The usefulness of Poynting's theorem in magnetic turbulence

TL;DR

This paper revisits Poynting's theorem to clarify the roles of electric and magnetic fluctuations in turbulent plasma, deriving new expressions for turbulent conductivity and discussing their application to solar wind turbulence.

Contribution

It explicitly incorporates relativistic transformations and mechanical contributions into Poynting's theorem for turbulent plasma analysis, extending previous work.

Findings

Derived expressions for turbulent conductivity spectra in different turbulence regimes.

Clarified the role of electric fluctuations as intermediate in turbulence analysis.

Discussed the application of these theoretical results to solar wind turbulence.

Abstract

We rewrite Poynting's theorem, already used in a previous publication (Treumann & Baumjohann 2017) to derive relations between the turbulent magnetic and electric power spectral densities, to make explicit where the mechanical contributions enter. We then make explicit use of the relativistic transformation of the turbulent electric fluctuations to obtain expressions which depend only on the magnetic and velocity fluctuations. Any electric fluctuations play just an intermediate role. Equations are constructed for the turbulent conductivity spectrum in Alfv\'enic and non-Alfv\'enic turbulence in extension of the results in the above citation. An observation-based discussion of their use in application to solar wind turbulence is given. The inertial range solar wind turbulence exhibits signs of chaos and self-organisation.