The Solar Wind as a Turbulence Laboratory

Annual Review of Astronomy and Astrophysics, 1995

Recent work in describing the solar wind as an MHD turbulent fluid has shown that the magnetic fluctuations are adequately described as time stationary and to some extent as spatially homogeneous. Spectra of the three rugged invariants of incompressible MHD are the principal quantities used to characterize the velocity and magnetic field fluctuations. Unresolved issues concerning the existence of actively developing turbulence are discussed. INTRODUCTION To describe a fluid system as turbulent is to say that the dynamical fluid variables exhibit complex and essentially non-reproducible behavior as a function of time. This is generally due to the presence of nonlinearities in the fluid equations which strongly couple a large number of degrees of freedom. Turbulent systems are usually very far from equilibrium states for which detailed analytically tractable theories might exist. By all appearances, the solar wind plasma flow and the interplanetary magnetic field carried along with it are such a turbulent system. In the zero momentum frame, the magnetic and velocity field fluctuations are energetically comparable to the mean magnetic field over length scales of order I AU and display the type of complicated behavior expected of turbulence. velocity and magnetic fields in magnetohydrodynamie turbulence, EOS,

Physical Review Letters, 2009

Incompressible and isotropic magnetohydrodynamic turbulence in plasmas can be described by an exact relation for the energy flux through the scales. This Yaglom-like scaling law has been recently observed in the solar wind above the solar poles observed by the Ulysses spacecraft, where the turbulence is in an Alfvénic state. An analogous phenomenological scaling law, suitably modified to take into account compressible fluctuations, is observed more frequently in the same dataset. Large scale density fluctuations, despite their low amplitude, play thus a crucial role in the basic scaling properties of turbulence. The turbulent cascade rate in the compressive case can moreover supply the energy dissipation needed to account for the local heating of the non-adiabatic solar wind. PACS numbers: 96.50.Ci; 47.27.Gs; 96.50.Tf; 52.35.Ra The interplanetary space is permeated by the solar wind [1], a magnetized, supersonic flow of charged particles originating in the high solar atmosphere and blowing away from the sun. Low frequency fluctuations of solar wind variables are often described in the framework of fully developed hydromagnetic (MHD) turbulence . The large range of scales involved, spanning from 1 AU (≃ 1.5 × 10 8 km) down to a few kilometers, make the solar wind the largest "laboratory" where MHD turbulence can be investigated using measurements collected in situ by instruments onboard spacecraft . MHD turbulence is often investigated through the Elsässer variables z ± = v ± (4πρ) −1/2 b, computed from the local plasma velocity v and magnetic field b, ρ being the plasma mass density. In terms of such variables, MHD equations can be rewritten as ∂ t z ± + z ∓ · ∇z ± = −∇P/ρ + diss, where P is the total hydromagnetic pressure, and diss indicates dissipative terms involving the viscosity and the magnetic diffusivity. As in the Navier-Stokes equations for neutral fluids, the nonlinear terms z ∓ · ∇z ± cause the turbulent energy transfer between different scales, at high Reynolds numbers where dissipative terms can be neglected. However, in the MHD case, they couple the two Elsässer variables, so that the Alfvénic MHD fluctuations z ± , propagating along the background magnetic field, are advected by fluctuations z ∓ propagating in the opposite direction. The presence of strong correlations (or anti-correlations) between velocity and magnetic fluctuations, along with a nearly constant magnetic intensity and low amplitude density fluctuations, is usually referred to as Alfvénic state of turbulence, and implies that one of the two modes z ± should be negligible, making the nonlinear term of MHD equations vanish for pure Alfvénic fluctuations. In that case, the turbulent energy transfer should also disappear . Alfvénic turbulence is observed almost ubiquitously in fast wind. This holds both in the ecliptic fast streams, and in the high latitude wind blowing directly from the sun coronal holes .

Nonlinear Processes in Geophysics, 2005

The solar wind serves as a laboratory for investigating magnetohydrodynamic turbulence under conditions irreproducible on the terra firma. Here we show that the frame work of Hall magnetohydrodynamics (HMHD), which can support three quadratic invariants and allows nonlinear states to depart fundamentally from the Alfvénic, is capable of reproducing in the inertial range the three branches of the observed solar wind magnetic fluctuation spectrum-the Kolmogorov branch f −5/3 steepening to f −α 1 with α 1 3−4 on the high frequency side and flattening to f −1 on the low frequency side. These fluctuations are found to be associated with the nonlinear Hall-MHD Shear Alfvén waves. The spectrum of the concomitant whistler type fluctuations is very different from the observed one. Perhaps the relatively stronger damping of the whistler fluctuations may cause their unobservability. The issue of equipartition of energy through the so called Alfvén ratio acquires a new status through its dependence, now, on the spatial scale.

Journal of Geophysical Research, 1984

Two time periods are studied for gomery, 1983) of interpreting solar wind observa- which a relatively complete set of magnetic field tions in terms of turbulence theory. MHD turbu- and plasma measurements are available at both 1 AU lence involves a dynamical transfer of energy (from IMP 8 and ISEE 3) and near 4 to 5 AU (from between various

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015

Physical Review Letters, 2012

A connection between kinetic processes and intermittent turbulence is observed in the solar wind plasma using measurements from the Wind spacecraft at 1 A.U. In particular, kinetic effects such as temperature anisotropy and plasma heating are concentrated near coherent structures, such as current sheets, which are nonuniformly distributed in space. Furthermore, these coherent structures are preferentially found in plasma unstable to the mirror and firehose instabilities. The inhomogeneous heating in these regions, which is present in both the magnetic field parallel and perpendicular temperature components, results in protons at least 3-4 times hotter than under typical stable plasma conditions. These results offer a new understanding of kinetic processes in a turbulent regime, where linear Vlasov theory is not sufficient to explain the inhomogeneous plasma dynamics operating near non-Gaussian structures.

Planetary and Space Science, 2011

The analysis of the transition from the large-scale fluid regime to the short-scale kinetic range of wavelengths in the development of the turbulent cascade of energy is nowadays subject of fervent discussion in the space plasmas scientific community. We make use of Hybrid Vlasov-Maxwell simulations where the full kinetic dynamics of ions is taken into account, while electrons are treated as a fluid. We investigate the development of turbulence in the solar wind, in 1D-3V phase space configuration and in the frequency range across the ion cyclotron frequency. These simulations allow for the analysis of the role of kinetic effects in the short-scale region of the energy spectra in the direction parallel to the background magnetic field. Our numerical results show the presence of a significant electrostatic activity at small wavelengths, triggered by the resonant interaction of ions with longitudinal waves. Our model does not allow to take into account the evolution of the turbulent spectra in the plane perpendicular to the ambient field, due to limited dimensionality in phase space. On the other hand, this model permits to isolate and study the possibility of transferring the electromagnetic large-scale energy on the small-scale kinetic electrostatic component of the spectrum. Peculiar features observed in the spacecraft data in the solar wind are qualitatively reproduced within the hybrid-Vlasov model, such as the generation of perpendicular temperature anisotropy and accelerated longitudinal beams of ions in the distribution of particle velocities as well as the appearance of a marked peak of electrostatic activity in the short-scale termination of the turbulent spectra.

Planetary and Space Science, 2011

The occurrence of a nonlinear turbulent energy cascade in solar wind plasma has been recently established through the observation of an exact law from spacecraft measurements. The main results obtained in the fast, polar wind measured by Ulysses spacecraft are reviewed here. In particular, the turbulent cascade is seen as the mean to provide the energy necessary for the local heating in the non-adiabatic expansion of the solar wind. The importance of the density fluctuations in enhancing the turbulent energy transport is also evidenced. The ecliptic wind data measured by Ulysses are studied here in the same framework. This has been done by separating fast and slow streams, in order to avoid mixing of different physical conditions. The results further support the need for separate analysis of the two types of wind.

The Astrophysical Journal, 2012

New aspects of the slow solar wind turbulent heating and acceleration are investigated. A physical meaning of the lower boundary of the Alfvén wave turbulent spectra in the solar atmosphere and the solar wind is studied and the significance of this natural parameter is demonstrated. Via an analytical and quantitative treatment of the problem we show that a truncation of the wave spectra from the lower frequency side, which is a consequence of the solar magnetic field structure and its cyclic changes, results in a significant reduction of the heat production and acceleration rates. An appropriate analysis is presented regarding the link of the considered problem with existing observational data and slow solar wind initiation scenarios.

Astrophysical Journal, 2008

Magnetic fluctuations in the solar wind are distributed according to Kolmogorov's power law f −5/3 below the ion cyclotron frequency f ci . Above this frequency, the observed steeper power law is usually interpreted in two different ways: a dissipative range of the solar wind turbulence or another turbulent cascade, the nature of which is still an open question. Using the Cluster magnetic data we show that after the spectral break the intermittency increases toward higher frequencies, indicating the presence of non-linear interactions inherent to a new inertial range and not to the dissipative range. At the same time the level of compressible fluctuations raises. We show that the energy transfer rate and intermittency are sensitive to the level of compressibility of the magnetic fluctuations within the small scale inertial range. We conjecture that the time needed to establish this inertial range is shorter than the eddy-turnover time, and is related to dispersive effects. A simple phenomenological model, based on the compressible Hall MHD, predicts the magnetic spectrum ∼ k −7/3+2α , which depends on the degree of plasma compression α.