Dynamo theories

Rincon, F.

doi:10.1017/s0022377819000539

Cited by 167 publications

(128 citation statements)

References 539 publications

(1,221 reference statements)

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“…The study explores physical effects over a range of Re M for Pr M ≥ 1. However, for Pr M > 1 at very high Re M ( 10 3 ), the fields might be unstable to fast magnetic reconnection [12]. This might change the morphology of magnetic fields, locally affect velocity fields and thus might alter the saturated state of the fluctuation dynamo.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

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Saturation mechanism of the fluctuation dynamo at PrM ≥ 1

et al. 2020

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The presence of magnetic fields in many astrophysical objects is due to dynamo action, whereby a part of the kinetic energy is converted into magnetic energy. A turbulent dynamo that produces magnetic field structures on the same scale as the turbulent flow is known as the fluctuation dynamo. We use numerical simulations to explore the nonlinear, statistically steady state of the fluctuation dynamo in driven turbulence. We demonstrate that as the magnetic field growth saturates, its amplification and diffusion are both affected by the back-reaction of the Lorentz force upon the flow. The amplification of the magnetic field is reduced due to stronger alignment between the velocity field, magnetic field, and electric current density. Furthermore, we confirm that the amplification decreases due to a weaker stretching of the magnetic field lines. The enhancement in diffusion relative to the field line stretching is quantified by a decrease in the computed local value of the magnetic Reynolds number. Using the Minkowski functionals, we quantify the shape of the magnetic structures produced by the dynamo as magnetic filaments and ribbons in both kinematic and saturated dynamos and derive the scalings of the typical length, width, and thickness of the magnetic structures with the magnetic Reynolds number. We show that all three of these magnetic length scales increase as the dynamo saturates. The magnetic intermittency, strong in the kinematic dynamo (where the magnetic field strength grows exponentially) persists in the statistically steady state, but intense magnetic filaments and ribbons are more volume-filling.

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Section: Conclusion and Discussionmentioning

confidence: 99%

“…For spiral galaxies, the mean and fluctuating fields have comparable magnitudes and thus both kinds of fields are equally important for the galactic dynamics [6]. There are a number of reviews covering the theoretical, numerical, and observational aspects of the subject [7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Saturation mechanism of the fluctuation dynamo at PrM ≥ 1

et al. 2020

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“…It is believed that, for systems without any large-scale features such as rotational shear or net helicity, weak seed fields are amplified and sustained by the fluctuation (or small-scale) dynamo (Kulsrud & Zweibel 2008), in which a random turbulent flow amplifies a weak seed magnetic field to near-equipartition energies (Batchelor 1950; Zel'dovich et al. 1984; Childress & Gilbert 1995; Rincon 2019; Tobias 2019). This process is thought to be particularly important in the intracluster medium (ICM), a hot (temperatures keV) and diffuse (densities ) ionized plasma that sits in the dark-matter-dominated gravitational potential of a galaxy cluster (Fabian 1994).…”

Section: Introductionmentioning

confidence: 99%

Fluctuation dynamo in a weakly collisional plasma

et al. 2020

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The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. In all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

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“…This approximation is equivalent to neglecting the term in (3.3); in the context of large-scale kinematic dynamo theory, it is often called the first-order smoothing approximation (FOSA) or the second-order correlation approximation (SOCA). In the dynamo-theory context, it is employed in the small-scale part of the induction equation to neglect a similar ‘fluctuating part of the product of two fluctuations’ term, allowing the small-scale induction equation to be solved for the small-scale magnetic field, which can then be used to compute the growth of the large-scale field (for a review, see Rincon (2019)). Our use of this approximation is directly complementary: instead of solving an equation for the small-scale magnetic field given a prescribed flow, we use the FOSA to solve an equation for a small-scale flow given a known small-scale magnetic-field configuration, .…”

Section: Analytic Theory Of An Inhomogeneous Tanglementioning

confidence: 99%

“…In § 3.3, we develop a mean-field formalism based on an approximation that assumes the coupling of different Fourier modes of the small-scale motions to each other to be small. This treatment is equivalent to the first-order smoothing approximation (FOSA) commonly employed in large-scale dynamo theory (Moffatt 1978; Krause & Raedler 1980; Brandenburg & Subramanian 2005; see Rincon (2019) for a review), and allows the dispersion relation for magnetoelastic waves to be expressed in terms of statistical properties of the magnetic-field configuration.…”

Section: Introductionmentioning

confidence: 99%

Elasticity of tangled magnetic fields

Hosking

Schekochihin

2020

J. Plasma Phys.

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The fundamental difference between incompressible ideal magnetohydrodynamics and the dynamics of a non-conducting fluid is that magnetic fields exert a tension force that opposes their bending; magnetic fields behave like elastic strings threading the fluid. It is natural, therefore, to expect that a magnetic field tangled at small length scales should resist a large-scale shear in an elastic way, much as a ball of tangled elastic strings responds elastically to an impulse. Furthermore, a tangled field should support the propagation of ‘magnetoelastic waves’, the isotropic analogue of Alfvén waves on a straight magnetic field. Here, we study magnetoelasticity in the idealised context of an equilibrium tangled field configuration. In contrast to previous treatments, we explicitly account for intermittency of the Maxwell stress, and show that this intermittency necessarily decreases the frequency of magnetoelastic waves in a stable field configuration. We develop a mean-field formalism to describe magnetoelastic behaviour, retaining leading-order corrections due to the coupling of large- and small-scale motions, and solve the initial-value problem for viscous fluids subjected to a large-scale shear, showing that the development of small-scale motions results in anomalous viscous damping of large-scale waves. Finally, we test these analytic predictions using numerical simulations of standing waves on tangled, linear force-free magnetic-field equilibria.

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Dynamo theories

Cited by 167 publications

References 539 publications

Saturation mechanism of the fluctuation dynamo at PrM ≥ 1

Saturation mechanism of the fluctuation dynamo at PrM ≥ 1

Fluctuation dynamo in a weakly collisional plasma

Elasticity of tangled magnetic fields

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