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Magnetorotational Turbulence and Dynamo in a Collisionless Plasma

Matthew W. Kunz, James M. Stone, and Eliot Quataert
Phys. Rev. Lett. 117, 235101 – Published 1 December 2016

Abstract

We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model of a collisionless accretion disk. The kinetic magnetorotational instability grows from a subthermal magnetic field having zero net flux over the computational domain to generate self-sustained turbulence and outward angular-momentum transport. Significant Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabilities through particle trapping and pitch-angle scattering. The latter endow the plasma with an effective viscosity that is biased with respect to the magnetic-field direction and spatiotemporally variable. Energy spectra suggest an Alfvén-wave cascade at large scales and a kinetic-Alfvén-wave cascade at small scales, with strong small-scale density fluctuations and weak nonaxisymmetric density waves. Ions undergo nonthermal particle acceleration, their distribution accurately described by a κ distribution. These results have implications for the properties of low-collisionality accretion flows, such as that near the black hole at the Galactic center.

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  • Received 28 August 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.235101

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Gravitation, Cosmology & AstrophysicsPlasma Physics

Authors & Affiliations

Matthew W. Kunz1,2,*, James M. Stone1, and Eliot Quataert3

  • 1Department of Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, New Jersey 08544, USA
  • 2Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543, USA
  • 3Department of Astronomy and Theoretical Astrophysics Center, University of California, 501 Campbell Hall #3411, Berkeley, California 94720-3411, USA

  • *mkunz@princeton.edu

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Issue

Vol. 117, Iss. 23 — 2 December 2016

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Images

  • Figure 1
    Figure 1

    Evolution of box-averaged (a) magnetic energy and thermal pressure, (b) kinetic energy, (c) pressure anisotropy (compared to magnetic energy), and (d) xy components of the total, Maxwell, viscous, and Reynolds stresses, all normalized to the initial thermal pressure p0. The inset in (c) shows a slice of the magnetic-field strength in the xz plane at the time marked by the dot; mirror-mode parasites, which feed off the pressure anisotropy generated by the MRI, are evident. The plus sign in panel (d) denotes the value of Txy/p0 obtained in a MHD simulation of the zero-net-flux MRI with Pm=16 [26].

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  • Figure 2
    Figure 2

    Distribution of the ion temperature anisotropy Ti/Ti vs the parallel ion βi (top left) initially, (top right) during the channel phase, (bottom left) at peak channel amplitude, and (bottom right) in the saturated state. The solid, dot-dashed, and dashed lines denote approximate mirror, ion-cyclotron, and firehose instability thresholds, respectively.

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  • Figure 3
    Figure 3

    x and y components of the magnetic field (normalized to B0) and the momentum (normalized to ni0vA0) at Ωrott=47.4.

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  • Figure 4
    Figure 4

    Slices of (left) Maxwell stress (normalized to p0), (left center) magnetic-field strength (normalized to B0), and (right center) density fluctuation (normalized to n0i) at z=0. Right: vertically averaged density fluctuation (normalized to n0i). All frames are taken at Ωrott=47.4.

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  • Figure 5
    Figure 5

    Energy spectra of (top) magnetic fluctuations and (bottom) velocity and density fluctuations in the saturated state, defined by EA(k)dΩk(kH/2π)2|Ak|2 with d(kH/2π)EA(k)=A2. Characteristic slopes are shown as labeled dashed lines; the vertical dotted line marks kρi=1.

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  • Figure 6
    Figure 6

    Box-averaged ion distribution function at Ωrott=51 (solid line), binned logarithmically in ϵ(mi/2)|vui(r)|2. A κ=5 distribution and a Maxwell distribution, both with temperature Ti5.4T0i, are overlaid; the former is a good fit, indicating nonthermal particle acceleration.

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