Magnetohydrodynamic Turbulence Mediated by Reconnection
- Department of Physics, University of Wisconsin-Madison, Madison, WI 53706 (United States)
- Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge MA 02139 (United States)
Magnetic field fluctuations in magnetohydrodynamic turbulence can be viewed as current sheets that are progressively more anisotropic at smaller scales. As suggested by Loureiro and Boldyrev and Mallet et al., below a certain critical thickness, λ{sub c}, such current sheets become tearing-unstable. We propose that the tearing instability changes the effective alignment of the magnetic field lines in such a way as to balance the eddy turnover rate at all scales smaller than λ{sub c}. As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as θ∼(λ/λ{sub ∗}){sup −4/5+β}, where λ{sub ∗}∼L{sub 0}S{sub 0}{sup −3/4} is the resistive dissipation scale. Here L {sub 0} is the outer scale of the turbulence, S {sub 0} is the corresponding Lundquist number, and 0⩽β<4/5 is a parameter. The resulting Fourier energy spectrum is E(k{sub ⊥})∝k{sub ⊥}{sup −11/5+2β/3}, where k{sub ⊥} is the wavenumber normal to the local mean magnetic field, and the critical scale is λ{sub c}∼S{sub L}{sup −(4−5β)/(7−20β/3)}. The simplest model corresponds to β = 0, in which case the predicted scaling formally agrees with one of the solutions obtained in Mallet et al. from a discrete hierarchical model of abruptly collapsing current sheets, an approach different from and complementary to ours. We also show that the reconnection-mediated interval is non-universal with respect to the dissipation mechanism. Hyper-resistivity of the form η-tilde k{sup 2+2s} leads (in the simplest case of β = 0) to the different transition scale λ{sub c}∼L{sub 0} S-tilde {sub 0}{sup −4/(7+9s)} and the energy spectrum E(k{sub ⊥})∝k{sub ⊥}{sup −(11+9s)/(5+3s)}, where S-tilde {sub 0} is the corresponding hyper-resistive Lundquist number.
- OSTI ID:
- 22875967
- Journal Information:
- Astrophysical Journal, Journal Name: Astrophysical Journal Journal Issue: 2 Vol. 844; ISSN ASJOAB; ISSN 0004-637X
- Country of Publication:
- United States
- Language:
- English
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Magnetohydrodynamic Turbulence Mediated by Reconnection