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.

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 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 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.

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.

scholarly journals Path integrals for mean-field equations in nonlinear dynamos

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
Dmitry Sokoloff ◽  
Nobumitsu Yokoi
Keyword(s):  
Magnetic Field ◽  
Path Integrals ◽  
Mean Field ◽  
Three Dimensional ◽  
Field Equations ◽  
Mean Field Equations ◽  
The Mean ◽  
Path Integral Method ◽  
The Magnetic Field ◽  
Mean Field Dynamo

Mean-field dynamo equations are addressed with the aid of the path integral method. The evolution of magnetic field is treated as a three-dimensional Wiener random process, and the mean magnetic-field equations are obtained with the Wiener integrals taken over all the trajectories of the fluid particles. The form of the equations is just the same as the conventional mean-field equations, but here the equations are derived with the velocity field realisation affected by the force exerted by the magnetic field. In this sense, we derive nonlinear dynamo equations.

scholarly journals Modelling of the Magnetic Configuration of CP Stars from Polarimetric Observations

1998 ◽  
Vol 11 (2) ◽  
pp. 679-681
Author(s):  
M. Landolfi
Keyword(s):  
Magnetic Field ◽  
Stokes Parameter ◽  
Quadratic Field ◽  
Mean Field ◽  
Longitudinal Component ◽  
Stokes Parameters ◽  
Longitudinal Field ◽  
The Mean ◽  
The Magnetic Field ◽  
Polarized Radiation

The observational quantities commonly used to study the magnetic field of CP stars – the mean field modulus and the mean longitudinal field, as well as the ‘mean asymmetry of the longitudinal field’ and the ‘mean quadratic field’ recently introduced by Mathys (1995a,b) – are based either on the Stokes parameter / or on the Stokes parameter V. However, a complete description of polarized radiation requires the knowledge of the full Stokes vector: in other words, we should expect that useful information is also contained in linear polarization (the Stokes parameters Q and U); or rather we should expect the information contained in (Q, U) and in V to be complementary, since linear and circular polarization are basically related to the transverse and the longitudinal component of the magnetic field, respectively.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

scholarly journals Effect of fluctuations on mean-field dynamos

2018 ◽  
Vol 84 (4) ◽  
Author(s):  
A. Alexakis ◽  
S. Fauve ◽  
C. Gissinger ◽  
F. Pétrélis
Keyword(s):  
Turbulent Flows ◽  
Mean Field ◽  
Liquid Sodium ◽  
Mean Flow ◽  
Dynamo Action ◽  
Scale Separation ◽  
Turbulent Fluctuations ◽  
The Mean ◽  
The One ◽  
The Magnetic Field

We discuss the effect of different types of fluctuations on dynamos generated in the limit of scale separation. We first recall that the magnetic field observed in the VKS (von Karman flow of liquid sodium) experiment is not the one that would be generated by the mean flow alone and that smaller scale turbulent fluctuations therefore play an important role. We then consider how velocity fluctuations affect the dynamo threshold in the framework of mean-field magnetohydrodynamics. We show that the detrimental effect of turbulent fluctuations observed with many flows disappears in the case of helical flows with scale separation. We also find that fluctuations of the electrical conductivity of the fluid, for instance related to temperature fluctuations in convective flows, provide an efficient mechanism for dynamo action. Finally, we conclude by describing an experimental configuration that could be used to test the validity of mean-field magnetohydrodynamics in strongly turbulent flows.

scholarly journals The geometry of the magnetic field in the central molecular zone measured by PILOT

2019 ◽  
Vol 630 ◽  
pp. A74 ◽  
Author(s):  
A. Mangilli ◽  
J. Aumont ◽  
J.-Ph. Bernard ◽  
A. Buzzelli ◽  
G. de Gasperis ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Molecular Clouds ◽  
Angular Resolution ◽  
Galactic Center ◽  
Galactic Plane ◽  
Mean Field ◽  
Field Orientation ◽  
Center Region ◽  
The Mean ◽  
The Magnetic Field

We present the first far infrared (FIR) dust emission polarization map covering the full extent of Milky Way’s central molecular zone (CMZ). The data, obtained with the PILOT balloon-borne experiment, covers the Galactic center region − 2° < ℓ < 2°, − 4° < b < 3° at a wavelength of 240 μm and an angular resolution of 2.2′. From our measured dust polarization angles, we infer a magnetic field orientation projected onto the plane of the sky (POS) that is remarkably ordered over the full extent of the CMZ, with an average tilt angle of ≃22° clockwise with respect to the Galactic plane. Our results confirm previous claims that the field traced by dust polarized emission is oriented nearly orthogonally to the field traced by GHz radio synchrotron emission in the Galactic center region. The observed field structure is globally compatible with the latest Planck polarization data at 353 and 217 GHz. Upon subtraction of the extended emission in our data, the mean field orientation that we obtain shows good agreement with the mean field orientation measured at higher angular resolution by the JCMT within the 20 and 50 km s−1 molecular clouds. We find no evidence that the magnetic field orientation is related to the 100 pc twisted ring structure within the CMZ. The low polarization fraction in the Galactic center region measured with Planck at 353 GHz combined with a highly ordered projected field orientation is unusual. This feature actually extends to the whole inner Galactic plane. We propose that it could be caused by the increased number of turbulent cells for the long lines of sight towards the inner Galactic plane or to dust properties specific to the inner regions of the Galaxy. Assuming equipartition between magnetic pressure and ram pressure, we obtain magnetic field strength estimates of the order of 1 mG for several CMZ molecular clouds.

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