The Dynamo Problem of Magnetohydrodynamics

Krause, F.; Rädler, K.-H.

doi:10.1016/b978-0-08-025041-0.50014-7

Cited by 250 publications

(414 citation statements)

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“…Our finding for the stochastic parametric instability can be straightforwardly applied to partial differential equations (2) in which case one has to consider the coupled system for eigenmodes [12]. In this respect the two equations (7), (8) can be regarded as a dynamical system for first eigenmodes (order parameters), where the influence of other degrees of freedom is parameterized by additive and multiplicative noises.…”

Section: Discussionmentioning

confidence: 99%

“…It should be noted that this result is different from analogous in [16] since we consider here the second moments of the random magnetic field. Certainly, the predictions obtained here for the simplified stochastic model should be ultimately extended to more realistic systems of partial differential equations (2). However, for now we use the no−z model as a simplified tool to observe the noise effects on the generation of magnetic energy in the subcritical case.…”

Section: Multiplicative Noise: Stochastic Instabilitymentioning

confidence: 99%

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Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo

Fedotov

Bashkirtseva

Ryashko

2004

Physica A: Statistical Mechanics and its Applications

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We present and analyze a simplified stochastic αΩ−dynamo model which is designed to assess the influence of additive and multiplicative noises, non-normality of dynamo equation, and nonlinearity of the α−effect and turbulent diffusivity, on the generation of a large-scale magnetic field in the subcritical case. Our model incorporates random fluctuations in the α−parameter and additive noise arising from the small-scale fluctuations of magnetic and turbulent velocity fields. We show that the noise effects along with non-normality can lead to the stochastic amplification of the magnetic field even in the subcritical case. The criteria for the stochastic instability during the early kinematic stage are established and the critical value for the intensity of multiplicative noise due to α−fluctuations is found. We obtain numerical solutions of nonlinear stochastic differential equations and find the series of phase transitions induced by random fluctuations in the α−parameter.

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Section: Discussionmentioning

confidence: 99%

Section: Multiplicative Noise: Stochastic Instabilitymentioning

confidence: 99%

Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo

Fedotov

Bashkirtseva

Ryashko

2004

Physica A: Statistical Mechanics and its Applications

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“…Flow Dominated: For this subclass, the input energy is kinetic energy dominated and the EMF can be sustained, for example, by kinetic helicity, as in the classic Parker-type solar dynamo and its extensions (e.g. Moffatt 1978;Parker 1979;Krause & Rädler 1980;Pouquet et al 1976;Blackman & Brandenburg 2002). Alternatively, there is emerging agreement that a combination of shear and fluctuating kinetic helicity can conspire to produce an LSD (Vishniac & Brandenburg 1997;Brandenburg 1995;Brandenburg 2005;Yousef et al 2008;Heinemann et al 2011;Mitra & Brandenburg 2012;Sridhar & Singh 2013).…”

Section: Types Of Dynamos and Approaches To Study Themmentioning

confidence: 99%

“…The 20th century textbook mean field dynamo theory (MFDT) of standard textbooks (Moffatt 1978;Parker 1979;Krause & Rädler 1980) is a practical approach to modeling LSDs in turbulent rotators. These approaches focused mostly on initially globally reflection asymmetric rotators where the the EMF is sustained by kinetic helicity.…”

Section: Th Century Vs 21st Century Dynamos: Physical Role Of Magnmentioning

confidence: 99%

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Blackman¹

2016

Space Sciences Series of ISSI

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Magnetic fields of laboratory, planetary, stellar, and galactic plasmas commonly exhibit significant order on large temporal or spatial scales compared to the otherwise random motions within the hosting system. Such ordered fields can be measured in the case of planets, stars, and galaxies, or inferred indirectly by the action of their dynamical influence, such as jets. Whether large scale fields are amplified in situ or a remnant from previous stages of an object's history is often debated for objects without a definitive magnetic activity cycle. Magnetic helicity, a measure of twist and linkage of magnetic field lines, is a unifying tool for understanding large scale field evolution for both mechanisms of origin. Its importance stems from its two basic properties: (1) magnetic helicity is typically better conserved than magnetic energy; and (2) the magnetic energy associated with a fixed amount of magnetic helicity is minimized when the system relaxes this helical structure to the largest scale available. Here I discuss how magnetic helicity has come to help us understand the saturation of and sustenance of large scale dynamos, the need for either local or global helicity fluxes to avoid dynamo quenching, and the associated observational consequences. I also discuss how magnetic helicity acts as a hindrance to turbulent diffusion of large scale fields, and thus a helper for fossil remnant large scale field origin models in some contexts. I briefly discuss the connection between large scale fields and accretion disk theory as well. The goal here is to provide a conceptual primer to help the reader efficiently penetrate the literature.

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“…Conventional mean field dynamo theory (see [62,65,49] for reviews) allows a large-scale magnetic field to grow exponentially from a seed field (see [69,51]) at the expense of small-scale turbulent energy through a process of spiral twisting and reconnection, illustrated in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Problems and Progress in Astrophysical Dynamos

Vishniac

Lazarían²,

Cho³

Turbulence and Magnetic Fields in Astrophysics

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Abstract. Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux threading a fluid element, or the field topology. Classical dynamo theory evades this limit by assuming that magnetic reconnection is fast, even for vanishing resistivity, and that the large scale field can be generated by the action of kinetic helicity. Both these claims have been severely criticized, and the latter appears to conflict with strong theoretical arguments based on magnetic helicity conservation and a series of numerical simulations. Here we discuss recent efforts to explain fast magnetic reconnection through the topological effects of a weak stochastic magnetic field component. We also show how mean-field dynamo theory can be recast in a form which respects magnetic helicity conservation, and how this changes our understanding of astrophysical dynamos. Finally, we comment briefly on why an asymmetry between small scale magnetic and velocity fields is necessary for dynamo action, and how it can arise naturally.

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The Dynamo Problem of Magnetohydrodynamics

Cited by 250 publications

References 0 publications

Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo

Stochastic analysis of subcritical amplification of magnetic energy in a turbulent dynamo

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

Problems and Progress in Astrophysical Dynamos

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