Evaluation of Reduced Power Spectra from Three-Dimensional k-Space

Friday, 19 December 2014
Michael von Papen and Joachim Saur, University of Cologne, Cologne, Germany
We present a new tool to evaluate one dimensional reduced power spectral densities (PSD) from arbitrary energy distributions in k-space. This enables us to calculate the power spectra as they are measured in spacecraft frame for any given measurement geometry assuming Taylor's frozen-in approximation. It is possible to seperately calculate the diagonal elements of the spectral tensor and also to insert additional, non-turbulent energy in k-space (e.g.\ mirror mode waves). Given a critically balanced turbulent cascade with kkα, we explore the implications on the spectral form of the PSD and the functional dependence of the spectral index κ on the field-to-flow angle θ between plasma flow and background magnetic field. We show that critically balanced turbulence develops a θ-independent cascade with the spectral slope of the perpendicular cascade κ(θ=90). This happens at frequencies f>fmax, where fmax(L,α,θ) is a function of outer scale L, critical balance exponent α and field-to-flow angle θ. We also discuss potential damping terms acting on the k-space distribution of energy and their effect on the PSD. Further, we show that the functional dependence κ(θ) as found by \textit{Horbury et al.} (2008) and \textit{Chen et al.} (2010) can be explained with a damped critically balanced turbulence model.