Hydromagnetic Dynamo Models
About: This article is published in The Astrophysical Journal.The article was published on 1955-09-01. It has received 1882 citations till now. The article focuses on the topics: Solar dynamo & Dynamo theory.
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TL;DR: The current understanding of astrophysical magnetic fields is reviewed in this paper, focusing on their generation and maintenance by turbulence, where analytical and numerical results are discussed both for small scale dynamos, which are completely isotropic, and for large scale dynamo, where some form of parity breaking is crucial.
1,548 citations
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05 Mar 2001TL;DR: An introductory text on magnetohydrodynamics (MHD) is presented in this paper, which is intended to serve as an introductory text for advanced undergraduates and postgraduate students in physics, applied mathematics and engineering.
Abstract: Magnetic fields influence many natural and man-made flows. They are routinely used in industry to heat, pump, stir and levitate liquid metals. There is the terrestrial magnetic field which is maintained by fluid motion in the earth's core, the solar magnetic field, which generates sunspots and solar flares, and the galactic field which influences the formation of stars. This is an introductory text on magnetohydrodynamics (MHD) - the study of the interaction of magnetic fields and conducting fluids. This book is intended to serve as an introductory text for advanced undergraduates and postgraduate students in physics, applied mathematics and engineering. The material in the text is heavily weighted towards incompressible flows and to terrestrial (as distinct from astrophysical) applications. The final sections of the text also contain an outline of the latest advances in the metallurgical applications of MHD and so are relevant to professional researchers in applied mathematics, engineering and metallurgy.
1,060 citations
TL;DR: In this paper, it was shown that spiral waves churn the stars and gas in a manner that largely preserves the overall angular momentum distribution and leads to little increase in random motion, and that changes in the angular momenta of individual stars are typically as large as ∼50 per cent over the lifetime of the disc.
Abstract: We show that spiral waves in galaxy discs churn the stars and gas in a manner that largely preserves the overall angular momentum distribution and leads to little increase in random motion. Changes in the angular momenta of individual stars are typically as large as ∼50 per cent over the lifetime of the disc. The changes are concentrated around the corotation radius for an individual spiral wave, but since transient waves with a wide range of pattern speeds develop in rapid succession, the entire disc is affected. This behaviour has profound consequences for the metallicity gradients with radius in both stars and gas, since the interstellar medium is also stirred by the same mechanism. We find observational support for stirring, propose a simple model for the distribution of stars over metallicity and age, and discuss other possible consequences.
1,001 citations
Cites background from "Hydromagnetic Dynamo Models"
...Standard αΩ-dynamo theory (Parker 1955) is thought to yield too low a growth rate to achieve the present-day observed field strengths (Beck, et al. 1996) from the likely seed fields....
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TL;DR: In this paper, a nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions.
Abstract: To understand the turbulent generation of large-scale magnetic fields and to advance beyond purely kinematic approaches to the dynamo effect like that introduced by Steenbeck, Krause & Radler (1966)’ a new nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions. For this, techniques introduced for ordinary turbulence in recent years by Kraichnan (1971~~)’ Orszag (1970, 1976) and others are generalized to MHD; in particular we make use of the eddy-damped quasi-normal Markovian approximation. The resulting closed equations for the evolution of the kinetic and magnetic energy and helicity spectra are studied both theoretically and numerically in situations with high Reynolds number and unit magnetic Prandtl number. Interactions between widely separated scales are much more important than for non-magnetic turbulence. Large-scale magnetic energy brings to equipartition small-scale kinetic and magnetic excitation (energy or helicity) by the ‘AlfvBn effect ’; the small-scale ‘residual’ helicity, which is the difference between a purely kinetic and a purely magnetic helical term, induces growth of largescale magnetic energy and helicity by the ‘helicity effect’. In the absence of helicity an inertial range occurs with a cascade of energy to small scales; to lowest order it is a - power law with equipartition of kinetic and magnetic energy spectra as in Kraichnan (1965) but there are - 2 corrections (and possibly higher ones) leading to a slight excess of magnetic energy. When kinetic energy is continuously injected, an initial seed of magnetic field willgrow to approximate equipartition, at least in the small scales. If in addition kinetic helicity is injected, an inverse cascade of magnetic helicity is obtained leading to the appearance of magnetic energy and helicity in ever-increasing scales (in fact, limited by the size of the system). This inverse cascade, predicted by Frisch et aZ. (1975), results from a competition between the helicity and Alfvh effects and yields an inertial range with approximately - 1 and - 2 power laws for magnetic energy and helicity. When kinetic helicity is injected at the scale Zinj and the rate k (per unit mass), the time of build-up of magnetic energy with scale L 9 Zinl is t % L( prp;nj)-k 21 FLM 77
982 citations
TL;DR: In this article, it is argued that a turbulent hydromagnetic dynamo of some kind and an inverse cascade of magnetic energy gives the most plausible explanation for the regular galactic magnetic fields.
Abstract: ▪ Abstract We discuss current observational and theoretical knowledge of magnetic fields, especially the large-scale structure in the disks and halos of spiral galaxies. Among other topics, we consider the enhancement of global magnetic fields in the interarm regions, magnetic spiral arms, and representations as superpositions of azimuthal modes, emphasizing a number of unresolved questions. It is argued that a turbulent hydromagnetic dynamo of some kind and an inverse cascade of magnetic energy gives the most plausible explanation for the regular galactic magnetic fields. Primordial theory is found to be unsatisfactory, and fields of cosmological origin may not even be able to provide a seed field for a dynamo. Although dynamo theory has its own problems, the general form of the dynamo equations appears quite robust. Finally, detailed models of magnetic field generation in galaxies, allowing for factors such as spiral structure, starbursts, galactic winds, and fountains, are discussed and confronted with...
977 citations
Cites methods from "Hydromagnetic Dynamo Models"
...The amplifying e ect of swirling motions onthe large-scale eld is described by the -e ect (Parker 1955, Steenbeck et al 1966, Mo att 1978)....
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