Simulations of Incompressible Magnetohydrodynamic Turbulence

Maron, Jason; Goldreich, Peter

doi:10.1086/321413

Cited by 571 publications

(772 citation statements)

References 24 publications

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“…GS95 predictions have been confirmed numerically (Cho & Vishniac 2000;Maron & Goldreich 2001;Cho, Lazarian & Vishniac 2002, 2003; they are in good agreement with observed and inferred astrophysical spectra (see …”

Section: What Do We Know About Mhd Turbulence?supporting

confidence: 75%

Theoretical approaches to particle propagation and acceleration in turbulent intergalactic medium

Lazarían

2006

Astron Nachr

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Abstract.Intercluster medium is expected to be turbulent with turbulence being superAlfvenic at large scales. Magnetic fields substantially modify the turbulent cascade when the turbulence reaches the scales at which the fluctuation velocity gets less than the Alfven velocity. At those scales it is possible to consider three cascades, of fast, slow and Alfven modes with little energy exchange between them. As Alfvenic and slow modes are anisotropic they marginally scatter and accelerate cosmic rays, while fast modes dominate the processes. However, in the presence of cosmic rays the turbulence is modified as cosmic rays transfer the energy of compressible motions (i.e. slow and fast modes) from large scales to the scale of cosmic ray Larmor radius. This results in generation of a new small-scale Alfvenic component which is not a part of the ordinary MHD cascade. This component does scatter and accelerate cosmic rays. In addition, magnetic reconnection in turbulent medium accelerates cosmic rays. The complexity of the interacluster turbulence calls for observational studies. A new technique Velocity Coordinate Spectrum (VCS) is particularly promising for studies of velocity fluctuations with a new generation of X-ray observatories.Key words: galaxies:clusters:general,turbulence, plasmas, intergalactic medium, galaxies: magnetic fields, MHD c 0000 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Do we expect IGM to be turbulent?A fluid of viscosity ν becomes turbulent when the rate of viscous dissipation, which is ∼ ν/L 2 at the energy injection scale L, is much smaller than the energy transfer rate ∼ V L /L, where V L is the velocity dispersion at the scale L. The ratio of the two rates is the Reynolds number Re = V L L/ν. In general, when Re is larger than Re crit ∼ 10 − 100 the system becomes turbulent. Chaotic structures develop gradually as Re increases, and those with Re ∼ 10 3 are appreciably less chaotic than those with Re ∼ 10 8 .It is widely accepted that medium in clusters should be turbulent. Mergers of galactic subclusters may be one of the major energy injection mechanism (see Sarazin 2002, Brunetti 2003 and references therein). The details of the injection and the energy transfer are poorly understood. A crude picture includes the energy injection scale of 100-500 kpc and the injection velocity of the order of 10 3 km/s.A difficulty that one faces trying to understand turbulence is clusters is that the diffusivity is very different along and perpendicular to magnetic field. This is related to the fact that the mean free path of ions is substantial. For non-magnetized Correspondence to: lazarian@astro.wisc.edu intracluster gas the Re number is only marginally larger than Re crit and therefore formally is only just sufficient for initiating the turbulence. At the same time, even small magnetization makes the Reynolds number for the motions perpendicular to magnetic field very large (e.g. more than 10 10 ). This poses the question of what a reasonable choice of the Reynolds number is for intracluster medium....

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Section: What Do We Know About Mhd Turbulence?supporting

confidence: 75%

Theoretical approaches to particle propagation and acceleration in turbulent intergalactic medium

Lazarían

2006

Astron Nachr

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“…Large values of k ⊥ could be the consequence of refraction [21,22], resonant absorption [23][24][25], and turbulent cascade [26]. This result is supported by numerical simulations of magnetized turbulence with a dynamically strong mean field [27,28]. In situ measurements of turbulence in the solar wind and observations of interstellar scintillation also show similar evidence for the theoretical results above [29][30][31][32][33][34].…”

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confidence: 66%

Exact solutions of dispersion equation for MHD waves with short-wavelength modification

Ling

2011

Chin. Sci. Bull.

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Dispersive magnetohydrodynamic (MHD) waves with short-wavelength modification have an important role in transforming energy from waves into particles. In this paper, based on the two-fluid mode, a dispersion equation, including the short-wavelength effect, and its exact solution are presented. The outcome is responsible for the short-wavelength modification versions of the three ideal MHD modes (i.e. the fast, slow and Alfvén). The results show that the fast and Alfvén modes are modified considerably by the shortwavelength effect mainly in the quasi-parallel and quasi-perpendicular propagation directions, respectively, while the slow mode can be affected by the short-wavelength effect in all propagation directions. On the other hand, the dispersive modification occurs primarily in the finite-β regime of 0.001 < β < 1 for the fast mode and in the high-β regime of 0.1 < β < 10 for the slow mode. For the Alfvén mode, the dispersive modification occurs from the low-β regime of β < 0.001 through the high-β regime of β > 1. It is well known that there are three ideal magnetohydrodynamic (MHD) modes: the fast, slow and Alfvén waves in the low-frequency limit (much lower than the ion cyclotron frequency ω ci ) and the long-wavelength limit (much longer than the ion Larmor radius ρ i ). When wavelengths reduce to the characteristic length scales, such as λ e and ρ i , where λ e is the electron inertial length, the ions are free while the electrons are tightly bound to magnetic field lines because their Larmor radius is much smaller than that of the ions (i.e. ρ e ρ i ). This leads to the presence of spatial charge and the dispersion of the MHD waves. In the case of the Alfvén wave, the dispersive wave is called the kinetic Alfvén wave (KAW). In the KAW, the perturbed electric fields have a non-zero component parallel to the background magnetic field that may cause efficient heating and acceleration of the plasma particles [1][2][3][4].KAWs have been extensively discussed because of their potential importance in the particle energization of plasmas.*Corresponding author (email: djwu@pmo.ac.cn) Also, they have been applied to laboratory, space and astrophysical plasmas, such as tokamak plasma heating [5][6][7], auroral electron acceleration [8][9][10][11], solar coronal plasma heating [12][13][14], and abnormal heating of heavy ions in the extended corona [15,16]. On the other hand, the other two modes, the fast and slow waves, have been given little attention. Some recent studies on the MHD turbulence in interstellar and interplanetary spaces show that the energy cascades primarily by developing small-scales structures perpendicular to the local field, with k ⊥ k [17][18][19][20]. Large values of k ⊥ could be the consequence of refraction [21,22], resonant absorption [23][24][25], and turbulent cascade [26]. This result is supported by numerical simulations of magnetized turbulence with a dynamically strong mean field [27,28]. In situ measurements of turbulence in the solar wind and observations of interstellar scintillat...

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“…The importance of the local field for the turbulence anisotropy analysis has been pointed out already in Cho and Vishniac (2000), Maron and Goldreich (2001), Milano et al (2001). The method proposed by Horbury et al (2008), and used by Wicks et al (2010) in Fig.…”

Section: Magnetic Fluctuationsmentioning

confidence: 90%

Solar Wind Turbulence and the Role of Ion Instabilities

et al. 2013

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Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: (i) weakness of collisional dissipation and (ii) presence of several characteristic space and time scales. In this paper we discuss observational properties of solar wind turbulence in a large range from the MHD to the electron scales. At MHD scales, within the inertial range, turbulence cascade of magnetic fluctuations develops mostly in the plane perpendicular to the mean field, with the Kolmogorov scaling k −5/3 ⊥ for the perpendicular cascade and k −2 for the parallel one. Solar wind turbulence is compressible in nature: density fluctuations at MHD scales have the Kolmogorov spectrum. Velocity fluctuations do not follow magnetic field ones: their spectrum is a power-law with a −3/2 spectral index. Probability distribution functions of different plasma parameters are not Gaussian, indicating presence of intermittency. At the moment there is no global model taking into account all these observed properties of the inertial range. At ion scales, turbulent spectra have a break, compressibility increases and the density fluctuation spectrum has a local flattening. Around ion scales, magnetic spectra are variable and ion instabilities occur as a function of the local plasma parameters. Between ion and electron scales, a small scale turbulent cascade seems to be established. It is characterized by a well defined power-law spectrum in magnetic and density fluctuations with a spectral index close to −2.8. Approaching electron scales, the fluctuations are no more self-similar: an exponential cut-off is usually observed (for time intervals without quasi-parallel whistlers) indicating an onset of dissipation. The small scale inertial range between ion and electron scales and the electron dissipation range can be together described by ∼ k −α ⊥ exp(−k ⊥ d ), with α 8/3 and the dissipation scale d close to the electron Larmor radius d ρ e . The nature of this small scale cascade and a possible dissipation mechanism are still under debate.

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Simulations of Incompressible Magnetohydrodynamic Turbulence

Cited by 571 publications

References 24 publications

Theoretical approaches to particle propagation and acceleration in turbulent intergalactic medium

Theoretical approaches to particle propagation and acceleration in turbulent intergalactic medium

Exact solutions of dispersion equation for MHD waves with short-wavelength modification

Solar Wind Turbulence and the Role of Ion Instabilities

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