The uniform magnetic field coils within the magnetic shielding layer find numerous applications, particularly in miniature nuclear magnetic resonance gyroscope (NMRG) sensors. However, the target magnetic field generated by the designed coils is inevitably distorted due to the adjacent ferromagnetic material that attracts the magnetic field. To address this issue, a novel image method based on uniqueness principle is proposed, which takes into account the coupling effect between the magnetic shielding box (MSB) and the coils. The particle swarm optimization (PSO) algorithm is employed to assist the novel image method in designing highly uniform axial magnetic field coils within a compact MSB. The validity and uniformity of the designed coils are verified by the finite element method (FEM), demonstrating that the maximum relative uniformity error of magnetic flux density <inline-formula> <tex-math notation="LaTeX">${B}_{z}$ </tex-math></inline-formula> is <inline-formula> <tex-math notation="LaTeX">$2.6\times 10^{-4}$ </tex-math></inline-formula> compared to the original point. Moreover, two classic configurations of uniform magnetic field coils, the Helmholtz coils and the 9449 coils, are introduced to compare the uniformity with the designed coils. Finally, the designed scheme was measured both within and without MSB, and the experimental results indicated that the relative uniformity error of <inline-formula> <tex-math notation="LaTeX">${B}_{z}$ </tex-math></inline-formula> was in good agreement with the reference values. These findings further substantiate the applicability of the proposed method to miniature atomic sensors that require generating a highly uniform magnetic field within the MSB.

The magnetic flux leakage (MFL) testing methods have been extensively used to detect defects in ferromagnetic materials. However, variations in the thickness of the surface paint layers or wax deposition can lead to unknown lift-off, which results in significant depth quantification errors. To address the challenge of quantifying the depths of internal or external defects under unknown lift-off conditions, this study introduces a new evaluation method based on time-domain features. Theoretical analysis combining the magnetic field phase reversal phenomenon and the magnetic shielding effect reveals why the rising time of the internal defect signals remains unaffected by lift-off. The simulation results verified the insensitivity of the time features to lift-off. In this experiment, a cross correlation algorithm was used to align different datasets. Wavelet analysis was employed to extract the rising time points, and a linear regression algorithm was applied to establish a depth quantification model under varying lift-off conditions. Finally, the validation of the pipeline samples demonstrated that the depth quantification error for defects under unknown lift-off conditions did not exceed 13%.

Magnetic shielding is a crucial aspect of many electronic devices and sensors. In this article, we investigate the magnetic shielding properties of ferromagnetic washers in a planar geometry in view of integration with on-chip devices, focusing on the transverse configuration, i.e., with the applied field parallel to the plane of the washer. We show that, in this configuration, the shielding factor of a washer can exceed the predictions of previous studies. We argue that the magnetic shielding results from the capture of the external magnetic flux by the upper and lower faces of the washer, and its subsequent channeling through the washer material and around the central hole. We present experimental results and numerical simulations and discuss the influence of the geometry of the washer, the permeability, and the saturation of the ferromagnetic material. We propose an explanation for the observed behavior and provide empirical formulas to estimate different quantities characterizing the shielding properties of washers in the transverse configuration.

<h4>Background and purpose</h4>Very high energy electron (VHEE) radiotherapy gained interest owing to technical advances and its potential for FLASH radiotherapy. Magnetically focused VHEE (fVHEE) beams showed promises in preliminary investigations in water phantoms. However, inverse treatment planning for fVHEE remains unexplored in clinically motivated scenarios. This study presented first inverse-optimized fVHEE treatment planning, permitting comparison to the current clinical benchmark, volumetric modulated arc therapy (VMAT), independent of FLASH considerations.<h4>Material and methods</h4>Seven cases across five sites (brain, head and neck, lung, prostate, and femoral head) were investigated. fVHEE plans were generated using Monte Carlo-based beamlet dose calculations and in-house inverse optimization. Plans employed 250 MeV electrons focused via idealized magnetic lenses. Plan quality was compared regarding target coverage and organ-at-risk (OAR) sparing.<h4>Results</h4>fVHEE achieved equivalent or improved target coverage in four sites, with V_95% increasing by up to 4.5% in lung cases. Notable OAR sparing occurred, including D_2% reductions of 0.2-7.6 Gy for the spinal canal and esophagus versus VMAT. The femoral head case's D_2% to the rectum/bladder decreased by 1.3 Gy/2.6 Gy. Compared to VMAT, fVHEE enabled dose deposition via limited beam angles, reducing OAR dose at selected angles and to contralateral structures in lateralized tumors. Prostate cases showed less benefit due to target-OAR proximity in multiple directions, limiting directional selectivity.<h4>Conclusions</h4>First results on inverse-optimized fVHEE planning are encouraging, particularly for lateralized targets or directionally isolated OARs. fVHEE demonstrates potential for selective dose sculpting, further comparison to VHEE is required to isolate fVHEE-specific benefits.