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 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 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.

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 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.

scholarly journals Application of a helicity proxy to edge-on galaxies

2020 ◽  
Vol 496 (4) ◽  
pp. 4749-4759
Author(s):  
Axel Brandenburg ◽  
Ray S Furuya
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Numerical Results ◽  
Magnetic Helicity ◽  
The Galaxy ◽  
Rotationally Invariant ◽  
The Magnetic Field ◽  
Mean Field Dynamo

ABSTRACT We study the prospects of detecting magnetic helicity in galaxies by observing the dust polarization of the edge-on galaxy NGC 891. Our numerical results of mean-field dynamo calculations show that there should be a large-scale component of the rotationally invariant parity-odd B polarization that we predict to be negative in the first and third quadrants, and positive in the second and fourth quadrants. The large-scale parity-even E polarization is predicted to be negative near the axis and positive further away in the outskirts. These properties are shown to be mostly a consequence of the magnetic field being azimuthal and the polarized intensity being maximum at the centre of the galaxy and are not a signature of magnetic helicity.

scholarly journals On Magnetic Inhibition of Thermal Convection

1972 ◽  
Vol 25 (6) ◽  
pp. 703 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy ◽  
EA Spiegel
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Quantitative Estimates ◽  
Wide Range ◽  
The Face ◽  
The Mean ◽  
The Magnetic Field

The effect of an imposed vertical magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. Solutions are found over a wide range of conditions, for free boundaries, by a combination of numerical and analytic techniques. Quantitative estimates are made of the significant modifications to the heat transfer which are brought about by the presence of the magnetic field. It is found that the general properties of nonlinear steady cellular convection seem to persist in the face of magnetic inhibition.

scholarly journals General Relativistic Mean-Field Dynamo Model for Proto-Neutron Stars

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 83 ◽  
Author(s):  
Kevin Franceschetti ◽  
Luca Del Zanna
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Growth Rates ◽  
Exponential Growth ◽  
Mean Field ◽  
Dynamo Model ◽  
Time Interval ◽  
General Relativistic ◽  
The Magnetic Field ◽  
Mean Field Dynamo

Neutron stars, and magnetars in particular, are known to host the strongest magnetic fields in the Universe. The origin of these strong fields is a matter of controversy. In this preliminary work, via numerical simulations, we study, for the first time in non-ideal general relativistic magnetohydrodynamic (GRMHD) regime, the growth of the magnetic field due to the action of the mean-field dynamo due to sub-scale, unresolved turbulence. The dynamo process, combined with the differential rotation of the (proto-)star, is able to produce an exponential growth of any initial magnetic seed field up to the values required to explain the observations. By varying the dynamo coefficient we obtain different growth rates. We find a quasi-linear dependence of the growth rates on the intensity of the dynamo. Furthermore, the time interval in which exponential growth occurs and the growth rates also seems to depend on the initial configuration of the magnetic field.

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