Correction to “Homotopy formulas for the magnetic vector potential and magnetic helicity: The Parker spiral interplanetary magnetic field and magnetic flux ropes”

2011 ◽  
Vol 116 (A11) ◽  
pp. n/a-n/a ◽  
Author(s):  
G. M. Webb ◽  
Q. Hu ◽  
B. Dasgupta ◽  
G. P. Zank
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Interplanetary Magnetic Field ◽  
Vector Potential ◽  
Magnetic Helicity ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Magnetic Flux Ropes ◽  
Parker Spiral ◽  
Flux Ropes

Modeling of an inductively coupled system

2018 ◽  
Vol 37 (4) ◽  
pp. 1500-1514 ◽  
Author(s):  
Rafael Psiuk ◽  
Alisa Artizada ◽  
Daniel Cichon ◽  
Hartmut Brauer ◽  
Hannes Toepfer ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Vector Potential ◽  
Coupled Systems ◽  
Magnetic Flux Density ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Content Type ◽  
Primary Loop ◽  
Inductively Coupled

Purpose This paper aims to provide a flexible model for a system of inductively coupled loops in a quasi-static magnetic field. The outlined model is used for theoretical analyses on the magnetic field-based football goal detection system called as GoalRef, where a primary loop generates a magnetic field around the goal. The passive loops are integrated in the football, and a goal is deduced from induced voltages in loop antennas mounted on the goal frame. Design/methodology/approach Based on the law of Biot–Savart, the magnetic vector potential of a primary current loop is calculated. The induced voltages in secondary loops are derived by Faraday’s Law. Expressions to calculate induced voltages in elliptically shaped loops and their magnetic field are also presented. Findings The induced voltages in secondary loops close to the primary loop are derived by either numerically integrating the primary magnetic flux density over the area of the secondary loop or by integrating the primary magnetic vector potential over the boundary of that loop. Both approaches are examined and compared with respect to accuracy and calculation time. It is shown that using the magnetic vector potential instead of the magnetic flux density can decrease the processing time by a factor of around 100. Research limitations/implications Environmental influences like conductive or permeable obstacles are not considered in the model. Practical implications The model can be used to investigate the theoretical behavior of inductively coupled systems. Originality/value The proposed model provides a flexible, fast and accurate tool for calculations of inductively coupled systems, where the loops can have arbitrary shape, position and orientation.

scholarly journals A new technique for observationally derived boundary conditions for space weather

2018 ◽  
Vol 8 ◽  
pp. A26 ◽  
Author(s):  
Paolo Pagano ◽  
Duncan Hendry Mackay ◽  
Anthony Robinson Yeates
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Boundary Conditions ◽  
Space Weather ◽  
Weather Forecasting ◽  
Interplanetary Space ◽  
Time Dependent ◽  
Magnetic Flux Ropes ◽  
Mhd Simulations ◽  
Flux Ropes

Context. In recent years, space weather research has focused on developing modelling techniques to predict the arrival time and properties of coronal mass ejections (CMEs) at the Earth. The aim of this paper is to propose a new modelling technique suitable for the next generation of Space Weather predictive tools that is both efficient and accurate. The aim of the new approach is to provide interplanetary space weather forecasting models with accurate time dependent boundary conditions of erupting magnetic flux ropes in the upper solar corona. Methods. To produce boundary conditions, we couple two different modelling techniques, MHD simulations and a quasi-static non-potential evolution model. Both are applied on a spatial domain that covers the entire solar surface, although they extend over a different radial distance. The non-potential model uses a time series of observed synoptic magnetograms to drive the non-potential quasi-static evolution of the coronal magnetic field. This allows us to follow the formation and loss of equilibrium of magnetic flux ropes. Following this a MHD simulation captures the dynamic evolution of the erupting flux rope, when it is ejected into interplanetary space. Results.The present paper focuses on the MHD simulations that follow the ejection of magnetic flux ropes to 4 R⊙. We first propose a technique for specifying the pre-eruptive plasma properties in the corona. Next, time dependent MHD simulations describe the ejection of two magnetic flux ropes, that produce time dependent boundary conditions for the magnetic field and plasma at 4 R⊙ that in future may be applied to interplanetary space weather prediction models. Conclusions. In the present paper, we show that the dual use of quasi-static non-potential magnetic field simulations and full time dependent MHD simulations can produce realistic inhomogeneous boundary conditions for space weather forecasting tools. Before a fully operational model can be produced there are a number of technical and scientific challenges that still need to be addressed. Nevertheless, we illustrate that coupling quasi-static and MHD simulations in this way can significantly reduce the computational time required to produce realistic space weather boundary conditions.

scholarly journals Sunquake with a second bounce, other sunquakes, and emission associated with the X9.3 flare of 6 September 2017

2020 ◽  
Vol 639 ◽  
pp. A78 ◽  
Author(s):  
Sergei Zharkov ◽  
Sarah Matthews ◽  
Valentina Zharkova ◽  
Malcolm Druett ◽  
Satoshi Inoue ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
White Light ◽  
Light Emission ◽  
Line Emission ◽  
White Light Emission ◽  
Seismic Sources ◽  
X Ray ◽  
Magnetic Flux Ropes ◽  
Flux Ropes

Aims. The 6 September 2017 X9.3 solar flare produced very unique observations of magnetic field transients and a few seismic responses, or sunquakes, detected by the Helioseismic and Magnetic Imager (HMI) instrument aboard Solar Dynamic Observatory (SDO) spacecraft, including the strongest sunquake ever reported. This flare was one of a few flares occurring within a few days or hours in the same active region. Despite numerous reports of the fast variations of magnetic field, and seismic and white light emission, no attempts were made to interpret the flare features using multi-wavelength observations. In this study, we attempt to produce the summary of available observations of the most powerful flare of the 6 September 2017 obtained using instruments with different spatial resolutions (this paper) and to provide possible interpretation of the flaring events, which occurred in the locations of some seismic sources (a companion Paper II). Methods. We employed non-linear force-free field extrapolations followed by magnetohydrodynamic simulations in order to identify the presence of several magnetic flux ropes prior to the initiation of this X9.3 flare. Sunquakes were observed using the directional holography and time–distance diagram detection techniques. The high-resolution method to detect the Hα line kernels in the CRISP instrument at the diffraction level limit was also applied. Results. We explore the available γ-ray (GR), hard X-ray (HXR), Lyman-α, and extreme ultra-violet (EUV) emission for this flare comprising two flaring events observed by space- and ground-based instruments with different spatial resolutions. For each flaring event we detect a few seismic sources, or sunquakes, using Dopplergrams from the HMI/SDO instrument coinciding with the kernels of Hα line emission with strong redshifts and white light sources. The properties of sunquakes were explored simultaneously with the observations of HXR (with KONUS/WIND and the Reuven Ramaty High Energy Solar Spectroscopic Imager payload), EUV (with the Atmospheric Imaging Assembly (AIA/SDO and the EUV Imaging Spectrometer aboard Hinode payload), Hα line emission (with the CRisp Imaging Spectro-Polarimeter (CRISP) in the Swedish Solar Telescope), and white light emission (with HMI/SDO). The locations of sunquake and Hα kernels are associated with the footpoints of magnetic flux ropes formed immediately before the X9.3 flare onset. Conclusions. For the first time we present the detection of the largest sunquake ever recorded with the first and second bounces of acoustic waves generated in the solar interior, the ripples of which appear at a short distance of 5–8 Mm from the initial flare location. Four other sunquakes were also detected, one of which is likely to have occurred 10 min later in the same location as the largest sunquake. Possible parameters of flaring atmospheres in the locations with sunquakes are discussed using available temporal and spatial coverage of hard X-ray, GR, EUV, hydrogen Hα-line, and white light emission in preparation for their use in an interpretation to be given in Paper II.

Transient magnetic field formulation for solid source conductors

2020 ◽  
Vol 64 (1-4) ◽  
pp. 1539-1545
Author(s):  
Georg Wimmer ◽  
Sebastian Lange
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Numerical Scheme ◽  
Eddy Currents ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Time Step ◽  
Azimuthal Component ◽  
Transient Magnetic Fields

The formulation for the azimuthal component of the magnetic vector potential for axisymmetric magnetostatic applications is well known. However for transient magnetic fields with solid source conductors and eddy currents the formulation has to be revised. A variable transformation is introduced to remove the singularity from the numerical scheme. The numerical error cannot accumulate and is put instead to the postprocessing at every time step.

The evolution of magnetic flux ropes in sheared plasma flows

2000 ◽  
Vol 64 (1) ◽  
pp. 41-55 ◽  
Author(s):  
J. M. SCHMIDT ◽  
P. J. CARGILL
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Shear Layer ◽  
Cross Section ◽  
Circular Cross Section ◽  
Flux Rope ◽  
Plasma Pressure ◽  
Magnetic Flux Ropes ◽  
Flux Ropes ◽  
The Magnetic Field

The evolution of magnetic flux ropes in a sheared plasma flow is investigated. When the magnetic field outside the flux rope lies parallel to the axis of the flux rope, a flux rope of circular cross-section, whose centre is located at the midpoint of the shear layer, has its shape distorted, but remains in the shear layer. Small displacements of the flux-rope centre above or below the midpoint of the shear layer lead to the flux-rope being expelled from the shear layer. This motion arises because small asymmetries in the plasma pressure around the flux-rope boundary leads to a force that forces the flux rope into a region of uniform flow. When the magnetic field outside the flux rope lies in a plane perpendicular to the flux-rope axis, the flux rope and external magnetic field reconnect with each other, leading to the destruction of the flux rope.

scholarly journals Non-Gaussianity and cross-scale coupling in interplanetary magnetic field turbulence during a rope–rope magnetic reconnection event

2018 ◽  
Vol 36 (2) ◽  
pp. 497-507 ◽  
Author(s):  
Rodrigo A. Miranda ◽  
Adriane B. Schelin ◽  
Abraham C.-L. Chian ◽  
José L. Ferreira
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Magnetic Reconnection ◽  
Coherent Structures ◽  
Flux Rope ◽  
Inertial Subrange ◽  
Order Moment ◽  
Magnetic Flux Ropes ◽  
Flux Ropes ◽  
Non Gaussian

Abstract. In a recent paper (Chian et al., 2016) it was shown that magnetic reconnection at the interface region between two magnetic flux ropes is responsible for the genesis of interplanetary intermittent turbulence. The normalized third-order moment (skewness) and the normalized fourth-order moment (kurtosis) display a quadratic relation with a parabolic shape that is commonly observed in observational data from turbulence in fluids and plasmas, and is linked to non-Gaussian fluctuations due to coherent structures. In this paper we perform a detailed study of the relation between the skewness and the kurtosis of the modulus of the magnetic field |B| during a triple interplanetary magnetic flux rope event. In addition, we investigate the skewness–kurtosis relation of two-point differences of |B| for the same event. The parabolic relation displays scale dependence and is found to be enhanced during magnetic reconnection, rendering support for the generation of non-Gaussian coherent structures via rope–rope magnetic reconnection. Our results also indicate that a direct coupling between the scales of magnetic flux ropes and the scales within the inertial subrange occurs in the solar wind. Keywords. Space plasma physics (turbulence)

scholarly journals Vector Potential, Magnetic Field, Mutual Inductance, Magnetic Force, Torque and Stiffness Calculation between Current-Carrying Arc Segments with Inclined Axes in Air

2021 ◽  
Author(s):  
Slobodan Babic
Keyword(s):  
Magnetic Field ◽  
Numerical Integration ◽  
Vector Potential ◽  
Magnetic Force ◽  
Analytical Form ◽  
Mutual Inductance ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Special Cases ◽  
Incomplete Elliptic Integrals

In this paper we give the improved and new analytical and semi-analytical expression for calcu-lating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air. The expressions are ob-tained either in the analytical form over the incomplete elliptic integrals of the first and the sec-ond time or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the special cases when the inclined circular loops are treated. We mention that all formulas are obtain by the integral ap-proach except the stiffness which is found by the derivative of the magnetic force.

The Analysis of Pressure Capability of Different Teeth Structures in Ferrofluid Seal

2010 ◽  
Vol 146-147 ◽  
pp. 1278-1284 ◽  
Author(s):  
Fei Fei Xing ◽  
De Cai Li ◽  
Wen Ming Yang
Keyword(s):  
Magnetic Field ◽  
Finite Element Method ◽  
Finite Element ◽  
Theoretical Model ◽  
Vector Potential ◽  
Potential Method ◽  
Magnetic Vector Potential ◽  
Magnetic Vector ◽  
Two Sides ◽  
Sealing Gap

Theoretical model of calculating magnetic field of typical ferrofluid sealing structures with magnetic vector potential method is built. Based on the theoretical model, magnetic field distribution of rectangular teeth, two-sides dilated shape and one-side dilated shape teeth structures with common other conditions were calculated using finite element method when the sealing gap was 0.1mm and 0.12mm. The comparison of their results with the same sealing gap showed that one-side dilated shape teeth structure had higher pressure capability than other shape teeth under reasonable design.

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