Anomalous Viscosity of the Quark-Gluon Plasma

The shear viscosity of the quark-gluon plasma is predicted to be lower than the collisional viscosity for weak coupling. The estimated ratio of the shear viscosity to entropy density is rather close to the ratio calculated by N = 4 super Yang-Mills theory for strong coupling, which indicates that the quark-gluon plasma might be strongly coupled. However, in presence of momentum anisotropy, the Weibel instability can arise and drive the turbulent transport. Shear viscosity can be lowered by enhanced collisionality due to turbulence, but the decorrelation time and its relation to underlying dynamics and color-magnetic fields have not been calculated self-consistently. In this paper, we use resonance broadening theory for strong turbulence to calculate the anomalous viscosity of the quark-gluon plasma for nonequilibrium. For saturated Weibel instability, we estimate the scalings of the decorrelation rate and viscosity and compare these with collisional transport. This calculation yields an explicit connection between the underlying momentum space anisotropy and the viscosity anomaly.Comment: 16 pages, 2 figure

Theory of Two Dimensional Mean Field Electron Magnetohydrodynamics

The theory of mean field electrodynamics for diffusive processes in Electron Magnetohydrodynamic (EMHD) model is presented. In contrast to Magnetohydrodynamics (MHD) the evolution of magnetic field here is governed by a nonlinear equation in the magnetic field variables. A detailed description of diffusive processes in two dimensions are presented in this paper. In particular, it has been shown analytically that the turbulent magnetic field diffusivity is suppressed from naive quasilinear estimates. It is shown that for complete whisterlization of the spectrum, the turbulent diffusivity vanishes. The question of whistlerization of the turbulent spectrum is investigated numerically, and a reasonable tendency towards whisterlization is observed. Numerical studies also show the suppression of magnetic field diffusivity in accordance with the analytical estimates.Comment: 18 pages, 6 figure

Turbulence model reduction by deep learning

A central problem of turbulence theory is to produce a predictive model for turbulent fluxes. These have profound implications for virtually all aspects of the turbulence dynamics. In magnetic confinement devices, drift-wave turbulence produces anomalous fluxes via cross-correlations between fluctuations. In this work, we introduce a new, data-driven method for parameterizing these fluxes. The method uses deep supervised learning to infer a reduced mean-field model from a set of numerical simulations. We apply the method to a simple drift-wave turbulence system and find a significant new effect which couples the particle flux to the local \emph{gradient} of vorticity. Notably, here, this effect is much stronger than the oft-invoked shear suppression effect. We also recover the result via a simple calculation. The vorticity gradient effect tends to modulate the density profile. In addition, our method recovers a model for spontaneous zonal flow generation by negative viscosity, stabilized by nonlinear and hyperviscous terms. We highlight the important role of symmetry to implementation of the new method.Comment: To be published in Phys. Rev. E Rap. Comm. 6 pages, 7 figure

Suppression of Cross-Field Transport of a Passive Scalar in Two-Dimensional Magnetohydrodynamic Turbulence

The theory of passive scalar transport in two dimensional turbulent fluids is generalized to the case of 2D MHD. Invariance of the cross correlation of scalar concentration and magnetic potential produces a novel contribution to the concentration flux. This pinch effect is proportional to the mean potential gradient, and is shown to drastically reduce transport of the passive scalar across the mean magnetic field when . Transport parallel to the mean magnetic field is unchanged. Implications for models of transport in turbulent magnetofluids are discussed. PAC NOS. 47.25.Jn, 47.65.+aComment: uuencoded compressed postscript fil

Potential Vorticity Mixing in a Tangled Magnetic Field

A theory of potential vorticity (PV) mixing in a disordered (tangled) magnetic field is presented. The analysis is in the context of $\beta$-plane MHD, with a special focus on the physics of momentum transport in the stably stratified, quasi-2D solar tachocline. A physical picture of mean PV evolution by vorticity advection and tilting of magnetic fields is proposed. In the case of weak-field perturbations, quasi-linear theory predicts that the Reynolds and magnetic stresses balance as turbulence Alfv\'enizes for a larger mean magnetic field. Jet formation is explored quantitatively in the mean field-resistivity parameter space. However, since even a modest mean magnetic field leads to large magnetic perturbations for large magnetic Reynolds number, the physically relevant case is that of a strong but disordered field. We show that numerical calculations indicate that the Reynolds stress is modified well before Alfv\'enization -- i.e. before fluid and magnetic energies balance. To understand these trends, a double-average model of PV mixing in a stochastic magnetic field is developed. Calculations indicate that mean-square fields strongly modify Reynolds stress phase coherence and also induce a magnetic drag on zonal flows. The physics of transport reduction by tangled fields is elucidated and linked to the related quench of turbulent resistivity. We propose a physical picture of the system as a resisto-elastic medium threaded by a tangled magnetic network. Applications of the theory to momentum transport in the tachocline and other systems are discussed in detail.Comment: 17 pages, 10 figures, 2 table

Impact of Resonant Magnetic Perturbations on Zonal Modes, Drift-Wave Turbulence and the L-H Transition Threshold

We study the effects of Resonant Magnetic Perturbations (RMPs) on turbulence, flows and confinement in the framework of resistive drift-wave turbulence. This work was motivated, in parts, by experiments reported at the IAEA 2010 conference [Y. Xu {\it et al}, Nucl. Fusion \textbf{51}, 062030] which showed a decrease of long-range correlations during the application of RMPs. We derive and apply a zero-dimensional predator-prey model coupling the Drift-Wave Zonal Mode system [M. Leconte and P.H. Diamond, Phys. Plasmas \textbf{19}, 055903] to the evolution of mean quantities. This model has both density gradient drive and RMP amplitude as control parameters and predicts a novel type of transport bifurcation in the presence of RMPs. This model allows a description of the full L-H transition evolution with RMPs, including the mean sheared flow evolution. The key results are: i) The L-I and I-H power thresholds \emph{both} increase with RMP amplitude |\bx|, the relative increase of the L-I threshold scales as \Delta P_{\rm LI} \propto |\bx|^2 \nu_*^{-2} \gyro^{-2}, where $\nu_*$ is edge collisionality and \gyro is the sound gyroradius. ii) RMPs are predicted to \emph{decrease} the hysteresis between the forward and back-transition. iii) Taking into account the mean density evolution, the density profile - sustained by the particle source - has an increased turbulent diffusion compared with the reference case without RMPs which provides one possible explanation for the \emph{density pump-out} effect.Comment: 30 pages, IAEA-based articl