scholarly journals Euler potentials for two layers with non-constant current densities in the ambient magnetic field aligned to the layers

2016 ◽  
Vol 34 (12) ◽  
pp. 1165-1173
Author(s):  
Marek Vandas ◽  
Eugene P. Romashets
Keyword(s):  
Magnetic Field ◽  
Current Density ◽  
Previous Treatment ◽  
Homogeneous Magnetic Field ◽  
Constant Current ◽  
Constant Current Density ◽  
New Approach ◽  
Current Densities ◽  
The Magnetic Field ◽  
Birkeland Currents

Abstract. The Euler potentials for two current layers aligned to an ambient homogeneous magnetic field are found. Previous treatment of such a system assumed constant current density in the layers. However, the magnetic field becomes infinite at the edges. The new approach eliminates this inconsistency by introducing an inhomogeneous current density. Euler potentials are constructed semi-analytically for such a system. Charged-particle motion and trapping in it are examined by this representation. Using Euler potentials, the influence of current sheets of zero and non-zero thicknesses on energetic-particle fluxes is investigated, and characteristic flux variations near the sheets are presented. The results can be applied to Birkeland currents.

scholarly journals Continuum sensitivity and design optimization of superconducting systems under critical current densities with magnetic field dependence

2021 ◽  
Author(s):  
Kyungsik Seo ◽  
Tim Coombs ◽  
Il Han Park
Keyword(s):  
Magnetic Field ◽  
Design Optimization ◽  
Critical Current ◽  
Current Density ◽  
State Equation ◽  
Design Sensitivity ◽  
Continuum Sensitivity ◽  
Current Densities ◽  
The Magnetic Field ◽  
The Continuum

AbstractThis paper presents an approach for deriving the continuum sensitivity of superconducting systems operating at critical current densities and an optimization method based on the continuum sensitivity. In the sensitivity problem, the superconducting systems is represented by a variational state equation, wherein the magnetic permeability depends on the magnetic field, which is transformed from a state equation with a field-dependent source. The design sensitivity is derived using the material derivative concept of continuum mechanics and the adjoint variable method. The adjoint system has a material property represented as a symmetric tensor that contains the sensitivity of the current density with respect to the magnetic field. The design sensitivity is represented in the analytical form of a surface integral on the interface between the superconducting material and its surroundings, which depends on the sensitivity of the current density. The optimization scheme is constructed based on the continuum design sensitivity. In the design optimization, the level set method is used to express the shape variation of the superconducting materials. The numerical example of infinite solenoids demonstrates that the design sensitivity provides an accurate design solution considering the critical current condition. In addition, the design example of a magnetic resonance imaging solenoid shows that the derived design sensitivity has the inherent ability for attaining the compact design by treating the input current of a superconducting system as a critical condition.

Critical Current Densities in Bi2Sr2Cacu2O8+D

1989 ◽  
Vol 169 ◽  
Author(s):  
Shunji Nomura ◽  
Yutaka Yamada ◽  
Tomohisa Yamashita ◽  
Eriko Yoneda ◽  
Hisashi Yoshino ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Critical Current Density ◽  
Critical Current ◽  
Current Density ◽  
Flux Pinning ◽  
Pinning Force ◽  
Critical Fields ◽  
Current Densities ◽  
Upper Critical Fields ◽  
The Magnetic Field

AbstractCritical current densities and upper critical fields were measured for a single crystal of the high Tc oxide superconductor, Bi2Sr2CaCu2O8+d, within the ab basal plane and along the c axis. The anisotropy in critical current densities was observed to be Jc⊥/Jc//=10 in agreement with the anisotropy in resistivity for the normal state. The magnetic field dependence of the critical current densities can be interpreted by the anisotropy in the upper critical fields. The scaling of the critical current density with the magnetic field was found. The critical current density scaled to zero at fields Bc2 in the ab plane and along the c axis which were in good agreement with the upper critical fields measured by transport.The anisotropy in flux pinning force density along the b axis, Fp//b, and along the a axis, Fp//a, was found to be Fp//b/Fp//a=3. The data provided strong evidence for flux pinning by the modulated structure in this system.

scholarly journals Magnetic nulls in interacting dipolar fields

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Todd Elder ◽  
Allen H. Boozer
Keyword(s):  
Magnetic Field ◽  
Current Density ◽  
Magnetic Flux Tube ◽  
Electron Inertia ◽  
Characteristic Spatial Scale ◽  
Field Lines ◽  
Dipolar Fields ◽  
Time Required ◽  
Magnetic Null ◽  
The Magnetic Field

The prominence of nulls in reconnection theory is due to the expected singular current density and the indeterminacy of field lines at a magnetic null. Electron inertia changes the implications of both features. Magnetic field lines are distinguishable only when their distance of closest approach exceeds a distance $\varDelta _d$ . Electron inertia ensures $\varDelta _d\gtrsim c/\omega _{pe}$ . The lines that lie within a magnetic flux tube of radius $\varDelta _d$ at the place where the field strength $B$ is strongest are fundamentally indistinguishable. If the tube, somewhere along its length, encloses a point where $B=0$ vanishes, then distinguishable lines come no closer to the null than $\approx (a^2c/\omega _{pe})^{1/3}$ , where $a$ is a characteristic spatial scale of the magnetic field. The behaviour of the magnetic field lines in the presence of nulls is studied for a dipole embedded in a spatially constant magnetic field. In addition to the implications of distinguishability, a constraint on the current density at a null is obtained, and the time required for thin current sheets to arise is derived.

scholarly journals Finite Element Analysis of Magnetic Field Exciter for Direct Testing of Magnetocaloric Materials’ Properties

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2792
Author(s):  
Wieslaw Lyskawinski ◽  
Wojciech Szelag ◽  
Cezary Jedryczka ◽  
Tomasz Tolinski
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Magnetic Circuit ◽  
Homogeneous Magnetic Field ◽  
Element Analysis ◽  
Mcm Testing ◽  
Testing Region ◽  
Magnetocaloric Materials ◽  
Field Excitation ◽  
The Magnetic Field

The paper presents research on magnetic field exciters dedicated to testing magnetocaloric materials (MCMs) as well as used in the design process of magnetic refrigeration systems. An important element of the proposed test stand is the system of magnetic field excitation. It should provide a homogeneous magnetic field with a controllable value of its intensity in the MCM testing region. Several concepts of a magnetic circuit when designing the field exciters have been proposed and evaluated. In the MCM testing region of the proposed exciters, the magnetic field is controlled by changing the structure of the magnetic circuit. A precise 3D field model of electromagnetic phenomena has been developed in the professional finite element method (FEM) package and used to design and analyze the exciters. The obtained results of the calculations of the magnetic field distribution in the working area were compared with the results of the measurements carried out on the exciter prototype. The conclusions resulting from the conducted research are presented and discussed.

scholarly journals The effect of simplifications of a numerical mesh on the results of electromagnetic analysis of the Nuclotron-type cable

2018 ◽  
Vol 177 ◽  
pp. 08004
Author(s):  
Łukasz Tomków
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Current Density ◽  
Electric Current Density ◽  
Electromagnetic Analysis ◽  
First Case ◽  
Single Region ◽  
The Magnetic Field

The model of a single Nuclotron-type cable is presented. The goal of this model is to assess the behaviour of the cable under different loads. Two meshes with different simplifications are applied. In the first case, the superconductor in the cable is modelled as single region. Second mesh considers individual strands of the cable. The significant differences between the distributions of the electric current density obtained with both models are observed. The magnetic field remains roughly similar.

scholarly journals Comparison of the measured and modelled electron densities and temperatures in the ionosphere and plasmasphere during 20-30 January, 1993

2000 ◽  
Vol 18 (10) ◽  
pp. 1257-1262 ◽  
Author(s):  
A. V. Pavlov ◽  
T. Abe ◽  
K.-I. Oyama
Keyword(s):  
Magnetic Field ◽  
Heat Flux ◽  
Electron Temperature ◽  
Field Line ◽  
Electron Density ◽  
Magnetic Field Line ◽  
New Approach ◽  
Additional Heating ◽  
Vibrational Levels ◽  
The Magnetic Field

Abstract. We present a comparison of the electron density and temperature behaviour in the ionosphere and plasmasphere measured by the Millstone Hill incoherent-scatter radar and the instruments on board of the EXOS-D satellite with numerical model calculations from a time-dependent mathematical model of the Earth's ionosphere and plasmasphere during the geomagnetically quiet and storm period on 20–30 January, 1993. We have evaluated the value of the additional heating rate that should be added to the normal photoelectron heating in the electron energy equation in the daytime plasmasphere region above 5000 km along the magnetic field line to explain the high electron temperature measured by the instruments on board of the EXOS-D satellite within the Millstone Hill magnetic field flux tube in the Northern Hemisphere. The additional heating brings the measured and modelled electron temperatures into agreement in the plasmasphere and into very large disagreement in the ionosphere if the classical electron heat flux along magnetic field line is used in the model. A new approach, based on a new effective electron thermal conductivity coefficient along the magnetic field line, is presented to model the electron temperature in the ionosphere and plasmasphere. This new approach leads to a heat flux which is less than that given by the classical Spitzer-Harm theory. The evaluated additional heating of electrons in the plasmasphere and the decrease of the thermal conductivity in the topside ionosphere and the greater part of the plasmasphere found for the first time here allow the model to accurately reproduce the electron temperatures observed by the instruments on board the EXOS-D satellite in the plasmasphere and the Millstone Hill incoherent-scatter radar in the ionosphere. The effects of the daytime additional plasmaspheric heating of electrons on the electron temperature and density are small at the F-region altitudes if the modified electron heat flux is used. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calculated. The present study suggests that these deviations are not significant at the first vibrational levels of N2 and O2 and the second level of O2, and the calculated distributions of N2(v) and O2(v) are highly non-Boltzmann at vibrational levels v > 2. The resulting effect of N2(v > 0) and O2(v > 0) on NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 1.5. The modelled electron temperature is very sensitive to the electron density, and this decrease in electron density results in the increase of the calculated daytime electron temperature up to about 580 K at the F2 peak altitude giving closer agreement between the measured and modelled electron temperatures. Both the daytime and night-time densities are not reproduced by the model without N2(v > 0) and O2(v > 0), and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement.Key words: Ionosphere (ionospheric disturbances; ionosphere-magnetosphere interactions; plasma temperature and density)  

Study on Special Morphology Hydroxyapatite Bioactive Coating by Electrochemical Deposition

2013 ◽  
Vol 537 ◽  
pp. 256-260
Author(s):  
Cai Ge Gu ◽  
Qian Gang Fu ◽  
He Jun Li ◽  
Jin Hua Lu ◽  
Lei Lei Zhang
Keyword(s):  
Electrochemical Deposition ◽  
Current Density ◽  
Electrolyte Concentration ◽  
Spherical Particles ◽  
Constant Current ◽  
Constant Current Density ◽  
Depth Direction ◽  
Special Morphology ◽  
Calcium Phosphate Coatings ◽  
Coating Weight

Bioactive calcium phosphate coatings were deposited on carbon/carbon（C/C） composites using electrochemical deposition technique. The effects of electrolyte concentration and constant current density on morphology, structure and composition of the coating were systematically investigated using scanning electron microscopy (SEM), X-ray diffraction (XRD) and Fourier transformed infrared (FTIR) spectroscopy. The results show that, the coating weight elevated gradually with the increase of electrolyte concentration, and the morphology of coatings changed from spherical particles to nanolamellar crystals with interlocking structure initially. Then the coating transformed into seaweed-like and nano/micro-sized crystals along the depth direction of the coating. The coatings showed seaweed-like morphology as the deposition current density was less than 20mA. With the less current density, the coating became more homogenous. However, the coating was fiakiness crysal, with needlike crystal stacked upside as the current density reached to 20mA/cm2. The coating weight was improved gradually when the current density increased from 2.5mA/cm2 to 10mA/cm2, then reduced with the increasing current density in the range of 10 to 20mA/cm2.

The Critical Current Density and the Curvature of the Magnetic Field in Epitaxial YBaCuO Films

1992 ◽  
Vol 170 (2) ◽  
pp. 549-562 ◽  
Author(s):  
D. Glatzer ◽  
A. Forkl ◽  
H. Theuss ◽  
H. U. Habermeier ◽  
H. Kronmüller
Keyword(s):  
Magnetic Field ◽  
Critical Current Density ◽  
Critical Current ◽  
Current Density ◽  
The Magnetic Field

scholarly journals Statistical analysis of the dependence of large-scale Birkeland currents on solar wind parameters

2010 ◽  
Vol 28 (2) ◽  
pp. 515-530 ◽  
Author(s):  
H. Korth ◽  
B. J. Anderson ◽  
C. L. Waters
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Mach Number ◽  
Electric Field ◽  
Large Scale ◽  
Dynamic Pressure ◽  
Dominant Factor ◽  
Total Current ◽  
Current Densities ◽  
Birkeland Currents

Abstract. The spatial distributions of large-scale field-aligned Birkeland currents have been derived using magnetic field data obtained from the Iridium constellation of satellites from February 1999 to December 2007. From this database, we selected intervals that had at least 45% overlap in the large-scale currents between successive hours. The consistency in the current distributions is taken to indicate stability of the large-scale magnetosphere–ionosphere system to within the spatial and temporal resolution of the Iridium observations. The resulting data set of about 1500 two-hour intervals (4% of the data) was sorted first by the interplanetary magnetic field (IMF) GSM clock angle (arctan(By/Bz)) since this governs the spatial morphology of the currents. The Birkeland current densities were then corrected for variations in EUV-produced ionospheric conductance by normalizing the current densities to those occurring for 0° dipole tilt. To determine the dependence of the currents on other solar wind variables for a given IMF clock angle, the data were then sorted sequentially by the following parameters: the solar wind electric field in the plane normal to the Earth–Sun line, Eyz; the solar wind ram pressure; and the solar wind Alfvén Mach number. The solar wind electric field is the dominant factor determining the Birkeland current intensities. The currents shift toward noon and expand equatorward with increasing solar wind electric field. The total current increases by 0.8 MA per mV m−1 increase in Eyz for southward IMF, while for northward IMF it is nearly independent of the electric field, increasing by only 0.1 MA per mV m−1 increase in Eyz. The dependence on solar wind pressure is comparatively modest. After correcting for the solar dynamo dependencies in intensity and distribution, the total current intensity increases with solar wind dynamic pressure by 0.4 MA/nPa for southward IMF. Normalizing the Birkeland current densities to both the median solar wind electric field and dynamic pressure effects, we find no significant dependence of the Birkeland currents on solar wind Alfvén Mach number.

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