Saturation mechanism of the fluctuation dynamo at 
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Seta, Amit; Bushby, P. J.; Shukurov, Anvar; Wood, Toby S.

doi:10.1103/physrevfluids.5.043702

Cited by 53 publications

(44 citation statements)

References 92 publications

(118 reference statements)

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“…Similar p.d.f.s were calculated recently for the isotropic-MHD dynamo by Seta et al. (2020), whose results agree broadly with those presented here in figures 15 and 16 for isotropic MHD.…”

supporting

confidence: 92%

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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“…Similar p.d.f.s were calculated recently for the isotropic-MHD dynamo by Seta et al. (2020), whose results agree broadly with those presented here in figures 15 and 16 for isotropic MHD.…”

supporting

confidence: 92%

Fluctuation dynamo in a weakly collisional plasma

et al. 2020

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“…Once the mean magnetic energy becomes comparable to the energy of the viscous-scale motions (viz., B 2 rms ∼ U 2 Re −1/2 ), the kinematic stage ends and the dynamo becomes nonlinear. Namely, the Lorentz force due to the spatially coherent magnetic folds back-reacts on the viscous-scale motions and suppresses their ability to amplify the magnetic field [17,[33][34][35][36][37][38][39]. As a result, progressively larger (and slower) eddies are responsible for amplifying the field, while the eddies whose energies are lower,…”

Section: A Generation and Persistence Of Magnetic Foldsmentioning

confidence: 99%

Tearing instability and current-sheet disruption in the turbulent dynamo

Galishnikova¹,

Kunz²,

Schekochihin³

2022

Preprint

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Turbulence in a conducting plasma can amplify seed magnetic fields in what is known as the turbulent, or small-scale, dynamo. The associated growth rate and emergent magnetic-field geometry depend sensitively on the material properties of the plasma, in particular on the Reynolds number Re, the magnetic Reynolds number Rm, and their ratio Pm ≡ Rm/Re. For Pm > 1, the amplified magnetic field is gradually arranged into a folded structure, with direction reversals at the resistive scale and field lines curved at the larger scale of the flow. As the mean magnetic energy grows to come into approximate equipartition with the fluid motions, this folded structure is thought to persist. Using analytical theory and high-resolution MHD simulations with the Athena++ code, we show that these magnetic folds become unstable to tearing during the nonlinear stage of the dynamo for Rm 10 4 and Re 10 3 . An Rm-and Pm-dependent tearing scale, at and below which folds are disrupted, is predicted theoretically and found to match well the characteristic fieldreversal scale measured in the simulations. The disruption of folds by tearing increases the ratio of viscous-to-resistive dissipation. In the saturated state, the magnetic-energy spectrum exhibits a sub-tearing-scale steepening to a slope consistent with that predicted for tearing-mediated Alfvénic turbulence. Its spectral peak appears to be independent of the resistive scale and comparable to the driving scale of the flow, while the magnetic energy resides in a broad range of scales extending down to the field-reversal scale set by tearing. Emergence of a degree of large-scale magnetic coherence in the saturated state of the turbulent dynamo may be consistent with observations of magnetic-field fluctuations in galaxy clusters and recent laboratory experiments.

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“…The two approaches produce concordant results wherever their domains of applicability overlap (Chertkov et al 1999;Il'yn et al 2021), they are also verified by numerical simulations (Mason et al 2011;Schekochihin et al 2004;Seta et al 2020). However, there remains the domain where neither of them can be applied: processes with non-Gaussian and/or not δ-correlated velocity statistics cannot be analyzed at late (inertial) stage of their evolution neither by the Lagrangian deformations approach nor by the classical Kazantsev method.…”

Section: Introductionmentioning

confidence: 69%

Non-Gaussian generalization of the Kazantsev-Kraichnan model

Kopyev,

Kiselev,

Il'yn

et al. 2021

Preprint

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We consider a natural generalization of the Kazantsev-Kraichnan model for small-scale turbulent dynamo. This generalization takes account of statistical time asymmetry of a turbulent flow, and, thus, allows to describe velocity fields with energy cascade. For three-dimensional velocity field, generalized Kazantsev equation is derived, and evolution of the second order magnetic field correlator is investigated for large but finite magnetic Prandtl numbers. It is shown that as P r m → ∞, the growth increment tends to the limit known from the T-exponential (Lagrangian deformation) method. Magnetic field generation is shown to be weaker than that in the Gaussian velocity field for any direction of the energy cascade, and depends essentially on the Prandtl number.

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Saturation mechanism of the fluctuation dynamo at PrM ≥ 1

Cited by 53 publications

References 92 publications

Fluctuation dynamo in a weakly collisional plasma

Fluctuation dynamo in a weakly collisional plasma

Tearing instability and current-sheet disruption in the turbulent dynamo

Non-Gaussian generalization of the Kazantsev-Kraichnan model

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