Magnetic Field Growth and Saturation in Plasmas with Large Magnetic Prandtl Number. I. The Two‐dimensional Case

Kinney, R.; Chandran, Benjamin D. G.; Cowley, S. C.; McWilliams, James C.

doi:10.1086/317824

Cited by 28 publications

(59 citation statements)

References 28 publications

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“…This regime corresponds to what is sometimes referred to as the the viscous relaxation effect (Chandran 1998;Kinney et al 2000). Substituting the expression (19) for À1 r ðBÞ into equation (16), we find a Gaussian PDF (cf.…”

Section: A Model Of Back-reactionmentioning

confidence: 88%

The Small‐Scale Structure of Magnetohydrodynamic Turbulence with Large Magnetic Prandtl Numbers

Schekochihin

Maron

Cowley

et al. 2002

ApJ

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We study the intermittency and field-line structure of the MHD turbulence in plasmas with very large magnetic Prandtl numbers. In this regime, which is realized in the interstellar medium, some accretion disks, protogalaxies, galaxy-cluster gas, the early universe, etc., magnetic fluctuations can be excited at scales below the viscous cutoff. The salient feature of the resulting small-scale magnetic turbulence is the folded structure of the fields. It is characterized by very rapid transverse spatial oscillation of the field direction, while the field lines remain largely unbent up to the scale of the flow. Quantitatively, the fluctuation level and the field-line geometry can be studied in terms of the statistics of the field strength and of the field-line curvature. In the kinematic limit, the distribution of the field strength is an expanding lognormal, while that of the field-line curvature K is stationary and has a power tail $K À13/7 . The field strength and curvature are anticorrelated, i.e., the growing fields are mostly flat, while the sharply curved fields remain relatively weak. The field, therefore, settles into a reduced-tension state. Numerical simulations demonstrate three essential features of the nonlinear regime. First, the total magnetic energy is equal to the total kinetic energy. Second, the intermittency is partially suppressed compared to the kinematic case, as the fields become more volume-filling and their distribution develops an exponential tail. Third, the folding structure of the field is unchanged from the kinematic case: the anticorrelation between the field strength and the curvature persists, and the distribution of the latter retains the same power tail. We propose a model of back-reaction based on the folding picture that reproduces all of the above numerical results.

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Section: A Model Of Back-reactionmentioning

confidence: 88%

The Small‐Scale Structure of Magnetohydrodynamic Turbulence with Large Magnetic Prandtl Numbers

Schekochihin

Maron

Cowley

et al. 2002

ApJ

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“…Indeed, the velocity field that arises in the Kolmogorov turbulence is neither Gaussian nor δ correlated in time: its intermittent character is well known and its correlation time is naturally estimated to be of the same order as its eddy-turnover time. However, the Kazantsev-Kraichnan model, while by no means a controlled approximation [39], appears to correctly capture most of the physics of the passive advection on at least a semiquantitative level and has survived a number of reality tests, numerical [7][8][9] and, in the case of scalar turbulence, also experimental (see, e.g., the review [40] and references therein). Indeed, as was reported in the preceding sections, our results are in a very good agreement with numerical simulations, where the velocity field derives from the forced Navier-Stokes equation and has a realistic correlation time.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…However, developing such a nonlinear theory of the magnetic-field evolution will require a thorough understanding of its linear (kinematic) precursor. In fact, this point holds with greater force in view of the recent theoretical and numerical advances which suggest that the saturated spectra of magnetic fluctuations are largely determined by the turbulent advection processes that drive the kinematic dynamo [7][8][9]. In this work, we study the geometrical structure of the fluctuating small-scale magnetic fields produced by the kinematic stage of the high-Pr dynamo.…”

Section: Introductionmentioning

confidence: 99%

Structure of small-scale magnetic fields in the kinematic dynamo theory

et al. 2001

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A weak fluctuating magnetic field embedded into a turbulent conducting medium grows exponentially while its characteristic scale decays. In the interstellar medium and protogalactic plasmas, the magnetic Prandtl number is very large, so a broad spectrum of growing magnetic fluctuations is excited at small (subviscous) scales. The condition for the onset of nonlinear back reaction depends on the structure of the field lines. We study the statistical correlations that are set up in the field pattern and show that the magnetic-field lines possess a folding structure, where most of the scale decrease is due to the field variation across itself (rapid transverse direction reversals), while the scale of the field variation along itself stays approximately constant. Specifically, we find that, though both the magnetic energy and the mean-square curvature of the field lines grow exponentially, the field strength and the field-line curvature are anticorrelated, i.e., the curved field is relatively weak, while the growing field is relatively flat. The detailed analysis of the statistics of the curvature shows that it possesses a stationary limiting distribution with the bulk located at the values of curvature comparable to the characteristic wave number of the velocity field and a power tail extending to large values of curvature where it is eventually cut off by the resistive regularization. The regions of large curvature, therefore, occupy only a small fraction of the total volume of the system. Our theoretical results are corroborated by direct numerical simulations. The implication of the folding effect is that the advent of the Lorentz back reaction occurs when the magnetic energy approaches that of the smallest turbulent eddies. Our results also directly apply to the problem of statistical geometry of the material lines in a random flow. PACS number(s): 47.27. Gs, 98.35.Eg, 47.65.+a, 05.10.Gg

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“…Instability of density perturbations of accretion disks caused by their float ability is also sensitive to the effect of the Hall electric field [3]. A large number of studies concentrated on investigation of the role of Hall effects in interstellar medium [4], early universe [5], neutron stars [6][7][8], as well as in magnetic field generation under turbulent dynamo [9]. The Hall current determines the differ ence of phase velocities of low frequency left and right polarized electromagnetic waves propagating in weakly ionized plasma along the magnetic field [2] and their parametric instability in molecular clouds [10] and the solar photosphere [11].…”

Section: Introductionmentioning

confidence: 99%

Instability of a magnetic drift wave in the vicinity of the dust-ion hybrid resonance

Prudskikh¹

2012

Plasma Phys. Rep.

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Low frequency electromagnetic waves propagating perpendicular to the gradients of the density and magnetic field in an inhomogeneous dusty plasma whose mass density is determined primarily by the dust component are analyzed. It is shown that, in analyzing the dispersion properties of inhomogeneous plasma, it is important to take into account the dynamic properties of ions in the vicinity of the dust-ion hybrid res onance. The conditions for the onset of instability of a magnetic drift wave are investigated for different rela tions between parameters of the inhomogeneity and the value of the Alfvén velocity. The differences from the previous results, as well as possible astrophysical applications, are discussed.

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Magnetic Field Growth and Saturation in Plasmas with Large Magnetic Prandtl Number. I. The Two‐dimensional Case

Cited by 28 publications

References 28 publications

The Small‐Scale Structure of Magnetohydrodynamic Turbulence with Large Magnetic Prandtl Numbers

The Small‐Scale Structure of Magnetohydrodynamic Turbulence with Large Magnetic Prandtl Numbers

Structure of small-scale magnetic fields in the kinematic dynamo theory

Instability of a magnetic drift wave in the vicinity of the dust-ion hybrid resonance

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