Magnetohydrodynamic turbulence mediated by reconnection

Abstract

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 $\theta \sim (\lambda /{\lambda }_{\ast }{)}^{-4/5+\beta }$, where ${\lambda }_{\ast }\sim L_0{S}_0^{-3/4}$ is the resistive dissipation scale. Here $L_0$ is the outer scale of the turbulence, $S_0$ is the corresponding Lundquist number, and {$0\le \beta <4/5$} 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.

submitted for publication

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• Identification of active magnetic reconnection using magnetic flux transport in plasma turbulence
• Space-filter techniques for quasi-neutral hybrid-kinetic models
• Spatial intermittency of particle distribution in relativistic plasma turbulence
• On the Effect of Driving Turbulent-like Fluctuations on a Harris-Current Sheet Configuration and the Formation of Plasmoids
• PATOKA: Simulating Electromagnetic Observables of Black Hole Accretion