Three Dimensional AnisotropickSpectra of Turbulence at Subproton Scales in the Solar Wind

Abstract

We show the first three dimensional (3D) dispersion relations and k spectra of magnetic turbulence in the solar wind at subproton scales. We used the Cluster data with short separations and applied the k-filtering technique to the frequency range where the transition to subproton scales occurs. We show that the cascade is carried by highly oblique kinetic Alfvén waves with ω(plas) ≤ 0.1ω(ci) down to k(⊥) ρ(i)∼2. Each k spectrum in the direction perpendicular to B0 shows two scaling ranges separated by a breakpoint (in the interval [0.4,1]k(⊥)ρ(i): a Kolmogorov scaling k(⊥)⁻¹ⁱ⁷ followed by a steeper scaling ∼k(⊥)⁻⁴ⁱ⁵. We conjecture that the turbulence undergoes a transition range, where part of the energy is dissipated into proton heating via Landau damping and the remaining energy cascades down to electron scales where electron Landau damping may predominate.

Turbulent spectra and spectral kinks in the transition range from MHD to kinetic Alfvén turbulence

“…However, observations of power law spectra at k ⊥ ρ p 1 (Sahraoui et al, , 2010Alexandrova et al, 2009;Kiyani et al, 2009) suggest a continuation of the cascade that is consistent with the theoretical picture of KAWs (Bale et al, 2005;Schekochihin et al, 2009;Sahraoui et al, 2010). It has been envisaged that the nonlinear evolution and related wavenumber spectra in the range below k ⊥b are dominated by MHD-type nonlinear interactions among Alfvén waves, and that the spectra for k ⊥ > k ⊥b are determined by KAW properties (Schekochihin et al, 2009).…”

“…As has been first shown by Matthaeus et al (1990), followed by many others (see e.g. recent papers by Osman and Horbury (2009), Sahraoui et al (2010), Luo and Wu (2010), and references therein), solar wind turbulence is dominated by large perpendicular wavenumbers k ⊥ k z . In these conditions, satellites measure perpendicular wavenumber spectra, f ∝ k ⊥ , except for rare cases of B 0 V SW , where frequency measures parallel wavenumber, f ∝ k z .…”

“…There are numerous observational and theoretical indications that MHD Alfvén turbulence in the solar wind cascades towards high k ⊥ and eventually reaches the KAW wavenumber range at the proton gyroradius scales, k ⊥ ρ p ∼ 1 Bale et al, 2005;Alexandrova et al, 2008a;Sahraoui et al, 2009Sahraoui et al, , 2010. It is not yet certain what happens next with these KAWs: do they dissipate by heating the plasma , or do they interact nonlinearly among themselves and cascade further towards higher k ⊥ , ultimately reaching electron scales (Sahraoui et al, , 2010Alexandrova et al, 2009). Spectra up to electron scales with Cluster were first studied in the Earth's magnetosheath (Mangeney et al, 2006;Alexandrova et al, 2008b).…”

“…In these conditions, satellites measure perpendicular wavenumber spectra, f ∝ k ⊥ , except for rare cases of B 0 V SW , where frequency measures parallel wavenumber, f ∝ k z . The spectral break f b is often associated with one of the proton kinetic scales, the proton gyroradius ρ p or the proton inertial length δ p = V A / p , such that the observed frequency of the break is 2πf b V SW /ρ p or V SW /δ p Bale et al, 2005;Alexandrova et al, 2010;Sahraoui et al, 2010). Perri et al (2010) show, however, that the break position is not sensitive to the radial dependence of the ion scales, whereas Markovskii et al (2008) argue that the break position depends upon a combination of the scale and the turbulent amplitudes at that scale.…”

“…In particular, a recent theoretical analysis by Podesta et al (2010) argues that the KAW cascade is subject to collisionless Landau damping and cannot reach electron scales in solar wind conditions. However, using Cluster data, Sahraoui et al (2009Sahraoui et al ( , 2010 and Alexandrova et al (2009Alexandrova et al ( , 2010 have shown that the spectra extend to electron scales, with spectral slopes −1.7 and −2.8 in the MHD range and in the range between ion and electron scales, respectively. Between these k −1.7 ⊥ and k −2.8 ⊥ spectra, Sahraoui et al (2010) also noticed much steeper…”