equal to the known result for a uniform excitation. The behavior of the SF measured with two widely used EEC configurations, a single coil and a symmetrical coil pair, is compared with respect to the field detector location inside the shield and the radius and position of the EEC.
We demonstrate the use of a hybrid
3
He/
87
magnetometer to measure absolute magnetic fields in the pT range. The measurements were undertaken by probing time-dependent
3
He magnetisation using
87
Rb ...zero-field magnetometers. Measurements were taken to demonstrate the use of the magnetometer in cancelling residual fields within a magnetic shield. It was shown that the absolute field could be reduced to the 10 pT level by using field readings from the magnetometer. Furthermore, the hybrid magnetometer was shown to be applicable for the reduction of gradient fields by optimising the effective
3
He
T
2
time. This procedure represents a convenient and consistent way to provide a near zero magnetic field environment which can be potentially used as a base for generating desired magnetic field configurations for use in precision measurements.
Graphical abstract
A partly analytical method for calculating the magnetic field generated by coils in a closed magnetic shield is presented. The field distortion caused by the high-permeability boundary is analyzed by ...using the improved mirror method combined with a finite element method. This approach leads to an analytical solution which can be calculated much faster than a full FEM solution. By applying this model, we could calculate the optimal parameters for a four square-coil setup to produce the most homogenous magnetic field in the center of the Berlin magnetically shielded room (BMSR-2) with acceptable accuracy.
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