Magnetic field growth and saturation in plasmas with large magnetic prandtl number. I. The two-dimensional case

R. M. Kinney, B. Chandran, S. Cowley, J. C. McWilliams

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24 Scopus citations


In turbulent plasmas, velocities at scales smaller than a scale lD are strongly damped by viscosity, ν, and magnetic fields below a scale lR are strongly dissipated by resistivity, η. In galaxies and protogalaxies, lD ≫ lR; i.e., the magnetic Prandtl number, PM = v/η = l2D//l2R, is very large. The limit of high magnetic Prandtl number in two dimensions is the focus of this paper. In the kinematic phase of magnetic field growth, when the field is loo weak to affect the flow, the field strength grows and the field scale length lB decreases. Much of the initial growth of the field happens at scales below lD. In this paper we examine numerically and analytically the growth and saturation of magnetic field on scales less than lD in two dimensions. If the initial seed field strength is very weak, the field grows and lB decreases down to the resistive scale lR before the Lorentz force can affect the magnetic field: once lB ∼ lR it damps out rapidly. However, if the initial seed field is large enough the field grows until it saturates at a scale lB with lD > lB > lR. In saturation the field strength remains constant and lB decreases on the resistive time of the saturation scale (i.e., l2B/η). The small-scale velocities are insufficient to unwind the small-scale field and produce any kind of inverse cascade. When the scale of the saturation field reaches lR, the field strength begins to decay. In the initial phase of decay, coherent loops of magnetic field that are formed during saturation persist and act to limit the rate of decay of magnetic energy. Only after these loops have resistively decayed can the final, rapid, kinematic decay take place.

Original languageEnglish (US)
Pages (from-to)907-921
Number of pages15
JournalAstrophysical Journal
Issue number2 PART 1
StatePublished - Dec 20 2000
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


  • ISM: magnetic fields
  • MHD
  • Magnetic fields
  • Turbulence


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