Inefficient Magnetic-Field Amplification in Supersonic Laser-Plasma Turbulence

We report a laser-plasma experiment that was carried out at the LMJ-PETAL facility and realized the first magnetized, turbulent, supersonic (Ma_{turb}≈2.5) plasma with a large magnetic Reynolds number (Rm≈45) in the laboratory. Initial seed magnetic fields were amplified, but only moderately so, and did not become dynamically significant. A notable absence of magnetic energy at scales smaller than the outer scale of the turbulent cascade was also observed. Our results support the notion that moderately supersonic, low-magnetic-Prandtl-number plasma turbulence is inefficient at amplifying magnetic fields compared to its subsonic, incompressible counterpart.

Supersonic plasma turbulence in the laboratory

The properties of supersonic, compressible plasma turbulence determine the behavior of many terrestrial and astrophysical systems. In the interstellar medium and molecular clouds, compressible turbulence plays a vital role in star formation and the evolution of our galaxy. Observations of the density and velocity power spectra in the Orion B and Perseus molecular clouds show large deviations from those predicted for incompressible turbulence. Hydrodynamic simulations attribute this to the high Mach number in the interstellar medium (ISM), although the exact details of this dependence are not well understood. Here we investigate experimentally the statistical behavior of boundary-free supersonic turbulence created by the collision of two laser-driven high-velocity turbulent plasma jets. The Mach number dependence of the slopes of the density and velocity power spectra agree with astrophysical observations, and supports the notion that the turbulence transitions from being Kolmogorov-like at low Mach number to being more Burgers-like at higher Mach numbers.

Magneto-immutable turbulence in weakly collisional plasmas

We propose that pressure anisotropy causes weakly collisional turbulent plasmas to self-organize so as to resist changes in magnetic-field strength. We term this effect "magneto-immutability" by analogy with incompressibility (resistance to changes in pressure). The effect is important when the pressure anisotropy becomes comparable to the magnetic pressure, suggesting that in collisionless, weakly magnetized (high-β) plasmas its dynamical relevance is similar to that of incompressibility. Simulations of magnetized turbulence using the weakly collisional Braginskii model show that magneto-immutable turbulence is surprisingly similar, in most statistical measures, to critically balanced MHD turbulence. However, in order to minimize magnetic-field variation, the flow direction becomes more constrained than in MHD, and the turbulence is more strongly dominated by magnetic energy (a nonzero "residual energy"). These effects represent key differences between pressure-anisotropic and fluid turbulence, and should be observable in the β ≳ 1 turbulent solar wind.

Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma

Magnetic fields are ubiquitous in the Universe. The energy density of these fields is typically comparable to the energy density of the fluid motions of the plasma in which they are embedded, making magnetic fields essential players in the dynamics of the luminous matter. The standard theoretical model for the origin of these strong magnetic fields is through the amplification of tiny seed fields via turbulent dynamo to the level consistent with current observations. However, experimental demonstration of the turbulent dynamo mechanism has remained elusive, since it requires plasma conditions that are extremely hard to re-create in terrestrial laboratories. Here we demonstrate, using laser-produced colliding plasma flows, that turbulence is indeed capable of rapidly amplifying seed fields to near equipartition with the turbulent fluid motions. These results support the notion that turbulent dynamo is a viable mechanism responsible for the observed present-day magnetization.

Publisher's Note: Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High-β Plasma [Phys. Rev. Lett. 119, 155101 (2017)]

This corrects the article DOI: 10.1103/PhysRevLett.119.155101.

Kinetic Simulations of the Interruption of Large-Amplitude Shear-Alfvén Waves in a High-β Plasma

Using two-dimensional hybrid-kinetic simulations, we explore the nonlinear "interruption" of standing and traveling shear-Alfvén waves in collisionless plasmas. Interruption involves a self-generated pressure anisotropy removing the restoring force of a linearly polarized Alfvénic perturbation, and occurs for wave amplitudes δB_{⊥}/B_{0}≳β^{-1/2} (where β is the ratio of thermal to magnetic pressure). We use highly elongated domains to obtain maximal scale separation between the wave and the ion gyroscale. For standing waves above the amplitude limit, we find that the large-scale magnetic field of the wave decays rapidly. The dynamics are strongly affected by the excitation of oblique firehose modes, which transition into long-lived parallel fluctuations at the ion gyroscale and cause significant particle scattering. Traveling waves are damped more slowly, but are also influenced by small-scale parallel fluctuations created by the decay of firehose modes. Our results demonstrate that collisionless plasmas cannot support linearly polarized Alfvén waves above δB_{⊥}/B_{0}∼β^{-1/2}. They also provide a vivid illustration of two key aspects of low-collisionality plasma dynamics: (i) the importance of velocity-space instabilities in regulating plasma dynamics at high β, and (ii) how nonlinear collisionless processes can transfer mechanical energy directly from the largest scales into thermal energy and microscale fluctuations, without the need for a scale-by-scale turbulent cascade.

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows

This paper presents a complete theoretical framework for studying turbulence and transport in rapidly rotating tokamak plasmas. The fundamental scale separations present in plasma turbulence are codified as an asymptotic expansion in the ratio ε = ρi/α of the gyroradius to the equilibrium scale length. Proceeding order by order in this expansion, a set of coupled multiscale equations is developed. They describe an instantaneous equilibrium, the fluctuations driven by gradients in the equilibrium quantities, and the transport-timescale evolution of mean profiles of these quantities driven by the interplay between the equilibrium and the fluctuations. The equilibrium distribution functions are local Maxwellians with each flux surface rotating toroidally as a rigid body. The magnetic equilibrium is obtained from the generalized Grad-Shafranov equation for a rotating plasma, determining the magnetic flux function from the mean pressure and velocity profiles of the plasma. The slow (resistive-timescale) evolution of the magnetic field is given by an evolution equation for the safety factor q. Large-scale deviations of the distribution function from a Maxwellian are given by neoclassical theory. The fluctuations are determined by the 'high-flow' gyrokinetic equation, from which we derive the governing principle for gyrokinetic turbulence in tokamaks: the conservation and local (in space) cascade of the free energy of the fluctuations (i.e. there is no turbulence spreading). Transport equations for the evolution of the mean density, temperature and flow velocity profiles are derived. These transport equations show how the neoclassical and fluctuating corrections to the equilibrium Maxwellian act back upon the mean profiles through fluxes and heating. The energy and entropy conservation laws for the mean profiles are derived from the transport equations. Total energy, thermal, kinetic and magnetic, is conserved and there is no net turbulent heating. Entropy is produced by the action of fluxes flattening gradients, Ohmic heating and the equilibration of interspecies temperature differences. This equilibration is found to include both turbulent and collisional contributions. Finally, this framework is condensed, in the low-Mach-number limit, to a more concise set of equations suitable for numerical implementation.

Linear structures in the core of the Coma cluster of galaxies

The hot x-ray-emitting plasma in galaxy clusters is predicted to have turbulent motion, which can contribute around 10% of the cluster's central energy density. We report deep Chandra X-ray Observatory observations of the Coma cluster core, showing the presence of quasi-linear high-density arms spanning 150 kiloparsecs, consisting of low-entropy material that was probably stripped from merging subclusters. Two appear to be connected with a subgroup of galaxies at a 650-kiloparsec radius that is merging into the cluster, implying coherence over several hundred million years. Such a long lifetime implies that strong isotropic turbulence and conduction are suppressed in the core, despite the unrelaxed state of the cluster. Magnetic fields are presumably responsible. The structures seen in Coma present insight into the past billion years of subcluster merger activity.

Fast collisionless reconnection and electron heating in strongly magnetized plasmas

Magnetic reconnection in strongly magnetized (low-beta), weakly collisional plasmas is investigated by using a novel fluid-kinetic model [Zocco and Schekochihin, Phys. Plasmas 18, 102309 (2011)] which retains nonisothermal electron kinetics. It is shown that electron heating via Landau damping (linear phase mixing) is the dominant dissipation mechanism. In time, electron heating occurs after the peak of the reconnection rate; in space, it is concentrated along the separatrices of the magnetic island. For sufficiently large systems, the peak reconnection rate is cE(∥)(max) ≈ 0.2v(A)B(y,0), where v(A) is the Alfvén speed based on the reconnecting field B(y,0). The island saturation width is the same as in magnetohydrodynamics models except for small systems, when it becomes comparable to the kinetic scales.

Experimental signatures of critically balanced turbulence in MAST

Beam emission spectroscopy (BES) measurements of ion-scale density fluctuations in the MAST tokamak are used to show that the turbulence correlation time, the drift time associated with ion temperature or density gradients, the particle (ion) streaming time along the magnetic field, and the magnetic drift time are consistently comparable, suggesting a "critically balanced" turbulence determined by the local equilibrium. The resulting scalings of the poloidal and radial correlation lengths are derived and tested. The nonlinear time inferred from the density fluctuations is longer than the other times; its ratio to the correlation time scales as ν(*i)(-0.8 ± 0.1), where ν(*i) = ion  collision rate/streaming rate. This is consistent with turbulent decorrelation being controlled by a zonal component, invisible to the BES, with an amplitude exceeding those of the drift waves by ∼ ν(*i)(-0.8).

Alignment and scaling of large-scale fluctuations in the solar wind

We investigate the dependence of solar wind fluctuations measured by the Wind spacecraft on scale and on the degree of alignment between oppositely directed Elsasser fields. This alignment controls the strength of the nonlinear interactions and, therefore, the turbulence. We find that at scales larger than the outer scale of the turbulence the Elsasser fluctuations become on average more antialigned as the outer scale is approached from above. Conditioning structure functions using the alignment angle reveals turbulent scaling of unaligned fluctuations at scales previously believed to lie outside the turbulent cascade in the "1/f range." We argue that the 1/f range contains a mixture of a noninteracting antialigned population of Alfvén waves and magnetic force-free structures plus a subdominant population of unaligned cascading turbulent fluctuations.

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

A two-dimensional (2D) linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of reduced magnetohydrodynamics. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al., Phys. Plasmas 14, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids (k(max)L(CS)~S(3/8), where k(max) is the wave number of fastest growing mode, S=L(CS)V(A)/η is the Lundquist number, L(CS) is the length of the sheet, V(A) is the Alfvén speed, and η is the plasma resistivity), which grows super Alfvénically fast (γ(max)τ(A)~S(1/4), where γ(max) is the maximum growth rate, and τ(A)=L(CS)/V(A)). For typical background profiles, the growth rate and the wave number are found to increase in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfvén speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability γ(max)τ(A)~k(max)L(CS)~S(1/2). The effect of viscosity (ν) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers Pm=ν/η, it is found that γ(max)~S(1/4)Pm(-5/8) and k(max)L(CS)~S(3/8)Pm(-3/16), leading to the prediction that the critical Lundquist number for plasmoid instability in the Pm>>1 regime is S(crit)~10(4)Pm(1/2). These results are verified via direct numerical simulation of the linearized equations, using an analytical 2D SP equilibrium solution.

Zero-turbulence manifold in a toroidal plasma

Sheared toroidal flows can cause bifurcations to zero-turbulent-transport states in tokamak plasmas. The maximum temperature gradients that can be reached are limited by subcritical turbulence driven by the parallel velocity gradient. Here it is shown that q/ϵ (magnetic field pitch/inverse aspect ratio) is a critical control parameter for sheared tokamak turbulence. By reducing q/ϵ, far higher temperature gradients can be achieved without triggering turbulence, in some instances comparable to those found experimentally in transport barriers. The zero-turbulence manifold is mapped out, in the zero-magnetic-shear limit, over the parameter space (γ(E), q/ϵ, R/L(T)), where γ(E) is the perpendicular flow shear and R/L(T) is the normalized inverse temperature gradient scale. The extent to which it can be constructed from linear theory is discussed.

Scaling of spontaneous rotation with temperature and plasma current in tokamaks

Using theoretical arguments, a simple scaling law for the size of the intrinsic rotation observed in tokamaks in the absence of a momentum injection is found: The velocity generated in the core of a tokamak must be proportional to the ion temperature difference in the core divided by the plasma current, independent of the size of the device. The constant of proportionality is of the order of 10 km·s(-1)·MA·keV(-1). When the intrinsic rotation profile is hollow, i.e., it is countercurrent in the core of the tokamak and cocurrent in the edge, the scaling law presented in this Letter fits the data remarkably well for several tokamaks of vastly different size and heated by different mechanisms.

Large-scale magnetic field generation by randomly forced shearing waves

A rigorous theory for the generation of a large-scale magnetic field by random nonhelically forced motions of a conducting fluid combined with a linear shear is presented in the analytically tractable limit of low magnetic Reynolds number (Rm) and weak shear. The dynamo is kinematic and due to fluctuations in the net (volume-averaged) electromotive force. This is a minimal proof-of-concept quasilinear calculation aiming to put the shear dynamo, a new effect recently found in numerical experiments, on a firm theoretical footing. Numerically observed scalings of the wave number and growth rate of the fastest-growing mode, previously not understood, are derived analytically. The simplicity of the model suggests that shear dynamo action may be a generic property of sheared magnetohydrodynamic turbulence.

Critically balanced ion temperature gradient turbulence in fusion plasmas

Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat fluxes on temperature gradient and magnetic field line pitch are found to agree with numerical results in both the driving and inertial ranges. Evidence is provided to support the critical balance conjecture that parallel streaming and nonlinear perpendicular decorrelation times are comparable at all spatial scales, leading to a scaling relationship between parallel and perpendicular spatial scales. This indicates that even strongly magnetized plasma turbulence is intrinsically three dimensional.

Gyrokinetic simulations of solar wind turbulence from ion to electron scales

A three-dimensional, nonlinear gyrokinetic simulation of plasma turbulence resolving scales from the ion to electron gyroradius with a realistic mass ratio is presented, where all damping is provided by resolved physical mechanisms. The resulting energy spectra are quantitatively consistent with a magnetic power spectrum scaling of k(-2.8) as observed in in situ spacecraft measurements of the "dissipation range" of solar wind turbulence. Despite the strongly nonlinear nature of the turbulence, the linear kinetic Alfvén wave mode quantitatively describes the polarization of the turbulent fluctuations. The collisional ion heating is measured at subion-Larmor radius scales, which provides evidence of the ion entropy cascade in an electromagnetic turbulence simulation.

Turbulent transport in tokamak plasmas with rotational shear

Nonlinear gyrokinetic simulations are conducted to investigate turbulent transport in tokamak plasmas with rotational shear. At sufficiently large flow shears, linear instabilities are suppressed, but transiently growing modes drive subcritical turbulence whose amplitude increases with flow shear. This leads to a local minimum in the heat flux, indicating an optimal E×B shear value for plasma confinement. Local maxima in the momentum fluxes are observed, implying the possibility of bifurcations in the E×B shear. The critical temperature gradient for the onset of turbulence increases with flow shear at low flow shears; at higher flow shears, the dependence of heat flux on temperature gradient becomes less stiff. The turbulent Prandtl number is found to be largely independent of temperature and flow gradients, with a value close to unity.

Momentum injection in tokamak plasmas and transitions to reduced transport

The effect of momentum injection on the temperature gradient in tokamak plasmas is studied. A plausible scenario for transitions to reduced transport regimes is proposed. The transition happens when there is sufficient momentum input so that the velocity shear can suppress or reduce the turbulence. However, it is possible to drive too much velocity shear and rekindle the turbulent transport. The optimal level of momentum injection is determined. The reduction in transport is maximized in the regions of low or zero magnetic shear.

Anisotropy of imbalanced Alfvénic turbulence in fast solar wind

We present the first measurement of the scale-dependent power anisotropy of Elsasser variables in imbalanced fast solar wind turbulence. The dominant Elsasser mode is isotropic at lower spacecraft frequencies but becomes increasingly anisotropic at higher frequencies. The subdominant mode is anisotropic throughout. There are two distinct subranges exhibiting different scalings within what is normally considered the inertial range. The low Alfvén ratio and the different scaling of the Elsasser modes suggests an interpretation of the observed discrepancy between the velocity and magnetic field scalings, the total energy is dominated by the latter. These results do not appear to be fully explained by any of the current theories of incompressible imbalanced MHD turbulence.

Fast magnetic reconnection in the plasmoid-dominated regime

A conceptual model of resistive magnetic reconnection via a stochastic plasmoid chain is proposed. The global reconnection rate is shown to be independent of the Lundquist number. The distribution of fluxes in the plasmoids is shown to be an inverse-square law. It is argued that there is a finite probability of emergence of abnormally large plasmoids, which can disrupt the chain (and may be responsible for observable large abrupt events in solar flares and sawtooth crashes). A criterion for the transition from the resistive magnetohydrodynamic to the collisionless regime is provided.

Transport bifurcation in a rotating tokamak plasma

The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all nonzero flow shear values, but that subcritical turbulence can be sustained nonlinearly at a wide range of temperature gradients. Flow shear increases the nonlinear temperature gradient threshold for turbulence but also increases the sensitivity of the heat flux to changes in the temperature gradient, except over a small range near the threshold where the sensitivity is decreased. A bifurcation in the equilibrium gradients is found: for a given input of heat, it is possible, by varying the applied torque, to trigger a transition to significantly higher temperature and flow gradients.

Anisotropy of solar wind turbulence between ion and electron scales

The anisotropy of turbulence in the fast solar wind, between the ion and electron gyroscales, is directly observed using a multispacecraft analysis technique. Second order structure functions are calculated at different angles to the local magnetic field, for magnetic fluctuations both perpendicular and parallel to the mean field. In both components, the structure function value at large angles to the field S{⊥} is greater than at small angles S{∥}: in the perpendicular component S{⊥}/S{∥}=5±1 and in the parallel component S{⊥}/S{∥}>3, implying spatially anisotropic fluctuations, k{⊥}>k{∥}. The spectral index of the perpendicular component is -2.6 at large angles and -3 at small angles, in broad agreement with critically balanced whistler and kinetic Alfvén wave predictions. For the parallel component, however, it is shallower than -1.9, which is considerably less steep than predicted for a kinetic Alfvén wave cascade.

Formation of plasmoid chains in magnetic reconnection

A detailed numerical study of magnetic reconnection in resistive MHD for very large, previously inaccessible, Lundquist numbers (10(4) <or= S <or= 10(8)) is reported. Large-aspect-ratio Sweet-Parker current sheets are shown to be unstable to super-Alfvénically fast formation of plasmoid (magnetic-island) chains. The plasmoid number scales as S(3/8) and the instability growth rate in the linear stage as S(1/4), in agreement with the theory by Loureiro et al. [Phys. Plasmas 14, 100703 (2007)]. In the nonlinear regime, plasmoids continue to grow faster than they are ejected and completely disrupt the reconnection layer. These results suggest that high-Lundquist-number reconnection is inherently time-dependent and hence call for a substantial revision of the standard Sweet-Parker quasistationary picture for S>10(4).

Nonlinear phase mixing and phase-space cascade of entropy in gyrokinetic plasma turbulence

Electrostatic turbulence in weakly collisional, magnetized plasma can be interpreted as a cascade of entropy in phase space, which is proposed as a universal mechanism for dissipation of energy in magnetized plasma turbulence. When the nonlinear decorrelation time at the scale of the thermal Larmor radius is shorter than the collision time, a broad spectrum of fluctuations at sub-Larmor scales is numerically found in velocity and position space, with theoretically predicted scalings. The results are important because they identify what is probably a universal Kolmogorov-like regime for kinetic turbulence; and because any physical process that produces fluctuations of the gyrophase-independent part of the distribution function may, via the entropy cascade, result in turbulent heating at a rate that increases with the fluctuation amplitude, but is independent of the collision frequency.

Generation of magnetic field by combined action of turbulence and shear

The feasibility of a mean-field dynamo in nonhelical turbulence with a superimposed linear shear is studied numerically in elongated shearing boxes. Exponential growth of the magnetic field at scales much larger than the outer scale of the turbulence is found. The characteristic scale of the field is lB proportional S(-1/2) and the growth rate is gamma proportional S, where S is the shearing rate. This newly discovered shear dynamo effect potentially represents a very generic mechanism for generating large-scale magnetic fields in a broad class of astrophysical systems with spatially coherent mean flows.

Nonlinear growth of firehose and mirror fluctuations in astrophysical plasmas

In turbulent high-beta astrophysical plasmas (exemplified by the galaxy cluster plasmas), pressure-anisotropy-driven firehose and mirror fluctuations grow nonlinearly to large amplitudes, deltaB/B approximately 1, on a time scale comparable to the turnover time of the turbulent motions. The principle of their nonlinear evolution is to generate secularly growing small-scale magnetic fluctuations that on average cancel the temporal change in the large-scale magnetic field responsible for the pressure anisotropies. The presence of small-scale magnetic fluctuations may dramatically affect the transport properties and, thereby, the large-scale dynamics of the high-beta astrophysical plasmas.

Kinetic simulations of magnetized turbulence in astrophysical plasmas

This Letter presents the first ab initio, fully electromagnetic, kinetic simulations of magnetized turbulence in a homogeneous, weakly collisional plasma at the scale of the ion Larmor radius (ion gyroscale). Magnetic- and electric-field energy spectra show a break at the ion gyroscale; the spectral slopes are consistent with scaling predictions for critically balanced turbulence of Alfvén waves above the ion gyroscale (spectral index -5/3) and of kinetic Alfvén waves below the ion gyroscale (spectral indices of -7/3 for magnetic and -1/3 for electric fluctuations). This behavior is also qualitatively consistent with in situ measurements of turbulence in the solar wind. Our findings support the hypothesis that the frequencies of turbulent fluctuations in the solar wind remain well below the ion cyclotron frequency both above and below the ion gyroscale.

Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers

Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rmc for dynamo on the hydrodynamic Reynolds number Re is obtained for 1 less than or similar Re less than or similar 6700. In the limit Pm<<1, Rmc is about 3 times larger than for the previously well-established dynamo at large and moderate Prandtl numbers: Rmc less than or similar 200 for Re greater than or similar 6000 compared to Rmc approximately 60 for Pm>or=1. It is not yet possible to determine numerically whether the growth rate of the magnetic energy is proportional, Rm1/2 in the limit Rm-->infinity, as it should be if the dynamo is driven by the inertial-range motions at the resistive scale.

X-point collapse and saturation in the nonlinear tearing mode reconnection

We study the nonlinear evolution of the resistive tearing mode in slab geometry in two dimensions. We show that, in the strongly driven regime (large delta'), a collapse of the X point occurs once the island width exceeds a certain critical value approximately 1/delta'. A current sheet is formed and the reconnection is exponential in time with a growth rate proportional eta(1/2), where eta is the resistivity. If the aspect ratio of the current sheet is sufficiently large, the sheet can itself become tearing-mode unstable, giving rise to secondary islands, which then coalesce with the original island. The saturated state depends on the value of delta'. For small delta', the saturation amplitude is proportional delta' and quantitatively agrees with the theoretical prediction. If delta' is large enough for the X-point collapse to have occurred, the saturation amplitude increases noticeably and becomes independent of delta'.

Saturated state of the nonlinear small-scale dynamo

We consider the problem of incompressible, forced, nonhelical, homogeneous, and isotropic MHD turbulence with no mean magnetic field and large magnetic Prandtl number. This type of MHD turbulence is the end state of the turbulent dynamo, which generates folded fields with small-scale direction reversals. We propose a model in which saturation is achieved as a result of the velocity statistics becoming anisotropic with respect to the local direction of the magnetic folds. The model combines the effects of weakened stretching and quasi-two-dimensional mixing and produces magnetic-energy spectra in remarkable agreement with numerical results at least in the case of a one-scale flow. We conjecture that the statistics seen in numerical simulations could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.

Geometric properties of passive random advection

Geometric properties of a random Gaussian short-time correlated velocity field are studied by considering the statistics of a passively advected metric tensor. That describes the universal properties of the fluctuations of tensor objects frozen into the fluid and passively advected by it. The problem of the one-point statistics of covariant and contravariant tensors is solved exactly, provided that the advected fields do not reach diffusive scales, which would break the symmetry of the problem.