A stable inner working environment is essential for NMR sensors, which requires the absence of remnant magnetic fields and fluctuations caused by the surrounding magnetic fields. In this study, we utilized analytical formulations to derive transverse and longitudinal magnetic shielding factors for multilayer cylindrical magnetic shielding. Subsequently, we proposed a novel method for designing and improving the shielding factor by optimizing the spacing of every pair of adjacent layers within a limited volume. The final design result of the multilayer cylindrical magnetic shielding features optimally designed varying layer spacing, which are associated with a specific length and diameter. After optimization, the transverse shielding factor increased by 5.53%, 8.99%, and 13.51% for the three-, four-, and five-layer shields, respectively, compared to traditional magnetic shielding. The opening in the axial center of the magnetic shielding barrel may cause leakage of the magnetic flux and inhomogeneous remnant magnetic induction. We introduced a stovepipe to the end cap of the axial shield based on the finite element method, resulting in an improvement in the homogeneity of remnant magnetic induction. This modification widened the axial uniform region of the innermost shielding layer by approximately 9 cm within 52.5 cm in our simulation. To implement our proposed optimization method, we established and manufactured a four-layer cylindrical magnetic shielding with stovepipes and varying layer spacing. Moreover, the results indicate that this optimal method works for other applications in which multilayer magnetic shielding is required.
Nuclear magnetic resonance gyroscopes (NMRGs) have broad application perspectives with the advantages of low cost, low power consumption, miniaturization-ability and high precision. The transverse relaxation rate of noble gas nuclear spins is used to evaluate the performance of vapor cell, which also affects the angle random walk (ARW) of NMRG systems. The inhomogeneity of electronic spin polarization spatial distribution is one of the essential sources of the transverse relaxation rate. In this paper, we study the influence of the pump power and beam diameter in the transverse relaxation rate of noble gas nuclear spins through numerical simulations of electronic spin polarization and experimental measurements of transverse relaxation time. Simulations of the electronic spin polarization spatial distribution are proposed based on the Bloch-Torrey equations. The transverse relaxation time of noble gas nuclear spins under different pump power and beam diameters is measured by the free induction decay (FID) method. Experimental results show that the transverse relaxation rate of nuclear spins increases with pump power. The relaxation rate with a 2.3mm pump beam diameter is larger than with a 1.3mm diameter. Furthermore, we innovatively find that the transverse relaxation rate shows a linear relationship with the electronic spin polarization obtained from the numerical simulation. This work provides a reference for the study of nuclear spin relaxation and the optimization of the parameters of the pump beam in NMRGs.
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