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 e.g. the brain. The limitation for the quality of such magnetic signals are gradients and drifts in the measuring environment. Our presented work 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 < 130 pT was repeatedly achieved over 0.5 m x 0.5 m x 0.5 m inside an easily accessible space, consistent with the numerical modeling.

Ultra-low magnetic fields have drawn lots of attention due to their important role in scientific and technological research. The combination of a magnetic shield and an active compensation coil is adopted in most high performance magnetically shielded rooms. Special consideration needs to be taken in the coil design since the magnetic shield significantly affects the uniformity of the magnetic field that is generated by the coil. An analytical model for the magnetic field calculation of the coil inside a cubic magnetic shield is proposed based on the generalized image method, which is validated by finite element analysis. A novel design method of the coil used in a cubic magnetic shield with a large homogeneous volume is proposed. The coil parameters are optimized to obtain a large cubic uniform volume with desired total deviation rate by discretizing the central volume in the coil. In the desired total deviation rate, the normalized usable volume of the new coil increases by 70% when compared with the Merritt coil. A coil system is developed according to the parameters obtained based on this method. The magnetic flux density and practical deviation rate of the coil are measured to validate the accuracy of this model and the feasibility of the design method. The experimental magnetic flux density agrees well with the analytical value. The maximum practical deviation rate of uniform volume of 0.8 × 0.8 × 0.8 m is in good agreement with the theoretical design value, taking into account the experiment errors.

In this article, a uniform magnetic field coil with a magnetic shield is presented and designed to cancel the geomagnetic field and the surrounding magnetic noises. First, an analytical model of the uniform magnetic field coil with the magnetic shield is developed, based on the Biot–Savart law and the traditional images method. Second, in order to improve the model accuracy, the influence of the noninfinite shield thickness on the magnetic field produced by the uniform magnetic coil is considered using the multireflection theory, and an improved analytical model is obtained. The improved analytical model is verified by the three-dimensional finite-element method, and its accuracy is significantly improved compared to the previous analysis model. Then, the characteristic analysis of the uniform magnetic field coil is carried out using the improved analytical model, and design criteria of the uniform magnetic field coils are given to obtain a large uniform field area. Finally, the uniform magnetic field coil with the magnetic shield was constructed and the resulting magnetic field was tested. The test results show that the improved analytical model can accurately predict the performance of such magnetic field coils with magnetic shields, and can be used for its preliminary design.

The minimization of the remanent magnetization of ferromagnetic materials is a prerequisite for a reproducible low magnetic field inside shields. To realistically describe this so-called magnetic equilibration procedure, this paper proposes two approaches for the calculation of time- and space-dependent fields in the presence of ferromagnetic materials like permalloy. The first method is based on the Jiles-Atherton model and also takes into account frequency dependent effects. The second method is the newly developed empirical phase shift model, tailored specially for the simulation of the equilibration procedure. Both approaches are compared to experimental tests and show good quantitative agreement.

The homogeneity of the magnetic field generated by a coil inside a magnetic shield is essential for many applications, such as ultra-low field nuclear magnetic resonance or spin precession experiments. In the course of upgrading the Berlin Magnetically Shielded Room (BMSR-2) with a new inserted Permalloy layer of side length 2.87 m, we designed a built-in coil consisting of four identical square windings attached to its inside walls. The spacings of the four windings were optimized using a recently developed semi-analytic model and finite element analysis. The result reveals a strong dependence of the field homogeneity on the asymmetric placement of the inner two windings and on the chosen material permeability value μ_s. However, our model calculations also show that these experimental variations can be counterbalanced by an adjustment of the inner winding positions in the millimeter range. Superconducting quantum interference device-based measurements yield for our implementation after fine adjustments of a single winding position a maximum field change of less than 10 pT for a total field of B₀ = 2.3 µT within a 10 cm region along the coil axis, which is already better than the residual field of the upgraded BMSR-2.1 after degaussing. Measurements of free spin precession decay signals of polarized ${}^{129}\text{Xe}$ nuclei show that the transverse relaxation time for the used cell is not limited by the inhomogeneity of the new built-in coil system.

This paper proposes a novel hybrid rotor permanent magnet (HRPM) machine for the performance of torque and overload capability with the constraint of the rotor diameter. In order to optimize the electromagnetic performance, an analytical model (AM) is built by the magnetic equivalent circuit (MEC) of the rotor and stator considering the saturation and leakage flux effect. A good prediction accuracy is verified by the finite element method (FEM), even in high saturation condition. Based on the AM, the characteristics of the hybrid magnetic pole rotor are analyzed by the equivalent strategy that equivalent PM remanence and thickness of single pole in rotor. Furthermore, a response surface method (RSM) for multi-variate and multi-objective optimization is adapted to improve the electromagnetic performance because of the high torque density and PM material utilization. Finally, a comparison of the torque, PM eddy current loss and anti-demagnetization performance is investigated among surface-mount PM (SPM) machine, spoke-type PM (STPM) machine and HRPM machine. The comparison results show the hybrid PM rotor machine enhances higher torque density and overload capability. Finally, a 12 slot/10 pole HRPM machine is prototyped and tested to validate the analyses.