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Title: Fluctuation dynamo in a weakly collisional plasma

Abstract

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. Finally, 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.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]
  1. Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ. of Oxford (United Kingdom)
  2. Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  3. Univ. of Otago, Dunedin (New Zealand)
  4. Univ. of Oxford (United Kingdom); Merton College, Oxford (United Kingdom)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE; UK STFC; Engineering and Physical Sciences Research Council (EPSRC); National Science Foundation (NSF)
OSTI Identifier:
1668042
Grant/Contract Number:  
AC02-09CH11466; UOO1727; ST/N000919/1; EP/M022331/1; EP/R034737/1; PHY-1748958
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 86; Journal Issue: 5; Journal ID: ISSN 0022-3778
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English

Citation Formats

St-Onge, D. A., Kunz, M. W., Squire, J., and Schekochihin, A. A. Fluctuation dynamo in a weakly collisional plasma. United States: N. p., 2020. Web. doi:10.1017/s0022377820000860.
St-Onge, D. A., Kunz, M. W., Squire, J., & Schekochihin, A. A. Fluctuation dynamo in a weakly collisional plasma. United States. doi:10.1017/s0022377820000860.
St-Onge, D. A., Kunz, M. W., Squire, J., and Schekochihin, A. A. Tue . "Fluctuation dynamo in a weakly collisional plasma". United States. doi:10.1017/s0022377820000860.
@article{osti_1668042,
title = {Fluctuation dynamo in a weakly collisional plasma},
author = {St-Onge, D. A. and Kunz, M. W. and Squire, J. and Schekochihin, A. A.},
abstractNote = {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. Finally, 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.},
doi = {10.1017/s0022377820000860},
journal = {Journal of Plasma Physics},
issn = {0022-3778},
number = 5,
volume = 86,
place = {United States},
year = {2020},
month = {9}
}

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