Magnetohydrodynamic Turbulence Mediated by Reconnection

Dataset · Thu Jan 10 00:00:00 EST 2019

DOI:https://doi.org/10.7910/DVN/0JQHWY· OSTI ID:1881002

Boldyrev, Stanislav; Loureiro, Nuno F.

Magnetic field fluctuations in MHD turbulence can be viewed as current sheets that are progressively more anisotropic at smaller scales. As suggested by Loureiro & Boldyrev 2017 and Mallet et al. 2017, below a certain critical thickness $$\lambda_c$$ 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 $$\lambda_c$$. As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as $$\theta \sim (\lambda/\lambda_*)^{-4/5+\beta}$$, where $$\lambda_*\sim L_0 S_0^{-3/4}$$ is the resistive dissipation scale. Here $$L_0$$ is the outer scale of the turbulence, $$S_0$$ is the corresponding Lundquist number, and {$$0\leq \beta <4/5$$} is a parameter. The resulting Fourier energy spectrum is $$E(k_\perp)\propto k_\perp^{-11/5+2\beta/3}$$, where $$k_\perp$$ is the wavenumber normal to the local mean magnetic field, and the critical scale is $$\lambda_c\sim S_L^{-(4-5\beta)/(7-{20\beta/3})}$$. The simplest model corresponds to $$\beta=0$$, in which case the predicted scaling formally agrees with one of the solutions obtained in (Mallet et al. 2017) from a discrete hierarchical model of abruptly collapsing current sheets, an approach different 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 $${\tilde \eta}k^{2+2s}$$ leads (in the simplest case of $$\beta=0$$) to the different transition scale $$\lambda_c\sim L_0{\tilde S}_0^{-4/(7+9s)}$$ and the energy spectrum $$E(k_\perp)\propto k_\perp^{-(11+9s)/(5+3s)}$$, where $${\tilde S}_0$$ is the corresponding hyper-resistive Lundquist number.

• Research Organization: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center
• Sponsoring Organization: USDOE Office of Science (SC), Fusion Energy Sciences (FES)
• DOE Contract Number: SC0016215
• OSTI ID: 1881002
• Country of Publication: United States
• Language: English

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79 ASTRONOMY AND ASTROPHYSICS