scholarly journals Kinematic dynamos in triaxial ellipsoids

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210252
Author(s):  
Jérémie Vidal ◽  
David Cébron
Keyword(s):  
Magnetic Fields ◽  
Boundary Conditions ◽  
Reynolds Numbers ◽  
Dynamo Action ◽  
Local Boundary ◽  
Electrically Conducting ◽  
Free Decay ◽  
Planetary Magnetic Fields ◽  
Induction Equation ◽  
The Magnetic Field

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo problem for prescribed flows. The new method is thoroughly compared with analytical solutions and standard finite-element computations, which are also used to model an insulating exterior. We obtain dynamo magnetic fields at low magnetic Reynolds numbers in ellipsoids, which could be used as simple benchmarks for future dynamo studies in such geometries. We finally discuss how the magnetic boundary conditions can modify the dynamo onset, showing that a perfectly conducting boundary can strongly weaken dynamo action, whereas pseudo-vacuum and insulating boundaries often give similar results.

scholarly journals Magneto-convection

2012 ◽  
Vol 370 (1970) ◽  
pp. 3070-3087 ◽  
Author(s):  
Robert F. Stein
Keyword(s):  
Magnetic Fields ◽  
Equations Of State ◽  
Three Dimensional ◽  
Dynamo Action ◽  
Spatial And Temporal Scales ◽  
Solar Observations ◽  
Wide Range ◽  
Induction Equation ◽  
The Magnetic Field ◽  
Three Dimensional Simulations

Convection is the transport of energy by bulk mass motions. Magnetic fields alter convection via the Lorentz force, while convection moves the fields via the curl( v × B ) term in the induction equation. Recent ground-based and satellite telescopes have increased our knowledge of the solar magnetic fields on a wide range of spatial and temporal scales. Magneto-convection modelling has also greatly improved recently as computers become more powerful. Three-dimensional simulations with radiative transfer and non-ideal equations of state are being performed. Flux emergence from the convection zone through the visible surface (and into the chromosphere and corona) has been modelled. Local, convectively driven dynamo action has been studied. The alteration in the appearance of granules and the formation of pores and sunspots has been investigated. Magneto-convection calculations have improved our ability to interpret solar observations, especially the inversion of Stokes spectra to obtain the magnetic field and the use of helioseismology to determine the subsurface structure of the Sun.

scholarly journals Decaying turbulence and magnetic fields in galaxy clusters

2019 ◽  
Vol 488 (3) ◽  
pp. 3439-3445 ◽  
Author(s):  
Sharanya Sur
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Galaxy Clusters ◽  
Power Law ◽  
Dynamo Action ◽  
Wide Range ◽  
Major Merger ◽  
Decaying Turbulence ◽  
Field Decay ◽  
The Magnetic Field

Abstract We explore the decay of turbulence and magnetic fields generated by fluctuation dynamo action in the context of galaxy clusters where such a decaying phase can occur in the aftermath of a major merger event. Using idealized numerical simulations that start from a kinetically dominated regime we focus on the decay of the steady state rms velocity and the magnetic field for a wide range of conditions that include varying the compressibility of the flow, the forcing wavenumber, and the magnetic Prandtl number. Irrespective of the compressibility of the flow, both the rms velocity and the rms magnetic field decay as a power law in time. In the subsonic case we find that the exponent of the power law is consistent with the −3/5 scaling reported in previous studies. However, in the transonic regime both the rms velocity and the magnetic field initially undergo rapid decay with an ≈t−1.1 scaling with time. This is followed by a phase of slow decay where the decay of the rms velocity exhibits an ≈−3/5 scaling in time, while the rms magnetic field scales as ≈−5/7. Furthermore, analysis of the Faraday rotation measure (RM) reveals that the Faraday RM also decays as a power law in time ≈t−5/7; steeper than the ∼t−2/5 scaling obtained in previous simulations of magnetic field decay in subsonic turbulence. Apart from galaxy clusters, our work can have potential implications in the study of magnetic fields in elliptical galaxies.

scholarly journals Enhancement of Galactic Dynamos by Density Waves

1990 ◽  
Vol 140 ◽  
pp. 127-130 ◽  
Author(s):  
Makoto Tosa ◽  
Masashi Chiba
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Density Wave ◽  
Wave Perturbation ◽  
Density Waves ◽  
Dynamo Action ◽  
Galactic Dynamos ◽  
The Magnetic Field ◽  
Effects Of Density

We examine effects of density waves on the local galactic αω-dynamo. Oscillations of the magnetic field and the dynamo parameters due to the density wave perturbation irreversibly couple with the dynamo action to enhance the growth of the magnetic fields.

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.

A mapping method for solving dynamo equations

1995 ◽  
Vol 448 (1932) ◽  
pp. 1-28 ◽  
Keyword(s):  
Magnetic Field ◽  
Decay Rate ◽  
Mapping Method ◽  
Three Dimensions ◽  
New Method ◽  
Dynamo Model ◽  
Dynamo Action ◽  
Electrically Conducting ◽  
Induction Equation ◽  
Conducting Fluids

A new method is presented for integration of the equations of magnetohydrody­namics in rapidly rotating, electrically conducting fluids, and in particular for studying dynamo action in such systems. Tests of the method are reported. The decay rate of magnetic field in a stationary sphere are recovered, as are the results of a number of α 2 - and αω -dynamos. These are solutions of the electrodynamic (induction) equation. An intermediate dynamo model, in which the dynamics are also partly allowed for, is also studied. This is due to Braginsky ( Geomag. Aero­naut . 18, 225 (1978)) and is of ‘model- Z type’. All models considered here are axisymmetric, but the possibility of generalization to three-dimensions is allowed for.

scholarly journals Structure of magnetic fields in spiral galaxies

2008 ◽  
Vol 4 (S259) ◽  
pp. 551-552
Author(s):  
Hanna Kotarba ◽  
H. Lesch ◽  
K. Dolag ◽  
T. Naab ◽  
P. H. Johansson ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Homogeneous Field ◽  
Field Equations ◽  
The Galaxy ◽  
Induction Equation ◽  
Tight Connection ◽  
Field Lines ◽  
The Magnetic Field ◽  
Direct Implementation

AbstractWe present a set of global, self-consistentN-body/SPH simulations of the dynamic evolution of galactic discs with gas and including magnetic fields. We have implemented a description to follow the ideal induction equation in the SPH part of the codeVine. Results from a direct implementation of the field equations are compared to a representation by Euler potentials, which pose a ∇ ċB-free description, a constraint not fulfilled for the direct implementation. All simulations are compared to an implementation of magnetic fields in the codeGadget. Starting with a homogeneous field we find a tight connection of the magnetic field structure to the density pattern of the galaxy in our simulations, with the magnetic field lines being aligned with the developing spiral pattern of the gas. Our simulations clearly show the importance of non-axisymmetry of the dynamic pattern for the evolution of the magnetic field.

Erklärung stellarer und planetarer Magnetfelder durch einen turbulenzbedingten Dynamomechanismus

1966 ◽  
Vol 21 (8) ◽  
pp. 1285-1296 ◽  
Author(s):  
M. Steenbeck ◽  
F. Krause
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Magnetic Fields ◽  
Cross Product ◽  
Skin Depth ◽  
Electrically Conducting ◽  
Magnetic Stars ◽  
The Magnetic Field ◽  
Component Parallel ◽  
Good Agreement

In a foregoing paper 1 the effects of a turbulent motion on magnetic fields were investigated. Especially turbulence was treated under the influence of CORIOLiS-forces and gradients of density and/or turbulence intensity. It was shown that on these conditions the average cross-product of velocity and magnetic field has a non-vanishing component parallel to the average magnetic field. Here we give the consequences of this effect for rotating, electrically conducting spheres.At first a sphere rotating with constant angular velocity is investigated. The quadratic effect provides for dynamo maintainance of the magnetic fields. A field of dipol-type has the weakest condition for maintainance. Applications to the magnetic field of the earth show a good agreement with the conceptions of the physical state of the earth’s core.For a second model differential rotation is included. We have also dynamo maintainance. Since we have to assume that generally the angular velocity is a function decreasing with the distance from the centre of the sphere, the calculations show that we have a preferred self-excited build-up of a quadrupol-type field. This model may be applicable to magnetic stars.Finally we look for dynamo maintainance of alternating fields. We consider the skin-depth to be small compared with the radius of the sphere, then we have plane geometry. The existence of periodical solutions is proved. Applications to the general magnetic field of the sun, which has a period of 22 years, are discussed.

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.

Magnetohydrodynamics: Overview

2020 ◽  
Author(s):  
E.R. Priest
Keyword(s):  
Magnetic Fields ◽  
Magnetic Energy ◽  
Liquid Metals ◽  
Plasma Heating ◽  
The Sun ◽  
Pressure Gradients ◽  
Dynamo Action ◽  
Electrically Conducting ◽  
Stellar Flares ◽  
Outer Atmosphere

Magnetohydrodynamics is sometimes called magneto-fluid dynamics or hydromagnetics and is referred to as MHD for short. It is the unification of two fields that were completely independent in the 19th, and first half of the 20th, century, namely, electromagnetism and fluid mechanics. It describes the subtle and complex nonlinear interaction between magnetic fields and electrically conducting fluids, which include liquid metals as well as the ionized gases or plasmas that comprise most of the universe. In places such as the Earth’s magnetosphere or the Sun’s outer atmosphere (the corona) where the magnetic field provides an important component of the free energy, MHD effects are responsible for much of the observed dynamic behavior, such as geomagnetic substorms, solar flares and huge eruptions from the Sun that dominate the Earth’s space weather. However, MHD is also of great importance in astrophysics, since many of the MHD processes that are observed in the laboratory or in the Sun and the magnetosphere also take place under different parameter regimes in more exotic cosmical objects such as active stars, accretion discs, and black holes. The different aspects of MHD include determining the nature of: magnetic equilibria under a balance between magnetic forces, pressure gradients and gravity; MHD wave motions; magnetic instabilities; and the important process of magnetic reconnection for converting magnetic energy into other forms. In turn, these aspects play key roles in the fundamental astrophysical processes of magnetoconvection, magnetic flux emergence, star spots, plasma heating, stellar wind acceleration, stellar flares and eruptions, and the generation of magnetic fields by dynamo action.

scholarly journals The nature of mean-field generation in three classes of optimal dynamos

2020 ◽  
Vol 86 (1) ◽  
Author(s):  
Axel Brandenburg ◽  
Long Chen
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Boundary Conditions ◽  
Magnetic Energy ◽  
Mean Field ◽  
Dynamo Action ◽  
Magnetic Diffusivity ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Field Dynamo

In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behaviour is different from that of an $\unicode[STIX]{x1D6FC}^{2}$ dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time dependent. The growing mean field can be modelled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23–45), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15 % supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests that negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.

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