New compact and singularity free formulations for the magnetic field produced by a finite cylinder considering linearly varying current density

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.

Download Full-text

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

EPJ Web of Conferences ◽

10.1051/epjconf/201817708004 ◽

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.

Download Full-text

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

physica status solidi (b) ◽

10.1002/pssb.2221700220 ◽

1992 ◽

Vol 170 (2) ◽

pp. 549-562 ◽

Cited By ~ 19

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

Download Full-text

Small, modular and economically attractive fusion enabled by high temperature superconductors

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2018.0354 ◽

2019 ◽

Vol 377 (2141) ◽

pp. 20180354 ◽

Cited By ~ 4

Author(s):

Dennis Whyte

Keyword(s):

Magnetic Field ◽

High Temperature ◽

Magnetic Fields ◽

Current Density ◽

High Temperature Superconductors ◽

Fusion Energy ◽

High Magnetic Fields ◽

Operating Temperatures ◽

The Magnetic Field ◽

Game Changer

The advantages of high magnetic fields in tokamaks are reviewed, and why they are important in leading to more compact tokamaks. A brief explanation is given of what limits the magnetic field in a tokamak, and why high temperature superconductors (HTSs) are a game changer, not just because of their higher magnetic fields but also for reasons of higher current density and higher operating temperatures. An accelerated pathway to fusion energy is described, defined by the SPARC and ARC tokamak designs. This article is part of a discussion meeting issue ‘Fusion energy using tokamaks: can development be accelerated?’.

Download Full-text

Study of the applicability of the curlometer technique with the four Cluster spacecraft in regions close to Earth

Annales Geophysicae ◽

10.5194/angeo-30-597-2012 ◽

2012 ◽

Vol 30 (3) ◽

pp. 597-611 ◽

Cited By ~ 9

Author(s):

S. Grimald ◽

I. Dandouras ◽

P. Robert ◽

E. Lucek

Keyword(s):

Magnetic Field ◽

Current Density ◽

Ring Current ◽

Current System ◽

Sufficient Conditions ◽

Magnetic Activity ◽

Inner Magnetosphere ◽

Good Proxy ◽

The Magnetic Field ◽

Magnetospheric Current System

Abstract. Knowledge of the inner magnetospheric current system (intensity, boundaries, evolution) is one of the key elements for the understanding of the whole magnetospheric current system. In particular, the calculation of the current density and the study of the changes in the ring current is an active field of research as it is a good proxy for the magnetic activity. The curlometer technique allows the current density to be calculated from the magnetic field measured at four different positions inside a given current sheet using the Maxwell-Ampere's law. In 2009, the CLUSTER perigee pass was located at about 2 RE allowing a study of the ring current deep inside the inner magnetosphere, where the pressure gradient is expected to invert direction. In this paper, we use the curlometer in such an orbit. As the method has never been used so deep inside the inner magnetosphere, this study is a test of the curlometer in a part of the magnetosphere where the magnetic field is very high (about 4000 nT) and changes over small distances (ΔB = 1nT in 1000 km). To do so, the curlometer has been applied to calculate the current density from measured and modelled magnetic fields and for different sizes of the tetrahedron. The results show that the current density cannot be calculated using the curlometer technique at low altitude perigee passes, but that the method may be accurate in a [3 RE; 5 RE] or a [6 RE; 8.3 RE] L-shell range. It also demonstrates that the parameters used to estimate the accuracy of the method are necessary, but not sufficient conditions.

Download Full-text