Three-dimensional Magnetic Field Research Articles

3-D nonlinear magnetic field analysis with a novel adaptive finite element method

In this paper, an adaptive degrees-of-freedom finite element method is extended to three-dimensional (3-D) nonlinear magnetic field analysis. The error distribution of the discrete solution changes along with the iterative process, and mesh coarsening or other operations with the same effect is needed to keep the scale of the problem small. In this proposed adaptive method, dispensable degrees of freedom (DoFs) are eliminated from the unknown list by constraining them with supplementary interpolation functions, which are formulated with master DoFs. Compared with mesh coarsening, the administration of DoFs and geometric data are no longer required, while the topology of the mesh is maintained. To extend to 3-D problems, a novel constraint, which produces accurate coefficients for an alterable number of master DoFs, is presented. The constraint is integrated into the element algebraic equation, followed by a conventional assembly. Other techniques for the adaptive algorithm are also included in this method. Several numerical examples are tested to showcase the effectiveness of this method in 3-D problems.

On the representation of dense plasma focus as a circuit element

The dense plasma focus is a plasma discharge powered by a capacitor bank. Standard diagnostics include the measurement of the time derivative of the current through and the voltage across its connections with the capacitor bank. Interpretation of this diagnostic data often involves some assumptions regarding the representation of the dense plasma focus as a time varying inductance. One of the characteristic features of the current derivative waveform is a relatively sharp dip and an associated sharp voltage spike. This has often been interpreted as a result of a rapid rise in the time varying inductance of the plasma. Sometimes, an anomalous plasma impedance is invoked. This Letter discusses instances where such interpretation creates conceptual difficulties. A first principles approach to the representation of the dense plasma focus as a circuit element reveals some fundamental problems with the traditional representation of plasma focus as a time varying inductance. The anomalous impedance is shown to be necessary to account for the difference in the motional impedance implied by a time-varying inductance in the circuit element representation and a first principles description based on Poynting's theorem. Dynamo effects that convert post-stagnation local motion of plasma into three-dimensional magnetic fields are shown to contribute to the effective inductance of the plasma focus and resolve the observed conceptual difficulties.

Data-driven MHD Simulation of Successive Solar Plasma Eruptions

Abstract Solar flares and plasma eruptions are sudden releases of magnetic energy stored in the plasma atmosphere. To understand the physical mechanisms governing their occurrences, three-dimensional magnetic fields from the photosphere up to the corona must be studied. The solar photospheric magnetic fields are observable, whereas the coronal magnetic fields cannot be measured. One method for inferring coronal magnetic fields is performing data-driven simulations, which involves time-series observational data of the photospheric magnetic fields with the bottom boundary of magnetohydrodynamic simulations. We developed a data-driven method in which temporal evolutions of the observational vector magnetic field can be reproduced at the bottom boundary in the simulation by introducing an inverted velocity field. This velocity field is obtained by inversely solving the induction equation and applying an appropriate gauge transformation. Using this method, we performed a data-driven simulation of successive small eruptions observed by the Solar Dynamics Observatory and the Solar Magnetic Activity Telescope in 2017 November. The simulation well reproduced the converging motion between opposite-polarity magnetic patches, demonstrating successive formation and eruptions of helical flux ropes.

Multi-layer quasi three-dimensional equivalent model of axial-flux permanent magnet synchronous machine

Axial-flux permanent magnet synchronous machine (AFPMSM) enjoys the merits of high torque density and high efficiency, which make it one good candidate in the direct-drive application. The AFPMSM is usually analyzed based on the three-dimensional finite element method (3D FEM) due to its three-dimensional magnetic field distribution. However, the 3D FEM suffers large amount of calculation, time-consuming and is not suitable for the optimization of AFPMSM. Addressing this issue, a multi-layer quasi three-dimensional equivalent model of the AFPMSM is investigated in this paper, which could take the end leakage into consideration. Firstly, the multi-layer quasi three-dimensional equivalent model of the AFPMSM with single stator and single rotor is derived in details, including the equivalent processes and conversions of structure dimensions, motion conditions and electromagnetic parameters. Then, to consider the influence of end leakage on the performance, a correction factor is introduced in the multi-layer quasi three-dimensional equivalent model. Finally, the proposed multi-layer quasi three-dimensional equivalent model is verified by the 3D FEM based on an AFPMSM under different structure parameters. It demonstrates that the errors of flux linkage and average torque obtained by the multi-layer quasi three-dimensional equivalent model and 3D FEM are only around 2% although the structure parameters of the AFPMSM are varied. Besides, the computation time of one case based on the multi-layer quasi three-dimensional equivalent model is only 6 min, which is much less than that of the 3D FEM, 1.8 h, under the same conditions. Thus, the proposed multi-layer quasi three-dimensional equivalent model could be used to optimize the AFPMSM and much time could be saved by this method compared with the 3D FEM.

Torsional waves with force-free magnetic fields in solar plasma structures

ABSTRACT The aim here is to model torsional waves in homogeneous and expanding twisted flux tubes of solar coronal magnetic plasma structures. For the sake of simplicity, a force-free condition applicable to solar magnetic structures is presented to determine the existing three-dimensional equilibrium magnetic fields. The determined magnetic field is implemented to study the effects of the magnetic twist parameter on the eigenvalues and eigenfunctions of torsional waves. Solenoidal and force-free conditions are applied to find the three-dimensional components of the magnetic field with respect to the numerical flux function. The obtained differential equation is linear where the technique of the separation of variables is implemented in order to solve it. The equilibrium magnetic field components and appropriate vector potential are extracted. Using the provided components in the magnetohydrodynamic theory, a differential equation that governs the frequency dependence of the torsional wave is obtained, whereby the differential transform method is solved. Both eigenvalues and eigenfunctions of torsional waves are calculated numerically. The obtained values for the frequency of the fundamental mode and its first harmonic, together with appropriate functions, exhibit a fine consistency with observations, with regards to the ratio of ω2/ω1, which is estimated to be around 2. At a fixed distance from the tube axis, the ratio increases with the increase of the twist parameter. The higher the applied twist parameter, the more variations of the ω2/ω1 ratio are observed. We cannot find significant variations of the eigenfunctions of torsional waves due to the twist parameter. The consistency between analytical results and observations proves adequate for implementing a force-free equilibrium magnetic field subject to conditions in solar plasma structures regarding torsional wave propagation.

Quantitative Research on Cracks in Pipe Based on Magnetic Field Response Method of Eddy Current Testing

The quantitative evaluation of defects in eddy current testing is of great significance. Impedance analysis, as a traditional method, is adopted to determine defects in the conductor, however, it is not able to depict the shape, size and location of defects quantitatively. In order to obtain more obvious characteristic quantities and improve the ability of eddy current testing to detect defects, the study of cracks in metal pipes is carried out by utilizing the analysis method of three-dimensional magnetic field in present paper. The magnetic field components in the space near the crack are calculated numerically by using finite element analysis. The simulation results confirm that the monitoring of the crack change can be achieved by measuring the magnetic field at the arrangement positions. Besides, the quantitative relationships between the shape, length of the crack and the magnetic field components around the metal pipe are obtained. The results show that the axial and radial magnetic induction intensities are affected more significantly by the cross-section area of the crack. Bz demonstrates obvious advantages in analyzing quantitatively crack circumference length. Therefore, the response signal in the three-dimensional direction of the magnetic field gets to intuitively reflect the change of the defect parameter, which proves the effectiveness and practicability of this method.

A spin–orbit torque device for sensing three-dimensional magnetic fields

A spin–orbit torque device for sensing three-dimensional magnetic fields

The Mechanical Performance evaluation of Vertical Stability Coil under Electromagnetic-structure Coupling Analyses

The vertical stability coil is a set of active feedback control coil that is used to deal with the vertical instability of plasma. To improve the response performance, the coil is mounted in the vacuum vessel, which denotes the coil-body will suffer from large electromagnetic force from the plasma current and poloidal field coils. Besides the current flowing in the feeder is nearly perpendicular with magnetic field originated from toroidal coil. It implies large electromagnetic force will be generated on the feeder. In order to withstand the impact from the electromagnetic force, a series of reinforce compo-nents are designed and installed on the coil. It is necessary to verify whether or not the coil conductor and auxiliary components could successfully bear the shock of large electromagnetic force. A three-dimensional magnetic field model is built to accurately calculate the magnetic field and electromag-netic force. Corresponding to the magnetic field calculation model, a more detailed me-chanical anal-ysis model is created to launch the electromagnetic-structural coupling analysis. Based on the stress analysis results, the local structure of the coil is optimized to decrease the peak stress. The updated model is reanalyzed and stress linearization is exerted to extract the different kinds of stress on the coil components. Finally, the stress is evaluated based on ASME analytical design. The evaluation result is helpful to guide the further design optimization.

Threaded-field-line Model for the Low Solar Corona Powered by the Alfvén Wave Turbulence

Abstract We present an updated global model of the solar corona, including the transition region. We simulate the realistic three-dimensional (3D) magnetic field using the data from the photospheric magnetic field measurements and assume the magnetohydrodynamic (MHD) Alfvén wave turbulence and its nonlinear dissipation to be the only source for heating the coronal plasma and driving the solar wind. In closed-field regions, the dissipation efficiency in a balanced turbulence is enhanced. In the coronal holes, we account for a reflection of the outward-propagating waves, which is accompanied by the generation of weaker counterpropagating waves. The nonlinear cascade rate degrades in strongly imbalanced turbulence, thus resulting in colder coronal holes. The distinctive feature of the presented model is the description of the low corona as almost-steady-state low-beta plasma motion and heat flux transfer along the magnetic field lines. We trace the magnetic field lines through each grid point of the lower boundary of the global corona model, chosen at some heliocentric distance, R = R b ∼ 1.1R ⊙, well above the transition region. One can readily solve the plasma parameters along the magnetic field line from 1D equations for the plasma motion and heat transport together with the Alfvén wave propagation, which adequately describe the physics within the heliocentric distance range R ⊙ < R < R b , in the low solar corona. By interfacing this threaded-field-line model with the full MHD global corona model at r = R b , we find the global solution and achieve a faster-than-real-time performance of the model on ∼200 cores.

Evolution of the Nonpotential Magnetic Field in the Solar Active Region 12673 Based on a Nonlinear Force-free Modeling

Abstract Active region (AR) 12673 has produced many M-class and several X-class flares, one of which being an X9.3 flare, which is recorded as the largest solar flare in solar cycle 24. We studied the evolution of the three-dimensional flare-productive magnetic field within AR 12673, using a time series of nonlinear force-free field extrapolations of every 12 hr from 2017 September 4 00:00 UT to 6 00:00 UT. Our analysis found that three magnetic flux ropes (MFRs) formed by September 4, one of which produced the X9.3 flare on September 6. One MFR has positive magnetic twist, which is a different sign from the other two MFRs. Since the temporal evolution of the magnetic flux of the MFR accumulating the positive twist is consistent with the profile of the GOES X-ray flux well observed from September 4 to 6, we suggest that the formation of the MFR having the positive twist is closely related to the occurrence of the M-class flares, including an M5.5 flare. We further found a magnetic null in the magnetic field surrounding the MFRs, in particular above the MFR having positive twist before the M5.5 flare, which is the largest M-flare observed during this period. By comparing with Atmospheric Imaging Assembly 1600 Å images, we found that the footpoints of the overlying field lines are anchored to the area where the brightening was initially observed. Therefore, we suggest that reconnection induced by the torus instability of the positively twisted MFR at the null possibly drove the M5.5 flare.

Maps of Magnetic Field Strength in the OMC-1 Using HAWC+ FIR Polarimetric Data

Abstract Far-infrared dust polarimetry enables the study of interstellar magnetic fields via tracing of the polarized emission from dust grains that are partially aligned with the direction of the field. The advent of high-quality polarimetric data has permitted the use of statistical methods to extract both the direction and magnitude of the magnetic field. In this work, the Davis–Chandrasekhar–Fermi technique is used to make maps of the plane-of-sky (POS) component of the magnetic field in the Orion Molecular Cloud (OMC-1) by combining polarization maps at 53, 89, 154 and 214 μm from HAWC+/SOFIA with maps of density and velocity dispersion. In addition, maps of the local dispersion of polarization angles are used in conjunction with Zeeman measurements to estimate a map of the strength of the line-of-sight (LOS) component of the field. Combining these maps, information about the three-dimensional magnetic field configuration (integrated along the LOS) is inferred over the OMC-1 region. POS magnetic field strengths of up to 2 mG are observed near the BN/KL object, while the OMC-1 bar shows strengths of up to a few hundred μG. These estimates of the magnetic field components are used to produce maps of the mass-to-magnetic-flux ratio (M/Φ)—a metric for probing the conditions for star formation in molecular clouds—and determine regions of sub- and supercriticality in OMC-1. Such maps can provide invaluable input and comparison to MHD simulations of star formation processes in filamentary structures of molecular clouds.

Field amplification effect of resonant magnetic perturbation on ion orbits in tokamak plasma

<sec> The fast ion transport associated with resonant magnetic perturbation (RMP) contains rich physical spanning single particle motion of fast particle and plasmas response physics with RMP and their interaction. Full numerical simulation considering such physical ingredients should be performed in a long run for clarifying the underlying physical features of the fast ion confinement with RMP. Thus, the appropriate application of RMP is not only to avoid the detrimental effects but also to serve as an actuator to exert targeted control over the energetic particle profile. To achieve this goal, a comprehensive knowledge of the effects of RMP including plasma response on fast ions is necessary. </sec> <sec> In this work, the plasma response to RMP in HL-2A device is simulated by the MARS-F code under different parameters including finite resistivity, toroidal rotation frequency and toroidal mode number, and the three-dimensional (3D) magnetic field topology considering RMP is obtained. Then, Boris algorithm is used to track the ion orbit under these 3D fields, and the physical mechanism of ion orbit characteristics changed by the perturbed field is explored in detail. It is found that with the increase of finite resistivity, the average value of perturbed magnetic field decreases, and the orbit radial expansion turns smaller. The variation of toroidal rotation frequency can change the distribution of perturbed magnetic field, resulting in different orbit radial expansions for different kinds of orbits. What is more, if the toroidal mode number increases, the amplitude of perturbed magnetic field after response decreases obviously, thus resulting in little effect on orbit radial expansion. In a word, the plasma responded RMP field enhances the orbit radial expansion, and the maximum orbital radial expansion increases with the augment of average value of perturbed magnetic field on the orbit. Meanwhile, the amplitude of orbit expansion increases significantly when the ions pass through the region where the perturbed magnetic field is strongly amplified. This effect can explain the increase of ion prompt loss and enhancement of plasma radial transport in edge localized mode mitigation experiments by RMP. </sec>

Improvement in the spatial resolution of heavy ion beam probe measurements through application of ion optics.

A technique for more accurately modeling and improving the spatial resolution of heavy ion beam probe measurements is described. We use a set of particle trajectories to numerically determine the focusing properties of a complicated three-dimensional magnetic field and characterize these properties with a transfer matrix. We then modify the transfer matrix approach of traditional ion optics to include a parameter that describes the ionization location of the detected ions. The ion optics model calculated using this technique enables a more accurate description of the particle trajectories than previously feasible. The model also allows one to easily determine an initial beam focus that could be used during experimental operation to optimize the spatial resolution of measurements. The technique has been applied to the design of a heavy ion beam probe diagnostic for the Wendelstein 7-X stellarator, and improvements in the modeled spatial resolution by a factor of about 2 over previous estimates are possible. The improved spatial resolution will enable measurements of plasma fluctuations with smaller wavelengths than would otherwise be possible.

Simulation of electromagnetic field and its effect during electromagnetic stirring in continuous casting mold

A mathematical model of in-mold electromagnetic stirrer has been developed to calculate the three-dimensional time-varying magnetic field for electromagnetic stirring in the continuous casting mold. The calculated magnetic field is coupled with the magneto-hydrodynamic and solidification model to analyze the effect of stirrer width at different current and frequency applied to the stirrer. The enthalpy porosity technique is used to track the liquid-solid transformation while the realizable k-ε turbulence model is used to account the turbulence in the fluid flow. The coupling of the time-varying electromagnetic field with solidification model makes the model complicate which leads to having divergence problem and large computation time. The model efficiently computes the electromagnetic field, fluid flow, solidification behavior of an electromagnetically stirred continuous casting mold, which have been validated against the reported results. From the initial results it is observed that magnetic flux density significantly increases with increase in stirrer width and current while, frequency has a marginal effect on magnetic flux density. The result obtained from coupled model shows that increase in frequency has a large influence on stirring intensity and hence on solidification behavior. However, stirrer width and current marginally affect the stirring intensity and solidification behavior.

An experimental study on characterizing damage and fracture of a rock-like material based on three-dimensional magnetic field imaging

PurposeThe results showed that the use of a magnetic marker could relatively accurately reflect the fracture pattern inside the rock-like material (RLM).Design/methodology/approachThis study investigated the internal structure and fracture pattern of a fractured RLM. Magnetized iron oxide powder, which was used as a magnetic marker, was mixed with water and glue to form a magnetic slurry, which was subsequently injected into a fractured RLM. After the magnetic slurry completely filled the cracks inside the RLM and became cemented, the distribution and magnitude of the magnetic field inside the RLM were determined using a three-dimensional (3D) magnetic field imaging system.FindingsA model for determining the magnetic field strength was developed using MATLAB.Originality/valueThis model of 3D magnetic will further be used as a finite element tool to simulate and image cracks inside the rock.

Localized Reconnection Heating Inferred from the Three-dimensional Locations of Bright Active Region Coronal Loops

Abstract Coronal loops observed in soft X-rays and extreme ultraviolet imaging data offer direct evidence that coronal plasma is heated by some mechanism. That mechanism appears to energize a particular bundle of field lines somehow selected from the magnetized coronal volume. Magnetic reconnection localized to a patch within a coronal current sheet is one mechanism that would select a flux bundle at the same time it energized it. Since magnetic reconnection occurs preferentially at topological boundaries, we would expect to find coronal loops concentrated there if it were at work. We explore this hypothesis using a data set, previously compiled by McCarthy et al., consisting of 301 coronal loops interconnecting a pair of active regions over a 48 hr period. That work computed the three-dimensional geometries and magnetic field strengths for most of the loops. This revealed many bright loops lying at the periphery of the interconnecting flux domain, possibly created and energized by the reconnection that created the interconnecting flux. There were, however, many loops well inside the domain which would be difficult to attribute to that mode of reconnection. Here we use detailed magnetic models of the interconnecting domain to show that these internal loops tend to occur along internal boundaries: separatrices. This offers a novel form of evidence that coronal loops are the products of patchy reconnection even under quiescent conditions.

Research on Three-Dimensional Magnetic Induced Error Model of Interferometric Fiber Optic Gyro

In practical, the Faraday effect-induced bias error is one of the main sources of bias error for the interferometric fiber optic gyroscope (IFOG). The Faraday effect-induced bias error impairs in the performance of IFOG. Normally, the Faraday effect-induced bias errors is hardly eliminated. To improve the performance of IFOG, the accurate model of Faraday effect-induced bias errors is necessary for its practical applications. In this paper, from the perspective of the finite element method, we calculate Faraday effect-induced bias errors of the fiber coil by the three-dimensional model in the radial magnetic field, and the axial magnetic field. Comparing with the traditional model, the differences mainly come from the size, and direction of the magnetic field, including the differences of the twist ratio, and the bending rate of each layer. Using the Jones matrix, we derive the three-dimensional magnetic field error model, further more theoretical results are obtained by simulation. The experiment with a 1024 m PM fiber coil are performed, and the experimental results support these theoretical predictions.

Rapid Scan EPR imaging as a Tool for Magnetic Field Mapping.

Functional four-dimensional spectral-spatial electron paramagnetic imaging (EPRI) is routinely used in biomedical research. Positions and widths of EPR lines in the spectral dimension report oxygen partial pressure, pH, and other important parameters of the tissue microenvironment. Images are measured in the homogeneous external magnetic field. An application of EPRI is proposed in which the field is perturbed by a magnetized object. A proof-of-concept imaging experiment was conducted, which permitted visualization of the magnetic field created by this object. A single-line lithium octa-n-butoxynaphthalocyanine spin probe was used in the experiment. The spectral position of the EPR line directly measured the strength of the perturbation field with spatial resolution. A three-dimensional magnetic field map was reconstructed as a result. Several applications of this technology can be anticipated. First is EPRI/MPI co-registration, where MPI is an emerging magnetic particle imaging technique. Second, EPRI can be an alternative to magnetic field cameras that are used for the development of high-end permanent magnets and their assemblies, consumer electronics, and industrial sensors. Besides the high resolution of magnetic field readings, EPR probes can be placed in the internal areas of various assemblies that are not accessible by the standard sensors. Third, EPRI can be used to develop systems for magnetic manipulation of cell cultures.

Torque Modelling and Validation for a Spherical Motor with Stepped Permanent Magnets

A spherical motor is an electromagnetic device with multi-degree-of-freedom motion. Three-dimensional (3-D) magnetic field analysis and torque analysis are needed for the design, optimization and control of the motor. Presently, these analyses are carried out by the finite-element method (FEM) with a large amount of calculation and time consumption. An analytical method (AM) can reduced the computational burden of the FEM without sacrifice of the accuracy. A stepped permanent magnet (PM) can obtain a large range of the magnetic field while effectively saving PM materials. However, its special structure causes difficulties in analytical modelling. This paper presents an AM for the 3-D magnetic field and torque of a permanent magnet spherical motor with stepped PMs. The analytical model of the 3-D magnetic field of the stepped PM is derived based on the loop current method, and the electromagnetic force of the stator coil is calculated based on the Lorentz force method. Thus the 3-D magnetic field and torque can be calculated efficiently with reasonable accuracy. The analytical model is verified by the FEM and experimental tests. The test results confirm the high accuracy of the developed model.

Research on High-Temperature Superconducting Machine With a Rotating-Pole Shoe

As a kind of high-power density machine, superconducting machines have important application prospects in the fields of aerospace, ship propulsion, and wind power generation. The existing semisuperconducting-type machines have great difficulties in design and application because of the need to use complicated structures such as brushes and rotating dewars. A rotating-pole-shoe-type high-temperature superconducting machine is proposed in this article. The machine separates the pole shoe from the magnetic pole and generates a magnetic field synchronized with the armature side by rotating the pole shoe. The excitation system of the machine consists of a rotating rotor and a stationary inner stator. The superconducting coil is placed on the inner stator, avoiding the use of complex structures such as brushes and rotary seals. Aiming at the special structure of the rotating-pole-shoe-type superconducting machine, a three-dimensional magnetic field analysis of the superconducting machine is performed to improve the machine structure. The output performance of the machine is calculated and compared with that of the semisuperconducting-type machine.