Abstract
Abstract. There is an increasing amount of observational evidence in space plasmas 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. In the present paper we consider a two-dimensional geometry with no wave vector component parallel to the magnetic field as is appropriate in Hall MHD. 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 a slope of -7/3 for compressible magnetic turbulence; they are flatter for the Hall electric field with a slope of -1/3. Our model for the Hall turbulence gives a possible explanation for the steepening of the magnetic energy spectra in the solar wind as an indication of neither 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's magnetopause.
Highlights
The power spectra of Hall turbulence are steep for the magnetic field with a slope of − 7/3 for compressible magnetic turbulence; they are flatter for the Hall electric field with a slope of −1/3
The recent availability of multi-spacecraft missions such as Cluster (Escoubet et al, 2001), THEMIS (Angelopoulos, 2008), and MMS (Burch et al, 2016) together with substantial advances in their instrumentation and the subsequent data analysis opened up the door to a more detailed study of space plasma turbulence on ion scales when ion inertia comes into play
We intend to determine the ratio δE/δB as well as the energy spectra in an attempt to obtain a scaled model of the ion-inertial-scale field fluctuations as the necessary step to derive the turbulent inertialrange power spectra of the fields on ion-inertial-scale lengths 1 kc/ωi < kc/ωe. To this end we turn to the application of a phenomenological turbulence model (Biskamp et al, 1996) in twodimensional electron magnetohydrodynamics which is appropriate in our case
Summary
The recent availability of multi-spacecraft missions such as Cluster (Escoubet et al, 2001), THEMIS (Angelopoulos, 2008), and MMS (Burch et al, 2016) together with substantial advances in their instrumentation and the subsequent data analysis opened up the door to a more detailed study of space plasma turbulence on ion scales when ion inertia comes into play. Ion-kinetic-scale power-law spectra (though limited to the frequency domain) were observationally obtained separately for the magnetic (Alexandrova et al, 2009; Sahraoui et al, 2009) and electric (Bale et al, 2005) fields. The study by Narita et al (2016) exhibits a frequency scattering in the observationally determined dispersion relation with an indication of a kinetic-drift mirror mode Based on these observations, we consider in the following a phenomenological turbulence model of stationary inertial-range spectra evolving in ion-scale turbulence. An important lesson from the model construction is that the Hall electric field is dependent on the wavenumber and the E–B ratio shows the wavenumber dependence
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