Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence

Wareing, C. J.; Hollerbach, Rainer

doi:10.1063/1.3111033

Cited by 36 publications

(50 citation statements)

References 17 publications

(60 reference statements)

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“…[10] Continuing with the second scenario, the forward cascade of lightly damped whistlers at W p < w r has been demonstrated by electron magnetohydrodynamic simulations in both two dimensions [Biskamp et al, 1996;Dastgeer et al, 2000;Wareing and Hollerbach, 2009] and three dimensions [Biskamp et al, 1999;Cho and Lazarian, 2004] as well as by the two-dimensional particle-in-cell (PIC) simulations of and Saito et al [2008]. These computations show that the whistler cascade leads to reduced spectra that are steeper functions of wave number than inertial range spectra, but that the fluctuation intensity is, like that of the inertial range, stronger at quasiperpendicular than at quasi-parallel propagation.…”

Section: Introductionmentioning

confidence: 92%

Short‐wavelength turbulence in the solar wind: Linear theory of whistler and kinetic Alfvén fluctuations

2009

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[1] There is a debate as to the identity of the fluctuations which constitute the relatively high-frequency plasma turbulence observed in the solar wind. One school holds that these modes are kinetic Alfvén waves, whereas another opinion is that they are whistler modes. Here linear kinetic theory for electromagnetic fluctuations in homogeneous, collisionless, magnetized plasmas is used to compute two dimensionless transport ratios, the electron compressibility C e and the magnetic compressibility C k for these two modes. The former is a measure of the amplitude of density fluctuations, and the latter indicates the relative energy in magnetic fluctuations in the component parallel to the background magnetic fieldwhistler , and the latter quantity is of order 0.5 at whistler propagation strongly oblique to B o . Such values of C k are sometimes measured at relatively high frequencies and b e ( 1 in the solar wind; thus, it is concluded that such observations correspond to whistler mode turbulence. But other solar wind observations indicate that kinetic Alfvén fluctuations also contribute to relatively high-frequency solar wind turbulence.

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Section: Introductionmentioning

confidence: 92%

Short‐wavelength turbulence in the solar wind: Linear theory of whistler and kinetic Alfvén fluctuations

2009

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“…Quasi-parallel magnetosonic modes are not damped at the above scale, so that a weak cascade of right-hand polarized fluctuations can generate a dispersive region of whistler modes (Stawicki et al, 2001;Borovsky, 2004, 2008;Goldstein et al, 1994). The cascade of weakly damped whistler modes has been reproduced through electron MHD numerical simulations (Biskamp et al, 1996(Biskamp et al, , 1999Wareing and Hollerbach, 2009;Cho and Lazarian, 2004) and Particle-in-Cell (PIC) codes Saito et al, 2008).…”

Section: Whistler Modes Scenariomentioning

confidence: 99%

The Solar Wind as a Turbulence Laboratory

Bruno

Carbone

2013

Living Rev. Solar Phys.

960

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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“…Goldreich & Reisenegger (1992) suggested that the Hall effect may lead to the formation of smaller scale structure through cascades, which have reduced Ohmic decay times, a result that has been followed up by numerical studies exploring Hall-induced turbulence (Biskamp et al 1996;Wareing & Hollerbach 2009. Another possibility ⋆ Email: K.N.Gourgouliatos@leeds.ac.uk is the development of instability of a state previously being in Hall equilibrium leading to smaller structure formation (Rheinhardt & Geppert 2002;Rheinhardt et al 2004;Pons & Geppert 2010).…”

Section: Introductionmentioning

confidence: 99%

Resistive tearing instability in electron MHD: application to neutron star crusts

Gourgouliatos¹,

Hollerbach²

2016

Mon. Not. R. Astron. Soc.

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We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the Electron-MHD limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as γ ∝ B 2/3 σ −1/3 where B is the magnetic field and σ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane parallel configuration where the magnetic field polarity reverses, through simulations of systems initiating in Hall equilibrium with some superimposed perturbation. Following a transient phase, during which there is some minor rearrangement of the magnetic field, the perturbation grows exponentially. Once the instability is fully developed the magnetic field forms the characteristic islands and X-type reconnection points, where Ohmic decay is enhanced. We discuss the implications of this instability for the local magnetic field evolution in neutron stars' crusts, proposing that it can contribute to heating near the surface of the star, as suggested by models of magnetar post-burst cooling. In particular, we find that a current sheet a few meters thick, covering as little as 1% of the total surface can provide 10 42 erg in thermal energy within a few days. We briefly discuss applications of this instability in other systems where the Hall effect operates such as protoplanetary discs and space plasmas.

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Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence

Cited by 36 publications

References 17 publications

Short‐wavelength turbulence in the solar wind: Linear theory of whistler and kinetic Alfvén fluctuations

Short‐wavelength turbulence in the solar wind: Linear theory of whistler and kinetic Alfvén fluctuations

The Solar Wind as a Turbulence Laboratory

Resistive tearing instability in electron MHD: application to neutron star crusts

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