Magnetohydrodynamic turbulence mediated by reconnection

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.Comment: submitted for publicatio

Role of reconnection in inertial kinetic-Alfven turbulence

In a weakly collisional, low-electron-beta plasma, large-scale Alfv\'en turbulence transforms into inertial kinetic-Alfv\'en turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tend to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale $a$ in the plane perpendicular to the guide field. This aspect ratio is defined by the balance of the eddy turnover rate and the tearing rate, and varies from $(d_e/a)^{1/2}$ to $d_e/a$ depending on the assumed profile of the current sheets. The energy spectrum of the resulting turbulence varies from $k^{-8/3}$ to $k^{-3}$, and the corresponding spectral anisotropy with respect to the strong background magnetic field from $k_z\lesssim k_\perp^{2/3}$ to $k_z\lesssim k_\perp$.Comment: published versio

Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale λ∼LS_{L}^{-4/7}, where S_{L} is the outer-scale (L) Lundquist number and λ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum E(k_{⊥})∝k_{⊥}^{-5/2}, where k_{⊥} is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas (Pm), where the reconnection scale is found to be λ/L∼S_{L}^{-4/7}Pm^{-2/7}.NSF-DOE Partnership in Basic Plasma Science and Engineering (Award No. DE-SC0016215)National Science Foundation (U.S.) (Grant No. NSF AGS-1261659)University of Wisconsin--Madison. Vilas Associates Awar

Toward the Theory of Turbulence in Magnetized Plasmas

The goal of the project was to develop a theory of turbulence in magnetized plasmas at large scales, that is, scales larger than the characteristic plasma microscales (ion gyroscale, ion inertial scale, etc.). Collisions of counter-propagating Alfven packets govern the turbulent cascade of energy toward small scales. It has been established that such an energy cascade is intrinsically anisotropic, in that it predominantly supplies energy to the modes with mostly field-perpendicular wave numbers. The resulting energy spectrum of MHD turbulence, and the structure of the fluctuations were studied both analytically and numerically. A new parallel numerical code was developed for simulating reduced MHD equations driven by an external force. The numerical setting was proposed, where the spectral properties of the force could be varied in order to simulate either strong or weak turbulent regimes. It has been found both analytically and numerically that weak MHD turbulence spontaneously generates a “condensate”, that is, concentration of magnetic and kinetic energy at small k{sub {parallel}}. A related topic that was addressed in the project is turbulent dynamo action, that is, generation of magnetic field in a turbulent flow. We were specifically concentrated on the generation of large-scale magnetic field compared to the scales of the turbulent velocity field. We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model

On the Nature of Magnetic Turbulence in Rotating, Shearing Flows

The local properties of turbulence driven by the magnetorotational instability (MRI) in rotating, shearing flows are studied in the framework of a shearing-box model. Based on numerical simulations, we propose that the MRI-driven turbulence comprises two components: the large-scale shear-aligned strong magnetic field and the small-scale fluctuations resembling magnetohydrodynamic (MHD) turbulence. The energy spectrum of the large-scale component is close to $k^{-2}$, whereas the spectrum of the small-scale component agrees with the spectrum of strong MHD turbulence $k^{-3/2}$. While the spectrum of the fluctuations is universal, the outer-scale characteristics of the turbulence are not; they depend on the parameters of the system, such as the net magnetic flux. However, there is remarkable universality among the allowed turbulent states -- their intensity $v_0$ and their outer scale $\lambda_0$ satisfy the balance condition $v_0/\lambda_0\sim \mathrm d\Omega/\mathrm d\ln r$, where $\mathrm d\Omega/\mathrm d\ln r$ is the local orbital shearing rate of the flow. Finally, we find no sustained dynamo action in the $\mathrm{Pm}=1$ zero net-flux case for Reynolds numbers as high as $45\,000$, casting doubts on the existence of an MRI dynamo in the $\mathrm{Pm}\leq 1$ regime.Comment: 5 pages, 6 figures, 1 tabl