Solar Wind Turbulence and the Role of Ion Instabilities

Abstract

Solar wind is probably the best laboratory to study turbulence in astrophysical plasmas. In addition to the presence of magnetic field, the differences with neutral fluid isotropic turbulence are: (i) weakness of collisional dissipation and (ii) presence of several characteristic space and time scales. In this paper we discuss observational properties of solar wind turbulence in a large range from the MHD to the electron scales. At MHD scales, within the inertial range, turbulence cascade of magnetic fluctuations develops mostly in the plane perpendicular to the mean field, with the Kolmogorov scaling k −5/3 ⊥ for the perpendicular cascade and k −2 for the parallel one. Solar wind turbulence is compressible in nature: density fluctuations at MHD scales have the Kolmogorov spectrum. Velocity fluctuations do not follow magnetic field ones: their spectrum is a power-law with a −3/2 spectral index. Probability distribution functions of different plasma parameters are not Gaussian, indicating presence of intermittency. At the moment there is no global model taking into account all these observed properties of the inertial range. At ion scales, turbulent spectra have a break, compressibility increases and the density fluctuation spectrum has a local flattening. Around ion scales, magnetic spectra are variable and ion instabilities occur as a function of the local plasma parameters. Between ion and electron scales, a small scale turbulent cascade seems to be established. It is characterized by a well defined power-law spectrum in magnetic and density fluctuations with a spectral index close to −2.8. Approaching electron scales, the fluctuations are no more self-similar: an exponential cut-off is usually observed (for time intervals without quasi-parallel whistlers) indicating an onset of dissipation. The small scale inertial range between ion and electron scales and the electron dissipation range can be together described by ∼ k −α ⊥ exp(−k ⊥ d ), with α 8/3 and the dissipation scale d close to the electron Larmor radius d ρ e . The nature of this small scale cascade and a possible dissipation mechanism are still under debate.

Dynamic properties of small-scale solar wind plasma fluctuations

“…The maximum of distributions of the P 1 slope are approximately −(1.6 to 1.7), and of the P 2 ∼ −(2.6 to 2.8). The average values of the slope of the low frequency range P 1 = −1.6 ± 0.2 are in a good agreement with the numerous experimental results of plasma and IMF parameters in SW obtained earlier (see the reviews [1,2] and references therein) and correspond approximately to the slope of the Kolmogorov model spectrum in the inertial range [12]. The average values of the slope at high-frequency range are equal P 2 = −2.9 ± 0.2.…”

Recent progress in astrophysical plasma turbulence from solar wind observations

“…It is therefore of interest to compare the scaling of the compressive fluctuations in the solar wind to that of the Alfvénic turbulence. While spectra of compressive fluctuations have long been measured in the solar wind (see reviews by Alexandrova et al 2013;Bruno & Carbone 2013), we have recently been able to investigate these with greater precision, to enable comparison to the Alfvénic turbulence. Chen et al (2011a) showed that the spectral indices of both δn and δ|B| are close to −5/3, similar to the magnetic field, rather than the velocity, which has a −3/2 spectral index.…”

“…the nonGaussian nature of the fluctuations. Intermittency has been well studied in the solar wind for kρ i < 1 (see reviews by Alexandrova et al 2013;Bruno & Carbone 2013), where most quantities are seen to become increasingly non-Gaussian towards smaller scales, a well-known feature of turbulence. This is related to the turbulent energy being concentrated into a smaller fraction of the volume as the cascade proceeds to smaller scales, and results in the formation of energetic structures within the plasma.…”

“…It is not intended to be a complete review; for general review papers on solar wind observations see, e.g. Alexandrova et al (2013), Bruno & Carbone (2013) and the collection of Kiyani, Osman & Chapman (2015). It also primarily summarises work in which I have been involved, with other results and theoretical background described for context.…”

Ideal MHD turbulence: the inertial range spectrum with collisionless dissipation

“…Kinetic Alfvén wave damping, in particular when resulting from nonlinear evolution, would be another option [15], in addition to causing anisotropy. Other suggestions favorise whistler wave damping [30] which, however, should be too weak for dissipating the input of mechanical turbulent energy.…”