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.     

Polarization of compressible turbulent fluctuations in the solar wind plasma

Compressible fluctuations in solar wind plasma are analyzed on the basis of the 1995–2010 WIND and Advanced Composition Explorer (ACE) spacecraft data. In the low-speed solar wind (V ₀ < 430 km/s), correlations between fluctuations in the magnetic field direction and plasma density, as well as between velocity fluctuations and plasma density, are found. The covariance functions of these parameters calculated as functions of the local magnetic field direction are axially symmetric relative to the axis, which is oriented nearly along the regular magnetic field of the heliosphere (the Parker spiral). Fluctuations in the magnetic field and velocity are polarized in the plane that is orthogonal to the axis of symmetry. Plasma oscillations of these properties can be caused by fast magnetosonic waves propagating from the Sun along the Parker spiral.     

Intermittency of the solar wind density near the interplanetary shock

The properties of turbulent fluctuations of the solar wind plasma near the interplanetary shock observed at September 12, 2014 by the BMSW instrument are considered. The spectra of the density fluctuations in the solar wind and their statistical characteristics up-and downstream of the shock front are analyzed. They are compared with each other and with characteristics corresponding to different turbulence models. It is shown that the spectral and statistical characteristics of the density fluctuations in the solar wind conserve their basic properties after the arrival of an interplanetary shock. Intermittency is observed both before and after the front, but its level increases on average in the second case. In both regions, the scaling of the structure functions of the density fluctuations in the solar wind differ from the scaling of the classical Kolmogorov model and can be described by the log-Poisson turbulence model. Parameterization of the scaling of the structure functions revealed the presence of filamentary structures in the solar wind plasma, which provide the density intermittency in the studied space regions.     

Forecast of the solar wind velocity and the interplanetary magnetic field radial component polarity at the phase of decay of solar cycle 23

The solar wind velocity and polarity of the B _x-component of the interplanetary magnetic field have been analyzed for the first eight months of 2005. The interplanetary magnetic field had a four-sector structure, which persisted during nine Carrington rotations. Three stable clusters of a high-speed solar wind stream and one cluster of a low-speed stream were observed during one solar rotation. These clusters were associated with the interplanetary magnetic field sectors. The predicted solar wind velocity was calculated since July 2005 one month ahead as an average over several preceding Carrington rotations. The polarity of the B _x-component of the interplanetary magnetic field was predicted in a similar way based on the concept of the sector structure of the magnetic field and its relation to maxima of the solar wind velocity. The results indicate a satisfactory agreement of the forecast for two rotations ahead in July–August 2005 and pronounced violation of agreement for the next rotation due to a sudden reconfiguration of the solar corona and strong sporadic processes in September 2005.     

Non-Gaussian probability distributions of solar wind fluctuations

The probability distributions of field differences x()=x(t+)-x(t), where the variable x(t) may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag , ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD) turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.     

Influence of Solar Wind Plasma Parameters on the Intensity of Isolated Magnetospheric Substorms

Parameters of the interplanetary magnetic field and solar wind plasma during periods of 163 isolated substorms have been studied. It is shown that the solar wind velocity V and plasma density N remain approximately constant for at least 3 h before substorm onset Т _o and 1 h after Т _o . On average, the velocity of the solar wind exhibits a stable trend toward anticorrelation with its density over the whole data array. However, the situation is different if the values of V and N are considered with respect to the intensity of substorms observed during that period. With the growth of substorm intensity, quantified as the maximum absolute value of AL index, an increase in both the solar wind plasma velocity and density, at which these substorms appear, is obsreved. It has been found that the magnitude of the solar wind dynamic pressure P is closely related to the magnetosphere energy load defined as averaged values of the Kan–Lee electric field E_KL and Newell parameter dΦ/dt averaged for 1 h interval before Т _o . The growth of the dynamic pressure is accompanied by an increase in the load energy necessary for substorm generation. This interrelation between P and values of EKL and dΦ/dt is absent in other, arbitrarily chosen periods. It is believed that the processes accompanying increasing dynamic pressure of the solar wind result in the formation of magnetosphere conditions that increasingly impede substorm generation. Thus, the larger is P, the more solar wind energy must enter the Earth’s magnetosphere during the period of the growth phase for substorm generation. This energy is later released during the period of the substorm expansion phase and creates even more intense magnetic bays.     

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.     

Density and magnetic field fluctuations observed by ISEE 1–2 in the quiet magnetosheath

We analyse the fluctuations of the electron density and of the magnetic field in the Earth’s magnetosheath to identify the waves observed below the proton gyrofrequency. We consider two quiet magnetosheath crossings i.e. 2 days characterized by small-amplitude waves, for which the solar wind dynamic pressure was low. On 2 August 1978 the spacecraft were in the outer magnetosheath. We compare the properties of the observed narrow-band waves with those of the unstable linear wave modes calculated for an homogeneous plasma with Maxwellian electron and bi-Maxwellian (anisotropic) proton and alpha particle distributions. The Alfvén ion cyclotron (AIC) mode appears to be dominant in the data, but there are also density fluctuations nearly in phase with the magnetic fluctuations parallel to the magnetic field. Such a phase relation can be explained neither by the presence of a proton or helium AIC mode nor by the presence of a fast mode in a bi-Maxwellian plasma. We invoke the presence of the helium cut-off mode which is marginally stable in a bi-Maxwellian plasma with <alpha> particles: the observed phase relation could be due to a hybrid mode (proton AIC + helium cut-off) generated by a non-Maxwellian or a non-gyrotropic part of the ion distribution functions in the upstream magnetosheath. On 2 September 1981 the properties of the fluctuations observed in the middle of the magnetosheath can be explained by pure AIC waves generated by protons which have reached a bi-Maxwellian equilibrium. For a given wave mode, the phase difference between B _\Vert and the density is sensitive to the shape of the ion and electron distribution functions: it can be a diagnosis tool for natural and simulated plasmas.     

Solar wind velocity distribution on the heliospheric current sheet during Carrington rotations 1787-1795

The solar wind velocity distribution in the heliosphere is best represented using a v-map, where velocity contours are plotted in heliographic latitude-longitude coordinates. It has already been established that low-speed regions of the solar wind on the source surface correspond to the maximum bright regions of the K-corona and the neutral line of the coronal magnetic field. In this analysis, v-maps on the source surface for Carrington rotations (CRs) 1787-1795, during 1987, have been prepared using the interplanetary scintillation measurements at Research Institute of Atmospherics (RIA), Nagoya Univ., Japan. These v-maps were then used to study the time evolution of the low-speed (\leq450 km s⁻¹) belt of the solar wind and to deduce the distribution of solar wind velocity on the heliospheric current sheet. The low-speed belt of the solar wind on the source surface was found to change from one CR to the next, implying a time evolution. Instead of a slow and systematic evolution, the pattern of distribution of solar wind changed dramatically at one particular solar rotation (CR 1792) and the distributions for the succeeding rotations were similar to this pattern. The low-speed region, in most cases, was found to be close to the solar equator and almost parallel to it. However, during some solar rotations, they were found to be organised in certain longitudes, leaving regions with longitudinal width greater than 30^○ free of low-speed solar wind, i.e. these regions were occupied by solar wind with velocities greater than 450 km s⁻¹. It is also noted from this study that the low-speed belt, in general, followed the neutral line of the coronal magnetic field, except in certain cases. The solar wind velocity on the heliospheric current sheet (HCS) varied in the range 300–585 km s⁻¹ during the period of study, and the pattern of velocity distribution varied from rotation to rotation.     

Dependence of geomagnetic disturbances on extreme values of the solar wind <Emphasis Type="Italic">E</Emphasis><Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> component

The dependence of the zonal geomagnetic indices (AE, Ap, Kp, Kn, and Dst) on the solar wind parameters (the electric field E _y component, dynamic pressure P _d and IMF irregularity σB) has been studied for two types of events: magnetic clouds and high-speed streams. Based on the empirical relationships, it has been established that the AE, Ap, Kp, and Kn indices are directly proportional to the E _y value at E _y < 12 mV m^?1 and are inversely proportional to this value at E _y > 12 mV m^?1 for the first-type events. On the contrary, the dependence of Dst on E _y is monotonous nonlinear. A linear dependence of all geomagnetic indices on E _y is typical of the second-type events. It has been indicated that the specific features of geoeffectiveness of magnetic clouds and high-speed solar wind streams are caused by the dependence of the electric field potential across the polar cap on the electric field, solar wind dynamic pressure, and IMF fluctuations.     

Variability of parameters of the F2-layer maximum in the quiet midlatitude ionosphere under low solar activity: 2. Strong fluctuations of critical frequency

This paper presents a qualitative analysis of the properties and particular examples of strong (10% < |δfoF2| < 30%) and very strong (|δfoF2| > 30%) fluctuations in the critical frequency of the F2 layer (foF2) of the quiet ionosphere at midlatitudes under low solar activity according to the Irkutsk station data for 2007–2008. It is found that strong day-to-day fluctuations in foF2 are mainly related to changes in thermospheric parameters, which have a nature of planetary waves and tides. Evidently, very strong day-to-day fluctuations in foF2 are caused by superposition of the effects in the ionosphere caused by changes in the thermospheric parameters and those related to a complex of processes of solar wind interaction with the magnetosphere, including the effects caused by the reversal of the vertical component of the solar wind magnetic field southwards. The increase in foF2 during nighttime hours in winter up to values typical for the daytime maximum in foF2 is the brightest example of very strong changes in foF2 in the quiet ionosphere.     

Experimental evidence for direct penetration of ULF waves from the solar wind and their possible effect on acceleration of radiation belt electrons

The event of March 12–19, 2009, when a moderately high-speed solar wind stream flew around the Earth’s magnetosphere and carried millihertz ultralow-frequency (ULF) waves, has been analyzed. The stream caused a weak magnetic storm (D _{st min} = −28 nT). Since March 13, fluxes of energetic (up to relativistic) electrons started increasing in the magnetosphere. Comparison of the spectra of ULF oscillations observed in the solar wind and magnetosphere and on the Earth’s surface indicated that a stable common spectral peak was present at frequencies of 3–4 mHz. This fact is interpreted as evidence that waves penetrated directly from the solar wind into the magnetosphere. Possible scenarios describing the participation of oscillations in the acceleration of medium-energy (E > 0.6 MeV) and high-energy (E > 2.0 MeV) electrons in the radiation belt are discussed. Based on comparing the event with the moderate magnetic storm of January 21–22, 2005, we concluded that favorable conditions for analyzing the interaction between the solar wind and the magnetosphere are formed during a deep minimum of solar activity.     

Effect of the solar wind and IMF parameters on the formation of long-period irregular pulsation burst regimes

The excitation of long-period irregular pulsations in the 2.0–6.0 mHz range (ipcl pulsation series) in the Earth’s magnetosphere, depending on the set of solar wind plasma and IMF parameters, has been studied experimentally. It has been found that burst regimes are observed when the solar wind dynamic pressure and velocity are higher than V ∼ 320 km/s and P ∼ 1 nPa, respectively. It has been indicated that the dynamics of the ipcl pulsation intensity and fractal structure largely depend on the solar wind plasma velocity and magnetic pressure, respectively. An analysis of the relationship between the appearance of ipcl pulsation burst series and large-scale solar wind streams and polar coronal holes made it possible to identify solar geoeffective regions, which can cause solar wind streams and Alfvén waves that promote the generation of burst regimes. On the basis of the studied conditions of the interplanetary medium, favourable for the excitation of ipcl pulsation burst series, and generalization of morphological patterns, the possible mechanisms of their generation have been considerded. It has been demonstrated that ipcl burst regimes are most probably generated as wind instability in hydrodynamics (the Miles-Phillips mechanism). The Miles-Phillips instability is related to different factors in the solar wind stream, among which turbulence, the threshold velocity value, and pressure fluctuations play a defining role. Precisely these regularities are typical of the ipcl burst regime generation conditions.     

Hard X-ray generation in the turbulent plasma of solar flares

The influence of scattering of accelerated electrons in the turbulent plasma on the transformation of their distribution function is studied. The turbulence is connected with the emergence of magnetic inhomogeneities and ion-sound mode. The level of ion-sound turbulence is specified by the ratio W ^s/nk _B T _e = 10^?3, while the value of magnetic fluctuations is δB/B = 10^–3. Different initial angular distributions of the function of accelerated-electron source are regarded: from isotropic to narrow directional distributions. For the chosen energy-density values of the ion-sound turbulence and the level of magnetic fluctuations, it is shown that both types of turbulence lead to a qualitative change in the hard X-ray brightness along the loop, moreover their influence was found to be different. Models with magnetic fluctuations and the ion sound can be distinguished not only by the difference in the hard X-ray distribution along the loop but also by the photon spectrum.     

A Note on the Estimation of Eddy Diffusivity and Dissipation Length in Low Winds over a Tropical Urban Terrain

— Urban terrain poses a challenge for modeling air pollutant diffusion. In tropics, because of the dominant low wind speed environment, the importance of understanding the turbulence diffusion is even more critical, and uncertain. The objective of this study is to estimate the vertical eddy diffusivity of an urban, tropical atmosphere in low–wind speeds. Turbulence measurements at 1 Hz were made at 4-m level over an urban terrain with a roughness length of 0.78 m during winter months. Eddy diffusivity is estimated from spectral quantities of the turbulence data involving turbulent kinetic energy (E) and its dissipation rate (?). The spectral information of the vertical velocity fluctuations is used to estimate the vertical length scale which provides information on the eddy diffusivity. In addition, the product of friction velocity and the vertical length scale has been used to non-dimensionalize the eddy diffusivity, which is shown to increase with increasing instability. Using the eddy diffusivity (K) estimates from the E – ? approach, a relation is suggested for the mixing length based eddy diffusivity models of the form: K = c _w .[2.5 ? 0.5(z/L)], where z is the measurement height, L is the Obukhov length, and c _w has an average value close to 1 for unstable and near 0.5 for stable conditions for the urban terrains.     

Long-period irregular pulsations under the conditions of a quiet magnetosphere

Simultaneous observations of high-latitude long-period irregular pulsations at frequencies of 2.0–6.0 mHz (ipcl) and magnetic field disturbances in the solar wind plasma at low geomagnetic activity (Kp ~ 0) have been studied. The 1-s data on the magnetic field registration at Godhavn (GDH) high-latitude observatory and the 1-min data on the solar wind plasma and IMF parameters for 2011–2013 were used in an analysis. Ipcl (irregular pulsations continuous, long), which were observed against a background of the IMF Bz reorientation from northward to southward, have been analyzed. In this case other solar wind plasma and IMF parameters, such as velocity V, density n, solar wind dynamic pressure P = ρV² (ρ is plasma density), and strength magnitude B, were relatively stable. The effect of the IMF Bz variation rate on the ipcl spectral composition and intensity has been studied. It was established that the ipcl spectral density reaches its maximum (~10–20 min) after IMF Bz sign reversal in a predominant number of cases. It was detected that the ipcl average frequency (f) is linearly related to the IMF Bz variation rate (ΔBz/Δt). It was shown that the dependence of f on ΔBz/Δt is controlled by the α = arctan(By/Bx) angle value responsible for the MHD discontinuity type at the front boundary of magnetosphere. The results made it possible to assume that the formation of the observed ipcl spectrum, which is related to the IMF Bz reorientation, is caused by solar wind plasma turbulence, which promotes the development of current sheet instability and surface wave amplification at the magnetopause.     

Variations in the polar precipitation equatorward boundary during the interaction between the Earth’s magnetosphere and solar wind streams from isolated solar sources

The position of the auroral luminosity equatorward boundary during the interaction between the Earth’s magnetosphere and isolated solar wind streams from different solar sources has been statistically studied based on the ground and satellite observations of auroras. These studies continue the series of the works performed in order to develop the technique for predicting auroras based on the characteristics of the interplanetary medium and auroral disturbances. The dependences of the minimal position of the auroral luminosity equatorward boundary (Φ′) on the values of the azimuthal component of the interplanetary electric field (E _y ) and AL indices of magnetic activity, averaged over 6 and 24 h, are presented. The distribution limits for each type of isolated solar wind streams on the Φ′-E _y and Φ′-AL planes have been determined.     

The qualitative character of the global electrical conductivity of the earth

A spectral stacking and smoothing procedure has been applied to unbroken hourly values of H and Z, for 1964 and 1965, from 17 observatories, in order to estimate the magnitude and phase of the P₁⁰ response of the Earth to long-period geomagnetic fluctuations. Exploratory techniques have been used to gauge when sufficient smoothing has been applied, and to identify the qualitative character of the global electrical conductivity of the Earth.     

Solar wind structure sources and periodicities of auroral electron power over three solar cycles

We assess the contributions of various types of solar wind structures (transients, coronal hole high-speed streams (HSS), and slow-speed wind) to hourly average auroral electron power (P_e). The time variation of the solar wind velocity (V_sw) and P_e are determined by HSS, which contribute ～47% to P_e and V_sw. Transients contribute ～42% of P_e in solar maxima, and ～6% in solar minimum. Cross-correlations of P_e with V_sw|B| for negative B_z are significant. P_e exhibits solar rotational periodicities similar to those for V_sw, with strong 7- and 9-day periodicities in 2005–2008 and equinox semiannual periodicities in 1995–1999.