Anisotropic Magnetic Turbulence Research Articles

Anisotropic Magnetic Turbulence in the Inner Heliosphere—Radial Evolution of Distributions Observed by Parker Solar Probe

Observations from Parker Solar Probe’s first five orbits are used to investigate the helioradial evolution of probability density functions (pdfs) of fluctuations of magnetic-field components between ∼28 and 200 R ⊙. Transformation of the magnetic-field vector to a local mean-field coordinate system permits examination of anisotropy relative to the mean magnetic-field direction. Attention is given to effects of averaging-interval size. It is found that pdfs of the perpendicular fluctuations are well approximated by a Gaussian function, with the parallel fluctuations less so: kurtoses of the latter are generally larger than 10, and their pdfs indicate increasing skewness with decreasing distance r from the Sun, with the latter observation possibly explained by the increasing Alfvénicity of the fluctuations. The ratio of perpendicular to parallel variances is greater than unity; this variance anisotropy becomes stronger with decreasing r. The ratio of the total rms fluctuation strength to the mean-field magnitude decreases with decreasing r, with a value ∼0.8 near 1 au and ∼0.5 at 0.14 au; the ratio is well approximated by an r 1/4 power law. These findings improve our understanding of the radial evolution of turbulence in the solar wind, and have implications for related phenomena such as energetic-particle transport in the inner heliosphere.

Polarized synchrotron X-ray emission from supernova shells: XIPE/IXPE perspective

Young supernova remnants are the sources of a broadband nonthermal synchrotron continuum emission from radio to X-rays produced by accelerated electrons. Diffusive shock acceleration (DSA) of relativistic particles is accompanied by strong amplification of the turbulent magnetic field. This is an intrinsic feature of an efficient DSA. Synchrotron X-rays are produced by the multi-TeV electrons which are concentrated in a narrow region near the shock due to the strong energy losses. The confinement of the X-ray emitting electrons in this region filled with highly fluctuating magnetic field results in a complex time dependent clumpy structure of the observed X-ray images of supernova shells. The lack of Faraday depolarization in X-rays makes X-ray polarimetry a powerful tool to study synchrotron structures in the young galactic shell type SNRs Cas A, Tycho, SN 1006, RX J1713.7–3946. We present here simulated synchrotron images of SNR shells for different models of isotropic and anisotropic magnetic turbulence in a shell and argue that polarized X-ray imaging can be constructed for Tycho and Cas A SNRs with the expected sensitivity and the angular resolution of the upcoming missions XIPE (ESA) and IXPE (NASA).

Experimental Observation of Anisotropic Magnetic Turbulence in a Reversed Field Pinch Plasma

In this Letter we report an experimental study of fully developed anisotropic magnetic turbulence in a laboratory plasma. The turbulence has broad (narrow) spectral power in the perpendicular (parallel) direction to the local mean magnetic field extending beyond the ion cyclotron frequency. Its k[see symbol] spectrum is asymmetric in the ion and electron diamagnetic directions. The wave number scaling for the short wavelength fluctuations shows exponential falloff indicative of dissipation. A standing wave structure is found for the turbulence in the minor radial direction of the toroidal plasma.

ELECTRON TRANSPORT IN CORONAL LOOPS: THE INFLUENCE OF THE EXPONENTIAL SEPARATION OF MAGNETIC FIELD LINES

Observations by the TRACE spacecraft have shown that coronal emission in the extreme ultraviolet is characterized by filamentary structures within coronal loops, with transverse sizes close to the instrumental resolution. Starting from the observed filament widths and using the concepts of braided magnetic fields, an estimate of the turbulence level in the coronal loops can be obtained. Magnetic turbulence in the presence of a background magnetic field can be strongly anisotropic, and such anisotropy influences the separation of magnetic field lines, as well as the magnetic field line diffusion coefficient. Careful computations of the magnetic field line diffusion coefficient Dm and of the rate of exponential separation of magnetic field lines h, also allowing for the possibility of anisotropic magnetic turbulence, enable computation of the effective perpendicular diffusion coefficient for electrons. When compared with observations this yields magnetic turbulence levels on the order of δB/B0 = 0.05–0.7, which are larger than previous estimates. These values of the magnetic fluctuation level support the idea that magnetic turbulence can contribute to coronal heating by means of MHD turbulence dissipation. It is also found that field line transport is not governed by the quasilinear regime, but by a nonlinear regime which includes an intermediate and the percolation regimes.

ANGULAR DEPENDENCE OF JITTER RADIATION SPECTRA FROM SMALL-SCALE MAGNETIC TURBULENCE

Jitter radiation is produced by relativistic electrons moving in turbulent small-scale magnetic fields such as those produced by streaming Weibel-type instabilities at collisionless shocks in weakly magnetized media. Here we present a comprehensive study of the dependence of the jitter radiation spectra on the properties of, in general, anisotropic magnetic turbulence. We have obtained that the radiation spectra do reflect, to some extent, properties of the magnetic field spatial distribution, yet the radiation field is anisotropic and sensitive to the viewing direction with respect to the field anisotropy direction. We explore the parameter space of the magnetic field distribution and its effect on the radiation spectrum. Some important results include: the presence of the harder-than-synchrotron segment below the peak frequency at some viewing angles, the presence of the high-frequency power-law tail even for a monoenergetic distribution of electrons, the dependence of the peak frequency on the field correlation length rather than the field strength, the strong correlation of the spectral parameters with the viewing angle. In general, we have found that even relatively minor changes in the magnetic field properties can produce very significant effects upon the jitter radiation spectra. We consider these results to be important for accurate interpretation of prompt gamma-ray burst spectra and possibly other sources.

Kolmogorov–Sinai entropy in field line diffusion by anisotropic magnetic turbulence

The Kolmogorov–Sinai (KS) entropy in turbulent diffusion of magnetic field lines is analyzed on the basis of a numerical simulation model and theoretical investigations. In the parameter range of strongly anisotropic magnetic turbulence the KS entropy is shown to deviate considerably from the earlier predicted scaling relations (1992 Rev. Mod. Phys. 64 961). In particular, a slowing down logarithmic behavior versus the so-called Kubo number R ≫ 1 (R = (δB/B0) (ξ∥/ξ⊥), where δB/B0 is the ratio of the rms magnetic fluctuation field to the magnetic field strength, and ξ⊥ and ξ∥ are the correlation lengths in respective dimensions) is found instead of a power-law dependence. These discrepancies are explained from general principles of Hamiltonian dynamics. We discuss the implication of Hamiltonian properties in governing the paradigmatic ‘percolation’ transport, characterized by R → ∞, associating it with the concept of pseudochaos (random non-chaotic dynamics with zero Lyapunov exponents). Applications of this study pertain to both fusion and astrophysical plasma and by mathematical analogy to problems outside the plasma physics.

Anomalous, non-Gaussian transport of charged particles in anisotropic magnetic turbulence

The transport of energetic particles in a mean magnetic field and in the presence of anisotropic magnetic turbulence is studied numerically, for parameter values relevant to astrophysical plasmas. A numerical realization of magnetic turbulence is set up, in which the degree of anisotropy is varied by changing the correlation lengths lx, ly, and lz. The ratio ρ∕λ of the particle Larmor radius ρ over the turbulence correlation length λ is also varied. It is found that for lx,ly⪢lz, and for ρ∕λ≲10−2 transport can be non-Gaussian, with superdiffusion along the average magnetic field and subdiffusion perpendicular to it. In addition, the spatial distribution of particles is clearly non-Gaussian. Such regimes are characterized by a Levy statistics, with diverging second-order moments. Decreasing the ratio lx∕lz, nearly Gaussian (normal) diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Changing the particle Larmor radius, normal diffusion is found for 10−2≲ρ∕λ≲1 because of increased pitch angle diffusion. New anomalous superdiffusive regimes appear when ρ∕λ≳1 showing that the interaction between particles and turbulence decreases in these cases. A new regime, called generalized double diffusion, is proposed for the cases when particles are able to trace back field lines. A summary of the physical conditions which lead to non-Gaussian transport is given.

Superdiffusive and Subdiffusive Transport of Energetic Particles in Solar Wind Anisotropic Magnetic Turbulence

The transport of energetic particles in a mean magnetic field and the presence of anisotropic magnetic turbulence are studied numerically, for parameter values relevant to the solar wind. A numerical realization of magnetic turbulence is set up in which we can vary the type of anisotropy by changing the correlation lengths lx, ly, lz. We find that for lx, ly lz, transport can be non-Gaussian, with superdiffusion along the average magnetic field and subdiffusion perpendicular to it. Decreasing the lx/lz ratio down to 0.3, Gaussian diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Implications for energetic particle propagation in the solar wind and for diffusive shock acceleration are discussed.

Anomalous particle diffusion and Lévy random walk of magnetic field lines in three-dimensional solar wind turbulence

Plasma transport in the presence of turbulence depends on a variety of parameters such as the fluctuation level, δB/B0, the ratio between the particle Larmor radius and the turbulence correlation length, and the turbulence anisotropy. In this paper, we present the results of numerical simulations of plasma and magnetic field line transport in the case of anisotropic magnetic turbulence, for parameter values close to those of the solar wind. We assume a uniform background magnetic field B0 = B0 ez and a Fourier representation for magnetic fluctuations, which includes wavectors oblique with respect to B0. The energy density spectrum is a power law, and in k space it is described by the correlation lengths lx, ly, lz, which quantify the anisotropy of turbulence. For magnetic field lines, transport perpendicular to the background field depends on the Kubo number R = (δB/B0) (lz/lx). For small Kubo numbers, R ≪ 1, anomalous, non-Gaussian transport regimes (both sub- and superdiffusive) are found, which can be described as a Lévy random walk. Increasing the Kubo number, i.e. the fluctuation level, δB/B0, or the ratio lz/lx, we find first a quasilinear regime and then a percolative regime, both corresponding to Gaussian diffusion. For particles, we find that transport parallel and perpendicular to the background magnetic field depends heavily on the turbulence anisotropy and on the particle Larmor radius. For turbulence levels typical of the solar wind, δB/B0≃ 0.5–1, when the ratio between the particle Larmor radius and the turbulence correlation lengths is small, anomalous regimes are found in the case lz/lx ⩽ 1, with a Lévy random walk (superdiffusion) along the magnetic field and subdiffusion in the perpendicular directions. Conversely, for lz/lx > 1 normal Gaussian diffusion is found. A possible expression for generalized double diffusion is discussed.

Energetic particle transport in anisotropic magnetic turbulence

We study energetic particle transport in a magnetic field configuration which models the solar wind magnetic turbulence plus the background field. A power-law Fourier amplitude is used for the fully 3D turbulence model, and in order to model anisotropic turbulence, the constant amplitude surfaces in k space are ellipsoids. The turbulence correlation lengths parallel (perpendicular) to the background magnetic field l ∥ ( l ⊥) are varied in a wide range, and proton energies from 1 MeV to 10 GeV are assumed. Considering propagation on a distance corresponding to 1 AU, it is found that transport parallel and perpendicular to the background field heavily depends on the turbulence anisotropy, that is on the ratio l ∥/ l ⊥. The spatial distribution of energetic particle follows the shape of magnetic flux tube up to about 10 MeV, while for larger energies the structure of the magnetic flux tube is progressively washed out. The scatterplots of particle distribution show intermittent, non Gaussian structures for l ∥ ≪ l ⊥ (quasi slab turbulence), while a more diffusive, Gaussian structure is obtained for l ∥ ≫ l ⊥ (quasi 2D turbulence). The long time behavior of transport shows that anomalous (subdiffusive perpendicular and superdiffusive parallel) transport regimes are obtained for l ∥ ≪ l ⊥, while Gaussian diffusive transport is obtained for both l ∥ ≫ l ⊥ and the isotropic turbulence case.

Numerical simulation of anomalous plasma transport in the presence of magnetic turbulence

The structure of plasma in the interplanetary space is briefly presented, and the problems related to the variability of solar activity are discussed. The features of magnetic turbulence in the solar wind are also described. Magnetic field fluctuations are one of the causes of enhanced transport both in laboratory and astrophysical plasmas. To a first approximation, the plasma particles follow the magnetic field lines, whose equations form a non-linear one and a half degrees of freedom system. Unless the fluctuation level is very low, numerical simulations are needed to study such a system. We review three-dimensional numerical simulations of field line transport in anisotropic magnetic turbulence. Several transport regimes are found: for low Kubo number, anomalous transport is obtained, featuring both subdiffusion, corresponding to trapping in cantori structures, and superdiffusion, corresponding to Levy flights in the stochastic layer. Increasing the Kubo number, and hence stochasticity, quasilinear, intermediate, and percolative regimes are found, in the order. An expression of the diffusion coefficient valid for generalized anisotropy is presented.

A Monte Carlo simulation of magnetic field line tracing in the solar wind

Abstract. It is well known that the structure of magnetic field lines in solar wind can be influenced by the presence of the magnetohydrodynamic turbulence. We have developed a Monte Carlo simulation which traces the magnetic field lines in the heliosphere, including the effects of magnetic turbulence. These effects are modelled by random operators which are proportional to the square root of the magnetic field line diffusion coefficient. The modelling of the random terms is explained, in detail, in the case of numerical integration by discrete steps. Furthermore, a proper evaluation of the diffusion coefficient is obtained by a numerical simulation of transport in anisotropic magnetic turbulence. The scaling of the fluctuation level and of the correlation lengths with the distance from the Sun are also taken into account. As a consequence, plasma transport across the average magnetic field direction is obtained. An application to the propagation of energetic particles from corotating interacting regions to high heliographic latitudes is considered.

Predictions for the propagation of energetic particles from the sun to the earth: influence of the magnetic turbulence

Energetic particle fluxes in the Earth's magnetosphere can seriously affect spacecraft operations as well as navigation and communication systems. To this end, and critical issue is to understand and predict whether particles accelerated at a solar flare will impinge on the Earth's magnetosphere. Energetic particle propagation depends on the magnetohydrodynamic turbulence in the solar wind. We present here a Monte Carlo simulation which traces the magnetic field line from the Earth to the solar corona, taking into account both the average Parker spiral magnetic field and the effects of magnetic turbulence. A proper evaluation of the diffusion coefficient is obtained by a numerical simulation of transport in anisotropic magnetic turbulence which takes into account the scaling of the fluctuation level and of the correlation lengths with the distance from the Sun. This numerical code allows to determine, from the observations of a solar flare at given heliographic latitude and longitude, whether energetic particles will come over the magnetosphere or not.

The Kubo number as a parameter governing the level of chaos in magnetic turbulence

It is well known that the Kubo number R allows to classify the transport regimes in turbulent systems. A small Kubo number leads to the so-called quasilinear diffusion coefficient, while a large Kubo number corresponds to the percolative diffusion coefficient. Here we show, by means of a numerical simulation of magnetic field line transport in a three-dimensional anisotropic magnetic turbulence, in which the magnetic fluctuating level and the correlation lengths can be varied independently of each other, that the Kubo number also determines the level of chaos of the magnetic-field lines. We find weak chaos, closed magnetic surfaces, and anomalous transport regimes for R⪡1; widespread chaos, destroyed magnetic surfaces, and quasilinear scaling of the diffusion coefficient for R≳0.3; and global stochasticity as well as the percolation scaling of the diffusion coefficient for R⪢1.