Persistence of small-scale anisotropy of magnetic turbulence as observed in the solar wind

Sorriso‐Valvo, L.; Carbone, V.; Bruno, R.; Veltri, P.

doi:10.1209/epl/i2006-10172-y

Cited by 31 publications

(43 citation statements)

References 23 publications

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“…It is seen most clearly in the spacecraft measurements of the turbulent fluctuations in the solar wind (Belcher & Davis 1971;Matthaeus et al 1990;Bieber et al 1996;Dasso et al 2005;Bigazzi et al 2006;Sorriso-Valvo et al 2006;Horbury et al 2005Horbury et al , 2008Osman & Horbury 2007;Hamilton et al 2008) and in the magnetosheath Sahraoui et al (2006); Alexandrova et al (2008b). In a recent key development, solar-wind data analysis by Horbury et al (2008) approaches quantitative corroboration of the critical balance conjecture by confirming the scaling of the spectrum with the parallel wave number ∼ k −2 that follows from the first scaling relation in Eq.…”

Section: Mhd Turbulence and Critical Balancementioning

confidence: 58%

Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades In Magentized Weakly Collisional Plasmas

Schekochihin¹,

Cowley²,

W.³

et al. 2009

156

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This paper presents a theoretical framework for understanding plasma turbulence in astrophysical plasmas. It is motivated by observations of electromagnetic and density fluctuations in the solar wind, interstellar medium and galaxy clusters, as well as by models of particle heating in accretion disks. All of these plasmas and many others have turbulent motions at weakly collisional and collisionless scales. The paper focuses on turbulence in a strong mean magnetic field. The key assumptions are that the turbulent fluctuations are small compared to the mean field, spatially anisotropic with respect to it and that their frequency is low compared to the ion cyclotron frequency. The turbulence is assumed to be forced at some system-specific outer scale. The energy injected at this scale has to be dissipated into heat, which ultimately cannot be accomplished without collisions. A kinetic cascade develops that brings the energy to collisional scales both in space and velocity. The nature of the kinetic cascade in various scale ranges depends on the physics of plasma fluctuations that exist there. There are four special scales that separate physically distinct regimes: the electron and ion gyroscales, the mean free path and the electron diffusion scale. In each of the scale ranges separated by these scales, the fully kinetic problem is systematically reduced to a more physically transparent and computationally tractable system of equations, which are derived in a rigorous way. In the "inertial range" above the ion gyroscale, the kinetic cascade separates into two parts: a cascade of Alfvénic fluctuations and a passive cascade of density and magnetic-fieldstrength fluctuations. The former are governed by the Reduced Magnetohydrodynamic (RMHD) equations at both the collisional and collisionless scales; the latter obey a linear kinetic equation along the (moving) field lines associated with the Alfvénic component (in the collisional limit, these compressive fluctuations become the slow and entropy modes of the conventional MHD). In the "dissipation range" below ion gyroscale, there are again two cascades: the kinetic-Alfvén-wave (KAW) cascade governed by two fluid-like Electron Reduced Magnetohydrodynamic (ERMHD) equations and a passive cascade of ion entropy fluctuations both in space and velocity. The latter cascade brings the energy of the inertial-range fluctuations that was Landau-damped at the ion gyroscale to collisional scales in the phase space and leads to ion heating. The KAW energy is similarly damped at the electron gyroscale and converted into electron heat. Kolmogorov-style scaling relations are derived for all of these cascades. The relationship between the theoretical models proposed in this paper and astrophysical applications and observations is discussed in detail.

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Section: Mhd Turbulence and Critical Balancementioning

confidence: 58%

Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades In Magentized Weakly Collisional Plasmas

Schekochihin¹,

Cowley²,

W.³

et al. 2009

156

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“…A different approach to anisotropic fluctuations in solar wind turbulence have been made by Bigazzi et al (2006) and Sorriso-Valvo et al (2006. In these studies the full tensor of Figure 31: Power density spectra of the three components of IMF after rotation into the minimum variance reference system.…”

Section: Fluctuations Anisotropymentioning

confidence: 99%

“…the mixed second-order structure functions has been used to quantitatively measure the degree of anisotropy and its effect on small-scale turbulence through a fit of the various elements of the tensor on a typical function (Sorriso-Valvo et al, 2006). Moreover three different regions of the near-Earth space have been studied, namely the solar wind, the Earth's foreshock and magnetosheath showing that, while in the undisturbed solar wind the observed strong anisotropy is mainly due to the largescale magnetic field, near the magnetosphere other sources of anisotropy influence the magnetic field fluctuations (Sorriso-Valvo et al, 2010b).…”

Section: Living Reviews In Solar Physicsmentioning

confidence: 99%

The Solar Wind as a Turbulence Laboratory

Bruno

Carbone

2013

Living Rev. Solar Phys.

969

957

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In this review we will focus on a topic of fundamental importance for both astrophysics and plasma physics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Helios inner heliosphere and Ulysses' high latitude observations, recent multi-spacecrafts measurements in the solar wind (Cluster four satellites) and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD) turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.

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“…On the other hand, it has also been shown [2] that magnetic field compressibility increases mainly at very small scales within the fast wind regime. It follows that the incompressibility assumption can be considered valid to a large extent for the analyzed interval and at intermediate scales.The large scale anisotropy, mainly due to the average magnetic field, is only partially lost at smaller scales, and a residual anisotropy is always present [24,25], generally breaking the local isotropy assumption. Thus, while inhomogeneity, compressibility and anisotropy could all be responsible for the loss of linear scaling, anisotropy probably is the main candidate within high latitude regions of the solar wind.…”

mentioning

confidence: 99%

Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Sorriso‐Valvo¹,

et al. 2007

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We show in this article direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), in the solar wind as observed by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom's law for MHD turbulence, we show that a linear relation is indeed observed for the scaling of mixed third order structure functions involving Elsässer variables. This experimental result, confirming the prescription stemming from a theorem for MHD turbulence, firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.Space flights have shown that the interplanetary medium is permeated by a supersonic, highly turbulent plasma flowing out from the solar corona, the so called solar wind [1,2]. The turbulent character of the flow, at frequencies below the ion gyrofrequency f ci ≃ 1Hz, has been invoked since the first Mariner mission [3]. In fact, velocity and magnetic fluctuations power spectra are close to the Kolmogorov's -5/3 law [2,6]. However, even if fields fluctuations are usually considered within the framework of magnetohydrodynamic (MHD) turbulence [2], a firm established proof of the existence of an energy cascade, namely the main characteristic of turbulence, remains a conjecture so far [4]. This apparent lack could be fulfilled through the evidence for the existence of the only exact and nontrivial result of turbulence [6], that is a relation between the third order moment of the longitudinal increments of the fields and the separation [5]. This observation would firmly put low frequency solar wind fluctuations within the framework of MHD turbulence. The importance of such question stands beyond the understanding of the basic physics of solar wind turbulence. For example, it is well known that turbulence is one of the main obstacles to the confinement of plasmas in the fusion devices [7,8]. The understanding of interplanetary turbulence and its effects on energetic particle transport is of great importance also for Space Weather research [9], which is a relevant issue for spacecrafts and communication satellites operations, and for the security of human beings. Finally, more theoretical problems are concerned, such as the puzzle of solar coronal heating due to the turbulent flux toward small scales [10].Incompressible MHD equations are more complicated than the standard neutral fluid mechanics equations because the velocity of the charged fluid is coupled with the magnetic field generated by the motion of the fluid itself. However, written in terms of the Elsässer variables defined as z ± = v ± (4πρ) −1/2 b (v and b are the velocity and magnetic field respectively and ρ the mass density), they have the same structure as the Navier-Stokes equations [4]where P is the total hydromagnetic pressure, while ν is the viscosity and κ the magnetic diffusivity. In particular, the nonlinear term appears as z ∓ · ∇z ± , suggesting the form of a transport process, in which Alfvé...

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Persistence of small-scale anisotropy of magnetic turbulence as observed in the solar wind

Cited by 31 publications

References 23 publications

Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades In Magentized Weakly Collisional Plasmas

Astrophysical Gyrokinetics: Kinetic and Fluid Turbulent Cascades In Magentized Weakly Collisional Plasmas

The Solar Wind as a Turbulence Laboratory

Observation of Inertial Energy Cascade in Interplanetary Space Plasma

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