Universality of Solar-Wind Turbulent Spectrum from MHD to Electron Scales

Abstract

To investigate the universality of magnetic turbulence in space plasmas, we analyze seven time periods in the free solar wind under different plasma conditions. Three instruments on Cluster spacecraft operating in different frequency ranges give us the possibility to resolve spectra up to 300 Hz. We show that the spectra form a quasiuniversal spectrum following the Kolmogorov's law approximately k(-5/3) at MHD scales, a approximately k(-2.8) power law at ion scales, and an exponential approximately exp[-sqrt[k(rho)e]] at scales k(rho)e approximately [0.1,1], where rho(e) is the electron gyroradius. This is the first observation of an exponential magnetic spectrum in space plasmas that may indicate the onset of dissipation. We distinguish for the first time between the role of different spatial kinetic plasma scales and show that the electron Larmor radius plays the role of a dissipation scale in space plasma turbulence.

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).…”

“…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 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…”

“…1). Alexandrova et al (2009Alexandrova et al ( , 2010 have demonstrated the universal character of the MHD k −1.7 ⊥ and kinetic k −2.8 ⊥ spectra and analyzed the non-universal transition between them. Kinetic spectrum ends up with a curved spectrum at electron scales, indicating dissipation.…”

Ideal MHD turbulence: the inertial range spectrum with collisionless dissipation

“…. The IK-like range is mapped less clearly with varying slopes ranging from extremely flat ∼ k −1 up to IK as, for instance, indicated in the CLUSTER observation in Figure 1 of Alexandrova et al [7], Horbury et al [24] and more pronounced in the MESSENGER/Ulysses observations [26] where the slope found was ∼ − 5 4 . At the high frequency end the spectrum enters a dissipation range, at 0.5 Hz < f < 0.8 Hz in Figure 1, still power law though from case to case exhibiting varying slopes −3 [e.g., 26,32], sometimes even much steeper.…”