Perpendicular Field Component Research Articles

Angle-dependent Hall resistivity and longitudinal resistivity of type-II superconductor

We use time-dependent Ginzburg–Landau theory in a three-dimensional model, including thermal noise, to analyze angle-dependent Hall resistivity and longitudinal resistivity of type-II superconductor. The Hall resistivity and longitudinal resistivity are calculated as functions of temperature, magnetic field and the angle θ between the magnetic field and the ab-plane in the vortex-liquid regime. Our theoretical calculations within a self-consistent fluctuation approximation for MgB2 and HgBa2CaCu2O6 materials are in good agreements with the experimental findings for both below and above the critical temperature Tc. We observe that when the field angle decreases, the transition temperature increases and the magnitude of longitudinal resistivity decreases, which is qualitatively comparable to decrease of the perpendicular field component. However, when the magnetic field direction approaches the layer surface, it shows a clear different effect from that of a perpendicular field with the same normal component.

The velocity-space signature of transit-time damping

Transit-time damping (TTD) is a process in which the magnetic mirror force – induced by the parallel gradient of magnetic field strength – interacts with resonant plasma particles in a time-varying magnetic field, leading to the collisionless damping of electromagnetic waves and the resulting energization of those particles through the perpendicular component of the electric field, $E_\perp$ . In this study, we utilize the recently developed field–particle correlation technique to analyse gyrokinetic simulation data. This method enables the identification of the velocity-space structure of the TTD energy transfer rate between waves and particles during the damping of plasma turbulence. Our analysis reveals a unique bipolar pattern of energy transfer in the velocity-space characteristic of TTD. By identifying this pattern, we provide clear evidence of TTD's significant role in the damping of strong plasma turbulence. Additionally, we compare the TTD signature with that of Landau damping (LD). Although they both produce a bipolar pattern of phase-space energy density loss and gain about the parallel resonant velocity of the Alfvénic waves, they are mediated by different forces and exhibit different behaviours as the perpendicular velocity $v_\perp \to 0$ . We also explore how the dominant damping mechanism varies with ion plasma beta $\beta _i$ , showing that TTD dominates over LD for $\beta _i > 1$ . This work deepens our understanding of the role of TTD in the damping of weakly collisional plasma turbulence and paves the way to seek the signature of TTD using in situ spacecraft observations of turbulence in space plasmas.

Design and simulation of a superconducting machine excitation system taking into account the three-dimensional magnetic leakage

The optimized design of a new high-temperature superconducting rotating pole machine is presented. Its main structural feature is the use of a double stator core which separates the synchronous machine pole shoe from the pole body to rotate separately as the machine rotor, allowing the superconducting coil to operate in a stationary state. The inner stator core, the stationary dewar and the rotor core together form the excitation system of the machine. The excitation coil windings adopt a rectangular cross-section, with flux divertor strategically placed between the high-temperature superconducting coils. This configuration aims to modulate the background magnetic field, specifically reducing the perpendicular magnetic field component. This mitigation minimizes the impact of ambient magnetic fields on the superconducting coil’s current carrying capacity, ensuring an optimized magnetic field environment for its operation. Through the integration of these modifications, the technical and economic parameters of the enhanced high-temperature superconducting machine have been significantly improved. The optimization of design, coupled with detailed calculations of the 3D electromagnetic field, was achieved utilizing the commercial software Ansys EM module.

Kinetic simulations comparing quasi-parallel and quasi-perpendicular piston-driven collisionless shock dynamics in magnetized laboratory plasmas

Magnetized collisionless shocks are common in astrophysical systems, and scaled versions can be created in laboratory experiments by utilizing laser-driven piston plasmas to create these shocks in a magnetized background plasma. A key parameter for these experiments is the angle θB between the shock propagation direction and the background magnetic field. We performed quasi-1D piston-driven shock simulations to explore shock formation, evolution, and key observables relevant to laboratory experiments for a range of shock angles between θB=90° to θB=30°. Our results show that the spatial and temporal scales of shock formation for all angles considered are similar when expressed in terms of the perpendicular component of the magnetic field. In a steady state, ion and electron temperatures become more isotropic, and the electron-to-ion temperature ratio is higher for smaller θB. At θB=30°, ion heating parallel to the magnetic field becomes dominant, associated with more ions being reflected at one discontinuity and subsequently trapped by the next discontinuity due to shock reformation.

The switchable chirality and optical properties of hexabenzo[a,c,k,m,u,w]trinaphthylene controlled by synergistic effect of static electric field and substituents: A DFT study

This work selected the planar molecule hexabenzo [a,c,k,m,u,w]trinaphthylene (HBTN) with electron donor and acceptor, and introduced static electric field perpendicular to the conjugation plane for its control over molecular physical properties. With the guidance of electron donor and acceptor, controllable chirality, charge polarization, obvious charge transfer transition, Cotton effect and large NLO coefficients of molecule were obtained. The necessity of substituents to realize the control of static electric field to molecular chirality and optical properties was further confirmed by their locations and species. The direction of static electric field was also tested, and the importance of perpendicular field component was stressed. At last, the conclusion obtained via the discussion of monomer could also be applied to both homodimer and heterodimer, where same or different fragments were stacked via π-π interaction respectively. Especially for heterodimer, the completely different optical properties such as UV–Vis absorption spectra, ECD spectra and NLO coefficients between P- and M-type conformations were observed, and made it easier to recognize the chirality of heterodimer. All above results were meaningful to promote the application of molecules as chiral photovoltaic devices.

Angular dependence of resistance and critical current of a Bi-2223 superconducting joint

Low resistance and high critical current are prerequisites for superconducting joints used in persistent-mode magnets. Herein, we use a joint resistance evaluation system, previously developed by us, to systematically evaluate the angular dependence of resistance and critical current of a Bi-2223 superconducting joint in a closed-loop sample. The current decay is measured by rotating the sample incrementally. The time dependence of the loop current is evaluated at 4 K, 0.15–0.28 T, and magnetic field angles ranging from 90° to 0, wherein 90° corresponds to the direction parallel to the tape surface. The results suggest that the resistance and critical current of the joint depend on the angle of the magnetic field. The evaluated critical current increases as the angle increases. The angular dependence of resistance can be divided into three regions: low-resistance, transition, and high-resistance regions. The low-resistance region exists at high angles close to 90°. In this region, the decay of the loop current is small, and the persistent current continues to flow. Furthermore, the joint resistance is less than 1.4 × 10−13 Ω. In the transition region, the joint resistance significantly increases by three orders of magnitude with sample rotation. This significant increase is attributed to an increase in the perpendicular component of the magnetic field, which decreases the critical current of the joint. At lower angles, the joint resistance remains high, ranging from 10−11 to 10−10 Ω. A significant decay in the loop current is observed in the high-resistance region. Based on these findings, we conclude that the design of a persistent-mode magnet must consider not only the magnitude but also the direction of the magnetic field applied to superconducting joints.

Indirect Observations of Electric Fields at Comet 67P

AbstractNo spacecraft visiting a comet has been equipped with instruments to directly measure the static electric field. However, the electric field can occasionally be estimated indirectly by observing its effects on the ion velocity distribution. We present such observations made by the Rosetta spacecraft on 19 April 2016, 35 km from the nucleus. At this time comet 67P was at a low outgassing rate and the plasma environment was relatively stable. The ion velocity distributions show the cometary ions on the first half of their gyration. We estimate the bulk drift velocity and the gyration speed from the distributions. By using the local measured magnetic field and assuming an E × B drift of the gyrocentre, we get an estimate for the average electric field driving this ion motion. We analyze a period of 13 hr, during which the plasma environment does not change drastically. We find that the average strength of the perpendicular electric field component is 0.21 mV/m. The direction of the electric field is mostly anti‐sunward. This is in agreement with previous results based on different methods.

Dynamic resistance and total loss in small REBCO pancake and racetrack coils carrying DC currents under an AC magnetic field

In many high-temperature superconducting applications, REBCO (Rare-earth barium copper oxide) coils carry DC currents under AC magnetic fields, such as the field winding of rotating machines, linear synchronous motors and the electro-dynamic suspension system of maglev. In such operating conditions, REBCO coils generate AC loss—total loss which includes the magnetization loss due to the shielding currents, and the dynamic loss arising from dynamic resistance caused by the interaction of DC currents and AC magnetic fields. In this work, dynamic resistance and total loss in a small double pancake coil (DPC) and a small double racetrack coil (DRC) are investigated via experiments in the temperature range between 77 K and 65 K. The DC currents are varied from zero to 70% of the self-field critical currents of the REBCO coils, with AC magnetic fields up to 100 mT. The experimental results in the DPC are well supported by the finite element simulation results using 3D T-A formulation. Our results show that the critical current of the DRC is approximately 2%–5% higher than that of the DPC in the temperature range. For given experimental conditions, the magnetization loss in both coils is much greater than the dynamic loss. The dynamic loss and magnetization loss in the DRC are greater than those in the DPC, which we attribute to the large perpendicular magnetic field component in the straight sections of the DRC.

Relationship between drift kinetics, gyrokinetics and magnetohydrodynamics in the long-wavelength limit

Gyrokinetic theories, even ‘global’ models, typically rely on a separation in scale (in perpendicular wavelength) between the fluctuations and the system scale. In such models direct simulation of system-scale dynamics like magnetohydrodynamic (MHD) motion is formally not consistent. Drift-kinetic theory, on the other hand, may be directly applied to model system-scale MHD-ordered behaviour. I review the long-wavelength limit of standard gyrokinetics and drift kinetics to present the relationships between these theories in an elementary fashion. This provides a pathway to global gyrokinetic modelling, resulting in an approach that is structurally similar to kinetic MHD, and I present dynamical equations for solving global field evolution in this framework. Departures from certain earlier global gyrokinetic theories include the appearance of magnetosonic (fast) modes, and the cross-coupling of the parallel and perpendicular currents with perpendicular and parallel magnetic field components. A periodic two-dimensional testcase is outlined as a benchmarking and implementation target, to help clarify practical aspects of these theories, with minimal complexity in terms of boundary conditions, and a proof-of-principle implementation of a field-solver is exhibited. To motivate this work, I first illustrate certain limitations of existing global gyrokinetic frameworks and directly identify how scale separation approximations lead to certain ‘missing’ system-scale field terms in global gyrokinetics, largely as a result of simplifications associated with the field representation in terms of $A_{\|}$ and $B_{\|}$ . As a result, the currents in the gyrokinetic Ampère's law resulting from a gyrokinetic equilibrium distribution do not match the currents implied by Ampère's law in a force-balance MHD equilibrium. I present a simple choice of equilibrium distribution function whose drift-kinetic currents are consistent with MHD currents; a specific Grad–Shafranov equilibrium is used to illustrate the size of the components of the parallel currents.

Effects of Field‐Aligned Cold Plasma Density Filaments on the Fine Structure of Chorus

AbstractThe whistler‐mode chorus emission, a major driver of radiation belt electron energization and precipitation, exhibits significant amplitude modulations on millisecond timescales. These subpacket modulations are accompanied by fast changes in the wave normal angle. Understanding the evolution of wave propagation properties inside chorus elements is essential for modeling nonlinear chorus‐electron interactions, but the origin of these rapid changes is unclear. We propose that the variations come from propagation inside thin, field‐aligned cold plasma enhancements (density ducts), which produce differing modulations in parallel and perpendicular wave magnetic field components. We show that a full‐wave simulation on a filamented density background predicts wave vector and amplitude evolution similar to Van Allen Probes spacecraft observations. We further demonstrate that the commonly assumed wide density ducts, in which wave propagation can be studied with ray tracing methods, cannot explain the observed behavior. This indirectly proves the existence of wavelength‐scale field‐aligned density fluctuations.

Scanning magnetometer based on magnetoimpedance sensor for measuring a remnant magnetization of printed toners

In this work, a scanning magnetometer based on a giant magnetoimpedance sensor was used to study the toner material of a black-and-white laser printer that contains iron oxide nanoparticles. We measured the local perpendicular magnetic field component of various sizes black toner strips, magnetized in a perpendicular magnetic field. Our calibration samples were two-wire current lines, which are the current analogue of magnetized toner strips. Magnetic images of the samples were obtained. It was found that investigated toner samples have an average concentration of magnetic nanoparticles per unit area of order of 6 μg/mm2. At this concentration of nanoparticles, the remnant magnetic moment of the sample 1.6 × 5 mm2 in size was about of 0.046 µA⋅m2 and could be reliably registered by the scanning magnetometer. The magnetic image of the toner sample was compared with a hysteresis loop obtained using a vibrating sample magnetometer.

Mechanism of Capacitive Coupling of Proximal Electromagnetic Sources With Biological Bodies.

This study investigates the absorption of the induced E-field in homogeneous biological tissue exposed to highly localized field sources in proximity of the body, such as the charged tips of antennas, where E-field coupling dominates. These conditions are relevant for compliance testing of modern mobile phones where exposure is evaluated at small separation between radiators and the body. We derive an approximation that characterizes the decay of the induced E-field in the tissue as a function of distance. The absorption is quantified in terms of the local specific absorption rate (SAR) at the tissue surface as a function of the charge at the antenna tip. The approximation is based on the analytical evaluation of the E-fields of a charged disk under quasi-static conditions. We validate this approximation using full-wave simulations of dipoles. We demonstrate that the coupling mechanism of the E-field is dominated by the perpendicular field component and that wave propagation need not be considered for the characterization of the exposure. The surface SAR decreases approximately with the fourth power of the distance and with the square of the ratio of the permittivities of the tissue and free-space. The approximation predicts the induced maximum E-field with an accuracy of better than 1.5 dB. © 2022 Bioelectromagnetics Society.

Measurement of In-Field E-J Characteristics in Multi-Filamentary Bi-2223 Tapes at Ultra-Low Electric-Field Down to Around 10−13 V/m

We have developed a method to investigate in-field electric-field v.s. current-density (E-J) characteristics at ultra low electric field criterion around 10-13 V/m in a multi filamentary Bi-2223 tape at 5 K based on scanning Hall probe microscopy (SHPM). Bi-2223 is widely used in high field applications, e.g. a 30.5 T NMR magnet system is currently being developed in Japan. Ultra-low electric field is induced in such magnets operating in persistent current mode with extremely steady field. Namely, E-J characteristics need to be clarified around that criterion. E-J characteristics can be estimated from decay of magnetization in the whole sample, assuming the uniformity of J. But for multi filamentary Bi-2223 tape, magnetization current path should be clarified. In this study, we measured local magnetic field profile as a function of time for Bi-2223 tapes using SHPM. Additionally, we carried out flux annealing measurements to realize ultra-low electric field induced in the tape. As a result, two main messages we obtained. Experimental field profile or sheet current density obtained from the inverted Biot-Savart law indicated that filaments remain coupled up to high field, and even at ultra-low E criterion. Moreover, local E-J characteristics around 10-13 V/m are obtained at 5 K and 4.5 T of perpendicular magnetic field, which is comparable perpendicular field component in a Bi-2223 insert coil in the high field NMR magnet system. Ic properties at 10-12 V/m decrease to nearly 50%, in comparison to the transport Ic properties at 10-4 V/m.

Orbital-induced crossover of the Fulde-Ferrell-Larkin-Ovchinnikov phase into Abrikosov-like states

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in superconductors for which the orbital critical field exceeds the Pauli limit. Here, we present angular-resolved specific-heat data of the quasi-two-dimensional organic superconductor $\kappa$-(ET)$_2$Cu(NCS)$_2$, with a focus on high fields in the regime of the FFLO transition. For an increasing out-of-plane tilt of the applied magnetic field, which leads to an increase of orbital contributions, we found that the nature of the superconducting transition changes from second to first order and that a further transition appears within the high-field superconducting phase. However, the superconducting state above the Pauli limit is stable for field tilt of several degrees. Since any finite perpendicular component of the magnetic field necessarily leads to quantization of the orbital motion, the resulting vortex lattice states compete with the modulated order parameter of the FFLO state leading to complex high-field superconducting phases. By solving the linearized self-consistency equation within weak-coupling BCS theory, we show that our results are clear experimental evidence of an orbital-induced transformation of the FFLO order-parameter into Abrikosov-like states of higher Landau levels.

Coherence of Ion Cyclotron Resonance in Damped Ion Cyclotron Waves in Space Plasmas

Abstract Ion cyclotron resonance is one of the fundamental energy-conversion processes through field–particle interaction in collisionless plasmas. However, the key evidence for ion cyclotron resonance (i.e., the coherence between electromagnetic fields and the ion phase-space density) and the resulting damping of ion cyclotron waves (ICWs) has not yet been directly observed. Investigating the high-quality measurements of space plasmas by the Magnetospheric Multiscale (MMS) satellites, we find that both the wave electromagnetic field vectors and the bulk velocity of the disturbed ion velocity distribution rotate around the background magnetic field. Moreover, we find that the absolute gyrophase angle difference between the center of the fluctuations in the ion velocity distribution functions and the wave electric field vectors falls in the range of (0, 90)°, consistent with an ongoing energy conversion from wave fields to particles. By invoking plasma kinetic theory, we demonstrate that the field–particle correlation for the damped ICWs in our theoretical model matches well with our observations. Furthermore, the wave electric field vectors ( δ E wave , ⊥ ′ ), ion current density (δ J i,⊥), and energy transfer rate ( δ J i , ⊥ · δ E wave , ⊥ ′ ) exhibit quasiperiodic oscillations, and the integrated work done by the electromagnetic field on the ions is positive, indicating that ions are mainly energized by the perpendicular component of the electric field via cyclotron resonance. Therefore, our combined analysis of MMS observations and kinetic theory provides direct, thorough, and comprehensive evidence for ICW damping in space plasmas.

Engineering-based design and fabrication procedure for mid-temperature REBCO magnets accommodating the strong Ic anisotropy

An engineering-feasible design and fabrication procedure for REB2aCu3O7-x (REBCO) magnets based on the strong Ic angle dependence at moderate temperatures (40–77 K) was developed. In this procedure, the Ic value of every REBCO coil of the magnet is calculated from the Ic (B,θ) data of REBCO tape at operating temperature with different applied fields, which is called the “full field-angle dependent Ic method.” This approach has significantly higher accuracy than the conventional method, which only focuses on the Ic value at the coil with the highest perpendicular field component. Additionally, the fitted lift factor at 45 K with different applied fields was closely related to the minimum Ic value at 77 K and 0.5 T. The engineering-feasible design and fabrication procedure for the REBCO magnet was developed on the basis of the Ic values calculated via the “full field-angle dependent Ic method” and lifting-factor fitted method, and it had a design error of <5%. The proposed technique is a more accurate method for the design and fabrication of cooling REBCO coils and will improve the applicability of REBCO magnets in this temperature range.

An investigation on AC loss reduction for permanent-magnet superconducting electrical machine

High temperature superconducting (HTS) tapes could be introduced into large scale electrical machines in order to improve the power density. However, the alternating current (AC) loss of HTS tapes will cause the reduction of efficiency. On the basis of analytical and numerical model calculations, this paper presents an optimal design of the HTS armature winding aiming at lower AC loss. The main contribution of this work is that the relationship between the installation parameters and the AC loss of such HTS armature windings has been figured out based on the analysis of the shape feature of the HTS tape and the external magnetic field. When the tape is placed along a particular direction where the perpendicular component of external magnetic field has the lowest amplitude, the AC loss is the smallest. The modified installation location and angle are found based on the proposed generator. These results are verified using finite element method (FEM).

Kinetic Plasma Turbulence Generated in a 3D Current Sheet With Magnetic Islands

In this article we aim to investigate the kinetic turbulence in a reconnecting current sheet (RCS) with X- and O-nullpoints and to explore its link to the features of accelerated particles. We carry out simulations of magnetic reconnection in a thin current sheet with 3D magnetic field topology affected by tearing instability until the formation of two large magnetic islands using particle-in-cell (PIC) approach. The model utilizes a strong guiding field that leads to the separation of the particles of opposite charges, the generation of a strong polarization electric field across the RCS, and suppression of kink instability in the “out-of-plane” direction. The accelerated particles of the same charge entering an RCS from the opposite edges are shown accelerated to different energies forming the “bump-in-tail” velocity distributions that, in turn, can generate plasma turbulence in different locations. The turbulence-generated waves produced by either electron or proton beams can be identified from the energy spectra of electromagnetic field fluctuations in the phase and frequency domains. From the phase space analysis we gather that the kinetic turbulence may be generated by accelerated particle beams, which are later found to evolve into a phase-space hole indicating the beam breakage. This happens at some distance from the particle entrance into an RCS, e.g. about 7di (ion inertial depth) for the electron beam and 12di for the proton beam. In a wavenumber space the spectral index of the power spectrum of the turbulent magnetic field near the ion inertial length is found to be −2.7 that is consistent with other estimations. The collective turbulence power spectra are consistent with the high-frequency fluctuations of perpendicular electric field, or upper hybrid waves, to occur in a vicinity of X-nullpoints, where the Langmuir (LW) can be generated by accelerated electrons with high growth rates, while further from X-nullponts or on the edges of magnetic islands, where electrons become ejected and start moving across the magnetic field lines, Bernstein waves can be generated. The frequency spectra of high- and low-frequency waves are explored in the kinetic turbulence in the parallel and perpendicular directions to the local magnetic field, showing noticeable lower hybrid turbulence occurring between the electron’s gyro- and plasma frequencies seen also in the wavelet spectra. Fluctuation of the perpendicular electric field component of turbulence can be consistent with the oblique whistler waves generated on the ambient density fluctuations by intense electron beams. This study brings attention to a key role of particle acceleration in generation kinetic turbulence inside current sheets.

Rapid Evolution of Bald Patches in a Major Solar Eruption

Abstract A bald patch (BP) is a magnetic topological feature where U-shaped field lines turn tangent to the photosphere. Field lines threading the BP trace a separatrix surface where reconnection preferentially occurs. Here we study the evolution of multiple, strong-field BPs in AR 12673 during the most intense, X9.3 flare of solar cycle 24. The central BP, located between the initial flare ribbons, largely “disintegrated” within 35 minutes. The more remote, southern BP survived. The disintegration manifested as a 9° rotation of the median shear angle; the perpendicular component of the horizontal field (with respect to the polarity inversion line) changed sign. The parallel component exhibited a step-wise, permanent increase of 1 kG, consistent with previous observations of the flare-related “magnetic imprint.” The observations suggest that magnetic reconnection during a major eruption may involve entire BP separatrices, leading to a change of magnetic topology from BPs to sheared arcades.

Study on screening current field of quasi-isotropic strand and directly stacked strand at different field orientations

REBCO tapes, the so-called second-generation high temperature superconductor, have wide application prospects in electrical engineering and high field magnets because of their high critical current density and superior mechanical and electromagnetic properties. However, a screening current field (SCF) can be induced by the perpendicular component of the magnetic field if the tapes are in a variable magnetic field since the width of the commercial tape is generally more than 2 mm. As a result, the SCF results in an uneven spatial distribution of the magnetic field. In this paper, the SCFs of the quasi-isotropic strand and the directly stacked strand, made of the REBCO tapes, are calculated at 77 K under different orientations of a 300 mT external magnetic field. Then, the experiments are conducted under the same conditions as the simulation. The experimental results are in good agreement with the calculated results. The conclusions of this paper are helpful to understand the SCFs of two kinds of strands and useful in the design of high field magnets in the future.