Magnetic Length Research Articles

Numerical study of turbulent eddy self-interaction in tokamaks with low magnetic shear. Part I: Linear simulations

Abstract This study examines the impact of low and zero magnetic shear, along with rational values of safety factor, on linear mode behavior in tokamak plasmas. We focus on how magnetic field line topology and parallel domain length influence linear mode structures and growth rates as magnetic shear decreases. Our results
show that as magnetic shear is reduced to low values, linear modes can transition between different branches, significantly affecting their characteristics. At zero magnetic shear, accurate modeling requires precisely capturing magnetic topology, as small deviations near rational surfaces can greatly impact growth rates. These findings are extended to nonlinear simulations in a companion paper (Volčokas, 2024), revealing that long turbulent eddies and magnetic field line topology play a crucial role in turbulence self-interaction and plasma transport.

Particle-Hole Asymmetric Ferromagnetism and Spin Textures in the Triangular Hubbard-Hofstadter Model

In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor ν≤1, bounded below by filling factor ν=1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors ν=1 and ν=3. The phases near ν=1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands. Published by the American Physical Society 2024

Origin of magnetism via cation vacancy defects in non-stoichiometric NiCo2O4 nanoparticles: A synchrotron-based x-ray absorption and x-ray magnetic circular dichroism spectroscopic study

The present study probes the effect of cation distributions in the structural, optical, electronic, and magnetic properties of mixed-valent inverse-spinel NiCo2O4 (NCO) nanoparticles (NPs). NCO NPs were prepared using the sol–gel combustion method and the grain size was obtained in the magnetic exchange length range assumed to be from single-ion anisotropy. The Raman and photoluminescence spectroscopies confirm the presence of an inverse-spinel structure with different oxidation states, and vibrating sample magnetometry clarifies the existence of ferromagnetism with the presence of magnetic anisotropy among the cations. These NPs annealed at a higher grain-growth temperature accumulate ferrimagnetic properties and produce magneto-crystalline anisotropy making NCO an assuring material for spintronic applications. A detailed x-ray absorption spectroscopy and x-ray magnetic circular dichroism studies reveal an indestructible correlation between the distribution of the present cations and the element-specific origin of ferrimagnetic behavior. Ni is found to be accountable for the magnetic moment and electronic conduction, whereas Co is associated mainly with the generation of the magnetic anisotropy even in the polycrystalline NP form. This describes the anti-ferromagnetic coupling between Co and Ni ions that is pivotal in demonstrating the exchange interaction between these cations. The above result signifies the site-dependent cation valence states for the magnetic properties, and the extent of growing conditions are related to such cation-site dysfunction. This depicts further tunability in NCO as a functional oxide material.

Aluminum's role in tailoring the characteristics of room temperature co-sputtered gadolinium and aluminum-doped ZnO thin films

This study investigated the characteristics of gadolinium (Gd) and aluminum (Al) co-doped ZnO synthesized by co-sputtering at varying concentrations of Al. FESEM images revealed a morphology containing spherical-hexagonal nanostructures of different sizes based on the amount of Al. The EDS spectra clearly demonstrated the presence of Al, Gd, Zn, and O, confirming the successful incorporation of Gd and Al ions into the ZnO lattice in agreement with XRD profiles, not detecting any secondary phases. The photoluminescence study revealed that doping-induced defect states (oxygen vacancies, zinc vacancies, and zinc interstitial) were responsible for the many characteristic peaks of deep level emission observed in the photoluminescence spectra. Higher Al doping induced changes in magnetic characteristics as reflected in the greater root mean square value (δfrms), and the root mean square phase shift value (Φrms) in MFM analysis, whereas the magnetic correlation length (L) decreases. The incorporation of Al at higher concentrations into Gd-doped ZnO resulted in improved magnetic behavior suggesting the exchange interaction between Gd and Al ions mediated by oxygen vacancies. These results confirm that sufficient Al doping can efficiently improve the properties and magnetic behavior of ZnO-based DMS systems, which could potentially pave the way towards the realization of spin and/or optical based electronic devices.

Quantifying the topology of magnetic skyrmions in three dimensions.

Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number. However, in real systems with the finite thickness of the device material being larger than the magnetic exchange length, the skyrmion spin texture extends into the third dimension and cannot be assumed as homogeneous. Using soft x-ray laminography, we reconstruct with about 20-nanometer spatial (voxel) size the full three-dimensional spin texture of a skyrmion in an 800-nanometer-diameter and 95-nanometer-thin disk patterned into a 30× [iridium/cobalt/platinum] multilayered film. A quantitative analysis finds that the evolution of the radial profile of the topological skyrmion number is nonuniform across the thickness of the disk. Estimates of the micromagnetic energy densities suggest that the changes in topological profile are related to nonuniform competing energetic interactions. Our results provide a foundation for nanoscale metrology for spintronics devices using topology as a design parameter.

Access to an ELM-suppressed X-point radiator regime in TCV snowflake minus configurations

TCV’s operating regime with an X-point radiator (XPR) has been broadened by changing the magnetic geometry. XPRs have properties that could make them an attractive power exhaust solution for fusion reactors. These include the conversion of a high fraction of exhaust power into radiation. TCV had previously accessed the XPR regime only with difficulties, as predicted for plasmas where radiative losses are dominated by carbon impurities, that are ubiquitous in TCV. Guided by this theoretical model of the XPR, recent experiments employed TCV’s configurational versatility to demonstrate that XPR access can be facilitated by introducing a second X-point in the vicinity of the separatrix. This configuration, which has a snowflake-minus topology, features a particularly long magnetic connection length from the region just above the X-point to the outer midplane together with a wide geometrical interface with the private flux region that reaches high neutral pressure. Transitioning to this configuration in a high-power H-mode leads to a shift in the radiating region across the separatrix from the divertor to a volume above the X-point, i.e. within the last closed flux surface (LCFS). This displacement of the radiating region is co-incident with the disappearance of edge localised modes (ELMs), while retaining H-mode confinement, a behaviour only, to date, observed in devices with metallic walls. In contrast to observations in these other devices, on TCV, the primary strike points in these configurations remain attached. Detailed measurements of the plasma kinetic parameters inside and outside of the separatrix now challenge the models for access and stability of the XPR and ELMs alike.

Elliptical Halbach magnet and gradient modules for low-field portable magnetic resonance imaging.

This study aims to develop methods to design the complete magnetic system for a truly portable MRI scanner for neurological and musculoskeletal (MSK) applications, optimized for field homogeneity, field of view (FoV), and gradient performance compared to existing low-weight configurations. We explore optimal elliptic-bore Halbach configurations based on discrete arrays of permanent magnets. In this way, we seek to improve the field homogeneity and remove constraints to the extent of the gradient coils typical of Halbach magnets. Specifically, we have optimized a tightly packed distribution of magnetic Nd2Fe14B cubes with differential evolution algorithms and a second array of shimming magnets with interior point and differential evolution methods. We have also designed and constructed an elliptical set of gradient coils that extend over the whole magnet length, maximizing the distance between the lobe centers. These are optimized with a target field method minimizing a cost function that considers also heat dissipation. We have employed the new toolbox to build the main magnet and gradient modules for a portable MRI scanner designed for point-of-care and residential use. The elliptical Halbach bore has semi-axes of 10 and 14& cm, and the magnet generates a field of 87& mT homogeneous down to 5700& ppm (parts per million) in a 20-cm diameter FoV; it weighs 216& kg and has a width of 65& cm and a height of 72& cm. Gradient efficiencies go up to around 0.8& mT/m/A, for a maximum of 12& mT/m within 0.5& ms with 15& A and 15& V amplifier. The distance between lobes is 28& cm, significantly increased with respect to other Halbach-based scanners. Heat dissipation is around 25& W at maximum power, and gradient deviations from linearity are below 20% in a 20-cm sphere. Elliptic-bore Halbach magnets enhance the ergonomicity and field distribution of low-cost portable MRI scanners, while allowing for full-length gradient support to increase the FoV. This geometry can be potentially adapted for a prospective low-cost whole-body technology.

Origin and fate of the pseudogap in the doped Hubbard model

The relationship between the pseudogap and underlying ground-state phases has not yet been rigorously established. We investigated the doped two-dimensional Hubbard model at finite temperature using controlled diagrammatic Monte Carlo calculations, allowing for the computation of spectral properties in the infinite-size limit and with arbitrary momentum resolution. We found three distinct regimes as a function of doping and interaction strength: a weakly correlated metal, a correlated metal with strong interaction effects, and a pseudogap regime at low doping. We show that the pseudogap forms both at weak coupling, when the magnetic correlation length is large, and at strong coupling, when it is shorter. As the temperature goes to zero, the pseudogap regime extrapolates precisely to the ordered stripe phase found by ground-state methods.

An analytical model for a coaxial electromagnetic recuperator considering end effect

A coaxial electromagnetic recuperator (CER), leveraging the principle of tubular permanent magnet linear synchronous motor, has been introduced to mitigate the shortcomings of the traditional recuperator, including low reliability and uncontrollable counter-recoil motion. Firstly, the layout and structural scheme of the CER are presented, with the maximum recuperator force determined through a force analysis of the recoil process. Subsequently, by incorporating a virtual permanent magnet area at both ends of the permanent magnet array, a precise CER analysis model is developed. This model adeptly accounts for the end effect due to magnet length limitations and formulates expressions for air gap flux density, back electromotive force, and electromagnetic thrust. The analytical model’s accuracy is then validated against a finite element model. Finally, the key parameters influencing CER performance were improved, and the overall structure of the CER was refined, significantly enhancing its thrust capabilities.

Josephson effect in a fractal geometry

The Josephson effect is a hallmark signature of the superconducting state, which, however, has been sparsely explored in non-crystalline superconducting materials. Motivated by this, we consider a Josephson junction consisting of two superconductors with a fractal metallic interlayer, which is patterned as a Sierpiński carpet by removing atomic sites in a self-similar and scale-invariant manner. We here show that the fractal geometry has direct observable consequences on the Josephson effect. In particular, we demonstrate that the form of the supercurrent–magnetic field relation as the fractal generation number increases can be directly related to the self-similar fractal geometry of the normal metallic layer. Furthermore, the maxima of the corresponding diffraction pattern directly encode the self-repeating fractal structure in the course of fractal generation, implying that the corresponding magnetic length directly probes the shortest length scale in the given fractal generation. Our results should motivate future experimental efforts to verify these predictions in designer quantum materials and motivate future pursuits regarding fractal-based SQUID devices.

Microscopic solutions for vortex clustering in two-band type-1.5 superconductors

Two-band superconductors exhibit a distinct phase characterized by two correlation lengths, one smaller and the other larger than the magnetic field penetration length. This regime was coined type-1.5 superconductivity, with several unconventional properties, such as vortex clustering. However, a fully microscopic solution for vortex clusters has remained challenging due to computational complexities beyond quasiclassical models. This work presents numerical solutions obtained in a fully self-consistent two-band Bogoliubov–de Gennes model. We show the presence of discrepant correlation lengths leading to vortex clustering in two-band superconductors. Published by the American Physical Society 2024

A study on maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolator.

This paper aims to study the maglev force and vibration attenuation characteristics of quasi-zero stiffness cruciform maglev isolators (CMIs). The maglev force and stiffness of CMIs were analytically computed based on equivalent charge theory, and the transfer function of the system was conducted. The effects of magnet geometry parameters and air gap on the maglev force, stiffness, and vibration transmission characteristics of the CMI system were revealed through parametric analyses. With the increase in magnet length and width, the maximum value of maglev force increases, but the displacement range of near-zero stiffness, amplitude, and phase of the system gradually decrease. With the increase in magnet height, the displacement range of near-zero stiffness increases, while the variation in the amplitude and phase of the system has minimal impact. Meanwhile, in the Halbach array, the height variation of the magnet at different positions has different impacts on the magnetic force. As the air gap increases, the maximum value of maglev force decreases, but the amplitude and phase gradually increase, and the displacement range of near-zero stiffness first rises and then decreases. Finally, an experimental study was carried out to test the vibration attenuation characteristics of CMIs, in which sinusoidal excitation, hammer strike excitation, and random excitation were applied.

Oscillatory onset of rotating thermal convection subject to spatially varying magnetic fields and stable stratification

Convective fluid motions in deep planetary cores induce spatially and temporally varying magnetic fields observable as secular variation. Oscillatory instabilities occurring as onset modes in rapidly rotating thermal convection influenced by heterogeneous magnetic fields and stratification, investigated in this study, can be potentially linked to such observations. A plane layer approximation to near-polar and near-equatorial regions of the Earth's outer core is considered. In addition to penetrative convection and flow suppression effects, the simultaneous interaction of convective instabilities with asymmetrical magnetic fields and stable stratification is the focus of this study. The fundamental modes of magnetoconvection onset are preserved even under stable stratification, although the convection threshold is lowered irrespective of the parameter regime. The axial invariance of rapidly rotating columnar convection loses its midplane symmetry with intense localization of kinetic energy in the unstably stratified regions. The parameter regimes supporting the onset of the magnetically modified viscous oscillatory (mVO) modes are further extended toward Earthlike conditions such as high thermal conductivity (low Prandlt number, Pr) and magnetic dissipation (low Roberts number, q). Moreover, compared to fully unstable stratification, partial stable stratification enhances the range of imposed magnetic field length scale (δ) over which the onset of mVO modes is favored. The critical field length scale (δ⋆), above which the onset regime of the mVO modes is bounded by a minimum q, is determined. Irrespective of the rotation rate, below δ=δ⋆, the onset of the mVO mode is supported for asymptotically small q for Pr values close to the Earth's outer core.

Investigating the impact of magnetic air gap variations on short circuit characteristics of partially high temperature superconducting generator

Partially high-temperature superconducting generators (PHTSGs) feature large magnetic air gaps imposed by using cryostats for HTS field windings. This increased air gap significantly affects end winding inductance and can lead to elevated fault torque levels. This study investigates the influence of magnetic air gap variation on generator design and end winding inductance and its implications for short-circuit faults in PHTSGs. Through a combination of numerical simulations and analytical analysis, the study explores how changes in the magnetic air gap affect end winding inductance and subsequently influence short-circuit fault behavior. The results reveal a direct correlation between magnetic air gap length, end winding inductance, and key short-circuit parameters such as stator current, field currents, and electromagnetic torque. Notably, an increase in the magnetic air gap is observed to elevate stator and field currents and electromagnetic torque during short-circuit events. These insights underscore the importance of considering magnetic air gap variation and its impact on end winding inductance and its relationship with short circuit characteristics in the design and operation of PHTSGs, providing valuable insights for enhancing the resilience and performance of high-temperature superconductor-based generator systems.

Error analysis and correction strategy for measuring oriented silicon steel by SST method

AbstractTo accurately determine the relationship between magnetic polarisation and magnetic field strength in oriented silicon steel, the magnetic properties, such as power loss, were measured under different magnetisation conditions. This facilitates for the precise selection of iron core materials for distribution transformers. The deviation rate of measurement results for different magnetisation conditions in oriented silicon steel with varying thicknesses was analysed using the SST method. Additionally, the finite element simulation of MagNet was employed to further investigate this relationship. The causes of measurement errors in oriented silicon steel by the SST method are thoroughly studied, with a focus on 0.18 mm oriented silicon steel as an example. It is found that the main reason for the measurement error is the deviation between the actual effective magnetic path length and the conventional effective magnetic path length, which is caused by the uneven distribution of magnetic polarisation in oriented silicon steel. The main reason for the difference of magnetisation conditions is the change in the actual effective magnetic path length, which is mainly affected by changes in permeability. Combined with the magnetic field distribution inside the oriented silicon steel, the distribution coefficient of magnetic polarisation can be calculated, the actual effective magnetic path length under each condition can be calculated, and then the measurement results of the SST method can be modified. This research is expected to significantly contribute to the practical applications of oriented silicon steel in engineering.

Impact of the magnetic horizon on the interpretation of the Pierre Auger Observatory spectrum and composition data

The flux of ultra-high energy cosmic rays reaching Earth above the ankle energy (5 EeV) can be described as a mixture of nuclei injected by extragalactic sources with very hard spectra and a low rigidity cutoff.Extragalactic magnetic fields existing between the Earth and the closest sources can affect the observed CR spectrum by reducing the flux of low-rigidity particles reaching Earth. We perform a combined fit of the spectrum and distributions of depth of shower maximum measured with the Pierre Auger Observatory including the effect of this magnetic horizon in the propagation of UHECRs in the intergalactic space.We find that, within a specific range of the various experimental and phenomenological systematics, the magnetic horizon effect can be relevant for turbulent magnetic field strengths in the local neighbourhood in which the closest sources lieof order Brms ≃ (50–100) nG (20 Mpc/ds)( 100 kpc/Lcoh)1/2, with ds the typical intersource separation and Lcoh the magnetic field coherence length. When this is the case,the inferred slope of the source spectrum becomes softer and can be closer to the expectations of diffusive shock acceleration, i.e., ∝ E-2.An additional cosmic-ray population with higher source density and softer spectra, presumably also extragalactic and dominating the cosmic-ray flux at EeV energies, is also required to reproduce the overall spectrum and composition results for all energies down to 0.6 EeV.

Free convection in a square wavy porous cavity with partly magnetic field: a numerical investigation

Natural convection in a square porous cavity with a partial magnetic field is investigated in this work. The magnetic field enters a part of the left wall horizontally. The horizontal walls of the cavity are thermally insulated. The wave vertical wall on the right side is at a low temperature, while the left wall is at a high temperature. The Brinkman-Forchheimer-extended Darcy equation of motion is utilized in the construction of the fluid flow model for the porous media. The Finite Element Method (FEM) was used to solve the problem’s governing equations, and the current study was validated by comparing it to earlier research. On streamlines, isotherms, and Nusselt numbers, changes in the partial magnetic field length, Hartmann number, Rayleigh number, Darcy number, and number of wall waves have been examined. This paper will show that the magnetic field negatively impacts heat transmission. This suggests that the magnetic field can control heat transfer and fluid movement. Additionally, it was shown that heat transfer improved when the number of wall waves increased.

Chaotic vibration of a curved CNT conveying magnetic fluid in the thermo-magnetic field considering the surface effects

The nonlinear chaotic vibration of curved single-walled carbon nanotube (CSWCNT) conveying magnetic fluid is studied based on the nonlocal Euler-Bernoulli beam model. The governing equation of CSWCNT is presented considering the axial thermo-magnetic load and the surface effect. By employing the Galerkin decomposition approximation method along with the admissible beam shape function satisfying the cantilevered beam boundary conditions, the nonlinear partial differential equation of the system is reduced to a nonlinear ordinary differential equation and numeric integration procedures are used to solve it. By considering the non-dimensional damping, cubic and quadratic terms, and amplitude of external force as controlling parameters, the bifurcation diagram and the largest Lyapunov exponent are employed to distinguish the chaotic, periodic, and quasi-periodic critical parameters of the curved CNT dynamics and validate the predicted results. Also, the phase plane and Poincare map for these critical parameters are provided. The results show that decreasing values of damping coefficient and quadratic term leads to quasi-periodic or chaotic motion, while system has periodic behaviour for smaller values of the external force and nonlinear cubic term. Also, magnetic field intensity and length of the CSWCNT help preventing the chaotic motion. Furthermore, adverse effects of higher values of temperature change, flow velocity and its correction factor are seen based on the obtained results.

Theoretical limits of magnetic detection of structural surface defects at the nanometre scale

ABSTRACT We present a theoretical study on the magnetic signals of structural surface defects like cracks or indents combined with inhomogeneities on the surface or subsurface inclusions of soft ferromagnetic metals like body-centred cubic Fe or amorphous CoFeB. We discuss limits of early detection of small surface defects on the basis of calculated magnetic stray fields few tens of nm above the surface. The considered surface imperfections have extensions of a few nm which correspond to low multiples of the magnetic exchange lengths of Fe or CoFeB. The detection of such small inhomogeneities requires that the sensor is about as close to the surface as the size of the inhomogeneity is. Furthermore, the step width of a scanning sensor must be of the same size as well. Both these requirements may be fulfilled for instance by scanning microscopy with diamond nitrogen-vacancy-centre quantum sensors.

Optimised design of aviation stainless steel sheet SH guided wave focusing PPM EMAT

ABSTRACT Electromagnetic Acoustic Transducer (EMAT) is an ultrasonic testing technique that generates sound in the part inspected instead of the transducer. Electromagnetic ultrasonic guided wave detection technology has problems such as low energy conversion efficiency and the great influence of environmental noise, resulting in low echo signal amplitude. When the two rows of permanent magnets are arranged non-parallel, the sound beam will be focused at the intersection point of the axes of the two rows of permanent magnets. This article uses this rule to optimise the design parameters of PPM EMAT. Distance amplitude curve (DAC) is a method of compensating. However, large-scale detection requires a flat DAC curve. In addition, the increase in the angle and length of the permanent magnets and the number of pairs of permanent magnets will improve the intensity of the defect wave indication intensity. However, the increase in the angle of the permanent magnets will increase the signal attenuation. After simulation and experiments, when the angle, length and number of permanent magnet pairs are 4°, 25 mm and 8 pairs, the corresponding EMAT has the optimal axis radiation sound field and a smoother DAC, which is more suitable for stainless steel sheets, long-distance rapid guided wave detection.