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Scaling laws in Hall inertial-range turbulence

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.
