Irregular Magnetic Field Research Articles

Applications of the landscape function for Schrödinger operators with singular potentials and irregular magnetic fields

We resolve both a conjecture and a problem of Z. Shen from the 90's regarding non-asymptotic bounds on the eigenvalue counting function of the magnetic Schrödinger operator La,V=−(∇−ia)2+V with a singular or irregular magnetic field B on Rn, n≥3. We do this by constructing a new landscape function for La,V, and proving its corresponding uncertainty principle, under certain directionality assumptions on B, but with no assumption on ∇B. These results arise as applications of our study of the Filoche-Mayboroda landscape function u, a solution to the equation LVu=−divA∇u+Vu=1, on unbounded Lipschitz domains in Rn, n≥1, and 0≤V∈Lloc1, under a mild decay condition on the Green's function. For LV, we prove a priori exponential decay of Green's function, eigenfunctions, and Lax-Milgram solutions in an Agmon distance with weight 1/u, which may degenerate. Similar a priori results hold for La,V. Furthermore, when n≥3 and V satisfies a scale-invariant Kato condition and a weak doubling property, we show that 1/u is pointwise equivalent to the Fefferman-Phong-Shen maximal function m(⋅,V) (also known as Shen's critical radius function); in particular this gives a setting where the Agmon distance with weight 1/u is not too degenerate. Finally, we extend results from the literature for La,V regarding exponential decay of the fundamental solution and eigenfunctions, to the situation of irregular magnetic fields with directionality assumptions.

Thermal-vibration correlation study for high-temperature superconducting maglev intelligent monitoring based on back propagation neural network analysis

The internal temperature rise inside the high-temperature superconducting (HTS) superconductor (SC) resulting from irregular magnetic field (MF) above the permanent magnet guideway is a major factor contributing to the decline of levitation performance. Real-time monitoring of the temperature rise inside YBCO SC is an important issue for the safe operation of the maglev train systems. However, the existing temperature rise testing method involves destructive intrusion less or more, easily affected by strong MF, occupying limited space and sensors prone to detachment. This paper innovatively proposes a non-contact internal temperature rise testing method combining artificial intelligence (AI) methods. Vibration is common signal of a maglev train system, which inspires to establish a fundamental thermal-dynamic levitation force synchronous testing device for YBCO SC. Then, a set of temperature rise-vibration dataset exposed to different alternating MF frequencies is created. The wavelet transform is chosen to extract the frequency band energy of vibration, and the backpropagation neural network is used to identify the corresponding temperature rise. The recognition accuracy can reach over 99.9%, which firstly proves the effectiveness of AI algorithms in the thermal-vibration correlation analysis for the HTS maglev system. The results can provide the foundation reference for the intelligent monitoring and fault diagnosis of thermal-dynamics stabilities of HTS maglev train in the future.

Solar energetic particles propagation during solar events at the beginning of the 25th solar cycle

Space weather is induced by solar events like solar flares, solar wind, the solar cycle, and coronal mass ejections. These solar events have the potential to affect various aspects of Earth, including radio communications, electric power failures, and navigation signals, and pose risks to spacecraft and astronauts. Solar activity is more or less intense according to the solar cycle. We are currently in the 25th solar cycle, which began in 2019. This research studies the space weather at the beginning of the 25th solar cycle using the distribution data obtained from spacecraft including the explosion on the Sun’s surface, by analyzing the solar energetic particles (SEPs) propagation. The distribution of SEPs with flux; F is given by a power law for solar events on November 29, 2020, July 3, 2021, and April 22, 2022, with indices 6.2, 4.5, and 1.8 depending on energy. The propagation of the SEPs was studied using Ruffolo’s transport equation, which was solved using the Finite-differences method. We found that solar flares with higher X-ray intensity have a longer movement along the irregular magnetic field and arrive at Earth more quickly than those with lower X-ray intensity. The SEPs are weaker and have no impact on Earth, although both events generated coronal mass ejection. The M-class and X-class solar flares occurred during the beginning of the 25th solar cycle, the position of explosion and injection time of particles resulted in space weather with little impact on Earth.

On the Propagation of Whistler‐Mode Waves in the Magnetic Ducts

AbstractThis paper studies extremely low frequency (ELF) whistler‐mode waves' behavior within small‐scale magnetic field irregularities in the Earth's magnetosphere, known as magnetic ducts. Based on the magnetic fields' magnitude inside and outside these ducts, they are categorized as high‐magnetic ducts and low‐magnetic ducts (LBD). Using the whistler‐mode dispersion relation analysis, our primary focus is to show that LBDs are prone to leak electromagnetic energy outside the duct. We further investigate the hypothesis that whistlers can propagate within LBDs without any signal loss when the width of the duct corresponds to an integer multiple of the perpendicular wavelengths of the waves inside it. This condition offers a straightforward and effective method for identifying non‐leaking eigenmodes of LBDs. Our analysis of this non‐leaking condition reveals that every LBD possesses a finite number of non‐leaking eigenmodes directly proportional to the duct's width and the magnitude of the ambient magnetic field within it. The analytical results are then validated using two‐dimensional, time‐dependent simulations of the electron‐Magnetohydrodynamics model. Also, we model the non‐leaking propagation of an ELF whistler‐mode wave observed inside the LBD by the NASA Magnetospheric Multiscale mission satellites.

Electromagnetic Behavior Simulation of REBCO Pancake Coils Considering REBCO Tape Rotation Under High Magnetic Field

Since the screening current induced in rare earth-barium-copper-oxide (REBCO) magnet generates an irregular magnetic field, a few screening current simulation methods have been proposed. For an insert REBCO magnet generating ultra-high magnetic field, a new screening current method has been proposed with consideration of the coil-deformation effect. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">In this paper, we have developed a new screening current method based on a partial element equivalent circuit (PEEC) model coupling with a two-dimensional stress finite element analysis to accurately the time-transient distribution of accurate screening current. In the presented method, the changes of self/mutual inductances are considered due to the coil deformation. As the simulation results, it was found that the coil deformation affected the screening current distribution. When considering the coil deformations, the screening current-induced fields to operating current are different for charging cycles. It is necessary to simulate the coil deformation to accurately estimate the screening current and the screening current-induced field.

The SCML-05 Developed for Studying the 3D Force and PMG Irregularities Characteristics of HTS Maglev

In order to promote the application of high temperature superconducting (HTS) maglev vehicle, the series of superconducting maglev (SCML) measurement devices — 01, 02 & 03 have been developed in Southwest Jiaotong University. During the course of research, the importance of three-dimensional (3D) study of the interaction between HTS bulks and permanent magnet guideways (PMGs) has become evident. More specifically, when the HTS vehicle is moving at a high speed, small irregularities of the PMG's magnetic field become the source of vibration. Therefore, in order to study the 3D force and the characteristics of HTS maglev under PMG irregularities, a new measurement device called SCML-05 was designed, constructed, and validated. This newly developed measurement device consists of two major parts. The first one is a closed-loop sliding platform providing 3D motion. The second part is measurement and data acquisition system with the software developed for this purpose. In addition, a laser displacement sensor is used to measure the geometry irregularities of the PMG. Overall, the SCML-05 is flexible and light. The force characteristics of the HTS bulks placed above the PMG can be precisely investigated by means of this system. Additionally, the PMG irregularities including geometry and magnetic field irregularities can be measured. These parameters are required to analyze the relationship between the PMG irregularities and the force of HTS maglev vehicle. The test process and typical results obtained by this system are presented in this paper.

On heat conduction in an irregular magnetic field. Part 1

Anisotropic heat conduction in a plasma embedded in a magnetic field with irregular, possibly chaotic, field lines is discussed. If the collisional mean free path exceeds the electron gyroradius, the heat conductivity is much larger along the field lines than across them, and this enhances the transport across a domain where good flux surfaces do not exist. Recognising that anisotropic heat conduction may be cast in a variational form, and by constructing increasingly sophisticated trial functions that are based on invariant and almost-invariant structures under the magnetic field-line flow, bounds are derived on this enhancement and on the temperature variation along the magnetic field. In this way, remarkably accurate approximations for the temperature can be rapidly constructed without solving the diffusion equation, even in the small perpendicular-diffusion limit when the solution for the temperature is dominated by the fractal structure the magnetic field lines.

Heat conduction in an irregular magnetic field. Part 2. Heat transport as a measure of the effective non-integrable volume

Given the large anisotropy of transport processes in magnetized plasmas, the magnetic field structure can strongly impact heat diffusion: magnetic surfaces and cantori form barriers to transport while chaotic layers and island structures can degrade confinement. When a small but non-zero amount of perpendicular diffusion is included, the structure of the magnetic field becomes less important, allowing pressure gradients to be supported across chaotic regions and island chains. We introduce a metric for the effective volume over which the local parallel diffusion dominates based on the solution to the anisotropic heat diffusion equation. To validate this metric, we consider model fields with a single island chain and a strongly chaotic layer for which analytic predictions of the relative parallel and perpendicular transport can be made. We also analyse critically chaotic fields produced from different sets of perturbations, highlighting the impact of the mode number spectrum on the heat transport. Our results indicate that this metric coincides with the effective volume of non-integrability in the limit $\kappa _{\perp } \rightarrow 0$ , where $\kappa_{\perp}$ is the perpendicular diffusion coefficient. We propose that this metric be used to assess the impact of non-integrability on the heat transport in stellarator equilibria.

Numerical Evaluation of Screening Current-Induced Magnetic Field in No-Insulation REBCO Coil Systems

We have been developing a no-insulation (NI) REBCO coil which is expected to be applied to medical accelerators and magnetic resonance imaging as a technology that can achieve both high thermal stability and high current density. Due to the flat shape and much greater, than the thickness, width of a REBCO-coated conductor, the screening currents are remarkably induced by changing the magnetic flux that penetrates the tape vertically. For insulated (INS) coils, this screening current causes an irregular magnetic field (screening current-induced magnetic field (SCIF)). Also, in the NI coil, an excitation delay occurs because of the current flowing in the radial direction with coil excitation. Therefore, as the cause of irregular magnetic field, it is necessary to simultaneously consider the influence of both the excitation delay and SCIF. In this study, we numerically investigate the magnetic field in the NI coil. The SCIF and an excitation delay reduce magnetic accuracy in the NI coil. Thus, we propose an energization waveform that can improve the magnetic field accuracy even if there is an excitation delay. Besides, we verified its effectiveness.

Numerical Evaluation of Screening Current-Induced Magnetic Field Considering Variable Output Energy in REBCO Coil System of Skeleton Cyclotron for Cancer Therapy

We have been developing a new-generation accelerator named “Skeleton Cyclotron”, which is an ultra-compact and high-intensity accelerator for the stable production of <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">211</sup> At used for targeted alpha-particle therapy. Coil system for Skeleton Cyclotron consists of circular and noncircular high-temperature superconducting magnets and it can cause the output energy to vary without being bounded by the non-linearity of the iron core. This will enable not only the production of <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">211</sup> At, but also the production of radioisotopes for positron emission tomography and neutron irradiation for boron neutron capture therapy with a single accelerator. A high-precision magnetic field distribution and a high temporal stability are required for stable beam acceleration, but the screening current, which is induced in the REBa <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Cu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> (REBCO, RE: Rare Earth) coated conductor, generates an irregular magnetic field and deteriorates the quality of the magnetic field spatially and temporally. In this study, we numerically evaluated the temporal stability and reproducibility of the screening current-induced field considering the variable energy operation for the Ultra-Baby Skeleton Cyclotron, which is a small demonstration model of Skeleton Cyclotron.

A simple screening current simulation method using equivalent circuit model for REBCO pancake coils

The screening current induced in rare-earth barium copper oxide (REBCO) tape generates an unwanted irregular magnetic field. The screening current-induced field (SCIF) is a challenging issue for MRI, NMR, and accelerators magnet composed of REBCO coils. A few FEM-based simulation methods have been proposed to estimate the SCIF; however, they require a long computation time.Recently, we have proposed a simple SCIF computation method based on the self and mutual inductances of REBCO pancake coils and screening current radial paths on the top and bottom of pancake coils. The accuracy of the proposed method is not excellent; however, the computation time is quite short. In this paper, we report an equivalent circuit model that includes the self and mutual inductances of a REBCO pancake coil and screening current radial path. Moreover, with this proposed method, we can compute the SCIF of no-insulation (NI) REBCO pancake coils, which is not the case with the previously proposed FEM-based simulation method. The proposed method has been validated by experimentation. The proposed method is available online.

Erratum: “The Acceleration of Charged Particles at a Spherical Shock Moving through an Irregular Magnetic Field” (2017, ApJ, 848, 123)

Erratum: “The Acceleration of Charged Particles at a Spherical Shock Moving through an Irregular Magnetic Field” (2017, ApJ, 848, 123)

Design and implementation of a single-side flat synchronous linear motor model

In recent decades, the demand for a linear motor has increased in various applications, due to its ability to develop a linear motion directly. One of the significant problems facing the operation of the linear motor is the presence of force ripple caused by the irregular magnetic field of the permanent magnets. Accordingly, a developed single-side permanent magnet synchronous flat linear motor (PMSLM) model has been designed based on minimizing its force ripple produced. A Maxwell ANSYS simulation is performed to study and enhance the dynamic characteristics and performance of the model and then verifying it with experimental measurements. Multi-objective optimization had been achieved through reducing the size of permanent magnets and reaction rail at specific rates with maintaining the required thrust and reducing the cogging force. The results of the improved model design showed that the maximum value of the force ripple is reduced by about 81.13% compared with the primary model at a smaller ripple coefficient of 0.22%. The comparison between the experimental measurements and numerical analysis showed a good agreement and accuracy of the analytical results.

Stress-Induced Magnetic Anisotropy Enabling Engineering of Magnetic Softness and GMI Effect of Amorphous Microwires

Stress-annealing enabled a considerable improvement in the GMI effect in both Fe- and Co-rich glass-coated microwires. Additionally, a remarkable magnetic softening can be achieved in stress-annealed Fe-rich microwires. Observed stress-annealing induced magnetic anisotropy is affected by annealing conditions (temperatures and stresses applied during annealing). The highest GMI ratio up to 310% was obtained in stress-annealed Co-rich microwires, although they presented rectangular hysteresis loops. A remarkable magnetic softness and improved GMI ratio over a wide frequency range were obtained in stress-annealed Fe-rich microwires. Irregular magnetic field dependence observed for some stress-annealing conditions is attributed to the contribution of both the inner axially magnetized core and outer shell, with transverse magnetic anisotropy.

Substorm Activity and Orientation of the Front of a Shock Wave of an Interplanetary Magnetic Cloud

The paper draws attention to the complex structure of the fast magnetic clouds of the solar wind, which, in addition to the actual cloud body, contain a turbulent transition layer (cloud sheath) with a large and irregular magnetic field following the shock wave. The orientation of the plane of the magnetic-cloud shock wave with respect to the interplanetary magnetic field modified by the shock wave propagating in the solar wind for 33 cases of the registration of fast magnetic clouds has been calculated. The dependence of the substorm activity in the auroral zone on the level of turbulent processes occurring in the sheath of magnetic clouds has been studied. It was taken into account that the turbulent phenomena in the sheath are largely determined by the orientation of the shock-wave plane with respect to the interplanetary magnetic field. It is shown that the level of magnetic activity in the auroral zone, which is characterized by the integral AL index, increases with a decrease in the angle between the direction normal to the shock-wave front and the vector of the interplanetary magnetic field. Thus, the most geoeffective are magnetic clouds with a quasi-parallel shock wave, and the least geoeffective are those with a quasi-perpendicular shock wave. It was concluded that the intensity of turbulent processes in the cloud sheath increases with a decrease in the magnetic field penetrating the sheath, which plays a stabilizing role for turbulent magnetohydrodynamic perturbations.

ANALISIS INDEKS AKTIVITAS GEOMAGNET PADA SAAT BADAI GEOMAGNET 13 OKTOBER 2016

Badai geomagnet terjadi akibat aktivitas abnormal di matahari yang mempengaruhi intensitas angin matahari. Badai ini ditandai dengan perubahan nilai variasi harian medan magnet bumi yang besar, cepat dan tidak beraturan. Efek badai geomagnet di sekitar bumi dapat berdampak pada aktivitas manusia di luar angkasa dan di permukaan bumi. Salah satu kejadian badai geomagnet yang pernah tercatat adalah pada tanggal 13 Oktober 2016. Dalam penentuan tingkat gangguan geomagnet digunakan indeks geomagnet. Indeks geomagnet merupakan ukuran sederhana yang menggambarkan aktivitas magnetis yang berasal dari ionosfer dan magnetosfer bumi. Penelitian ini bertujuan untuk menganalisis indeks geomagnet ketika terjadi badai tanggal 13 Oktober 2016. Indeks geomagnet yang dianalisis antara lain indeks K, indeks A dan indeks Dst khususnya di wilayah Sumatera. Data yang digunakan adalah data variasi harian komponen H medan magnet bumi dari rekaman sensor magnetometer BMKG di Stasiun Gunungsitoli, Tuntungan, Sicincin, Liwa dan Tangerang. Berdasarkan hasil analisis dapat diidentifikasi jika badai geomagnet pada tanggal 13 Oktober 2016 tersebut termasuk kriteria badai geomagnet kuat jika ditinjau dari nilai Dst indeks yang menyentuh angka dibawah -100 nT.

Cosmic-Ray Distribution Function under Anisotropic Scattering of Particles by Magnetic-Field Fluctuations

The acceleration of energetic particles and their propagation in magnetic fields of the solar wind and the Galaxy is a topical astrophysical problem. Cosmic rays (CR) affect communications and the operation of on-board spacecraft electronics and disturb the magnetosphere and the ionosphere of the Earth. The scattering of particles by magnetic-field irregularities is the primary mechanism governing the CR propagation in the interplanetary medium. If the scattering of energetic particles in the interplanetary medium is relatively inefficient (i.e., the mean free path is comparable to the heliocentric distance), a kinetic equation should be used to characterize the CR propagation. The Fokker–Planck kinetic equation is used to analyze the propagation of charged energetic particles in a magnetic field represented as a superposition of a mean uniform field and magnetic inhomogeneities of various scales. This kinetic equation corresponds to multiple small-angle scattering, and its collision integral characterizes particle diffusion in the momentum space. A system of differential equations for the spherical harmonics of the CR distribution function is obtained based on the kinetic equation. The CR transport equations are derived and solved. The evolution of the CR distribution function under anisotropic scattering of particles by magnetic-field fluctuations is examined. It is demonstrated that the angular distribution function of particles depends to a considerable extent on the degree of their scattering anisotropy. The temporal dependence of the CR distribution function is analyzed, and the parameter characterizing the scattering anisotropy is estimated.

Modeling and analysis of spoke-type permanent magnet vernier machine based on equivalent magnetic network method

In this paper, a new equivalent magnetic network(EMN) model is established for a spoke-type permanent magnet(PM) vernier(PMV) machine. Two different modeling methods are proposed for different parts of the PMV machine, considering that their magnetic field distributions are quite different. Hierarchical modeling method is proposed for the modeling of the rotor as the magnetic intensity of the rotor iron core presents gradient distribution along the radial direction. Mesh based reluctance network method is used for the modeling of flux modulation poles with irregular and unstable magnetic field distributions. Moreover, accurate PM leakage permeance calculation formulae are deduced to improve the simulation precision. The electromagnetic parameters, such as flux linkage, back electromagnetic force, electromagnetic torque and iron loss are predicted by the proposed EMN model. Finally, finite element analysis(FEA) and experimental results are given to verify the effectiveness of the proposed methods.

New Model for Ionospheric Irregularities at Mars

AbstractA new model for ionospheric irregularities at Mars is presented. It is shown that wind‐driven currents in the dynamo region of the Martian ionosphere can be unstable to the electromagnetic gradient drift instability. This plasma instability can generate ionospheric density and magnetic field irregularities with scale sizes of approximately 15–20 km down to a few kilometers. We show that the instability‐driven magnetic field fluctuation amplitudes relative to background are correlated with the ionospheric density fluctuation amplitudes relative to background. Our results can explain recent observations made by the Mars Atmosphere and Volatile EvolutioN spacecraft in the Martian ionosphere dynamo region.

An Extended Thin Approximation Method to Simulate Screening Current Induced in REBCO Coils

Superconducting magnets wound with second-generation high-temperature superconductors, i.e., REBa2Cu3O7– x (REBCO, RE = Rare Earth) tapes, are desired to apply high magnetic field nuclear magnetic resonance, MRI, and accelerators. However, a major problem for practical application is an undesirable irregular magnetic field caused by screening currents induced in REBCO tapes. To investigate the screening current-induced magnetic field, a few simulation methods have been proposed. One of the effective simulation methods employs a finite-element method with a thin approximation method. Although the thin approximation method was developed to simulate eddy currents in magnetic steel sheets, and it is not applicable to REBCO tapes carrying a transport current. Therefore, the thin approximation method is extended to simulate screening currents in REBCO tapes considering a carrying transport current. To show the validity of the proposed extended thin approximation method, the screening currents of an REBCO magnet are computed, and the results are compared with the measurement and simulation results of the conventional thin approximation method. The more accurate solution is available by using the proposed methods.