Influence of the Hall effect on the mean field dynamo
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The magnetic field dynamo is a mechanism which occurs in several different environments, such as the interior of stars, accretion disks or the interstellar medium. Because of this diversity, the equations which describe its behavior should incorporate the peculiarities of such different regions. For example, particles in low ionized and strongly magnetized objects, such as protostellar accretion disks, should be subject to the Hall effect, which modifies the Ohm’s law. In this work, we study how the Hall effect alters the equations that govern the turbulent mean field dynamo. We derive the equations for the e.m.f, cross helicity and for the small and large scale magnetic helicities. We consider a two scale model in which turbulent is induced in a scale lS and the magnetic field is generated at a larger scale lL and the Hall effect is relevant in a intermediate scale lH. We obtain that even in the presence of Hall effect the mechanism responsible for the dynamo action is still the inverse cascade of magnetic helicity. As in previous results without the Hall term, the numerical solutions with Hall effect show an oscillatory behavior. However, the amplitude of the oscillations is smaller and the e.m.f. is damped earlier. This result confirms previous numerical simulations. We conclude that Hall dynamo theory should be taken into account in order to correctly describe the evolution of the magnetic field in low in low ionized media.Keywords:
Solar dynamo
Magnetic helicity
Helicity
A magnetic field that is maintained by the dynamo action of a conducting fluid must have a nonvanishing magnetic helicity. The constraint of helicity preservation implies that a dynamo is more easily produced if the electric potential varies in the surface of the dynamo. For the Earth the north–south potential variation should be of the order of a hundred volts. The energetics and thermodynamic efficiency of a heat-driven dynamo are also considered.
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Abstract We give a short introduction to the subject and review advances in understanding the basic ingredients of the mean-field dynamo theory. The discussion includes the recent analytic and numerical work in developments for the mean electromotive force of the turbulent flows and magnetic field, the nonlinear effects of the magnetic helicity, the non-local generation effects in the dynamo. We give an example of the mean-field solar dynamo model that incorporates the fairly complete expressions for the mean-electromotive force, the subsurface shear layer and the conservation of the total helicity. The model is used to shed light on the issues in the solar dynamo and on the future development of this field of research.
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Solar dynamo
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Mean field theory
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We study a simple model for the solar dynamo in the framework of the Parker migratory dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We find a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic alpha-quenching. We compare the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. On one hand, our simulated data demonstrate behaviour comparable with the observed phenomenology, provided that a suitable set of governing dynamo parameters is chosen. On the other hand, the observational data are shown to be rich enough to reject some other sets of governing parameters. We conclude that, in spite of the very preliminary state of the observations and the crude nature of the model, the idea of using observational data to constrain our ideas concerning magnetic field generation in the framework of the solar dynamo appears promising.
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Magnetic helicity
Helicity
Solar dynamo
Saturation (graph theory)
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It is believed that magnetic helicity conservation is an important constraint on large-scale astrophysical dynamos. In this paper, we study a mean-field solar dynamo model that employs two different formulations of the magnetic helicity conservation. In the first approach, the evolution of the averaged small-scale magnetic helicity is largely determined by the local induction effects due to the large-scale magnetic field, turbulent motions, and the turbulent diffusive loss of helicity. In this case, the dynamo model shows that the typical strength of the large-scale magnetic field generated by the dynamo is much smaller than the equipartition value for the magnetic Reynolds number 106. This is the so-called catastrophic quenching (CQ) phenomenon. In the literature, this is considered to be typical for various kinds of solar dynamo models, including the distributed-type and the Babcock–Leighton-type dynamos. The problem can be resolved by the second formulation, which is derived from the integral conservation of the total magnetic helicity. In this case, the dynamo model shows that magnetic helicity propagates with the dynamo wave from the bottom of the convection zone to the surface. This prevents CQ because of the local balance between the large-scale and small-scale magnetic helicities. Thus, the solar dynamo can operate in a wide range of magnetic Reynolds numbers up to 106.
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Mercury's magnetic field
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Many astrophysical bodies possess magnetic fields. The Earth has one, the geomagnetic field, and it is apparently as old as the Earth. Since the temperature throughout most of the Earth is above the Curie points of all known materials, the Earth is not a permanent magnet. The geomagnetic field must be produced by electric currents flowing mainly within its core, which is a good electrical conductor. Lacking sources, such currents would die out in about 10,000 years. It is now believed that the currents are maintained by electromagnetic induction, as in a commercial dynamo, the moving parts of the geodynamo being motions in the outer core, which is fluid. The first question in dynamo theory is whether self-excitation is possible in a body having such a low degree of symmetry as the Earth's core. This well-studied "kinematic dynamo problem" defines a nontrivial non-self adjoint eigenvalue problem, which will be discussed after the basic electrodynamic theory has been summarized. The second question is whether motions of sufficient vigor, and which have the "helicity" required for field generation, would arise naturally in the Earth's outer core. This nonlinear "magnetohydrodynamic dynamo problem" raises some interesting questions in rotating magnetoconvection. The third question is whether the required energy source is available to power the dynamo. For bodies such as the solar convection zone, energy is available in abundance, but the geodynamo's needs are less easily met. Other topics will be touched on, including fast dynamos, auto-reversing dynamos, and chaotic dynamos.
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Ionospheric dynamo region
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The role of magnetic helicity in astrophysical large-scale dynamos is reviewed and compared with cases where there is no energy supply and an initial magnetic field can only decay. In both cases magnetic energy tends to get redistributed to larger scales. Depending on the efficiency of magnetic helicity fluxes the decay of a helical field can speed up. Likewise, the saturation of a helical dynamo can speed up through magnetic helicity fluxes. The astrophysical importance of these processes is reviewed in the context of the solar dynamo and an estimated upper limit for the magnetic helicity flux of 1046 Mx2/cycle is given.
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Saturation (graph theory)
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Helicity
Magnetic helicity
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Solar dynamo
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Helicity
Magnetic helicity
Solar dynamo
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We study a simple model for the solar dynamo in the framework of the Parker dynamo, with a nonlinear dynamo saturation mechanism based on magnetic helicity conservation arguments. We find a parameter range in which the model demonstrates a cyclic behaviour with properties similar to that of Parker dynamo with the simplest form of algebraic -quenching. We compare the nonlinear current helicity evolution in this model with data for the current helicity evolution obtained during 10 years of observations at the Huairou Solar Station of China. We conclude that, in spite of the very preliminary state of the observations and the crude nature of the model, the idea of using observational data to constrain our ideas concerning magnetic field generation in the framework of the solar dynamo appears promising.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html
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Helicity
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