The Anisotropy of Electron Magnetohydrodynamic Turbulence

Cho, Jungyeon; Lazarían, A.

doi:10.1086/425215

Cited by 187 publications

(266 citation statements)

References 17 publications

(31 reference statements)

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“…Its linear modes are the whistler waves with ω ± = ±k d i k ⊥ . Some key properties of the EMHD turbulence have been investigated both numerically and theoretically, suggesting that the Kolmogorov type arguments work fine (Biskamp et al 1999;Ng et al 2003;Cho & Lazarian 2004. A calculation along the lines of the one below for KAWs, shows that the energy spectrum for whistler wave turbulence is…”

Section: Two-fluid Plasma Dynamicsmentioning

confidence: 99%

Parallel electric field generation by Alfvén wave turbulence

Bian¹,

Kontar²,

Brown³

2010

A&A

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Aims. This work aims to investigate the spectral structure of the parallel electric field generated by strong anisotropic and balanced Alfvénic turbulence in relation with the problem of electron acceleration from the thermal population in solar flare plasma conditions. Methods. We consider anisotropic Alfvénic fluctuations in the presence of a strong background magnetic field. Exploiting this anisotropy, a set of reduced equations governing non-linear, two-fluid plasma dynamics is derived. The low-β limit of this model is used to follow the turbulent cascade of the energy resulting from the non-linear interaction between kinetic Alfvén waves, from the large magnetohydrodynamics (MHD) scales with k ⊥ ρ s 1 down to the small "kinetic" scales with k ⊥ ρ s 1, ρ s being the ion sound gyroradius. Results. Scaling relations are obtained for the magnitude of the turbulent electromagnetic fluctuations, as a function of k ⊥ and k , showing that the electric field develops a component parallel to the magnetic field at large MHD scales. Conclusions. The spectrum we derive for the parallel electric field fluctuations can be effectively used to model stochastic resonant acceleration and heating of electrons by Alfvén waves in solar flare plasma conditions

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Section: Two-fluid Plasma Dynamicsmentioning

confidence: 99%

Parallel electric field generation by Alfvén wave turbulence

Bian¹,

Kontar²,

Brown³

2010

A&A

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“…As with the MHD scale cascade, there are a number of observational and theoretical works, which identify turbulent fluctuations at small scales as having properties of linear wave modes (e.g., Denskat et al 1983;Goldstein et al 1994;Ghosh et al 1996;Biskamp et al 1996Biskamp et al , 1999Leamon et al 1998;Cho and Lazarian 2004;Bale et al 2005;Galtier 2006;Sahraoui et al 2010Howes et al 2006Howes et al , 2008Howes et al , 2012bSchekochihin et al 2009;Gary and Smith 2009;Chandran et al 2009;Chen et al 2010bChen et al , 2013a. A recent analysis by Chen et al (2013c) showed that the ratio of density to magnetic fluctuations in the range between ion and electron scales is very close to that expected for kinetic Alfvén waves, and not whistler waves, and concluded that the fluctuations in this range are predominantly strong kinetic Alfvén turbulence.…”

Section: Ion Scale Instabilities Driven By Solar Wind Expansion and Cmentioning

confidence: 99%

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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“…We found no evidence, in either 2D or 3D, of a dissipative cutoff, implying that the Hall term is able to dominate on all scales and that the coupling is nonlocal in Fourier space. Additional evidence of the nonlocal nature of the Hall cascade comes from the strong anisotropy in the presence of a uniform field found by ourselves and others (Cho & Lazarian 2004, 2009; if the coupling were purely local in Fourier space, then including a uniform field would have no effect at all on small scales, in contrast to what is observed.…”

Section: Article Published By Edp Sciencesmentioning

confidence: 71%

“…None of the fully nonlinear calculations, of ourselves or numerous other authors (Biskamp et al 1996(Biskamp et al , 1999Dastgeer et al 2000;Dastgeer & Zank 2003;Cho & Lazarian 2004;Shaikh & Zank 2005;Cho & Lazarian 2009), which have a broad variety of different initial conditions including sufficiently strong magnetic fields, have ever found anything other than a standard Hall cascade. Cumming et al (2004) also consider the possibility of a Hall instability, and its relevance for the evolution of neutron star magnetic fields.…”

Section: Discussionmentioning

confidence: 95%

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Hall cascades versus instabilities in neutron star magnetic fields

Wareing¹,

Hollerbach²

2009

A&A

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Context. The Hall effect is an important nonlinear mechanism affecting the evolution of magnetic fields in neutron stars. Studies of the governing equation, both theoretical and numerical, have shown that the Hall effect proceeds in a turbulent cascade of energy from large to small scales. Aims. We investigate the small-scale Hall instability conjectured to exist from the linear stability analysis of Rheinhardt and Geppert. Methods. Identical linear stability analyses are performed to find a suitable background field to model Rheinhardt and Geppert's ideas. The nonlinear evolution of this field is then modelled using a three-dimensional pseudospectral numerical MHD code. Combined with the background field, energy was injected at the ten specific eigenmodes with the greatest positive eigenvalues as inferred by the linear stability analysis. Results. Energy is transferred to different scales in the system, but not into small scales to any extent that could be interpreted as a Hall instability. Any instabilities are overwhelmed by a late-onset turbulent Hall cascade, initially avoided by the choice of background field, but soon generated by nonlinear interactions between the growing eigenmodes. The Hall cascade is shown here, and by several authors elsewhere, to be the dominant mechanism in this system.

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The Anisotropy of Electron Magnetohydrodynamic Turbulence

Cited by 187 publications

References 17 publications

Parallel electric field generation by Alfvén wave turbulence

Parallel electric field generation by Alfvén wave turbulence

Solar Wind Turbulence and the Role of Ion Instabilities

Hall cascades versus instabilities in neutron star magnetic fields

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