Magnetohydrodynamic Turbulence Research Articles

Energy partition between Alfvénic and compressive fluctuations in magnetorotational turbulence with near-azimuthal mean magnetic field

The theory of magnetohydrodynamic (MHD) turbulence predicts that Alfvénic and slow-mode-like compressive fluctuations are energetically decoupled at small scales in the inertial range. The partition of energy between these fluctuations determines the nature of dissipation, which, in many astrophysical systems, happens on scales where plasma is collisionless. However, when the magnetorotational instability (MRI) drives the turbulence, it is difficult to resolve numerically the scale at which both types of fluctuations start to be decoupled because the MRI energy injection occurs in a broad range of wavenumbers, and both types of fluctuations are usually expected to be coupled even at relatively small scales. In this study, we focus on collisional MRI turbulence threaded by a near-azimuthal mean magnetic field, which is naturally produced by the differential rotation of a disc. We show that, in such a case, the decoupling scales are reachable using a reduced MHD model that includes differential-rotation effects. In our reduced MHD model, the Alfvénic and compressive fluctuations are coupled only through the linear terms that are proportional to the angular velocity of the accretion disc. We numerically solve for the turbulence in this model and show that the Alfvénic and compressive fluctuations are decoupled at the small scales of our simulations as the nonlinear energy transfer dominates the linear coupling below the MRI-injection scale. In the decoupling scales, the energy flux of compressive fluctuations contained in the small scales is almost double that of Alfvénic fluctuations. Finally, we discuss the application of this result to prescriptions of ion-to-electron heating ratio in hot accretion flows.

Comparing Quasi-Parallel and Quasi-Perpendicular Configuration in the Terrestrial Magnetosheath: Multifractal Analysis

The terrestrial magnetosheath is characterized by large-amplitude magnetic field fluctuations. In some regions, and depending on the bow-shock geometry, these can be observed on several scales, and show the typical signatures of magnetohydrodynamic turbulence. Using Cluster data, magnetic field spectra and flatness are observed in two intervals separated by a sharp transition from quasi-parallel to quasi-perpendicular magnetic field with respect to the bow-shock normal. The multifractal generalized dimensions Dq and the corresponding multifractal spectrum f(α) were estimated using a coarse-graining method. A p-model fit was used to obtain a single parameter to describe quantitatively the strength of multifractality and intermittency. Results show a clear transition and sharp differences in the intermittency properties for the two regions, with the quasi-parallel turbulence being more intermittent.

Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: Toward linking energy cascade and instabilities.

We derive an exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new incompressible source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.

A Comparison with Theory of Computation and Estimation of Pitch-Angle Diffusion Coefficients from Simulations in Noisy Reduced Magnetohydrodynamic Turbulence

The transport of energetic charged particles in turbulent magnetic fields is a topic of interest in various astrophysical and laboratory plasma contexts. In order to estimate the mean free path λ∥ of a particle in the direction parallel to the mean magnetic field, one can use theoretical expressions that include the pitch-angle diffusion coefficient Dμμ. In this work we evaluate theories for Dμμ in the context of the noisy reduced magnetohydrodynamic (NRMHD) model where turbulent fluctuations are absent at large parallel wavenumbers. For most turbulence models, the standard quasilinear theory predicts zero pitch-angle diffusion only for particles with a 90◦ pitch angle, but for NRMHD a range of pitch angles is affected, leading to infinite λ∥. We examine two theories that include resonance broadening which yield finite λ∥ and compare them with test-particle computer simulations in which the parallel mean free path can be readily obtained. We find that both theories are quite accurate in some regions of the parameter space considered, but neither is particularly good when the particle Larmor radius RL becomes much smaller than the quasilinear resonance limit.

Reconciling cosmic ray transport theory with phenomenological models motivated by Milky-Way data

ABSTRACT Phenomenological models of cosmic ray (CR) transport in the Milky Way can reproduce a wide range of observations assuming that CRs scatter off of magnetic-field fluctuations with spectrum ∝ k−δ and δ ∼ [1.4, 1.67]. We study the extent to which such models can be reconciled with current microphysical theories of CR transport, specifically self-confinement due to the streaming instability and/or extrinsic turbulence due to a cascade of magnetohydrodynamic (MHD) fast modes. We first review why it is that on their own neither theory is compatible with observations. We then highlight that CR transport is a strong function of local plasma conditions in the multiphase interstellar medium, and may be diffusive due to turbulence in some regions and streaming due to self-confinement in others. A multiphase combination of scattering mechanisms can in principle reproduce the main trends in the proton spectrum and the boron-to-carbon ratio. However, models with a combination of scattering by self-excited waves and fast-mode turbulence require significant fine-tuning due to fast-mode damping, unlike phenomenological models that assume undamped Kolmogorov turbulence. The assumption that fast modes follow a weak cascade is also not well justified theoretically, as the weak cascade is suppressed by wave steepening and weak-shock dissipation even in subsonic turbulence. These issues suggest that there may be a significant theoretical gap in our understanding of MHD turbulence. We discuss a few topics at the frontier of MHD turbulence theory that bear on this (possible) gap and that may be relevant for CR scattering.

Measurement of MHD Turbulence Properties by Synchrotron Radiation Techniques

It is well known that magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical environments. The correct understanding of the fundamental properties of MHD turbulence is a pre-requisite for revealing many key astrophysical processes. The development of observation-based measurement techniques has significantly promoted MHD turbulence theory and its implications in astrophysics. After describing the modern understanding of MHD turbulence based on theoretical analysis and direct numerical simulations, we review recent developments related to synchrotron fluctuation techniques. Specifically, we comment on the validation of synchrotron fluctuation techniques and the measurement performance of several properties of magnetic turbulence based on data cubes from MHD turbulence simulations and observations. Furthermore, we propose to strengthen the studies of the magnetization and 3D magnetic field structure’s measurements of interstellar turbulence. At the same time, we also discuss the prospects of new techniques for measuring magnetic field properties and understanding astrophysical processes, using a large number of data cubes from the Low-Frequency Array (LOFAR) and the Square Kilometre Array (SKA).

Damping of Alfvén Waves in MHD Turbulence and Implications for Cosmic Ray Streaming Instability and Galactic Winds

Alfvénic component of MHD turbulence damps Alfvénic waves. The consequences of this effect are important for many processes, from cosmic ray (CR) propagation to launching outflows and winds in galaxies and other magnetized systems. We discuss the differences in the damping of the streaming instability by turbulence and the damping of a plane parallel wave. The former takes place in the system of reference aligned with the local direction of magnetic field along which CRs stream. The latter is in the reference frame of the mean magnetic field and traditionally considered in plasma studies. We also compare the turbulent damping of streaming instability with ion-neutral collisional damping, which becomes the dominant damping effect at a sufficiently low ionization fraction. Numerical testing and astrophysical implications are also discussed.

Studying Interstellar Turbulence Driving Scales Using the Bispectrum

We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify nonlinear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies turbulence-driving scales using density and column density fields. In particular, it shows that the driving scale is phase-coupled to scales present in the turbulent cascade. We also find that the presence of an ordered magnetic field at large scales enhances phase coupling as compared to a pure hydrodynamic case. We therefore suggest the bispectrum and bicoherence as tools for searching for non-locality for wave interactions in MHD turbulence.

The incompressible energy cascade rate in anisotropic solar wind turbulence

Context. The presence of a magnetic guide field induces several types of anisotropy in solar wind turbulence. The energy cascade rate between scales in the inertial range depends strongly on the direction of this magnetic guide field, splitting the energy cascade according to the parallel and perpendicular directions with respect to magnetic guide field. Aims. Using more than two years of Parker Solar Probe (PSP) observations, the isotropy and anisotropy energy cascade rates are investigated. The variance and normalized fluctuation ratios, the kinetic and magnetic energies, and the normalized cross-helicity and residual energy are studied. The connection between the heliocentric distance, the local temperature of the plasma, and the energy cascade components is made. Methods. Using exact relations for fully developed incompressible magnetohydrodynamic (MHD) turbulence, the incompressible energy cascade rate is computed. In particular, using the isotropy and 2D and slab assumptions, the isotropic, perpendicular, and parallel energy cascade rate components are estimated. Results. The variance anisotropy ratios, for both velocity and magnetic fields, do not exhibit a dependence with respect to the heliocentric distance r between 0.2 and 0.8 au. While the velocity normalized fluctuation ratio shows a dependence with r, the magnetic normalized fluctuation ratio does not. A strong correlation between the isotropic and anisotropic energy cascade rates and the temperature is found. A clear dominance of the perpendicular cascades over the parallel cascades as PSP approaches the Sun is observed. A dominant 2D cascade and/or geometry over the slab component in slow solar wind turbulence in the largest MHD scales is observed.

Decomposing magnetic fields in three dimensions over the central molecular zone

ABSTRACT Measuring magnetic fields in the interstellar medium and obtaining their distribution along line-of-sight (LOS) is very challenging with the traditional techniques. The Velocity Gradient Technique (VGT), which utilizes anisotropy of magnetohydrodynamic turbulence, provides an attractive solution. Targeting the central molecular zone (CMZ), we test this approach by applying the VGT to $\rm ^{12}CO$ and $\rm ^{13}CO$ (J = 1–0) data cubes. We first used the scousepy algorithm to decompose the CO line emissions into separate velocity components, and then we constructed pseudo-Stokes parameters via the VGT to map the plane-of-the-sky magnetic fields in three-dimension. We present the decomposed magnetic field maps and investigate their significance. While the LOS integrated magnetic field orientation is shown to be consistent with the polarized dust emission from the Planck survey at 353 GHz, individual velocity components may exhibit different magnetic fields. We present a scheme of magnetic field configuration in the CMZ based on the decomposed magnetic fields. In particular, we observe a nearly vertical magnetic field orientation in the dense clump near the Sgr B2 and a change in the outflow regions around the Sgr A*. Two high-velocity structures associated with an expanding ring in the CMZ show distinct swirling magnetic field structures. These results demonstrate the potential power of the VGT to decompose velocity or density-dependent magnetic structures.

Von Karman correlation similarity in solar wind magnetohydrodynamic turbulence.

A major development underlying hydrodynamic turbulence theory is the similarity decay hypothesis due to von Karman and Howarth, here extended empirically to plasma turbulence in the solar wind. In similarity decay the second-order correlation experiences a continuous transformation based on a universal functional form and a rescaling of energy and characteristic length. Solar wind turbulence follows many principles adapted from classical fluid turbulence, but previously this similarity property has not been examined explicitly. Here, we analyze an ensemble of Elsässer autocorrelation functions computed from Advanced Composition Explorer data at 1 astronomical unit (AU), and demonstrate explicitly that the two-point correlation functions undergo a collapse to a similarity form of the type anticipated from von Karman's hypothesis applied to weakly compressive magnetohydrodynamic turbulence. This provides a firm empirical basis for employing the similarity decay hypothesis to the Elsässer correlations that represent the incompressive turbulence cascade. This approach is of substantial utility in space turbulence data analysis, and for adopting von Karman-type heating rates in global and subgrid-scale dynamical modeling.

Fundamental scales in the kinematic phase of the turbulent dynamo

ABSTRACT The turbulent dynamo is a powerful mechanism that converts turbulent kinetic energy to magnetic energy. A key question regarding the magnetic field amplification by turbulence, is, on what scale, kp, do magnetic fields become most concentrated? There has been some disagreement about whether kp is controlled by the viscous scale, kν (where turbulent kinetic energy dissipates), or the resistive scale, kη (where magnetic fields dissipate). Here, we use direct numerical simulations of magnetohydrodynamic turbulence to measure characteristic scales in the kinematic phase of the turbulent dynamo. We run 104-simulations with hydrodynamic Reynolds numbers of 10 ≤ Re ≤ 3600, and magnetic Reynolds numbers of 270 ≤ Rm ≤ 4000, to explore the dependence of kp on kν and kη. Using physically motivated models for the kinetic and magnetic energy spectra, we measure kν, kη, and kp, making sure that the obtained scales are numerically converged. We determine the overall dissipation scale relations $k_\nu = (0.025^{+0.005}_{-0.006})\, k_\text{turb}\, \mbox{Re}^{3/4}$ and $k_\eta = (0.88^{+0.21}_{-0.23})\, k_\nu \, \mbox{Pm}^{1/2}$, where kturb is the turbulence driving wavenumber and Pm = Rm/Re is the magnetic Prandtl number. We demonstrate that the principle dependence of kp is on kη. For plasmas, where Re ≳ 100, we find that $k_p= (1.2_{-0.2}^{+0.2})\, k_\eta$, with the proportionality constant related to the power-law ‘Kazantsev’ exponent of the magnetic power spectrum. Throughout this study, we find a dichotomy in the fundamental properties of the dynamo where Re > 100, compared to Re < 100. We report a minimum critical hydrodynamic Reynolds number, Recrit = 100 for bonafide turbulent dynamo action.

Test Particle Energization of Heavy Ions in Magnetohydrodynamic Turbulence

Abstract In the present work, we study the energization and displacement of heavy ions through the use of test particles interacting with the electromagnetic fields of magnetohydrodynamic (MHD) turbulence. These fields are obtained from pseudospectral direct numerical solutions of the compressible three-dimensional MHD equations with a strong background magnetic field. We find particle energization to be predominantly perpendicular as the ions become heavier (lower charge-to-mass ratio) and that high displacement is detrimental for perpendicular energization. On the other hand, perpendicular displacement is unaffected by the charge-to-mass ratio, which we explain with a simple guide center model. Using Voronoi tessellation along with this model, we analyze preferential concentration and find that particles behave as tracers in the perpendicular plane, clustering in regions with ∇⊥ · u ⊥ < 0. These regions also have (∇ × E ) z < 0, which is optimal for perpendicular energization, thus providing a mechanism to understand precedent results.

An In-depth Numerical Study of Exact Laws for Compressible Hall Magnetohydrodynamic Turbulence

Abstract Various exact laws governing compressible magnetohydrodynamic (MHD) and compressible Hall-MHD (CHMHD) turbulence have been derived in recent years. Other than their fundamental theoretical interest, these laws are generally used to estimate the energy dissipation rate from spacecraft observations in order to address diverse problems related, e.g., to heating of the solar wind and magnetospheric plasmas. Here we use various 10243 direct numerical simulation data of free-decay isothermal CHMHD turbulence obtained with the GHOST code (Geophysical High-Order Suite for Turbulence) to analyze two of the recently derived exact laws. The simulations reflect different intensities of the initial Mach number and the background magnetic field. The analysis demonstrates the equivalence of the two laws in the inertial range and relates the strength of the Hall effect to the amplitude of the cascade rate at sub-ion scales. When taken in their general form (i.e., not limited to the inertial range), some subtleties regarding the validity of the stationarity assumption or the absence of the forcing in the simulations are discussed. We show that the free-decay nature of the turbulence induces a shift from a large-scale forcing toward the presence of a scale-dependent reservoir of energy fueling the cascade or dissipation. The reduced form of the exact laws (valid in the inertial range) ultimately holds even if the stationarity assumption is not fully verified.

Relativistic Particle Transport and Acceleration in Structured Plasma Turbulence

Abstract We discuss the phenomenon of energization of relativistic charged particles in three-dimensional incompressible MHD turbulence and the diffusive properties of the motion of the same particles. We show that the random electric field induced by turbulent plasma motion leads test particles moving in a simulated box to be accelerated in a stochastic way, a second-order Fermi process. A small fraction of these particles happen to be trapped in large-scale structures, most likely formed due to the interaction of islands in the turbulence. Such particles get accelerated exponentially, provided their pitch angle satisfies some conditions. We discuss at length the characterization of the accelerating structure and the physical processes responsible for rapid acceleration. We also comment on the applicability of the results to realistic astrophysical turbulence.

The Yaglom Scaling of the Third-order Structure Functions in the Inner Heliosphere Observed by Helios 1 and 2

Abstract The third-order scaling law, Yaglom law, of Elsässer fluctuations in the solar wind is believed to reflect the inertial range energy cascade of the MHD turbulence and provides an approach to evaluate the cascade rate. However, the occurrence ratio with the Yaglom scaling law, the fraction of the intervals where the Yaglom linear scaling is observed, is reported to be low (0.05–0.30) in the high-latitude solar wind observed by the Ulysses spacecraft. Whether the occurrence ratio could be higher in other conditions remains unknown. Here, we analyze the occurrence of the third-order scaling in the inner heliosphere with the first 100 days of observation of the Helios 1 and Helios 2 spacecraft. We investigate 162 intervals in the leading edges and 323 intervals in the trailing edges of the high-speed streams, respectively. All of these intervals have a time duration of 9 hr. We find that in the inner heliosphere the occurrence ratio is relatively high in the leading edges (0.58) and moderate in the trailing edges (0.45). Among the data intervals with the Yaglom scaling in the leading edges, 94.7% of intervals give positive rates, while in the trailing edges 78.6% give negative rates. The variations of the occurrence ratio with various turbulence parameters are shown. The cascade rate is found to be higher than the proton heating rate calculated from the data, which have third-order scaling. These new results raise several questions related to the nature and origin of the third-order scaling law and may initiate new studies on solar wind turbulence.

How Transverse Waves Drive Turbulence in the Solar Corona

Oscillatory power is pervasive throughout the solar corona, and magnetohydrodynamic (MHD) waves may carry a significant energy flux throughout the Sun’s atmosphere. As a result, over much of the past century, these waves have attracted great interest in the context of the coronal heating problem. They are a potential source of the energy required to maintain the high-temperature plasma and may accelerate the fast solar wind. Despite many observations of coronal waves, large uncertainties inhibit reliable estimates of their exact energy flux, and as such, it remains unclear whether they can contribute significantly to the coronal energy budget. A related issue concerns whether the wave energy can be dissipated over sufficiently short time scales to balance the atmospheric losses. For typical coronal parameters, energy dissipation rates are very low and, thus, any heating model must efficiently generate very small-length scales. As such, MHD turbulence is a promising plasma phenomenon for dissipating large quantities of energy quickly and over a large volume. In recent years, with advances in computational and observational power, much research has highlighted how MHD waves can drive complex turbulent behaviour in the solar corona. In this review, we present recent results that illuminate the energetics of these oscillatory processes and discuss how transverse waves may cause instability and turbulence in the Sun’s atmosphere.

Superdiffusion of cosmic rays in compressible magnetized turbulence

ABSTRACT Owing to the complexity of turbulent magnetic fields, modelling the diffusion of cosmic rays is challenging. Based on the current understanding of anisotropic magnetohydrodynamic (MHD) turbulence, we use test particles to examine the cosmic rays’ superdiffusion in the direction perpendicular to the mean magnetic field. By changing Alfvén Mach number MA and sonic Mach number MS of compressible MHD simulations, our study covers a wide range of astrophysical conditions including subsonic warm gas phase and supersonic cold molecular gas. We show that freely streaming cosmic rays’ perpendicular displacement increases as 3/2 to the power of the time travelled along local magnetic field lines. This power-law index changes to 3/4 if the parallel propagation is diffusive. We find that the cosmic rays’ parallel mean free path decreases in a power-law relation of $M_\mathrm{ A}^{-2}$ in supersonic turbulence. We investigate the energy fraction of slow, fast, and Alfvénic modes and confirm the dominance of Alfvénic modes in the perpendicular superdiffusion. In particular, the energy fraction of fast mode, which is the main agent for pitch-angle scattering, increases with MA, but is insensitive to MS ≥ 2. Accordingly, our results suggest that the suppressed diffusion in supersonic molecular clouds arises primarily due to the variations of MA instead of MS.

Cosmic-ray Transport in Magnetohydrodynamic Turbulence

Abstract This paper studies cosmic-ray (CR) transport in magnetohydrodynamic (MHD) turbulence. CR transport is strongly dependent on the properties of the magnetic turbulence. We perform test particle simulations to study the interactions of CR with both total MHD turbulence and decomposed MHD modes. The spatial diffusion coefficients and the pitch angle scattering diffusion coefficients are calculated from the test particle trajectories in turbulence. Our results confirm that the fast modes dominate the CR propagation, whereas Alfvén and slow modes are much less efficient and have shown similar pitch-angle scattering rates. We investigate the cross field transport on large and small scales. On large/global scales, normal diffusion is observed and the diffusion coefficient is suppressed by M A ζ compared to the parallel diffusion coefficients, with ζ closer to 4 in Alfvén modes than that in total turbulence, as theoretically expected. For the CR transport on scales smaller than the turbulence injection scale, both the local and global magnetic reference frames are adopted. Superdiffusion is observed on such small scales in all the cases. Particularly, CR transport in Alfvén modes show clear Richardson diffusion in the local reference frame. The diffusion transitions smoothly from the Richardson’s one with index 1.5 to normal diffusion as the particle mean free path decreases from λ ∥ ≫ L to λ ∥ ≪ L, where L is the injection/coherence length of turbulence. Our results have broad applications to CRs in various astrophysical environments.

Three-dimensional magnetohydrodynamic flow around a 180° sharp bend under transverse magnetic field

This study attempts to characterize the variation of pressure loss and the evolution of vortex structures in the steady three-dimensional flow around a 180° sharp bend under a transverse magnetic field. This study is conducted with the Reynolds number, 100≤Re≤400, and Hartmann number, 0≤Ha≤2000. This range of Re and Ha captures both complex three-dimensional structures and the inception of quasi-two-dimensional flows. Numerical simulations display how the pressure loss across the bend region (Δp0) and the vortex structures undergo four regimes by increasing Ha for fixed Re. These regimes are referred to as regimes I–IV. N1c, N2c, and N3c, the critical values of interaction number Nc for the first appearance of regimes II–IV, are recognized at values 0.8, 3.2, and 40, respectively. In regime I (N≤0.8), Δp0 increases slightly and the magnetohydrodynamic flow promotes the recirculating bubble. In regime II (0.8<N≤3.2), as Δp0 decreases, the scope of the recirculating bubble reaches its peak. In regime III (3.2<N≤40), Δp0 grows, while the shrinkage of the recirculating bubble is triggered. Simultaneously, the flow tends to be two-dimensional [J. Sommeria and R. Moreau, “Why, how, and when, MHD turbulence becomes two-dimensional,” J. Fluid Mech. 118, 507 (1982)]. In regime IV (40<N), Δp0 is linearly dependent on Ha/Re. The non-monotonic behavior of the recirculating bubble length is caused by the redistribution of momentum at low Ha and by the predominant effect of the Lorentz force at large Ha. The law of how to distinguish the three-dimensional (3D) flow and quasi-two-dimensional (Q2D) flow is discovered by assessing the recirculating bubble length in the center plane.