Lin, Rong; He, Jiansen; Zhu, Xingyu; Zhang, Lei; Duan, Die; Sahraoui, Fouad; Verscharen, Daniel; (2022) Power Anisotropy, Dispersion Signature and Turbulence Diffusion Region in the 3D Wavenumber Domain of Space Plasma Turbulence. The Astrophysical Journal , 939 (2) , Article 121. 10.3847/1538-4357/ac8e07.

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Abstract

We explore the multifaceted important features of turbulence (e.g., anisotropy, dispersion, and diffusion) in the three-dimensional (3D) wavenumber domain (k ∥, k ⊥,1, k ⊥,2), by employing the k-filtering technique to high-quality measurements of fields and particles from the Magnetospheric Multiscale Mission (MMS) multi-spacecraft constellation. We compute the 3D power spectral densities (PSDs) of magnetic and electric field fluctuations (marked as PSD(δ B ( k )) and <?CDATA $\mathrm{PSD}(\delta {{\boldsymbol{E}}}_{\langle {{\boldsymbol{v}}}_{{\rm{i}}}\rangle }^{{\prime} }({\boldsymbol{k}}))$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>PSD</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="bold-italic">E</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">〈</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="bold-italic">v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">〉</mml:mo> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="bold-italic">k</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:math> , respectively), both of which show a prominent spectral anisotropy in the sub-ion range. We give the first 3D image of the bifurcation between the power spectra of the electric and magnetic fluctuations, by calculating the ratio between <?CDATA $\mathrm{PSD}(\delta {{\boldsymbol{E}}}_{\langle {{\boldsymbol{v}}}_{{\rm{i}}}\rangle }^{{\prime} }({\boldsymbol{k}}))$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>PSD</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="bold-italic">E</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">〈</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="bold-italic">v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">〉</mml:mo> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi mathvariant="bold-italic">k</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:math> and PSD(δ B ( k )), the distribution of which is related to the nonlinear dispersion relation. We also compute the ratio between electric spectra in different reference frames defined by the ion bulk velocity, <?CDATA $\mathrm{PSD}(\delta {{\boldsymbol{E}}}_{\mathrm{local}\ {{\boldsymbol{v}}}_{{\rm{i}}}}^{{\prime} })/\mathrm{PSD}(\delta {{\boldsymbol{E}}}_{\langle {{\boldsymbol{v}}}_{{\rm{i}}}\rangle }^{{\prime} })$?> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>PSD</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="bold-italic">E</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>local</mml:mi> <mml:mspace width="0.33em" /> <mml:msub> <mml:mrow> <mml:mi mathvariant="bold-italic">v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>PSD</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>δ</mml:mi> <mml:msubsup> <mml:mrow> <mml:mi mathvariant="bold-italic">E</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">〈</mml:mo> <mml:msub> <mml:mrow> <mml:mi mathvariant="bold-italic">v</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">i</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">〉</mml:mo> </mml:mrow> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">)</mml:mo> </mml:math> , to visualize the turbulent ion diffusion region (T-IDR) in wavenumber space. The T-IDR has an anisotropy and a preferential direction of wavevectors, which is generally consistent with the plasma wave theory prediction based on the dominance of kinetic Alfvén waves. This work demonstrates the worth of the k-filtering technique in diagnosing turbulence comprehensively, especially when the electric field is involved.

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