In this review we will focus on a topic of fundamental importance for both plasma physics and astrophysics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Ulysses’ high latitude observations and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD) turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.

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The Solar Wind as a Turbulence Laboratory

A comprehensive overview is presented of recent observational and theoretical results on solar wind structures and fluctuations and magnetohydrodynamic waves and turbulence, with preference given to phenomena in the inner heliosphere. Emphasis is placed on the progress made in the past decade in the understanding of the nature and origin of especially small-scale, compressible and incompressible fluctuations. Turbulence models to describe the spatial transport and spectral transfer of the fluctuations in the inner heliosphere are discussed, and results from direct numerical simulations are dealt with. Intermittency of solar wind fluctuations and their statistical distributions are briefly investigated. Studies of the heating and acceleration effects of the turbulence on the background wind are critically surveyed. Finally, open questions concerning the origin, nature and evolution of the fluctuations are listed, and possible avenues and perspectives for future research are outlined.

MHD structures, waves and turbulence in the solar wind : observations and theories

Such nonthermal features as temperature anisotropies, heat fluxes, and proton double streams have been observed by a Helios solar probe survey of solar wind three-dimensional proton velocity distributions between 0.3 and 1 AU. It is found that a strong anisotropy in the core of proton distributions, with a temperature that is larger perpendicular rather than parallel to the magnetic field, is a persistent feature of high-speed streams, becoming most pronounced in the perihelion, or about 0.3 AU. Isotropic distributions have been detected only close to, and at, magnetic sector boundaries, and the flattest radial temperature profiles are found in high-speed streams. These observations indicate that local heating or proton heat conduction occurs in the solar wind.

Solar wind protons: Three-dimensional velocity distributions and derived plasma parameters measured between 0.3 and 1 AU

Assuming that the slab and isotropic models of solar wind turbulence need modification (largely due to the observed anisotropy of the interplanetary fluctuations and the results of laboratory plasma experiments), this paper proposes a model of the solar wind. The solar wind is seen as a fluid which contains both classical transverse Alfvenic fluctuations and a population of quasi-transverse fluctuations. In quasi-two-dimensional turbulence, the pitch angle scattering by resonant wave-particle interactions is suppressed, and the direction of minimum variance of interplanetary fluctuations is parallel to the mean magnetic field. The assumed incompressibility is consistent with the fact that the density fluctuations are small and anticorrelated, and that the total pressure at small scales is nearly constant.

Evidence for the presence of quasi‐two‐dimensional nearly incompressible fluctuations in the solar wind

A Helios solar probe survey of solar wind helium ion velocity distributions and derived parameters between 0.3 and 1 AU is presented. Distributions in high-speed wind are found to generally have small total anisotropies, with some indication that, in the core part, the temperatures are greater parallel rather than perpendicular to the magnetic field. The anisotropy tends to increase with heliocentric radial distance, and the average dependence of helium ion temperatures on radial distance from the sun is described by a power law. Differential ion speeds with values of more than 150 km/sec are observed near perihelion, or 0.3 AU. The role of Coulomb collisions in limiting differential ion speeds and the ion temperature ratio is investigated, and it is found that collisions play a distinct role in low-speed wind, by limiting both differential ion velocity and temperature.

Solar wind helium ions - Observations of the Helios solar probes between 0.3 and 1 AU

To obtain information on the temporal and spatial evolution of MHD waves and discontinuities in the solar wind, we studied by means of statistical methods magnetic field fluctuations measured by the two HELIOS spacecraft in the frequency range between 2.4×10−5 Hz and 1.3×10−2 Hz at distances from the sun between 0.29 AU and 1.0 AU. Some statistical properties as magnetic field variances show the fluctuations remaining very similar on their way out from the sun. A different picture of the fluctuations emerges from analyzing the spectral properties of the magnetic field: The slope of the power spectral densities (both the vector components and the magnitude of the magnetic field) as a function of frequency becomes steeper with increasing heliographic distance—the solar wind seems to act as a low-pass filter. The major changes occur within a heliographic distance up to about 0.4 AU. Field magnitude fluctuations fall off less rapidly with increasing radius than do fluctuations in the vector components. Cross spectral analysis between magnetic field components reveal the fluctuations as generally being field magnitude conserving.

Statistical properties of low‐frequency magnetic field fluctuations in the solar wind from 0.29 to 1.0 AU during solar minimum conditions: HELIOS 1 and HELIOS 2

MHD turbulence is studied by analyzing magnetic field and plasma observations from Helios-1 and -2 at minimum solar activity. The steady conditions in the plasma flows and the magnetic field sector structure in 1975/1976 facilitate an investigation of the radial evolution of the turbulence from 0.29 to 1AU. In high speed streams the fluctuations in the solar wind velocity v and the magnetic field b are highly correlated (the correction coefficient almost being one), which indicates that the turbulence is mainly Alfvenic in high speed plasma. While some general fluctuation properties remain essentially unchanged from 0.29 to 1AU, power spectral analysis reveals a different frequency composition of the Alfvenic turbulence at different heliocentric distances. At 0.3AU much more 'high' frequency fluctuations contribute to the total power in the magnetic field and velocity fluctuations than at 1AU. The contributions of field magnitude fluctuations are found to be distance and frequency dependent. Magnetic field spectra with an extended frequency range up to 470Hz show certain frequency bands, where the steepness of the spectra is independent of the helicocentric distance.

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K. U. Denskat

Papers

Statistical properties of low‐frequency magnetic field fluctuations in the solar wind from 0.29 to 1.0 AU during solar minimum conditions: HELIOS 1 and HELIOS 2

Observations of hydromagnetic turbulence in the solar wind

Properties of ``Alfvenic'' fluctuations near the sun: Helios-1 and Helios-2