Magnetic Field Gradient Tensor Research Articles

Kinetic-scale Topological Structures Associated with Energy Dissipation in the Turbulent Reconnection Outflow

Assisted by the Magnetospheric Multiscale mission capturing unprecedented high-resolution data in the terrestrial magnetotail, we apply a local streamline-topology classification methodology to investigate the categorization of the magnetic field topological structures at kinetic scales in the turbulent reconnection outflow. It is found that strong correlations exist between the straining and rotational part of the velocity gradient tensor as well as the magnetic field gradient tensor. Strong energy dissipation prefers to occur at regions with high magnetic stress or current density, which is contributed mainly by O-type topologies. These results indicate that the kinetic structures with O-type topology play a more important role in energy dissipation in turbulent reconnection outflow.

A New Correction Method of Distributed Magnetic Sensor System Based on Magnetic Shielding Room

Distributed Magnetic Sensor System (DMSS) can measure vector magnetic field and magnetic gradient tensor (MGT) and is widely used in magnetoencephalography, geological exploration, magnetic navigation, magnetic positioning, and other fields. The posture and position of the magnetic sensor are the key factors that affect measurement accuracy. For the first time, using a magnetic shielding room (MSR) and a composite coil that can switch between uniform and gradient fields in situ, a new correction method for various errors is proposed to reduce vector measurement errors. In addition, sensor position deviation can also lead to MGT calculation errors. This paper establishes a compensation model by using the magnetic field gradient formula. The simulation results show that the average calibration errors of the posture and position of the magnetic sensor are 0.08% and 0.53%, respectively, and the measurement error of the MGT is reduced by four times. Experimental results in the MSR show that the measurement error of the vector magnetic field is reduced by two orders of magnitude and that of the MGT by one order of magnitude. Therefore, the new calibration method can effectively enhance the measurement accuracy of the DMSS.

Magnetic Anomalies Caused by 3D Polyhedral Structures With Arbitrary Polynomial Magnetization

AbstractMagnetization is a natural property of magnetic materials which is widely used to analyze paramagnetic data, locate unexploded ordnance, explore mineral deposits and gas resources, and image anomalous magnetic structures in the Earth's crust. An essential and challenging task is to compute accurate magnetic anomalies caused by realistic magnetic 3D structures. In this study, for the first time, we derive the analytical expressions of magnetic potential, magnetic field and magnetic gradient tensor for magnetic materials with 3D polyhedral shapes and magnetization vectors that may vary in the space following polynomial trends. The order of polynomials can vary from one to high positive integers in both horizontal and vertical directions. Synthetic and realistic deposit models are used to validate our analytical solutions. We release the open‐source code in C++.

Secular variation signals in magnetic field gradient tensor elements derived from satellite-based geomagnetic virtual observatories

SUMMARYWe present local time-series of the magnetic field gradient tensor elements at satellite altitude derived using a Geomagnetic Virtual Observatory (GVO) approach. Gradient element time-series are computed in 4-monthly bins on an approximately equal-area distributed worldwide network. This enables global investigations of spatio-temporal variations in the gradient tensor elements. Series are derived from data collected by the Swarm and CHAMP satellite missions, using vector field measurements and their along-track and east–west differences, when available. We find evidence for a regional secular variation impulse (jerk) event in 2017 in the first time derivative of the gradient tensor elements. This event is located at low latitudes in the Pacific region. It has a similar profile and amplitude regardless of the adopted data selection criteria and is well fit by an internal potential field. Spherical harmonic models of the internal magnetic field built from the GVO gradient series show lower scatter in near-zonal harmonics compared with models built using standard GVO vector field series. The GVO gradient element series are an effective means of compressing the spatio-temporal information gathered by low-Earth orbit satellites on geomagnetic field variations, which may prove useful for core flow inversions and in geodynamo data assimilation studies.

The magnetic field and magnetic gradient tensor for a right circular cylinder

Expressions for the magnetic scalar potential, the magnetic field vector and the magnetic gradient tensor due to a uniformly magnetised semi-infinite right circular vertical cylinder are presented based on an application of Poisson’s relation to the gravity gradient tensor. The superposition principle allows for the theory to be extended to finite length and concentrically zoned right circular cylinders. This formulation provides an accurate and computationally efficient means of modelling the magnetic response of vertical or plunging right circular cylinders or pipes in which the total magnetisation is assumed to be homogeneous. This modelling technique lends itself to inversion applications in magnetic exploration. Furthermore, the theory presented here considers some important special cases including expressions for the magnetic gradient tensor on the axis of a vertical cylinder or pipe. This leads to expressions for estimating the direction of magnetisation within a uniformly magnetised pipe. This theory provides a basis for mapping magnetisation directions over quasi-vertical pipe-like bodies.

Detection technology of multi-magnetic source in spacecraft based on magnetic field gradient tensor

Multi-magnetic source resolution in spacecraft has been a difficult problem in the field of magnetic survey. Detection technology of magnetic gradient tensor is available to the problem for its high resolution and precision. A spacecraft magnetic source model is established, and a multi-magnetic source model fitting method for spacecraft is presented. The principal invariants of the magnetic field gradient tensor are introduced to ascertain the number and horizontal location of the source, and the Euler equations are combined to complete the multi-magnetic source depth calculation, the best resolution is up to 0.012m, meeting the engineering requirements. The study opens up a new way of multi-magnetic source target detection in spacecraft.

Fast 3D forward modeling of the magnetic field and gradient tensor on an undulated surface

Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy for forward modeling. For arbitrarily distributed susceptibility data on an undulated surface, we propose a fast 3D forward modeling method in the wavenumber domain based on (1) the wavenumber-domain expression of the prism combination model and the Gauss–FFT algorithm and (2) cubic spline interpolation. We apply the proposed 3D forward modeling method to synthetic data and use weighting coefficients in the wavenumber domain to improve the modeling for multiple observation surfaces, and also demonstrate the accuracy and efficiency of the proposed method.

Calculation and correction of magnetic object positioning error caused by magnetic field gradient tensor measurement

Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object (2.44 Am 2 @1 kHz) can be increased from (0.45 m, 0.75 m), (0°, 25°) to (0.30 m, 0.80 m), (0°, 80°), respectively.

Eliminating magnetic disturbance of satellites by method of magnetic field gradient tensor measurement

Eliminating magnetic disturbance of satellites by method of magnetic field gradient tensor measurement

Estimating rock-vector magnetization from coincident measurements of magnetic field and gravity gradient tensor

Poisson’s theorem relating components of the magnetic field to components of the gradient of the gravity vector assuming a common source has been cast into a general form. A given magnetization distribution in the terrain or in the underlying crust is propagated into the corresponding magnetic field through the gravity gradient tensor. Conversely, measured magnetic field anomalies and measured gravity gradient tensor anomalies can be used to estimate the unknown magnetization vectors without knowledge of the geometry of the sources. We have tested the method on recently acquired data over a greenstone belt in Northern Sweden. The topographic relief was sufficiently variable to dominate the measured gravity gradient tensor. In practice, we have concentrated on areas where the norm of the gravity gradient tensor reached a maximum so that there was a better chance of identifying isolated sources with well-defined density and magnetization. We have surrounded the selected points by a small window and used all the data lying within that window to estimate the magnetization vectors. We have compared the estimated amplitudes and directions of magnetization with those measured from selected rock samples in the area and found a relatively modest agreement. We have interpreted this as a result of two effects: (1) Measured magnetizations are generally lower than those estimated by this method, and we believe that this is related to the fact that the collection of samples in the field is biased because of a small number of outcrops in most parts of the area. (2) This analysis is biased toward high-amplitude magnetic anomalies; i.e., the estimation procedure works best for high-amplitude magnetic anomalies, in which case, the influence of neighboring anomalies is reduced. The estimated magnetization directions show a strong dominance of remanent magnetization over induced magnetization in agreement with laboratory measurements on rock samples from the area.

Magnetic tensor gradiometry using Ramsey interferometry of spinor condensates

We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate $^{87}$Rb spin-1 condensates in freefall and infer their relative Larmor phase -- and thus the differential magnetic field strength -- with a common-mode phase noise suppression exceeding $50\,\mathrm{dB}$. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure the magnetic field gradient tensor of ambient and applied magnetic fields with a nominal precision of $30\,\mathrm{\mu G\,cm^{-1}}$ and a sensor volume of $2\times10^{-5}\,\mathrm{mm}^3$. We predict a spin-projection noise limited magnetic energy resolution of order $\hbar$ for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle inherent to BEC experiments.

A regularity criterion for 2D MHD flows with horizontal dissipation and horizontal magnetic diffusion

This paper concerns the conditional global regularity of incompressible MHD equations with horizontal dissipation and horizontal magnetic diffusion in two dimension. When only horizontal dissipation and horizontal magnetic diffusion are present, there is no control on the vertical derivatives of velocity field and magnetic field, which is the main difficulty to establish the global regularity. In this paper, we establish a global regularity criterion in terms of one entry of the velocity gradient tensor or one entry of the magnetic field gradient tensor, which extends the recent work (Fan and Ozawa, 2014).

Inversion of geo-magnetic full-tensor gradiometer data

Abstract The fast and sensitive SQUID (Superconducting Quantum Interference Device) system, which was developed at IPHT Jena, allows the geo-magnetic prospection of large land areas. The system's simultaneous high-resolution recording of all components of the Earth's magnetic field gradient tensor represents a high-quality data base for precise inversion calculations. Thus, we developed a software tool for the fast and direct inversion of full-tensor data from especially dipole-like sources. Our motivation is to localize buried magnetic objects and inhomogeneities in the underground only by measuring the gradient components at the surface. The application of the algorithm will be shown by two examples, first on a synthetic data set and second on a real data set measured at the IPHT test site with well-defined buried targets.

Determining the full magnetic field gradient from two spacecraft measurements under special constraints

In this exploration, it is revealed for the first time that the full magnetic field gradient and current density distribution can be derived from two spacecraft magnetic field measurements under the assumptions that the magnetic field is approximately stationary and force‐free, conditions which are particularly relevant to low altitude regions of the Earth's magnetosphere and in the regions containing the field aligned current systems. The magnetic field gradients along the spacecraft line, spacecraft velocity direction and the normal direction can be defined so that the full magnetic field gradient tensor is determined, projected into any coordinate system. One test for an ideal situation has been made, which confirms the validity of this approach with very high accuracy. This method can be applied to the determination of the magnetic field gradient tensor and current density for the forthcoming multispacecraft Swarm mission.

First-Order Planar Superconducting Quantum Interference Device Gradiometers With Long Baseline

We have developed several types of low-Tc first-order planar gradiometers with long baselines ranging from 3.6 cm to 4 cm. Thin-film planar gradiometers are very attractive for measurements of the off-diagonal components of the magnetic field gradient tensor in noisy environments because of the high intrinsic balance that can be achieved with the precision photolithographic techniques used to fabricate these devices. The gradiometer pickup loops are series configured and connected to the input circuit of a dual-washer gradiometric dc SQUID. Series and parallel SQUID washer configurations have been investigated. For a given chip size, model calculations using a magnetic dipole point source and a distributed current dipole source show that gradiometer performance can be improved by increasing the size of the pickup loops at the expense of a small reduction of the baseline length. Based on these results, an improved planar gradiometer has been developed with 1.175 cm times 1.175 cm square pickup loops integrated with a series-configured dual washer SQUID on a 1.2 cm x 4.8 cm chip. The white flux noise of the improved gradiometer with 3.6 cm baseline is as low as 2.4 muPhi0/Hz1/2 (rms), and the magnetic field sensitivity referred to one pickup loop is 0.63 nT/Phi0. This results in a magnetic field gradient noise of 0.42 fT/cm - Hz1/2. The gradiometers are operable unshielded in typical laboratory environments without losing lock.

Thin-Film Planar Gradiometer with Long Baseline

Gradiometers are attractive for magnetic field measurements in noisy environments. Thin-film planar gradiometers are in particular attractive for measurements of the off-diagonal components of the magnetic field gradient tensor, and they can be fabricated with high intrinsic balance owing to the precision photolithographic techniques used to fabricate these devices. We have developed a low-Tc first-order planar gradiometer with a long baseline of 4 cm. The pickup loops are series configured and connected to the input circuit of a dual washer gradiometric dc SQUID. The white rms flux noise measured in a shielded environment is 1.6 µΦ0/Hz½. The magnetic field sensitivity referred to one pickup loop is 2 nT/Φ0, resulting in an rms magnetic field noise referred to one pickup loop of 3.2 fT/Hz½ and an rms gradient noise of 0.8 fT/cm-Hz½. Based on the lithographic methods used to fabricate the gradiometers, the expected balance level is 1 part in 24, 000 or 0.004%. The gradiometer is operable without shielding in typical laboratory environments without losing lock, with an rms white noise at 10 kHz of 3.5 µΦ0/Hz½.

Room temperature three sensor magnetic field gradiometer

We have constructed a portable magnetic field gradiometer from fluxgate magnetometers using a novel common-mode rejection method. The sensor, known as a room temperature Three Sensor Gradiometer (rtTSG), is, as far as we know, the first hand-held gradiometer that can measure all components of the magnetic field gradient tensor. The rtTSG can measure these components in motion at a noise level of about 1.4×10−10 T/m√Hz at 1 Hz. Real time tracking of magnetic dipoles while the gradiometer is in motion has been demonstrated.