Strong Magnetohydrodynamic Turbulence Research Articles

Identification of the weak-to-strong transition in Alfvénic turbulence from space plasma

AbstractPlasma turbulence is a ubiquitous dynamical process that transfers energy across many spatial and temporal scales in astrophysical and space plasma systems. Although the theory of anisotropic magnetohydrodynamic (MHD) turbulence has successfully described natural phenomena, its core prediction of an Alfvénic transition from weak to strong MHD turbulence when energy cascades from large to small scales has not been observationally confirmed. Here we report evidence for the Alfvénic weak-to-strong transition in small-amplitude, turbulent MHD fluctuations in Earth’s magnetosheath using data from four Cluster spacecraft. Our observations demonstrate the universal existence of strong turbulence accompanied by weak turbulent fluctuations on large scales. Moreover, we find that the nonlinear interactions of MHD turbulence are crucial to the energy cascade, as they broaden the cascade directions and fluctuating frequencies. The observed connection between weak and strong MHD turbulence systems may be present in many astrophysical environments, such as star formation, energetic particle transport, turbulent dynamos, and solar corona or solar wind heating.

First-Principles Fermi Acceleration in Magnetized Turbulence.

This Letter provides a concrete implementation of Fermi's model of particle acceleration in magnetohydrodynamic (MHD) turbulence, connecting the rate of energization to the gradients of the velocity of magnetic field lines, which it characterizes within a multifractal picture of turbulence intermittency. It then derives a transport equation in momentum space for the distribution function. This description is shown to be substantiated by a large-scale numerical simulation of strong MHD turbulence. The present general framework can be used to model particle acceleration in a variety of environments.

Particle acceleration in strong MHD turbulence

Nonthermal acceleration of particles in magnetohydrodynamic (MHD) turbulence plays a central role in a wide variety of astrophysical sites. This physics is addressed here in the context of a strong turbulence, composed of coherent structures rather than waves, beyond the realm of quasilinear theory. The present description tracks the momentum of the particle through a sequence of frames in which the electric field vanishes, in the spirit of the original Fermi scenario. It connects the sources of energy gain (or loss) to the gradients of the velocity of the magnetic field lines, in particular the acceleration and the shear of their velocity flow projected along the field line direction, as well as their compression in the transverse plane. Those velocity gradients are subject to strong intermittency: they are spatially localized, and their strengths obey power law distributions, as demonstrated through direct measurements in the incompressible MHD simulation of the Johns Hopkins University database. This intermittency impacts the acceleration process in a significant way, which opens up prospects for a rich phenomenology. In particular, the momentum distribution, which is here captured through an analytical random walk model, displays extended power law tails with soft-to-hard evolution in time, in general agreement with recent kinetic numerical simulations. Extensions to this description and possible avenues of exploration are discussed.

Eulerian space-time correlation of strong magnetohydrodynamic turbulence

In this work the scale-dependent temporal decorrelation of incompressible MHD turbulence is investigated by means of high-resolution numerical simulations and phenomenological modeling. The simulations show that counterpropagating Alfv\'enic fluctuations at each scale decorrelate at the same rate in both balanced and imbalanced turbulence, and consistent with random advection of small-scale eddies by the velocity of the energy containing scales.

Alfvénic Fluctuations Associated With Jupiter's Auroral Emissions

AbstractThe Alfvén wave mode transmits field‐aligned currents and large‐scale turbulence throughout Jupiter's magnetosphere. Magnetometer data from the Juno spacecraft have provided the first observations of Alfvénic fluctuations along the polar magnetic flux tubes connected to Jupiter's main auroral oval and the Jovian satellites. Transverse magnetic field perturbations associated with Io are observed up to ~90° away from main Io footprint, supporting the presence of extended Alfvénic wave activity throughout the Io footprint tail. Additional broadband fluctuations measured equatorward of the statistical auroral oval are composed of incompressible magnetic turbulence that maps to Jupiter's equatorial plasma sheet at radial distances within ~20 RJ. These fluctuations exhibit a k|| power spectrum consistent with strong magnetohydrodynamic turbulence. This turbulence can generate up to ~100 mW/m2 of Poynting flux to power the Jovian aurora in regions connected to the inner magnetosphere's central plasma sheet.

Magnetic field amplification and high-energy emission properties of compact galactic clusters

The observed appearance of the high-energy gamma-ray emission from galactic star clusters is determined by the geometry of the cluster and the distribution of the energy sources inside the cluster. A large number of massive stars with strong winds and supernova explosions lead to the formation of multidirectional plasma flows, shocks and strong magnetohydrodynamic turbulence. Magnetic turbulence is the main factor which determine the maximal energies of the accelerated particles and the power of the source. Here we discuss an effect of the efficient magnetic field amplification at the supernova shocks due to the cosmic-ray driven plasma instabilities on the gamma-ray and neutrino fluxes from massive star clusters. We show here that the photon flux attenuation by the e± pair production is important for this kind of sources in the photon energy range 1015 — 1016 eV. The ratio of the gamma-ray to the neutrino fluxes is a declining function of the distance to the source at 5-15 kpc and the photon flux can be several times lower than the corresponding neutrino flux from the hadron interactions.

Direct Evidence of the Transition from Weak to Strong Magnetohydrodynamic Turbulence.

One of the most important predictions in magnetohydrodynamics is that in the presence of a uniform magnetic field b_{0}e[over ^]_{∥} a transition from weak to strong wave turbulence should occur when going from large to small perpendicular scales. This transition is believed to be a universal property of several anisotropic turbulent systems. We present, for the first time, direct evidence of such a transition using a decaying three-dimensional direct numerical simulation of incompressible balanced magnetohydrodynamic turbulence with a grid resolution of 3072^{2}×256. From large to small scales, the change of regime is characterized by (i)a change of slope in the energy spectrum going from approximately -2 to -3/2, (ii)an increase of the ratio between the wave and nonlinear times, with a critical ratio of χ_{c}∼1/3, (iii)a modification of the isocontours of energy revealing a transition from a purely perpendicular cascade to a cascade compatible with the critical-balance-type phenomenology, and (iv)an absence followed by a dramatic increase of the communication between Alfvén modes. The changes happen at approximately the same transition scale and can be seen as manifest signatures of the transition from weak to strong wave turbulence. Furthermore, we observe a significant nonlocal three-wave coupling between strongly and weakly nonlinear modes resulting in an inverse transfer of energy from small to large scales.

On the nature of magnetic turbulence in rotating, shearing flows

Abstract 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 v0 and their outer scale λ0 satisfy the balance condition v0/λ0 ∼ dΩ/dln r, where dΩ/dln r is the local orbital shearing rate of the flow. Finally, we find no sustained dynamo action in the 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 Pm ≤ 1 regime.

Energy dynamics and current sheet structure in fluid and kinetic simulations of decaying magnetohydrodynamic turbulence

Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfvén waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation, whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of k⊥−1.3. The kinetic code shows a spectral slope of k⊥−1.5 for smaller simulation domain, and k⊥−1.3 for larger domain. We estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. This work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.

IMBALANCED RELATIVISTIC FORCE-FREE MAGNETOHYDRODYNAMIC TURBULENCE

When magnetic energy density is much larger than that of matter, as in pulsar/black hole magnetospheres, the medium becomes force-free and we need relativity to describe it. As in non-relativistic magnetohydrodynamics (MHD), Alfv\'enic MHD turbulence in the relativistic limit can be described by interactions of counter-traveling wave packets. In this paper we numerically study strong imbalanced MHD turbulence in such environments. Here, imbalanced turbulence means the waves traveling in one direction (dominant waves) have higher amplitudes than the opposite-traveling waves (sub-dominant waves). We find that (1) spectrum of the dominant waves is steeper than that of sub-dominant waves, (2) the anisotropy of the dominant waves is weaker than that of sub-dominant waves, and (3) the dependence of the ratio of magnetic energy densities of dominant and sub-dominant waves on the ratio of energy injection rates is steeper than quadratic (i.e., \$b_+^2/b_-^2 \propto (\epsilon_+/\epsilon_-)^n \$ with n>2). These results are consistent with those obtained for imbalanced non-relativistic Alfv\'enic turbulence. This corresponds well to the earlier reported similarity of the relativistic and non-relativistic balanced magnetic turbulence.

Numerical simulations of strong incompressible magnetohydrodynamic turbulence

Magnetised plasma turbulence pervades the universe and is likely to play an important role in a variety of astrophysical settings. Magnetohydrodynamics (MHD) provides the simplest theoretical framework in which phenomenological models for the turbulent dynamics can be built. Numerical simulations of MHD turbulence are widely used to guide and test the theoretical predictions; however, simulating MHD turbulence and accurately measuring its scaling properties is far from straightforward. Computational power limits the calculations to moderate Reynolds numbers and often simplifying assumptions are made in order that a wider range of scales can be accessed. After describing the theoretical predictions and the numerical approaches that are often employed in studying strong incompressible MHD turbulence, we present the findings of a series of high-resolution direct numerical simulations. We discuss the effects that insufficiencies in the computational approach can have on the solution and its physical interpretation.

Strong magnetohydrodynamic turbulence with cross helicity

Magnetohydrodynamics (MHD) provides the simplest description of magnetic plasma turbulence in a variety of astrophysical and laboratory systems. MHD turbulence with nonzero cross helicity is often called imbalanced, as it implies that the energies of Alfvén fluctuations propagating parallel and antiparallel the background field are not equal. Recent analytical and numerical studies have revealed that at every scale, MHD turbulence consists of regions of positive and negative cross helicity, indicating that such turbulence is inherently locally imbalanced. In this paper, results from high resolution numerical simulations of steady-state incompressible MHD turbulence, with and without cross helicity are presented. It is argued that the inertial range scaling of the energy spectra (E±) of fluctuations moving in opposite directions is independent of the amount of cross helicity. When cross helicity is nonzero, E+ and E− maintain the same scaling, but have differing amplitudes depending on the amount of cross helicity.

NUMERICAL SIMULATIONS OF IMBALANCED STRONG MAGNETOHYDRODYNAMIC TURBULENCE

Magnetohydrodynamics (MHD) is invoked to address turbulent fluctuations in a variety of astrophysical systems. MHD turbulence in nature is often anisotropic and imbalanced, in that Alfvenic fluctuations moving in opposite directions along the background magnetic field carry unequal energies. This work formulates specific requirements for effective numerical simulations of strong imbalanced MHD turbulence with a guide field B0 High-resolution simulations are then performed and they suggest that the spectra of the counter-propagating Alfven modes do not differ from the balanced case, while their amplitudes and the corresponding rates of energy cascades are significantly affected by the imbalance. It is further proposed that the stronger the imbalance the larger the magnetic Reynolds number that is required in numerical simulations in order to correctly reproduce the turbulence spectrum. This may explain current discrepancies among numerical simulations and observations of imbalanced MHD turbulence.

DYNAMIC ALIGNMENT AND EXACT SCALING LAWS IN MAGNETOHYDRODYNAMIC TURBULENCE

Magnetohydrodynamic (MHD) turbulence is pervasive in astrophysical systems. Recent high-resolution numerical simulations suggest that the energy spectrum of strong incompressible MHD turbulence is E(k ⊥) ∝ k –3/2 ⊥. So far, there has been no phenomenological theory that simultaneously explains this spectrum and satisfies the exact analytic relations for MHD turbulence due to Politano & Pouquet. Indeed, the Politano-Pouquet relations are often invoked to suggest that the spectrum of MHD turbulence instead has the Kolmogorov scaling –5/3. Using geometrical arguments and numerical tests, here we analyze this seeming contradiction and demonstrate that the –3/2 scaling and the Politano-Pouquet relations are reconciled by the phenomenon of scale-dependent dynamic alignment that was recently discovered in MHD turbulence.

Scale‐dependent angle of alignment between velocity and magnetic field fluctuations in solar wind turbulence

Under certain conditions, freely decaying magnetohydrodynamic (MHD) turbulence evolves in such a way that velocity and magnetic field fluctuations δv and δB approach a state of alignment in which δv ∝ δB. This process is called dynamic alignment. Boldyrev has suggested that a similar kind of alignment process occurs as energy cascades from large to small scales through the inertial range in strong incompressible MHD turbulence. In this study, plasma and magnetic field data from the Wind spacecraft, data acquired in the ecliptic plane near 1 AU, are employed to investigate the angle θ(τ) between velocity and magnetic field fluctuations in the solar wind as a function of the time scale τ of the fluctuations and to look for the scaling relation 〈θ(τ)〉 ∼ τ1/4 predicted by Boldyrev. We find that the angle 〈θ(τ)〉 appears to scale like a power law at large inertial range scales, but then deviates from power law behavior at medium to small inertial range scales. We also find that small errors in the velocity vector measurements can lead to large errors in the angle measurements at small time scales. As a result, we cannot rule out the possibility that the observed deviations from power law behavior arise from errors in the velocity measurements. When we fit the data from 2 × 103 s to 2 × 104 s with a power law of the form 〈θ(τ)〉 ∝ τp, our best fit values for p are in the range 0.27–0.36.

Nonlinear Dynamics of the Parker Scenario for Coronal Heating

The Parker or field line tangling model of coronal heating is studied comprehensively via long-time high-resolution simulations of the dynamics of a coronal loop in Cartesian geometry within the framework of reduced magnetohydrodynamics. Slow photospheric motions induce a Poynting flux which saturates by driving an anisotropic turbulent cascade dominated by magnetic energy. In physical space this corresponds to a magnetic topology where magnetic field lines are barely entangled; nevertheless, current sheets (corresponding to the original tangential discontinuities hypothesized by Parker) are continuously formed and dissipated. Current sheets are the result of the nonlinear cascade that transfers energy from the scale of convective motions (~1000 km) down to the dissipative scales, where it is finally converted to heat and/or particle acceleration. Current sheets constitute the dissipative structure of the system, and the associated magnetic reconnection gives rise to impulsive bursty heating events at the small scales. This picture is consistent with the slender loops observed by state-of-the-art (E)UV and X-ray imagers which, although apparently quiescent, shine brightly in these wavelengths with little evidence of entangled features. The different regimes of weak and strong magnetohydrodynamic turbulence that develop and their influence on coronal heating scalings are shown to depend on the loop parameters, and this dependence is quantitatively characterized: weak turbulence regimes and steeper spectra occur in stronger loop fields and lead to larger heating rates than in weak field regions.

Numerical measurements of the spectrum in magnetohydrodynamic turbulence

We report the results of an extensive set of direct numerical simulations of forced, incompressible, magnetohydrodynamic (MHD) turbulence with a strong guide field. The aim is to resolve the controversy regarding the power-law exponent (alpha, say) of the field-perpendicular energy spectrum E(k) proportional variant k(alpha). The two main theoretical predictions alpha=-3/2 and alpha=-5/3 have both received some support from differently designed numerical simulations. Our calculations have a resolution of 512(3) mesh points, a strong guide field, and an anisotropic simulation domain and implement a broad range of large-scale forcing routines, including those previously reported in the literature. Our findings indicate that the spectrum of well-developed, strong incompressible MHD turbulence with a strong guide field is E(k) proportional variant k(-3/2).

Particle Acceleration by Magnetohydrodynamic Turbulence

Recent advances in understanding of magnetohydrodynamic (MHD) turbulence call for revisions in the picture of particle acceleration. We make use of the recently established scaling of slow and fast MHD modes in strong and weak MHD turbulence to provide a systematic study of particle acceleration in magnetic pressure (low-$\beta$) and gaseous pressure (high-$\beta$) dominated plasmas. We consider the acceleration by large scale compressions in both slow and fast particle diffusion limits. We compare the results with the acceleration rate that arises from resonance scattering and Transit-Time Damping (TTD). We establish that fast modes accelerate particles more efficiently than slow modes. We find that particle acceleration by pitch-angle scattering and TTD dominates acceleration by slow or fast modes when the spatial diffusion rate is small. When the rate of spatial diffusion of particles is high, we establish an enhancement of the efficiency of particle acceleration by slow and fast modes in weak turbulence. We show that highly supersonic turbulence is an efficient agent for particle acceleration. We find that even incompressible turbulence can accelerate particles on the scales comparable with the particle mean free path.

Generation of compressible modes in MHD turbulence

Astrophysical turbulence is magnetohydrodynamic (MHD) in nature. We discuss fundamental properties of MHD turbulence and in particular the generation of compressible MHD waves by Alfvénic turbulence and show that this process is inefficient. This allows us to study the evolution of different types of MHD perturbations separately. We describe how to separate MHD fluctuations into three distinct families: Alfvén, slow, and fast modes. We find that the degree of suppression of slow and fast modes production by Alfvénic turbulence depends on the strength of the mean field. We review the scaling relations of the modes in strong MHD turbulence. We show that Alfvén modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfvén modes. However, fast modes exhibit isotropy and a scaling similar to that of acoustic turbulence both in high and low β plasmas. We show that our findings entail important consequences for star formation theories, cosmic ray propagation, dust dynamics, and gamma ray bursts. We anticipate many more applications of the new insight to MHD turbulence and expect more revisions of the existing paradigms of astrophysical processes as the field matures.

On the spectrum of high-energy cosmic rays produced by supernova remnants in the presence of strong cosmic-ray streaming instability and wave dissipation

The cosmic-ray streaming instability creates strong magnetohydrodynamic turbulence in the precursor of a SN shock. The level of turbulence determines the maximum energy of cosmic-ray particles accelerated by the diffusive shock accelera- tion mechanism. In this paper we present the continuation of previous work (Ptuskin & Zirakashvili 2003). We assume that Kolmogorov type nonlinear wave interactions together with ion-neutral collisions restrict the amplitude of the random mag- netic field. As a result, the maximum energy of the accelerated particles strongly depends on the age of a SNR. The average spectrum of cosmic rays injected in the interstellar medium in the course of the adiabatic SNR evolution (the Sedov stage) is approximately Q(p)p 2 ∝ p −2 at energies larger than 10−30 GeV/nucleon and with a maximum particle energy that is close to the position of the knee in the cosmic-ray spectrum observed at ∼4 × 10 15 eV. At an earlier stage of SNR evolution - the ejecta-dominated stage described by the Chevalier-Nadyozhin solution, the particles are accelerated to higher energies and have a rather steep power-law distribution. These results suggest that the knee may mark the transition from the ejecta-dominated to the adiabatic evolution of SNR shocks which accelerate cosmic rays.