Non-dipole Components Research Articles

The magnetic gradient tensor of a right circular cylinder: theoretical considerations in the determination of magnetisation direction

This paper investigates the use of the magnetic gradient tensor and its eigenvectors to derive expressions for estimating the direction of magnetisation of a uniformly magnetised right circular vertical cylinder. Expressions for the gradient tensor, the eigenvalues and eigenvectors, the normalised source strength (NSS), and the direction of magnetisation on the axis of a vertical cylinder are shown to be identical in form to those previously derived for a magnetised sphere or dipole. However, the off-axis gradient tensor field of a vertical cylinder is significantly different to that of a magnetic sphere or dipole particularly at low observation heights. These differences lessen with increasing observation height and in more compact pipes. The normalised source strength displays a directional asymmetry in the eigenvector field of the gradient tensor above a pipe which is related to the direction of magnetisation. This azimuthal asymmetry in the NSS results exclusively from the horizontal components of magnetisation, which are perpendicular to the longitudinal face of the vertical cylinder. In contrast, the vertical component of magnetisation is normal to the circular planar face and produces radial symmetry in the NSS. Additionally, the paper details some unusual properties of the NSS which are attributable to non-dipole field components in the gradient tensor field which cause pairs of eigenvectors to interchange directions when ordered by their eigenvalues, as is done when calculating the NSS. This results in spatial discontinuities in the eigenvector fields arising from crossovers in the ordered eigenvalue surfaces which vary with both magnetisation direction and observation height. This phenomenon is not present in a dipole field and thus provides direct evidence of non-dipole field components. Understanding this complexity in the eigenvector field is essential to designing methodologies which can successfully estimate the direction of magnetisation over a uniformly magnetised cylinder. One proposed method based on the peak NSS, uses airborne gradient tensor data to accurately estimate magnetisation direction over a reversely magnetised pipe-like body in the Diavik diamond field of north-western Canada. The results are verified using a full tensor inversion.

Comparative Evolutionary Analysis of Dipole and Non-Dipole Components of Geomagnetic Energy

The total energy of the potential geomagnetic field (up to the core-mantle boundary) is divided into dipole and non-dipole parts, which are determined by their evolution and frequency properties. The calculations presented here are based on the available and sufficiently reliable COV-OBS.x2 geomagnetic field model that covers the period of 1840–2020. The proposed approximations for longer periods are preliminary, as further work is required to estimate errors through comparison with other historical observational and paleomagnetic models of the geomagnetic field, as well as with numerical models of the geodynamo. The actual dipole energy (about 5 EJ) turned out to be only three times higher than the non-dipole energy, rather than the previously reported one order or more. It was found that the dipole energy decreases relatively slowly and monotonically, while the non-dipole part changes much faster and quasi-periodically. Therefore, the characteristic times are on the order of one thousand years for the dipole component and on the order of hundreds of years for the non-dipole component, respectively. If the quadrupole and octupole contributions to the geomagnetic field are only considered, which is a natural limitation for paleoand archaeomagnetologists, then the energy of such a “truncated” non-dipole part increases monotonically, and its evolutionary and frequency characteristics become different from the full (up to the 14th spherical harmonic) non-dipole part. The results show that the power or the time derivative of energy varies more significantly compared to the energy, being on the order of one hundred MW for both the dipole and non-dipole parts. Frequency values were obtained by analyzing the power/ energy ratios.

WEPAPIS 70 (Western Pacific paleointensity-stacking for the last 70 ka)

Earth's magnetic field comprises dipoles and non-dipole components. In some cases, the non-dipole magnetic fields can be detected only in certain areas. Some changes in the magnetic field might occur and be recorded only in certain regions, so it is necessary to make relative paleointensity stacking for regions to observe events that may not be recorded in other regions. To find out about these changes in the Western Pacific, a record called WEPAPIS-70 (Western Pacific Paleointensity Stacking for the Last 70 ka) was made by stacking the paleointensity record from twelve marine and lake cores. WEPAPIS-70 is comparable to other global and regional paleointensity models but shows features that are possibly specific to the Western Pacific region. WEPAPIS-70 identifies the Tianchi excursion that was not recorded in the western hemisphere. WEPAPIS-70 also identifies short-lived events, such as the Rockall excursion.

Analysis of inhomogeneous magnetization using a spinner magnetometer

The assumption for measuring a discrete sample by spinner magnetometer in paleomagnetism is that the sample under study is a magnetic dipole so that the magnetization vector can be calculated by successive measurements of components along three orthogonal axes. This assumption may not hold for samples with inhomogeneous magnetization, irregular shape, or both, where non-dipole components are no longer ignorable. This study draws attention to their effect on the measurement of remanent magnetization based on an offset dipole model using multipole expansion of magnetic potential. Results from this model are compared with the experimental data measured by a new type of spinner magnetometer featured by high spatial resolution and the capability of measuring the fundamental wave component as well as the harmonic wave components. By using the relative amplitude of the harmonic waves to the fundamental wave, the contribution of non-dipole components can be quantified, leading to assessing how dipolar a sample is. The new analyses and instrumentation will be useful as a new diagnostic tool to obtain more reliable data from the samples collected from tectonically active regions with complicated geological histories.

Which Component of Solar Magnetic Field Drives the Evolution of Interplanetary Magnetic Field over the Solar Cycle?

The solar magnetic structure changes over the solar cycle. It has a dipole structure during solar minimum, where the open flux extends mainly from the polar regions into the interplanetary space. During maximum, a complex structure is formed with low-latitude active regions and weakened polar fields, resulting in spread open field regions. However, the components of the solar magnetic field that are responsible for long-term variations in the interplanetary magnetic field (IMF) are not clear, and the IMF strength estimated based on the solar magnetic field is known to be underestimated by a factor of 3–4 against the actual in situ observations (the open flux problem). To this end, we decomposed the coronal magnetic field into the components of the spherical harmonic function of degree and order (ℓ, m) using the potential field source surface model with synoptic maps from SDO/HMI for 2010–2021. As a result, we found that the IMF rapidly increased in 2014 December (7 months after the solar maximum), which coincided with the increase in the equatorial dipole, (ℓ, m) = (1, ±1), corresponding to the diffusion of active regions toward the poles and in the longitudinal direction. The IMF gradually decreased until 2019 December (solar minimum) and its variation corresponded to that of the nondipole component ℓ ≥ 2. Our results suggest that the understanding of the open flux problem may be improved by focusing on the equatorial dipole and the nondipole component and that the influence of the polar magnetic field is less significant.

Latitudinal Variations of the Geomagnetic Field

The model of variations in the Earth’s magnetic field with random Gaussian coefficients is considered. It is shown that at small amplitudes of random nondipole field component σ, the scatter of the direction of the virtual geomagnetic pole grows with increasing latitude. At large σ, the scatter does not change much and its maximum is located at middle latitudes.

Quantum droplets with topological textures in a dipolar condensate

We investigate a spin–orbit coupled Bose–Einstein condensate containing both dipolar and non-dipolar components. Combined with Rashba spin–orbit coupling, the competition between contact and dipolar interaction reveals four distinctive exotic phases: droplet lattice phase, stripe phase, oblique stripe phase, and labyrinthine stripe phase. In particular, we adopt a condensate order parameter ansatz to characterize the superstripe phase in a harmonic trap through minimizing the analytical total energy. Furthermore, we find that the energy analysis of the dipolar condensate in the trap uncovers a higher order transition from lattice to stripe phases when contact interaction increases. Our results demonstrate the possibility for physicists to realize a wealth of controllable configurations in spin–orbit coupled dipolar condensates, including droplet lattice with topology and superstripe adjusted by changing the strength of contact and dipolar interactions. The topological phases we predict in this work can be realized by using state-of-the-art techniques in ultracold atomic experiments of chromium, erbium, or dysprosium condensates.

Alternating-domain supersolids in binary dipolar condensates

Two-component dipolar condensates are now experimentally producible, and we theoretically investigate the nature of supersolidity in this system. We predict the existence of a binary supersolid state in which the two components form a series of alternating domains, producing an immiscible double supersolid. Remarkably, we find that a dipolar component can even induce supersolidity in a nondipolar component. In stark contrast to single-component dipolar supersolids, alternating-domain supersolids do not require quantum stabilization, and the number of crystal sites is not strictly limited by the condensate populations, with the density hence being substantially lower. Our results are applicable to a wide range of dipole moment combinations, marking an important step towards long-lived bulk-supersolidity.

Abstract 12452: Relation of T-Wave Morphology And P-Wave Morphology Parameters With Left Ventricular Fibrosis in Sudden Cardiac Death Victims

Introduction: T-wave morphology and P-wave morphology have been observed to have prognostic significance. However, data about their relation with arrhythmic substrate represented by left ventricular fibrosis are limited. Methods: We evaluated associations of T- and P-wave morphology parameters analyzed from the standard 12-lead ECGs with left ventricular fibrosis in 379 victims of unexpected sudden cardiac death who underwent medico-legal autopsy. Results: T-wave and P-wave area dispersion (TWAd, PWAd) (low values abnormal), non-dipolar components of T-wave and P-wave morphology (T_NonDipolarABS, P_NonDipolarABS) (high values abnormal) all had a significant association with left ventricular fibrosis (p=0.008, p=0.011, p=0.027, p=0.005 between the groups with different stages of left ventricular fibrosis, respectively, post hoc Bonferroni p-values are shown in Figures). Conclusions: Abnormal values of T- and P-wave morphology are associated with arrhythmic substrate represented by ventricular fibrosis partly explaining the mechanism behind their prognostic significance.

Vortex, stripe, Skyrmion lattice, and localized states in a spin–orbit coupled dipolar condensate

We investigate a spin-1/2 system containing both dipolar and non-dipolar components in a 52Cr Bose–Einstein condensate with spin–orbit coupling. Combined with energy analysis, phase diagram between contact interaction and Rashba spin–orbit coupling reveals four distinctive ground-state phases: vortex state phase, stripe phase, Skyrmion lattice phase, and localized Skyrmion phase. We adopt the condensate order parameter to characterize the supersolidity and topological charges of the quantum states of matter. In particular, we predict the emergence of a Skyrmion lattice phase with supersolidity which is justified by calculating the crystalline order. Moreover, we find that the critical value of the spin–orbit coupling from stripe to Skyrmion lattice increases with decreasing relative strength of the dipolar and contact interactions. Our results demonstrate the possibility for physicists to realize a wealth of controllable topological configurations in dipolar condensates, including Skyrmion lattices with both supersolidity and different topological charges adjusted by changing the strength of spin–orbit coupling. The topological phases we predict in this work can be realized by using state-of-the-art techniques in ultracold atomic experiments, such as using pulsed magnetic fields to induce and adjust spin–orbit couplings on atom chips of chromium, erbium, or dysprosium condensates.

Novel spatiotemporal processing tools for body-surface potential map signals for the prediction of catheter ablation outcome in persistent atrial fibrillation.

Background: Signal processing tools are required to efficiently analyze data collected in body-surface-potential map (BSPM) recordings. A limited number of such tools exist for studying persistent atrial fibrillation (persAF). We propose two novel, spatiotemporal indices for processing BSPM data and test their clinical applicability through a comparison with the recently proposed non-dipolar component index (NDI) for prediction of single-procedure catheter ablation (CA) success rate in persAF patients. Methods: BSPM recordings were obtained with a 252-lead vest in 13 persAF patients (8 men, 63 ± 8 years, 11 ± 13 months sustained AF duration) before undergoing CA. Each recording was divided into seven 1-min segments of high signal quality. Spatiotemporal ventricular activity (VA) cancellation was applied to each segment to isolate atrial activity (AA). The two novel indices, called error-ratio, normalized root-mean-square error (ERNRMSE) and error-ratio, mean-absolute error (ERABSE), were calculated. These indices quantify the capacity of a subset of BSPM vest electrodes to accurately represent the AA, and AA dominant frequency (DF), respectively, on all BSPM electrodes over time, compared to the optimal principal component analysis (PCA) representation. The NDI, quantifying the fraction of energy retained after removal of the three largest PCs, was also calculated. The two novel indices and the NDI were statistically compared between patient groups based on single-procedure clinical CA outcome. Finally, their predictive power for univariate CA outcome classification was assessed using receiver operating characteristic (ROC) analysis with cross-validation for a logistic regression classifier. Results: Patient clinical outcomes were recorded 6 months following procedures, and those who had an arrhythmia recurrence at least 2 months post-CA were defined as having a negative outcome. Clinical outcome information was available for 11 patients, 6 with arrhythmia recurrence. Therefore, a total of 77 1-min AA-BSPM segments were available for analysis. Significant differences were found in the values of the novel indices and NDI between patients with arrhythmia recurrence post-ablation and those without. ROC analysis showed the best CA outcome predictive performance for ERNRMSE (AUC = 0.77 ± 0.08, sensitivity = 76.2%, specificity = 84.8%). Conclusion: Significant association was found between the novel indices and CA success or failure. The novel index ERNRMSE additionally shows good predictive power for single-procedure CA outcome.

Paleosecular variation record from Pleistocene-Holocene lava flows in southern Colombia

Improvements in the spatial and temporal coverage of paleomagnetic data are essential to better evaluate paleofield behaviour over the past 10 Myr, especially due to data scarcity at low latitudes in the South American region. Here, we provide new Pleistocene-Holocene (0–2 Ma age interval) paleodirectional data from three volcanic systems (Doña Juana Volcanic Complex, Galeras Volcanic Complex and Morasurco Volcano) in southwestern Colombia between latitudes 1.2 and 1.4°N. A total of 38 paleodirectional sites were studied using progressive alternating field and thermal demagnetization treatments. After excluding transitional data, we obtain thirty site-mean directions for analysis of paleosecular variation (PSV) and the time-averaged field (TAF) in the study area. The mean direction (Dec = 351.2°, Inc = −3.4°, α95 = 6.2°, k = 20.0) and the paleomagnetic pole (Plat = 80.7°N, Plon = 173.1°E, A95 = 5.2°, K = 29.1) of these sites are not statistically compatible with the expected geocentric axial dipole (GAD) field direction and geographic north pole, respectively. Virtual geomagnetic pole dispersion (SB) for our filtered dataset (SB(2Ma) = 15.212.017.6°) and the Brunhes chron (SB(Bru) = 16.011.619.1°) are consistent at the 95% confidence level with South American studies at equatorial latitudes and recent PSV models for the 0–10 Ma and Brunhes intervals. Likewise, the corresponding inclination anomaly (ΔI) for two age groups ΔI2Ma = − 5.9−12.10.3° and ΔIBru = − 5.3−13.73.1° suggests large deviations relative to the GAD model, in accordance with predictions from zonal TAF models. The high VGP dispersion could be linked to strong longitudinal variability of the magnetic equator position over South America. This feature reflects the presence of significant non-dipole field components in this region that have been detected in geomagnetic field models for the most recent centuries and millennia, probably associated with the presence of the South Atlantic Magnetic Anomaly in the South American region.

Variations of magnetic multipoles in the X-ray binary pulsars Her X-1 and A 0535+26

ABSTRACT The X-ray binaries (XRBs) Her X-1 and A 0535+26 have been extensively studied over the years during outbursts and in deep quiescence. Cyclotron resonance scattering features (CRSFs) have been observed in absorption correlating with X-ray luminosities, though recently, an anticorrelation was seen in the 2020 giant outburst of A 0535+26 at higher luminosities. These types of behaviour have been observed in several other XRBs, yet there are sources showing extended periods of no correlation at all. Such aperiodic changes and periods of no change in CRSFs can be explained by changes in the surface magnetic fields of the X-ray pulsars. In particular, we show here that CRSF variations occur in Her X-1 and A 0535+26 due to corresponding changes in the strong nondipolar components of their surface magnetic fields, while the magnetic dipoles reaching out to the accretion discs remain largely unchanged.

Geomagnetic field shielding over the last one hundred thousand years

The geomagnetic field prevents energetic particles, such as galactic cosmic rays, from directly interacting with the Earth’s atmosphere. The geomagnetic field is not static but constantly changing, and over the last 100,000 years, several geomagnetic excursions occurred. During geomagnetic field excursions, the field strength is significantly decreased and the field morphology is strongly influenced by non-dipole components, and more cosmic ray particles can access the Earth’s atmosphere. Paleomagnetic field models provide a global view of the long-term geomagnetic field evolution, however, with individual spatial and temporal resolution and uncertainties. Here, we reconstruct the geomagnetic shielding effect over the last 100,000 years by calculating the geomagnetic cutoff rigidity using four global paleomagnetic field models, i.e., the GGF100k, GGFSS70, LSMOD.2, and CALS10k.2 model. We compare results for overlapping periods and find that the model selection is crucial to constrain the cutoff rigidity variation. However, all models indicate that the non-dipole components of the geomagnetic field are not negligible for estimating the long-term geomagnetic shielding effect. We provide a combined record of global cutoff rigidities using the best available model for individual time intervals. Our results provide the possibility to estimate the cosmogenic isotope production rate and cosmic radiation dose rate covering the last 100,000 years according to the best current knowledge about geomagnetic field evolution, and will be useful in further long-term solar activity and climate change reconstruction.

On the association of predominant polarity of North-South component of IMF in the GSE system near 1 AU with solar polar magnetic fields during 1967–2020

The skewness of the monthly distribution of GSE latitudinal angles of Interplanetary Magnetic Field (IMF) observed near the Earth (Sk) is found to show anti-correlation with sunspot activity during the solar cycles 20–24. Sk can be considered as a measure of the predominant polarity of north-south component of IMF (Bz component) in the GSE system near 1 AU. Sk variations follow the magnitude of solar polar magnetic fields in general and polarity of south polar fields in particular during the years 1967–2020. Predominant polarity of Sk is found to be independent of the heliographic latitude of Earth. Sk basically reflects the variations of the solar dipolar magnetic field during a sunspot cycle. It is also found that IMF sector polarity variation is not a good indicator of the magnitude changes in solar polar magnetic fields during a sunspot cycle. This is possibly due to the influence of non-dipolar components of the solar magnetic field and the associated north-south asymmetries in the heliospheric current sheet.

Extending and refining the paleomagnetic secular variation database for south-eastern Africa (Madagascar) to 2500 cal BP

Today's knowledge about paleomagnetic secular variations in (southern) Africa is extremely limited. Here, we derive paleomagnetic records from independently radiocarbon dated sediment records from three maars in Madagascar: Andraikiba and Amparihibe are terrestrial maars located on the main island of Madagascar and on a small island in the Northwest, whereas Crater Lake is a maar which has an open connection to the Indian Ocean. Studied through alternating field demagnetization of u-channel samples, characteristic remanent magnetization (ChRM) directions document similar inclination and declination patterns in two of the archives for the past 2,500 years (except for the last 400 cal BP). These new data are the first allowing to test the reliability of previous records which often suffer from low resolution and other obstacles. This will further allow to start to distinguish between robustly confirmed paleomagnetic secular variation data for this region from potentially problematic data.Considering a much lower resolution and a shorter covered time interval of archaeomagnetic data from La Réunion, South Africa, Botswana and Zimbabwe the temporal successions of maxima and minima reveal a coherent picture. Although slightly shifted in time, similarities also exist to the global geomagnetic field reconstruction model SHAWQ2k (Campuzano et al., 2019) which includes the above mentioned data. Surprisingly also similarities, though only in declination, are observed to the CALS3K.4 model (Korte and Constable, 2011) which is used as Northern Hemisphere biased model example. In contrast to this, no declination similarities but remarkable inclination similarities are observed to a lake record from Lake Malawi. An analog inclination pattern is also observed in a record from the Makran Accretionary Wedge which is ∼5,000 km to the north of the investigated sites. Interestingly the spatial distribution of archives showing these inclination similarities resembles the spatial distribution of inclination anomalies detected in model predictions. PSV similarities over such a large area are suggestive of a large-scale core dynamic origin independent of westward drift of non-dipole field components often associated with PSV records. This study emphasizes the potential of maar lakes in Madagascar for paleo reconstructions but also suggests that shallow marine and marine-brackish systems should be avoided if possible when trying to expand the (South) African paleomagnetic database.

On the absolute geomagnetic intensity fluctuations in Mexico over the last three millennia

Earth Magnetic Field is characterized by continuous variations in terms of direction and intensity. These fluctuations occur with periodicities of the order of years to tens of thousands of years and constitute the principal characteristic of the geomagnetic field. Revealing such variations at a regional scale has a significant impact in geophysics, but also in archaeology and thus represents a clear example of interdisciplinary research. Due to the importance of non-dipole field components in the secular variation, reference curves can only be constructed for limited areas, commonly within less than 1200 km radius. Three recently reported paleosecular variation curves for most Mesoamerica show contradictory trends, probably due to inappropriate selection of data and the criteria applied to individual intensity determinations. The use of unpublished data, essentially reported in thesis, may lead the discrepancy over the reported curves. Here, we report a critical revaluation of existing published and unpublished data with particular emphasis on the sample-radiometric age relationship for the last 3600 years.

On the Rate of Crustal Failures in Young Magnetars

Abstract The activity of magnetars is powered by their intense and dynamic magnetic fields and has been proposed as the trigger to extragalactic fast radio bursts. Here we estimate the frequency of crustal failures in young magnetars, by computing the magnetic stresses in detailed magnetothermal simulations including Hall drift and ohmic dissipation. The initial internal topology at birth is poorly known but is likely to be much more complex than a dipole. Thus, we explore a wide range of initial configurations, finding that the expected rate of crustal failures varies by orders of magnitude depending on the initial magnetic configuration. Our results show that this rate scales with the crustal magnetic energy, rather than with the often used surface value of the dipolar component related to the spin-down torque. The estimated frequency of crustal failures for a given dipolar component can vary by orders of magnitude for different initial conditions, depending on how much magnetic energy is distributed in the crustal nondipolar components, likely dominant in newborn magnetars. The quantitative reliability of the expected event rate could be improved by a better treatment of the magnetic evolution in the core and the elastic/plastic crustal response, not included here. Regardless of that, our results are useful inputs in modeling the outburst rate of young Galactic magnetars, and their relation with the fast radio bursts in our and other galaxies.

Insights Into the Spatiotemporal Patterns of Complexity of Ventricular Fibrillation by Multilead Analysis of Body Surface Potential Maps.

BackgroundVentricular fibrillation (VF) is the main cause of sudden cardiac death, but its mechanisms are still unclear. We propose a noninvasive approach to describe the progression of VF complexity from body surface potential maps (BSPMs).MethodsWe mapped 252 VF episodes (16 ± 10 s) with a 252-electrode vest in 110 patients (89 male, 47 ± 18 years): 50 terminated spontaneously, otherwise by electrical cardioversion (DCC). Changes in complexity were assessed between the onset (“VF start”) and the end (“VF end”) of VF by the nondipolar component index (NDIBSPM), measuring the fraction of energy nonpreserved by an equivalent 3D dipole from BSPMs. Higher NDI reflected lower VF organization. We also examined other standard body surface markers of VF dynamics, including fibrillatory wave amplitude (ABSPM), surface cycle length (BsCLBSPM) and Shannon entropy (ShEnBSPM). Differences between patients with and without structural heart diseases (SHD, 32 vs. NSHD, 78) were also tested at those stages. Electrocardiographic features were validated with simultaneous endocardium cycle length (CL) in a subset of 30 patients.ResultsAll BSPM markers measure an increase in electrical complexity during VF (p < 0.0001), and more significantly in NSHD patients. Complexity is significantly higher at the end of sustained VF episodes requiring DCC. Intraepisode intracardiac CL shortening (VF start 197 ± 24 vs. VF end 169 ± 20 ms; p < 0.0001) correlates with an increase in NDI, and decline in surface CL, f-wave amplitude, and entropy (p < 0.0001). In SHD patients VF is initially more complex than in NSHD patients (NDIBSPM, p = 0.0007; ShEnBSPM, p < 0.0001), with moderately slower (BsCLBSPM, p = 0.06), low-amplitude f-waves (ABSPM, p < 0.0001). In this population, lower NDI (p = 0.004) and slower surface CL (p = 0.008) at early stage of VF predict self-termination. In the NSHD group, a more abrupt increase in VF complexity is quantified by all BSPM parameters during sustained VF (p < 0.0001), whereas arrhythmia evolution is stable during self-terminating episodes, hinting at additional mechanisms driving VF dynamics.ConclusionMultilead BSPM analysis underlines distinct degrees of VF complexity based on substrate characteristics.

The non-trivial magnetic configuration in neutron stars

AbstractWhile predominantly dipolar, large-scale magnetic fields are usually assumed in most studies involving neutron stars, there are multiple observational, theoretical hints and numerical simulations highlightening the importance of non-dipolar components. I review here the most important observational facts and numerical studies pointing towards the existence of magnetospheric currents and internal small-scale structures, arising from multipoles of poloidal and toroidal fields. This holds for all neutron star stages: at birth, during their lifetime and after a merger.