The spectrum of random magnetic fields in the mean field dynamo theory of the Galactic magnetic field

1992 ◽  
Vol 396 ◽  
pp. 606 ◽  
Author(s):  
Russell M. Kulsrud ◽  
Stephen W. Anderson
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Mean Field ◽  
Galactic Magnetic Field ◽  
Dynamo Theory ◽  
The Mean ◽  
Mean Field Dynamo

scholarly journals A dynamo amplifying the magnetic field of a Milky-Way-like galaxy

2020 ◽  
Vol 641 ◽  
pp. A165
Author(s):  
Evangelia Ntormousi ◽  
Konstantinos Tassis ◽  
Fabio Del Sordo ◽  
Francesca Fragkoudi ◽  
Rüdiger Pakmor
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Spiral Galaxies ◽  
Mean Field ◽  
Dark Matter Halo ◽  
Random Component ◽  
Galactic Magnetic Field ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Field Dynamo

Context. The magnetic fields of spiral galaxies are so strong that they cannot qualify as primordial. Their typical values are over one billion times higher than any value predicted for the early Universe. Explaining this immense growth and incorporating it in galaxy evolution theories is one of the long-standing challenges in astrophysics. Aims. So far, the most successful theory for the sustained growth of the galactic magnetic field is the alpha-omega dynamo. This theory predicts a characteristic dipolar or quadrupolar morphology for the galactic magnetic field, which has been observed in external galaxies. So far, however, there has been no direct demonstration of a mean-field dynamo operating in direct, multi-physics simulations of spiral galaxies. We carry out such a demonstration in this work. Methods. We employed numerical models of isolated, star-forming spiral galaxies that include a magnetized gaseous disk, a dark matter halo, stars, and stellar feedback. Naturally, the resulting magnetic field has a complex morphology that includes a strong random component. Using a smoothing of the magnetic field on small scales, we were able to separate the mean from the turbulent component and analyze them individually. Results. We find that a mean-field dynamo naturally occurs as a result of the dynamical evolution of the galaxy and amplifies the magnetic field by an order of magnitude over half a Gyr. Despite the highly dynamical nature of these models, the morphology of the mean component of the field is identical to analytical predictions. Conclusions. This result underlines the importance of the mean-field dynamo in galactic evolution. Moreover, by demonstrating the natural growth of the magnetic field in a complex galactic environment, it brings us a step closer to understanding the cosmic origin of magnetic fields.

Existence and Energy Balance of the Solar Dynamo

1993 ◽  
Vol 157 ◽  
pp. 19-23
Author(s):  
J.H.G.M. van Geffen
Keyword(s):  
Magnetic Field ◽  
Energy Balance ◽  
Energy Method ◽  
Magnetic Energy ◽  
Mean Field ◽  
Solar Dynamo ◽  
Ensemble Averaging ◽  
Dynamo Theory ◽  
The Magnetic Field ◽  
Mean Field Dynamo

The idea behind the use of ensemble averaging and the finite magnetic energy method of van Geffen and Hoyng (1992) is briefly discussed. Applying this method to the solar dynamo shows that the turbulence — an essential ingredient of traditional mean field dynamo theory — poses grave problems: the turbulence makes the magnetic field so unstable that it becomes impossible to recognize any period.

scholarly journals On the mean-field theory of the Karlsruhe Dynamo Experiment

2002 ◽  
Vol 9 (3/4) ◽  
pp. 171-187 ◽  
Author(s):  
K.-H. Rädler ◽  
M. Rheinhardt ◽  
E. Apstein ◽  
H. Fuchs
Keyword(s):  
Field Theory ◽  
Key Words ◽  
Mean Field Theory ◽  
Mean Field ◽  
Experimental Results ◽  
Dynamo Theory ◽  
The Mean ◽  
Earth’S Interior ◽  
Earth's Interior ◽  
Mean Field Dynamo

Abstract. In the Forschungszentrum Karlsruhe an experiment has been constructed which demonstrates a homogeneous dynamo as is expected to exist in the Earth's interior. This experiment is discussed within the framework of mean-field dynamo theory. The main predictions of this theory are explained and compared with the experimental results. Key words. Dynamo, geodynamo, dynamo experiment, mean-field dynamo theory, a-effect

scholarly journals Asymptotic Methods in the Nonlinear Mean-field Dynamo

1991 ◽  
Vol 130 ◽  
pp. 135-139
Author(s):  
D.D. Sokoloff ◽  
A. Shukurov ◽  
A.A. Ruzmaikin
Keyword(s):  
Magnetic Field ◽  
Spatial Distribution ◽  
Steady State ◽  
Main Part ◽  
Asymptotic Methods ◽  
Mean Field ◽  
Coriolis Forces ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Field Dynamo

AbstractWe discuss the methods and results of analysis of nonlinear mean-field dynamo models based on α-quenching in two asymptotic regimes, namely for weakly and highly supercritical excitation. In the former case the spatial distribution of the steady-state magnetic field is close to that given by the neutrally stable eigenfunction of the corresponding kinematic dynamo. In the latter case the magnetic field distribution within the main part of the dynamo volume is presumably determined by the balance between the Lorentz and Coriolis forces while near the boundaries boundary layers arise in which the field adjusts itself to the boundary conditions. The asymptotic behaviour of the highly supercritical αω-dynamos is sensitive to the particular form of dependence of the mean helicity on magnetic field while α2-dynamos are less sensitive to this dependence.

scholarly journals The Solar Dynamo

1990 ◽  
Vol 121 ◽  
pp. 385-402 ◽  
Author(s):  
K.-H. Rädler
Keyword(s):  
Magnetic Field ◽  
Differential Rotation ◽  
Mean Field ◽  
Solar Dynamo ◽  
Back Reaction ◽  
Dynamo Theory ◽  
Open Questions ◽  
Convective Motions ◽  
The Mean ◽  
Basic Ideas

AbstractThe phenomena of solar activity are connected with a general magnetic field of-the Sun which is due to a dynamo process essentially determined by the α-effect and the differential rotation in the convection zone. A few observational facts are summarized which are important for modelling this process. The basic ideas of the solar dynamo theory, with emphasis on the mean-field approach, are explained, and a critical review of the dynamo models investigated so far is given. Although several models reflect a number of essential features of the solar magnetic cycle there are many open questions. Part of them result from lack of knowledge of the structure of the convective motions and the differential rotation. Other questions concern, for example, details of the connection of the α-effect and related effects with the convective motions, or the way in which the behaviour of the dynamo is influenced by the back-reaction of the magnetic field on the motions.

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.

scholarly journals Turbulent transport coefficients in galactic dynamo simulations using singular value decomposition

2019 ◽  
Vol 491 (3) ◽  
pp. 3870-3883 ◽  
Author(s):  
Abhijit B Bendre ◽  
Kandaswamy Subramanian ◽  
Detlef Elstner ◽  
Oliver Gressel
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Turbulent Transport ◽  
Transport Coefficients ◽  
Mean Field ◽  
Dynamo Model ◽  
The Mean ◽  
Value Decomposition ◽  
Svd Method ◽  
Mean Field Dynamo

ABSTRACT Coherent magnetic fields in disc galaxies are thought to be generated by a large-scale (or mean-field) dynamo operating in their interstellar medium. A key driver of mean magnetic field growth is the turbulent electromotive force (EMF), which represents the influence of correlated small-scale (or fluctuating) velocity and magnetic fields on the mean field. The EMF is usually expressed as a linear expansion in the mean magnetic field and its derivatives, with the dynamo tensors as expansion coefficients. Here, we adopt the singular value decomposition (SVD) method to directly measure these turbulent transport coefficients in a simulation of the turbulent interstellar medium that realizes a large-scale dynamo. Specifically, the SVD is used to least-square fit the time series data of the EMF with that of the mean field and its derivatives, to determine these coefficients. We demonstrate that the spatial profiles of the EMF reconstructed from the SVD coefficients match well with that taken directly from the simulation. Also, as a direct test, we use the coefficients to simulate a 1D mean-field dynamo model and find an overall similarity in the evolution of the mean magnetic field between the dynamo model and the direct simulation. We also compare the results with those which arise using simple regression and the ones obtained previously using the test-field method, to find reasonable qualitative agreement. Overall, the SVD method provides an effective post-processing tool to determine turbulent transport coefficients from simulations.

scholarly journals Are GRMHD Mean-Field Dynamo Models of Thick Accretion Disks SANE?

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 259
Author(s):  
Niccolò Tomei ◽  
Luca Del Zanna ◽  
Matteo Bugli ◽  
Niccolò Bucciantini
Keyword(s):  
Magnetic Field ◽  
Accretion Disks ◽  
Mean Field ◽  
Dynamical Process ◽  
Magnetorotational Instability ◽  
Polarization Studies ◽  
The Mean ◽  
Sgr A ◽  
Mean Field Dynamo ◽  
Dynamo Process

The remarkable results by the Event Horizon Telescope collaboration concerning the emission from M87* and, more recently, its polarization properties, require an increasingly accurate modeling of the plasma flows around the accreting black hole. Radiatively inefficient sources such as M87* and Sgr A* are typically modeled with the SANE (standard and normal evolution) paradigm, if the accretion dynamics is smooth, or with the MAD (magnetically arrested disk) paradigm, if the black hole’s magnetosphere reacts by halting the accretion sporadically, resulting in a highly dynamical process. While the recent polarization studies seem to favor MAD models, this may not be true for all sources, and SANE accretion surely still deserves attention. In this work, we investigate the possibility of reaching the typical degree of magnetization and other accretion properties expected for SANE disks by resorting to the mean-field dynamo process in axisymmetric GRMHD simulations, which are supposed to mimic the amplifying action of an unresolved magnetorotational instability-driven turbulence. We show that it is possible to reproduce the main diagnostics present in the literature by starting from very unfavorable initial configurations, such as a purely toroidal magnetic field with negligible magnetization.

scholarly journals The Alpha-Effect in Galaxies is Highly Anisotropic

1990 ◽  
Vol 140 ◽  
pp. 113-114
Author(s):  
G. Rüdiger
Keyword(s):  
Large Scale ◽  
Rotation Axis ◽  
Mean Field ◽  
Dynamo Model ◽  
Mean Flow ◽  
Dynamo Theory ◽  
Input Quantity ◽  
Alpha Effect ◽  
The Mean ◽  
Mean Field Dynamo

Besides the mean flow the alpha is the other input quantity for any mean-field dynamo model. It describes the generation of turbulent electromotive force <u × B> from a large-scale field <B> for a given turbulence. The necessary helicity of the turbulence results from the joint action of Coriolis force and density stratification. The standard estimate of 1 km/s for alpha in galaxies is a surely well-established approximation. One of the essentials, however, remains open. Due to the extremely anisotropic structure of disks the tensorial character of alpha can no longer be ignored. In stellar applications anisotropy in the α-tensor leads to a preferred excitation of non-axisymmetric magnetic fields. That is true for α2 -dynamos if the alpha parallel to the rotation axis, α||, is much smaller than that in the equatorial plane, α⊥. The idea is that also for disk-like configurations a similar behaviour makes the existence of the observed large-scale non-axisymmetric magnetic BSS modes understandable within the frame of the mean-field dynamo theory.

scholarly journals Simulations of astrophysical dynamos

2010 ◽  
Vol 6 (S274) ◽  
pp. 402-409
Author(s):  
Axel Brandenburg
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Mean Field ◽  
Integral Kernel ◽  
Turnover Time ◽  
Dynamo Theory ◽  
Magnetic Prandtl Number ◽  
Artificial Diffusion ◽  
The Magnetic Field ◽  
Mean Field Dynamo

AbstractNumerical aspects of dynamos in periodic domains are discussed. Modifications of the solutions by numerically motivated alterations of the equations are being reviewed using the examples of magnetic hyperdiffusion and artificial diffusion when advancing the magnetic field in its Euler potential representation. The importance of using integral kernel formulations in mean-field dynamo theory is emphasized in cases where the dynamo growth rate becomes comparable with the inverse turnover time. Finally, the significance of microscopic magnetic Prandtl number in controlling the conversion from kinetic to magnetic energy is highlighted.

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