Conductivity spectrum and dispersion relation in solar wind turbulence

TL;DR

This paper models solar wind magnetic turbulence using electrodynamics, deriving the conductivity spectrum and dispersion relation from observations, revealing insights into turbulence dissipation and structure formation.

Contribution

It introduces a method to determine the turbulent conductivity spectrum and dispersion relation from electromagnetic spectral data in the solar wind inertial range.

Findings

Dispersion relation shows spatial scale decay with frequency.

Dissipation function suggests shot-noise spectrum of turbulent resistivity.

Indicates presence of discrete mode turbulence and nonlinear resonances.

Abstract

Magnetic turbulence in the solar wind is treated from the point of view of electrodynamics. This can be done based on the use of Poynting's theorem attributing all turbulent dynamics to the spectrum of turbulent conductivity. For two directions of propagation of the turbulent fluctuations of the electromagnetic field with respect to the mean plus external magnetic fields an expression is constructed for the spectrum of turbulent dissipation. Use of solar wind observations of electromagnetic power spectral densities in the inertial subrange then allows determination of the conductivity spectrum, the dissipative response function, in this range. It requires observations of the complete electromagnetic spectral energy densities including electric power spectral densities. The dissipative response function and dispersion relation of solar wind inertial range magnetic turbulence are obtained. The dispersion relation indicates the spatial scale decay with increasing frequency providing independent support for the use of Taylor's hypothesis. The dissipation function indicates an approximate shot-noise spectrum of turbulent resistivity in the inertial range suggesting progressive structure formation in the inertial range which hints on the presence of discrete mode turbulence and nonlinear resonances.