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Annales Geophysicae An interactive open-access journal of the European Geosciences Union
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© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: regular paper 17 May 2019

Submitted as: regular paper | 17 May 2019

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This discussion paper is a preprint. A revision of the manuscript is under review for the journal Annales Geophysicae (ANGEO).

Scaling laws in Hall-inertial range turbulence

Yasuhito Narita1, Wolfgang Baumjohann1, and Rudolf A. Treumann2,3 Yasuhito Narita et al.
  • 1Space Research Institute, Austrian Academy of Sciences, Schmiedlstraße 6, A-8042 Graz, Austria
  • 2International Space Science Institute, Hallerstraße 6, CH-3012, Berne, Switzerland
  • 3Geophysics Department, Ludwig-Maximilians-Universität, Theresienstraße 41, D-80333 Munich, Germany

Abstract. There is an increasing amount of observational evidence in space plasma for the breakdown of inertial-range spectra of magnetohydrodynamic (MHD) turbulence on spatial scales smaller than the ion inertial length. Magnetic energy spectra often exhibit a steepening, which is reminiscent of dissipation of turbulence energy, for example in wave-particle interactions. Electric energy spectra, on the other hand, tend to be flatter than those of MHD turbulence, which is indicative of a dispersive process converting magnetic into electric energy in electromagnetic wave excitation. Here we develop a model of the scaling laws and the power spectra for the Hall-inertial range in plasma turbulence. A phenomenological approach is taken. The Hall electric field attains an electrostatic component when the wave vectors are perpendicular to the mean magnetic field. The power spectra of Hall-turbulence are steep for the magnetic field with slope of −7/3 for compressible magnetic turbulence, they are flatter for the Hall electric field with slope −1/3. Our model for the Hall-turbulence serves as a likely candidate to explain the steepening of the magnetic energy spectra in the solar wind neither as indication of the dissipation range nor the dispersive range but as the Hall-inertial range. Our model also reproduces the shape of energy spectra in Kelvin-Helmholtz turbulence observed at the Earth magnetopause.

Yasuhito Narita et al.
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Yasuhito Narita et al.
Yasuhito Narita et al.
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Short summary
Scaling laws and energy spectra for the electric field, magnetic field, flow velocity, and density are theoretically derived for small-scale turbulence in space plasma on which the electrons behave as a fluid but the ions more as individual particles due to the difference in the mass (the Hall effect). Our spectrum model for small-scale turbulence can qualitatively explain the turbulence spectra measured in near-Earth space.
Scaling laws and energy spectra for the electric field, magnetic field, flow velocity, and...