Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. Using present experimental technology in solar wind measurements we cannot directly measure the real volumetric dissipation rate, <varepsilon>(t), but are constrained to represent it by its surrogate the energy flux near the dissipation range at the proton gyro scale. There is evidence for the multifractal nature of the so defined dissipation field <varepsilon>(t), a result derived from the scaling exponents of its statistical moments. The generalized dimension D _q has been determined and reveals that the dissipation field has a multifractal structure, which is not compatible with a scale-invariant cascade. The related multifractal spectrum f(<alpha>) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D _q can for turbulence in high-speed streams be fitted well by the functional dependence of the p-model with a comparatively large parameter p ₁=0.87, indicating a strongly intermittent multifractal energy cascade. The experimental value for D _p/3 used in the scaling exponent s(p) of the velocity structure function gives an exponent that can describe some of the observations. The scaling exponent <mu> of the autocorrelation function of <varepsilon>(t) has also been directly evaluated, being 0.37. Finally, the mean dissipation rate was determined, which could be used in solar wind heating models.     

Stationary strong magnetohydrodynamic discontinuities and pressure balanced structures in the solar wind stream

Strong disturbances of magnetic clouds in the solar wind stream are considered when solar MHD shock waves from the surrounding plasma collide with these inhomogeneities. The boundaries of the considered plasma inhomogeneities are presented as stationary tangential discontinuities. The collision of solar fast shock waves with the back and front boundaries is studied as a decomposition of an arbitrary discontinuity. It is asserted that secondary waves of rarefaction and reverse shock waves arise depending on the initial conditions. It is pointed out that a change occurs in the configuration of the plasma inhomogeneity under study, which is caused by the incoming perturbation repeatedly observed by spacecrafts.     

Broken ergodicity in magnetohydrodynamic turbulence

Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as “absolute equilibrium ensemble” theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field B _o. Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when B _o?=?0 and weakly broken when B _o?≠?0. Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector k ) can occur at low values of wavenumber k?=?| k |, especially when B _o?=?0. This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber k for 3-D cases, and at either lowest or highest k for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum k in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects.     

Cosmic rays and solar wind turbulence: Peculiarities of the 23rd solar cycle

This paper addresses observed variations in cosmic ray (CR) intensity, the interplanetary magnetic field (IMF), the solar wind (SW) turbulence energy spectrum, and the energy spectrum index of Forbush decreases in the 20th–23rd solar cycles. Unlike the previous three cycles, there are some distinctive features in the 23rd solar cycle. The entire cycle shows a considerable increase in the index of the SW turbulence energy spectrum inclination and an substantially harder energy spectrum of Forbush decreases. The anomalously high flux of high-energy CRs and the anomalously low level of the IMF strength were recorded at the end of this cycle. The conclusion has been made that such unusual CR behavior is associated with a decrease in the degree of scattering in the resonance interaction between CR fluxes and SW inhomogeneities with spatial scales of ∼10¹² cm.     

Response of the geomagnetic activity to solar wind turbulence during solar cycle 23

The solar wind–magnetosphere coupled system is characterized by dynamical processes. Recent works have shown that nonlinear couplings and turbulence might play a key role in the study of solar wind–magnetosphere interaction processes.Within this framework, this study presents a statistical analysis aimed to investigate the relationship between solar wind MHD turbulence and geomagnetic activity at high and low latitudes as measured by the AE and SYM-H indices, respectively. This analysis has been performed for different phases of solar cycle 23. The state of turbulence was characterized by means of 2-D histograms of the normalized cross-helicity and the normalized residual energy. The geomagnetic response was then studied in relation to those histograms.The results found clearly show that, from a statistical point of view, solar cycle 23 is somewhat peculiar. Indeed, good Alfvénic correlations are found unexpectedly even during solar activity maximum. This fact has implications on the geomagnetic response as well since a statistical relationship is found between Alfvénic fluctuations and auroral activity. Conversely, solar wind turbulence does not seem to play a relevant role in the geomagnetic response at low latitudes.     

Effect of the meridional velocity gradient on the anisotropy of turbulence in the solar wind

Geomagnetism and Aeronomy - In this paper, the heliolatitude dependence of the anisotropy of hourly interplanetary magnetic field fluctuations under conditions characteristic of low solar activity...     

The statistics of a passive scalar in field-guided magnetohydrodynamic turbulence

A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolution direct numerical simulations of incompressible, field-guided, MHD turbulence in order to establish the fundamental properties of passive scalar evolution. We study the scalar anisotropy, establish the scaling relation analogous to Yaglom’s law, and measure the intermittency of the passive scalar statistics. We also assess to what extent the pseudo Alfvén fluctuations in strong MHD turbulence can be modelled as a passive scalar. The results suggest that the dynamics of a passive scalar in MHD turbulence is considerably more complicated than in the hydrodynamic case.     

Analytic scaling laws in planetary dynamo models

ABSTRACT

Numerical models of planetary MHD dynamos have led to many advances in the last twenty years. However, the accessible parameter space of these models is somewhat limited due to computational constraints. A number of numerically based scaling laws have been proposed, but it has been difficult to reliably confirm them from the simulation data alone. Since these scaling laws have to be used to extend the numerical models into the planetary parameter regime, getting correct scalings is an important issue. Here some possible balances between the relevant terms in the dynamo equations are considered, and a number of different known and new scaling laws are proposed and justified from analytical point of view. Some of these laws are compatible with the widely known Christensen and Aubert (Geophys. J. Int. 2006, 166) scaling for the magnetic field strength. Plausible estimates of the typical values of the important quantities in the Earth's core and other Terrestrial planets are made, and the extent to which the various scaling laws are consistent with these estimates is discussed.     

Diagnostics of solar wind streams and their sources in the solar corona

The studies are based on the experimental mass sounding of the interplanetary plasma near the Sun at radial distances of R = 4−70 R _S, performed at Pushchino RAO, Russian Academy of Sciences, and on the calculated magnetic fields in the solar corona based on the magnetic field strength and structure measured on the Sun’s surface at J. Wilcox Solar Observatory, United States. The experimental data make it possible to localize the position of the boundary closest to the Sun of the transition transonic region of the solar wind in the near-solar space (R ≈ 10−20 R _S) and to perform an interrelated study of the solar wind structure and its sources, namely, the magnetic field components in the solar corona based on these data. An analysis of the evolution of the flow types in 2000–2007 makes it possible to formulate the physically justified criterion responsible for the time boundaries of different epochs in the solar activity cycle.     

Generation and propagation of solar disturbances: a magnetohydrodynamic simulation

It has been recognized that there are three basic physical agents, namely (i) electromagnetic radiation, (ii) high-energy charged particles, and (iii) enhanced solar wind, resulting from solar activity, which affect the near-Earth and terrestrial environment. In this paper, we restrict our discussion to the subject of the enhanced solar wind. In this context, it is well-known that the most appropriate tool to investigate the generation and propagation of solar disturbances is magnetohydrodynamic (MHD) theory. The most recent progress during the period of the Solar Terrestrial Energy Program (STEP) in these aspects will be presented. In particular, the induced transport of momentum and energy, by coronal mass ejections (CMEs), from the solar surface to the Earths environment (i.e. at 1 AU) will be illustrated by using a self-consistent MHD model of streamer and flux-rope interactions.     

The records of solar wind and solar flares in aubrites

A large number of individual enstatite crystals of the gas-rich aubrites Khor Temiki, Staroe Pesyanoe and Bustee was analyzed for implanted helium and for steep gradient ion tracks in order to investigate the relation between solar flare irradiation and solar wind implantation with extreme local resolution. Irradiated and non-irradiated crystals coexist within the gas-rich phases of the aubrites investigated. Statistically in a given meteorite the proportion of crystals with implanted solar wind is similar to the proportion of solar flare irradiated crystals. It varies from aubrite to aubrite in the sequence of their bulk contents of trapped rare gases.For nine enstatites, tracks and rare gases were subsequently measured within the same crystal. The results support the intimate association of solar flare tracks and implanted He. The⁴He-surface concentrations of irradiated crystals vary between <5 × 10^?7 and 10^?4 cm³ STP/cm².The absence of saturation effects together with the low degree of elemental gas fractionation indicates very short solar wind exposure times (< 100 yr) rather than strong diffusion losses. The evidence from tracks and rare gases can be understood in terms of an early simultaneous irradiation of aubritic crystals by solar wind and solar flare particles on top of a regolith-covered parent body.     

EISCAT measurements of the solar wind

EISCAT observations of interplanetary scintillation have been used to measure the velocity of the solar wind at distances between 15 and 130R (solar radii) from the Sun. The results show that the solar wind consists of two distinct components, a fast stream with a velocity of 800 km s^–1 and a slow stream at 400 kms^–1. The fast stream appears to reach its final velocity much closer to the Sun than expected. The results presented here suggest that this is also true for the slow solar wind. Away from interaction regions the flow vector of the solar wind is purely radial to the Sun. Observations have been made of fast wind/slow wind interactions which show enhanced levels of scintillation in compression regions.     

Analytic base of geodynamo-like scaling laws in the planets,geomagnetic periodicities and inversions

Scaling laws for hydromagnetic dynamo in planets initially express the characteristic strength of the magnetic field through the primary values, such as the size of the conductive core of the planet, the angular rotation rate, electrical conductivity and energy flows. Most of the earlier proposed scaling laws based only on observations and assumptions about force balances. Recent and my new approaches to fully take into account the energy and induction balance has additionally expressed here in terms of primary values such important characteristics as forces, magnitudes, energies, scales and orientations of hydromagnetic fields. The direct numerical simulation of the hydromagnetic dynamo and modeling ability in a fairly wide range of parameters for the first time allowed direct test such laws. The obtained numerical geodynamo-like results for the Earth, Jupiter and partially Saturn postulated previously not identified analytically simplest law that predicts the field strength is only depended on the specific energy density of convection and the size of the dynamo area. This simplest and already widely used law was original way analytically grounded here along with other previously known and new laws. This analytic identifies the physics determining geomagnetic periodicities for jerk, secular variations and inversions. Mean period between the inversions is found to be roughly proportional to the intensity of the geomagnetic field that is confirmed by some paleomagnetic researches. Possible dynamos in Mercury, Ganymede, Uranus and Neptune are also discussed.     

Ancient solar wind in lunar microbreccias

The Apollo 11 soil breccias are samplers of the ancient lunar environment due to their history in the regolith and their efficient closure to addition of recent solar wind upon compaction. These breccias contain the lowest¹⁵N/¹⁴N isotopic ratio yet reported for any lunar sample (in fact, for any natural sample). This extends the range of variation of¹⁵N/¹⁴N of the solar wind to greater than 30%, from a δ¹⁵N of ?190‰ in the past to +120‰ at present. No mechanism is yet known that is capable of accounting for such a large change in the¹⁵N/¹⁴N ratio without producing a substantial concomitant change in the¹³C/¹²C ratio, although some sort of nuclear reaction in the sun appears to be required. Apollo 11 soil breccias and 15086 are all formed by meteoritic impacts which compact the lower regolith against the basement rock without much heating. Rock 15086 formed from the layer of regolith between 100 and 200 cm depth, as shown by the close agreement between the nitrogen content and isotopic ratios of 15086 and those of the Apollo 15 deep drill core. Cosmic ray exposure ages, based on spallation-produced¹⁵N, are 2.3 ± 0.4 b.y. for Apollo 11 breccias. This age is much greater than the estimate from cosmogenic²¹Ne, presumably due to diffusive loss of neon.     

Compressive fluctuations in the solar wind and their polytropic index

Magnetohydrodynamic compressive fluctuations of the interplanetary plasma in the region from 0.3 to 1 AU have been characterized in terms of their polytropic index. Following Chandrasekhar’s approach to polytropic fluids, this index has been determined through a fit of the observed variations of density and temperature. At least three different classes of fluctuations have been identified: (1) variations at constant thermal pressure, in low-speed solar wind and without a significant dependence on distance, (2) adiabatic variations, mainly close to 1 AU and without a relevant dependence on wind speed, and (3) variations at nearly constant density, in fast wind close to 0.3 AU. Variations at constant thermal pressure are probably a subset of the ensemble of total-pressure balanced structures, corresponding to cases in which the magnetic field magnitude does not vary appreciably throughout the structure. In this case the pressure equilibrium has to be assured by its thermal component only. The variations may be related to small flow-tubes with approximately the same magnetic-field intensity, convected by the wind in conditions of pressure equilibrium. This feature is mainly observed in low-velocity solar wind, in agreement with the magnetic topology (small open flow-tubes emerging through an ensemble of closed structures) expected for the source region of slow wind. Variations of adiabatic type may be related to magnetosonic waves excited by pressure imbalances between contiguous flow-tubes. Such imbalances are probably built up by interactions between wind flows with different speeds in the spiral geometry induced by the solar rotation. This may account for the fact that they are mainly found at a large distance from the sun. Temperature variations at almost constant density are mostly found in fast flows close to the sun. These are the solar wind regions with the best examples of incompressible behaviour. They are characterized by very stable values for particle density and magnetic intensity, and by fluctuations of Alfvénic type. It is likely that temperature fluctuations in these regions are a remnant of thermal features in the low solar atmosphere. In conclusion, the polytropic index appears to be a useful tool to understand the nature of the compressive turbulence in the interplanetary plasma, as far as the frozen-in magnetic field does not play a crucial role.     

Multiparticle statistical model of the solar wind

A multiparticle statistical approach to plasma (gas) modeling is presented, in which the fact that the macroscopic parameters are measured with finite resolution scales is taken into account [Minkova, 2004; 2005; 2007]. This approach is based on the Liouville theorem formulated for a stationary open system in the approximation of detailed dynamic balance with its surroundings. When the finite resolution scales of measuring instruments are taken into account, the plasma (gas) is described by multiparticle distribution functions. The latter are used to derive the probability distribution functions of fluctuations and the average values of macroscopic parameters. The multiparticle statistical approach allows a stationary solar wind model to be constructed under a number of simplifying assumptions. Its results for the average values of macroscopic parameters coincide with those of the two-particle kinetic model [Vasenin et al., 2003] and agree with inecliptic observational data.     

Recent observations of MHD fluctuations in the solar wind

A short review of recent observations of solar wind fluctuations in the magnetohydrodynamic (MHD) range of scales is presented. In recent years, the use of high time-resolution data on an extended interval of heliocentric distance has allowed significant advances in our knowledge of MHD fluctuations. We first focus on the origin and evolution of the Alfvénic-type fluctuations. The role of interplanetary sources and the influence of interactions with structures convected by the solar wind are examined. Then compressive fluctuations are investigated, with special attention being given to their nature and origin. Observations are discussed in the light of recent theories and models. Finally, predictions for MHD turbulence in polar regions of the heliosphere are highlighted.     

The solar wind and the Sun–Earth link

Plasma streams out from the Sun in the form of the solar wind. Shadia Rifai Habbal and Richard Woo examine the workings of this enigmatic link between the Earth and the Sun.