617 research outputs found
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 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 . As a result, turbulent fluctuations become
progressively less anisotropic at smaller scales, with the alignment angle
increasing as , where
is the resistive dissipation scale. Here
is the outer scale of the turbulence, is the corresponding Lundquist
number, and {} is a parameter. The resulting Fourier energy
spectrum is , where is
the wavenumber normal to the local mean magnetic field, and the critical scale
is . The simplest model
corresponds to , 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 leads (in the simplest case of )
to the different transition scale
and the energy spectrum , where
is the corresponding hyper-resistive Lundquist number.Comment: submitted for publicatio
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
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