Transient magnetic energy growth in spherical stationary flows

2006 ◽  
Vol 462 (2072) ◽  
pp. 2457-2479 ◽  
Author(s):  
Philip W Livermore ◽  
Andrew Jackson
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Transient Effects ◽  
Physical Mechanisms ◽  
Stationary Flows ◽  
Induction Equation ◽  
Small Flow ◽  
Energy Amplification ◽  
The Magnetic Field

The non-normality associated with the induction equation may lead to subcritical growth of magnetic field structures even if all linear eigenmodes decay. We compute the magnitude of these transient effects for a collection of predominantly axisymmetric stationary spherical flows and find without exception the dominance of axisymmetric field growth above all other symmetries. The transient growth is robust under small flow perturbations and can be understood by simple physical mechanisms: either field line shearing or stretching. Magnetic energy amplification of is possible at magnetic Reynolds numbers of , and such effects could therefore lead the system from a principally non-magnetic state into one where the magnetic field plays a significant role in the dynamics.

scholarly journals General relativistic magnetic perturbations and dynamo effects in extragalactic radiosources

2010 ◽  
Vol 6 (S274) ◽  
pp. 393-397
Author(s):  
L. C. Garcia de Andrade
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Magnetic Fluctuations ◽  
Dynamo Action ◽  
Magnetic Contrast ◽  
Mhd Dynamo ◽  
Curvature Energy ◽  
Induction Equation ◽  
The Universe ◽  
The Magnetic Field

AbstractBy making use of the MHD self-induction equation in general relativity (GR), recently derived by Clarkson and Marklund (2005), it is shown that when Friedmann universe possesses a spatial section whose Riemannian curvature is negative, the magnetic energy bounds computed by Nuñez (2002) also bounds the growth rate of the magnetic field given by the strain matrix of dynamo flow. Since in GR-MHD dynamo equation, the Ricci tensor couples with the universe magnetic field, only through diffusion, and most ages are highly conductive the interest is more theoretical here, and only very specific plasma astrophysical problems can be address such as in laboratory plasmas. Magnetic fields and the negative curvature of some isotropic cosmologies, contribute to enhence the amplification of the magnetic field. Ricci curvature energy is shown to add to strain matrix of the flow, to enhance dynamo action in the universe. Magnetic fluctuations of the Clarkson-Marklund equations for a constant magnetic field seed in highly conductive flat universes, leads to a magnetic contrast of ≈ 2, which is well within observational limits from extragalactic radiosources of ≈ 1.7. In the magnetic helicity fluctuations the magnetic contrast shows that the dynamo effects can be driven by these fluctuations.

scholarly journals Magnetic relaxation and the Taylor conjecture

2015 ◽  
Vol 81 (6) ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Initial Phase ◽  
Magnetic Relaxation ◽  
Magnetic Energy ◽  
Magnetic Pressure ◽  
Second Phase ◽  
One Dimensional ◽  
Induction Equation ◽  
Two Phases ◽  
The Magnetic Field

A one-dimensional model of magnetic relaxation in a pressureless low-resistivity plasma is considered. The initial two-component magnetic field $\boldsymbol{b}(\boldsymbol{x},t)$ is strongly helical, with non-uniform helicity density. The magnetic pressure gradient drives a velocity field that is dissipated by viscosity. Relaxation occurs in two phases. The first is a rapid initial phase in which the magnetic energy drops sharply and the magnetic pressure becomes approximately uniform; the helicity density is redistributed during this phase but remains non-uniform, and although the total helicity remains relatively constant, a Taylor state is not established. The second phase is one of slow diffusion, in which the velocity is weak, though still driven by persistent weak non-uniformity of magnetic pressure; during this phase, magnetic energy and helicity decay slowly and at constant ratio through the combined effects of pressure equalisation and finite resistivity. The density field, initially uniform, develops rapidly (in association with the magnetic field) during the initial phase, and continues to evolve, developing sharp maxima, throughout the diffusive stage. Finally it is proved that, if the resistivity is zero, the spatial mean $\langle (\boldsymbol{b}\boldsymbol{\cdot }\boldsymbol{{\rm\nabla}}\times \boldsymbol{b})/b^{2}\rangle$ is an invariant of the governing one-dimensional induction equation.

scholarly journals High Resolution Observations of the Solar Corona

1992 ◽  
Vol 9 ◽  
pp. 659-660
Author(s):  
D. Gomez ◽  
L. Golub
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Solar Corona ◽  
Magnetic Energy ◽  
Intimate Relationship ◽  
X Ray ◽  
Physical Mechanisms ◽  
Convective Motions ◽  
The Magnetic Field ◽  
Intense Source

Soft X-ray images of the solar corona obtained during the last 20 years have systematically shown an intimate relationship between intense emitting structures and magnetic fields (Vaiana and Rosner 1978). The magnetic field confines a 106 K plasma, which is an intense source of soft X-ray photons. Therefore, it is natural to expect the bright X-ray structures to follow the field’s geometry. But this relationship does not seem to be just geometrical. It is generally believed that the energy necessary to heat the plasma comes from the dissipation of magnetic stresses, which are continually being re-generated by subphotospheric convective motions. However, there is still great uncertainty about the precise physical mechanisms involved in the production and release of the magnetic energy.

CHOICE OF CONDITIONS FOR MHD SIMULATIONS ABOVE THE ACTIVE REGION, ALLOWING THE STUDY OF THE SOLAR FLARE MECHANISM

2021 ◽  
Vol 44 ◽  
pp. 92-95
Author(s):  
A.I. Podgorny ◽  
◽  
I.M. Podgorny ◽  
A.V. Borisenko ◽  
N.S. Meshalkina ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Active Region ◽  
Solar Flare ◽  
Magnetic Energy ◽  
Solar Radius ◽  
Computational Domain ◽  
Mhd Simulations ◽  
Flare Energy ◽  
Numerical Instabilities ◽  
The Magnetic Field

Primordial release of solar flare energy high in corona (at altitudes 1/40 - 1/20 of the solar radius) is explained by release of the magnetic energy of the current sheet. The observed manifestations of the flare are explained by the electrodynamical model of a solar flare proposed by I. M. Podgorny. To study the flare mechanism is necessary to perform MHD simulations above a real active region (AR). MHD simulation in the solar corona in the real scale of time can only be carried out thanks to parallel calculations using CUDA technology. Methods have been developed for stabilizing numerical instabilities that arise near the boundary of the computational domain. Methods are applicable for low viscosities in the main part of the domain, for which the flare energy is effectively accumulated near the singularities of the magnetic field. Singular lines of the magnetic field, near which the field can have a rather complex configuration, coincide or are located near the observed positions of the flare.

scholarly journals The development of magnetic field line wander by plasma turbulence

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Gregory G. Howes ◽  
Sofiane Bourouaine
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Large Scale ◽  
Magnetic Energy ◽  
Plasma Turbulence ◽  
Alfven Wave ◽  
Astrophysical Plasmas ◽  
Field Lines ◽  
The Magnetic Field

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

On the level surfaces of the magnetic field in a resistive plasma

2001 ◽  
Vol 65 (3) ◽  
pp. 161-170
Author(s):  
MANUEL NÚÑEZ
Keyword(s):  
Magnetic Field ◽  
Current Sheets ◽  
Resistive Plasma ◽  
Induction Equation ◽  
The Magnetic Field

An analysis of the induction equation shows that the level surfaces of the magnetic field in a resistive plasma satisfy a certain bound upon the time means of their areas. When this bound is applied to some configurations typical of chaotic plasmas, it is shown that the number of bidimensional sheets where the field reaches a extremum is bounded, whereas the number of extremal ropes or points need not be. This also applies to current sheets.

scholarly journals Теплообмен при смешанной конвекции расплава соли в присутствии магнитных полей

2019 ◽  
Vol 45 (10) ◽  
pp. 27
Author(s):  
И.А. Беляев ◽  
Д.А. Бирюков ◽  
А.В. Котляр ◽  
Е.А. Белавина ◽  
П.А. Сардов ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Temperature Fluctuations ◽  
Reynolds Numbers ◽  
Transverse Magnetic ◽  
Statistical Characteristics ◽  
Transfer Coefficients ◽  
Gravitational Flow ◽  
Heat Transfer Coefficients ◽  
The Magnetic Field

The results of an experimental study of the salt melt downflow in a uniformly heated pipe under the influence of a strong transverse magnetic field are presented. The changes of heat transfer coefficients and statistical characteristics of temperature fluctuations under the influence of the magnetic field are investigated. The peculiarities of the transition of the viscous-gravitational flow in the viscous-inertial-gravitational flow at Reynolds numbers (Re=3000-5000) under the influence of the magnetic field (Ha=17) were studied.

Kinematic dynamo problem in a linear velocity field

1984 ◽  
Vol 144 ◽  
pp. 1-11 ◽  
Author(s):  
Ya. B. Zel'Dovich ◽  
A. A. Ruzmaikin ◽  
S. A. Molchanov ◽  
D. D. Sokoloff
Keyword(s):  
Magnetic Field ◽  
Spatial Distribution ◽  
Velocity Field ◽  
Random Matrix ◽  
Magnetic Energy ◽  
Linear Velocity ◽  
Finite Conductivity ◽  
Kinematic Dynamo ◽  
Linear Velocity Field ◽  
The Magnetic Field

A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Fast magnetic field penetration into low resistivity plasma

2017 ◽  
Vol 83 (1) ◽  
Author(s):  
Amnon Fruchtman
Keyword(s):  
Magnetic Field ◽  
Energy Dissipation ◽  
Electric Field ◽  
Density Gradient ◽  
Magnetic Energy ◽  
Measured Velocity ◽  
Magnetic Field Penetration ◽  
The Magnetic Field ◽  
Uniform Plasma ◽  
Field Penetration

Penetration of a magnetic field into plasma that is faster than resistive diffusion can be induced by the Hall electric field in a non-uniform plasma. This mechanism explained successfully the measured velocity of the magnetic field penetration into pulsed plasmas. Major related issues have not yet been resolved. Such is the theoretically predicted, but so far not verified experimentally, high magnetic energy dissipation, as well as the correlation between the directions of the density gradient and of the field penetration.

scholarly journals Estimation of Electrical Conductivity and Magnetization Parameter of Neutron Star Crusts and Applied to the High-Braking-Index Pulsar PSR J1640-4631

Universe ◽  
2020 ◽  
Vol 6 (5) ◽  
pp. 63
Author(s):  
Hui Wang ◽  
Zhi-Fu Gao ◽  
Huan-Yu Jia ◽  
Na Wang ◽  
Xiang-Dong Li
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Neutron Stars ◽  
General Expression ◽  
Equations Of State ◽  
Rotation Period ◽  
Ohmic Dissipation ◽  
Hartree Fock ◽  
Induction Equation ◽  
The Magnetic Field

Young pulsars are thought to be highly magnetized neutron stars (NSs). The crustal magnetic field of a NS usually decays at different timescales in the forms of Hall drift and Ohmic dissipation. The magnetization parameter ω B τ is defined as the ratio of the Ohmic timescale τ O h m to the Hall drift timescale τ H a l l . During the first several million years, the inner temperature of the newly born neutron star cools from T = 10 9 K to T = 1.0 × 10 8 K, and the crustal conductivity increases by three orders of magnitude. In this work, we adopt a unified equations of state for cold non-accreting neutron stars with the Hartree–Fock–Bogoliubov method, developed by Pearson et al. (2018), and choose two fiducial dipole magnetic fields of B = 1.0 × 10 13 G and B = 1.0 × 10 14 G, four different temperatures, T, and two different impurity concentration parameters, Q, and then calculate the conductivity of the inner crust of NSs and give a general expression of magnetization parameter for young pulsars: ω B τ ≃ ( 1 − 50 ) B 0 / ( 10 13 G) by using numerical simulations. It was found when B ≤ 10 15 G, due to the quantum effects, the conductivity increases slightly with the increase in the magnetic field, the enhanced magnetic field has a small effect on the matter in the low-density regions of the crust, and almost has no influence the matter in the high-density regions. Then, we apply the general expression of the magnetization parameter to the high braking-index pulsar PSR J1640-4631. By combining the observed arrival time parameters of PSR J1640-4631 with the magnetic induction equation, we estimated the initial rotation period P 0 , the initial dipole magnetic field B 0 , the Ohm dissipation timescale τ O h m and Hall drift timescale τ H a l l . We model the magnetic field evolution and the braking-index evolution of the pulsar and compare the results with its observations. It is expected that the results of this paper can be applied to more young pulsars.

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