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For the solar wind, a wealth of observational evidence indicates that turbulence is an important dynamical process for velocity (v), magnetic (b), and other related fluctuations at MHD (fluid) scales. Here we review such observations and turbulence features, including discussion of when wave or turbulence descriptions can (or cannot) explain the observations. The relevance of properties of MHD turbulence to the acceleration and transport of energetic particles is emphasized. A summary of different classes of models for solar wind fluctuations is presented, followed by reviews of transport models for (i) solar wind fluctuations and (ii) cosmic rays. In connection with cosmic ray transport models, recent developments in terms of cosmic ray transport coefficients, as well as their application in cosmic ray modulation models, are discussed in detail.

We employ spectral method numerical simulations to examine the dynamical development of anisotropy of the variance, or polarization, of the magnetic and velocity field in compressible magnetohydrodynamic (MHD) turbulence. Both variance anisotropy and spectral anisotropy emerge under influence of a large-scale mean magnetic field B0; these are distinct effects, although sometimes related. Here we examine the appearance of variance parallel to B0, when starting from a highly anisotropic state. The discussion is based on a turbulence theoretic approach rather than a wave perspective. We find that parallel variance emerges over several characteristic nonlinear times, often attaining a quasi-steady level that depends on plasma beta. Consistency with solar wind observations seems to occur when the initial state is dominated by quasi-two-dimensional fluctuations.

Measurements made with the Voyager 1 spacecraft indicate that significant levels of compressive fluctuations exist in the inner heliosheath. Some studies have already been performed with respect to the mirror-mode instability in the downstream region close to the solar wind termination shock, and here we extend the investigation to the whole inner heliosheath. We employ quasilinear theory and results from a global magnetohydrodynamic model of the heliosphere to compute the time evolution of both the temperature anisotropy and the energy density of the corresponding magnetic fluctuations, and we demonstrate their likely presence in the inner heliosheath. Furthermore, we compute the associated, locally generated density fluctuations. The results can serve as inputs for future models of the transport of compressible turbulence in the inner heliosheath., Comment: 7 pages, 5 figures

MHD-scale fluctuations in the velocity, magnetic, and density fields of the solar wind are routinely observed. The evolution of these fluctuations, as they are transported radially outwards by the solar wind, is believed to involve both wave and turbulence processes. The presence of an average magnetic field has important implications for the anisotropy of the fluctuations and the nature of the turbulent wavenumber cascades in the directions parallel and perpendicular to this field. In particular, if the ratio of the rms magnetic fluctuation strength to the mean field is small, then the parallel wavenumber cascade is expected to be weak and there are difficulties in obtaining a cascade in frequency. The latter has been invoked in order to explain the heating of solar wind fluctuations (above adiabatic levels) via energy transfer to scales where ion-cyclotron damping can occur.Following a brief review of classical hydrodynamic and magnetohydrodynamic (MHD) cascade theories, we discuss the distinct nature of parallel and perpendicular cascades and their roles in the evolution of solar wind fluctuations.

A review of spectral anisotropy and variance anisotropy for solar wind fluctuations is given, with the discussion covering inertial range and dissipation range scales. For the inertial range, theory, simulations and observations are more or less in accord, in that fluctuation energy is found to be primarily in modes with quasi-perpendicular wavevectors (relative to a suitably defined mean magnetic field), and also that most of the fluctuation energy is in the vector components transverse to the mean field. Energy transfer in the parallel direction and the energy levels in the parallel components are both relatively weak. In the dissipation range, observations indicate that variance anisotropy tends to decrease towards isotropic levels as the electron gyroradius is approached; spectral anisotropy results are mixed. Evidence for and against wave interpretations and turbulence interpretations of these features will be discussed. We also present new simulation results concerning evolution of variance anisotropy for different classes of initial conditions, each with typical background solar wind parameters.

An overview is given of important properties of spatial and temporal intermittency, including evidence of its appearance in fluids, magnetofluids and plasmas, and its implications for understanding of heliospheric plasmas. Spatial intermittency is generally associated with formation of sharp gradients and coherent structures. The basic physics of structure generation is ideal, but when dissipation is present it is usually concentrated in regions of strong gradients. This essential feature of spatial intermittency in fluids has been shown recently to carry over to the realm of kinetic plasma, where the dissipation function is not known from first principles. Spatial structures produced in intermittent plasma influence dissipation, heating, and transport and acceleration of charged particles. Temporal intermittency can give rise to very long time correlations or a delayed approach to steady-state conditions, and has been associated with inverse cascade or quasi-inverse cascade systems, with possible implications for heliospheric prediction. Fil: Matthaeus, W. H.. University of Delaware; Estados Unidos. Università della Calabria; Italia. Universita Degli Studi Di Firenze; Italia Fil: Minping Wan. University of Delaware; Estados Unidos Fil: Servidio, S.. Università della Calabria; Italia Fil: Greco, A.. Università della Calabria; Italia Fil: Osman, K. T.. University of Warwick; Reino Unido Fil: Oughton, S.. University of Waikato; Nueva Zelanda Fil: Dmitruk, Pablo Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

Spacecraft measurements in the solar wind offer the opportunity to study magnetohydrodynamic (MHD) turbulence in a collisionless plasma in great detail. We review some of the key results of the study of this medium: the presence of large amplitude Alfven waves propagating predominantly away from the Sun; the existence of an active turbulent cascade; and the presence of intermittency similar to that in neutral fluids. We also discuss the presence of anisotropy in wavevector space relative to the local magnetic field direction. Some models suggest that MHD turbulence can evolve to a state with power predominantly in wavevectors either parallel to the magnetic field ('slab' fluctuations) or approximately perpendicular to it ('2D'). We review the existing evidence for such anisotropy, which has important consequences for the transport of energetic particles. Finally, we present the first results of a new analysis which provides the most accurate measurements to date of the wave-vector anisotropy of wavevector power in solar wind MHD turbulence.

Originally proposed as an efficient approach to computation of nonlinear dynamics in tokamak fusion research devices, reduced magnetohydrodynamics (RMHD) has subsequently found application in studies of coronal heating, flux tube dynamics, charged particle transport, and, in general, as an approximation to describe plasma turbulence in space physics and astrophysics. Given the diverse set of derivations available in the literature, there has emerged some level of discussion and a lack of consensus regarding the completeness of RMHD as a turbulence model, and its applicability in contexts such as the solar wind. Some of the key issues in this discussion are examined here, emphasizing that RMHD is properly neither 2D nor fully 3D, being rather an incomplete representation that enforces at least one family of extraneous conservation laws. Fil: Oughton, S.. University Of Waikato; Nueva Zelanda Fil: Matthaeus, W. H.. University Of Delaware; Estados Unidos Fil: Dmitruk, Pablo Ariel. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina

We test a theory presented previously to account for the turbulent transport of magnetic fluctuation energy in the solar wind and the related dissipation and heating of the ambient ion population. This theory accounts for the injection of magnetic energy through the damping of large-scale flow gradients, such as wind shear and compression, and incorporates the injection of magnetic energy due to wave excitation by interstellar pickup ions. The theory assumes quasi-two-dimensional spectral transport of the fluctuation energy and subsequent dissipation that heats the thermal protons. We compare the predictions of this theory with Voyager 2 and Pioneer 11 observations of magnetic fluctuation energy, magnetic correlation lengths, and ambient proton temperatures. Near-Earth Omnitape observations are used to adjust for solar variability, and the possibility that high-latitude effects could mask possible radial dependences is considered. We find abundant evidence for in situ heating of the protons, which we quantify, and show that the observed magnetic energy is consistent with the ion temperatures.

Mechanisms for the deposition of heat in the lower coronal plasma are discussed, emphasizing recent attempts to reconcile the —uid and kinetic perspectives. Structures at magnetohydrodynamic (MHD) scales may drive a nonlinear cascade, preferentially exciting high perpendicular wavenumber —uctuations. Relevant dissipative kinetic processes must be identi—ed that can absorb the associated energy —ux. The relationship between the MHD cascade and direct cyclotron absorption, including cyclotron sweep, is discussed. We conclude that for coronal and solar wind parameters the perpendicular cascade cannot be neglected and may be more rapid than cyclotron sweep. Solar wind observational evidence suggests the relevance of the ion inertial scale, which is associated with current sheet thickness during reconnection. We conclude that a signi—cant fraction of dissipation in the corona and solar wind likely proceeds through a perpendicular cascade and small-scale reconnection, coupled to kinetic processes that act at oblique wavevectors. Subject headings: MHDsolar windSun: coronaSun: magnetic —eldsturbulence

A phenomenological theory describes radial evolution of plasma turbulence in the solar wind from 1 to 50 astronomical units. The theory includes a simple closure for local anisotropic magnetohydrodynamic turbulence, spatial transport, and driving by large-scale shear and pickup ions. Results compare well to plasma and magnetic field data from the Voyager 2 spacecraft, providing a basis for a concise, tractable description of turbulent energy transport in a variety of astrophysical plasmas.

In an evolving turbulent medium, a natural timescale can be defined in terms of the energy decay time. The time evolution may be complicated by other effects such as energy supply due to driving, and spatial inhomogeneity. In the solar wind the turbulence appears not to be simply engaging in free decay, but rather the energy level observed at a particular position in the hellosphere is affected by expansion, "mixing," and driving by stream shear. Here we discuss a new approach for estimating the "age" of solar wind turbulence as a function of heliocentric distance, using the local turbulent decay rate as the natural dock, but taking into account expansion and driving effects. The simplified formalism presented here is appropriate to low cross hellcity (non-Alfvnic) turbulence in the outer hellosphere especially at low hello-latitudes. We employ Voyager data to illustrate our method, which improves upon the familiar estimates in terms of local eddy turnover times.

Power spectra of the components of the magnetic field parallel (Pzz) and perpendicular (Pzz+Pyy) to the local mean magnetic field direction were determined by wavelet methods from Ulysses’ MAG instrument data during eighteen 10-day segments of its first North Polar pass at high latitude at solar minimum in 1995. The power depends on frequency f and the angle θ between the solar wind direction and the local mean field, and with distance from the Sun. This data includes the solar wind whose total power (Pxx + Pyy + Pzz) in magnetic fluctuations we previously reported depends on f and the angle θ nearly as predicted by the GS95 critical balance model of strong incompressible MHD turbulence. Results at much wider range of frequencies during six evenly-spaced 10-day periods are presented here to illustrate the variability and evolution with distance from the Sun. Here we investigate the aniso tropic scaling of Pzz(f,θ) in particular because it is a reduced form of the Poloidal (pseudo-Alfvenic) component of th...

The von Karman-Howarth (vKH) hierarchy of equations relate the second-order correlations of the turbulent fluctuations to the third-order ones, the third-order to the fourth-order, and so on. We recently demonstrated [1] that for MHD, self-similar solutions to the vKH equations seem to require at least two independent similarity lengthscales (one for each Elsasser energy), so that compared to hydrodynamics a richer set of behaviors seems likely to ensue. Moreover, despite the well-known anisotropy of MHD turbulence with a mean magnetic field (B0), the equation for the second-order correlation does not contain explicit dependence on B0. We show that there is, however, implicit dependence on B0 via the third-order correlations, which themselves have both explicit B0-dependence and also their own implicit dependence through fourth-order correlations. Some subtleties and consequences of this implicit-explicit balance are summarized here. In addition, we present an analysis of simulation results showing that t...

Direct spectral method simulation of the three-dimensional magnetohydrodynamics (MHD) equations is used to explore anisotropy that develops from initially isotropic fluctuations as a consequence of a uniform applied magnetic field. Spectral and variance anisotropies are investigated in both compressible and incompressible MHD. The nature of the spectral anisotropy is consistent with the model of Shebalin et al. [1983] in which the spectrum broadens in the perpendicular wavenumber direction, the anisotropy being greater for smaller wavenumbers. Here this effect is seen for both incompressible and polytropic compressible MHD. In contrast, the longitudinal (compressive) velocity fluctuations remain isotropic. Variance anisotropy is observed for low plasma beta compressible MHD but not for incompressible MHD. Solar wind observations are qualitatively consistent with both variance and spectral anisotropies of the type discussed here.

Solar wind fluctuations admit well-documented anisotropies of the variance matrix, or polarization, related to the mean magnetic field direction. Typically, one finds a ratio of perpendicular variance to parallel variance of the order of 9:1 for the magnetic field. Here we study the question of whether a kinetic plasma spontaneously generates and sustains parallel variances when initiated with only perpendicular variance. We find that parallel variance grows and saturates at about 5% of the perpendicular variance in a few nonlinear times irrespective of the Reynolds number. For sufficiently large systems (Reynolds numbers) the variance approaches values consistent with the solar wind observations.

We observe the anisotropy of the power spectral tensor of magnetic field fluctuations in the fast solar wind for the first time. In heliocentric RTN coordinates the power in each element of the tensor has a unique dependence on the angle between the magnetic field and velocity of the solar wind (\theta) and the angle of the vector in the plane perpendicular to the velocity (\phi). We derive the geometrical effect of the high speed flow of the solar wind past the spacecraft on the power spectrum in the frame of the plasma P(k) to arrive at the observed power spectrum P(f,\theta,\phi) based on a scalar field description of turbulence theory. This allows us to predict the variation in the \phi direction and compare it to the data. We then transform the observations from RTN coordinates to magnetic-field-aligned coordinates. The observed reduced power spectral tensor matches the theoretical predictions we derive in both RTN and field-aligned coordinates which means that the local magnetic field we calculate with wavelet envelope functions is an accurate representation of the physical axis of symmetry for the turbulence and implies that on average the turbulence is axi-symmetric. We also show that we can separate the dominant toroidal component of the turbulence from the smaller but significant poloidal component and that these have different power anisotropy. We also conclude that the magnetic helicity is anisotropic and mostly two-dimensional, arising from wavevectors largely confined to the plane perpendicular to B., Comment: 21 pages, 8 figures, 1 table

We present a new model for the transport of solar wind fluctuations which treats them as two interacting incompressible components: quasi-two-dimensional turbulence and a wave-like piece. Quantities solved for include the energy, cross helicity, and characteristic transverse length scale of each component, plus the proton temperature. The development of the model is outlined and numerical solutions are compared with spacecraft observations. Compared to previous single-component models, this new model incorporates a more physically realistic treatment of fluctuations induced by pickup ions and yields improved agreement with observed values of the correlation length, while maintaining good observational accord with the energy, cross helicity, and temperature.

We examine the effects of including effects of both protons and electrons on the heating of the fast solar wind through two different approaches. In the first approach, we incorporate the electron temperature in an MHD turbulence transport model for the solar wind. In the second approach, we adopt more empirically based methods by analyzing the measured proton and electron temperatures to calculate the heat deposition rates. Overall, we conclude that incorporating separate proton and electron temperatures and heat conduction effects provides an improved and more complete model of the heating of the solar wind.

We present a model for the transport of solar wind fluctuations, based on the assumption that they can be well‐represented using two distinct components: a quasi‐2D turbulence piece and a wave‐like piece. For each component, coupled transport equations for its energy, cross helicity, and characteristic lengthscale(s) are derived, along with an equation for the proton temperature. This energy‐containing “two‐component” model includes the effects of solar wind expansion and advection, driving by stream shear and pickup ions, and nonlinear cascades. Nonlinear effects are modeled using a recently developed one‐point phenomenology for such a two‐component model of homogeneous MHD turbulence [1]. Heating due to these nonlinear effects is included in the temperature equation. Numerical solutions are discussed and compared with observations.

A model is presented for generation of fast solar wind in coronal holes, relying on heating that is dominated by turbulent dissipation of MHD fluctuations transported upwards in the solar atmosphere. Scale-separated transport equations include large-scale fields, transverse Alfvenic fluctuations, and a small compressive dissipation due to parallel shears near the transition region. The model accounts for proton temperature, density, wind speed, and fluctuation amplitude as observed in remote sensing and in situ satellite data., accepted for publication in ApJL

We apply a recently developed 2‐component phenomenology to the turbulent heating of the core solar wind protons as seen at the Voyager 2 spacecraft. We find that this new description improves the model predictions of core temperature and correlation scale of the fluctuations, yielding excellent agreement with the Voyager measurements. However, the model fluctuation intensity substantially exceeds the Voyager measurements in the outer heliosphere, indicating that this picture needs further refinement.

Previous formulations of heating and transport associated with strong magnetohydrodynamic (MHD) turbulence are generalized to incorporate separate internal energy equations for electrons and protons. Electron heat conduction is included. Energy is supplied by turbulent heating that affects both electrons and protons, and is exchanged between them via collisions. Comparison to available Ulysses data shows that a reasonable accounting for the data is provided when (i) the energy exchange timescale is very long and (ii) the deposition of heat due to turbulence is divided, with 60% going to proton heating and 40% into electron heating. Heat conduction, determined here by an empirical fit, plays a major role in describing the electron data.

Recent observations at comets Giacobini-Zinner and Halley suggest that simple nonreacting gas dynamics or MHD is an inappropriate description for the bow shock. The thickness of the observed (sub)shock implies that mass-loading is an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot conditions possess source terms. This leads to shocks with properties similar to those of combustion shocks. The paper considers parallel magnetized shocks subjected to mass-loading, describes some properties which distinguish them from classical MHD parallel shocks, and establishes the existence of a new kind of MHD compound shock. These results will be of importance both to observations and numerical simulations of the comet-solar wind interaction.

[1] We employ a turbulence transport model to compute distributions of turbulence throughout the heliosphere. The model determines the radial dependence of three (coupled) quantities that characterize interplanetary turbulence, the energy per unit mass, the cross helicity or Alfvenicity, and a similarity length scale. A fourth integrated quantity, the plasma temperature, is modified by heat deposition due to turbulent dissipation. The model includes advection, expansion, and reflection effects as well as the tendency toward dynamic alignment, and a von Karman type dissipation function that represents decay of turbulence due to cascade to small scales. Two types of forcing are also featured, one a simple model of stream shear, and the other a driving in the outer heliosphere associated with wave energy injection due to pickup protons of interstellar origin. Parameters for the model have been tuned using observation data from Voyager and Ulysses. We analyze the constraining observations to provide boundary conditions and parameters that vary with heliocentric latitude, with some extrapolations. The fully assembled model permits the computation of the distribution of turbulence throughout the entire heliosphere, and we present solutions for several appropriate parameter sets.

We review the use of reduced magnetohydrodynamics (RMHD) in coronal heating models, with particular emphasis on models for magnetically open regions. A brief review of the nature of the coronal heating problem is presented first, followed by detailed discussion regarding the assumptions and features of RMHD and its applicability to the dynamics of the solar corona. We then review a class of heating models based on quasi-2D turbulent cascades driven by low-frequency Alfven waves.

[1] A transport theory including cross helicity, magnetohydrodynamic (MHD) turbulence, and driving by shear and pickup ions, is applied to the radial evolution of the solar wind. The radial decrease of cross helicity observed in the solar wind can be accounted for when sufficient driving is included to overcome the inherent tendency for MHD turbulence to produce Alfvenic states.

There is a growing body of literature that demonstrates the ability of a turbulent cascade within the solar wind to heat the thermal protons. Several sources of energy are required to accomplish the observed heating. Wind shear and shocks originating with the multiple source of wind plasma heat the wind inside ∼10 AU. However, beyond this distance little is left of these sources and all that remains is the energy injected into the plasma by the pickup of newborn protons originating from interstellar neutrals. Recent advances in the theory of wave excitation by the newborn protons allows us to return to the published heating theory and remove a previously unexplained parameterization of the heating due to pickup protons. Furthermore, recent observational evidence suggests that large‐scale correlations between the wind speed and the proton temperature exist into the distant outer heliosphere that motivate an attempt to connect the two within the structure of the heating theory.

We present a brief review of observations and theory regarding the nature and radial evolution of MHD‐scale solar wind fluctuations. Emphasis is placed on the fact that the fluctuations consist of both waves and turbulence, and on their dual dynamical roles.

In the presence of a weakly inhomogeneous background, magnetohydrodynamic fluctuations are transported, reflected and at small scales, dissipated. In contrast to orderings appropriate to outer solar wind conditions, here we explore transport in a regime relevant for solar coronal heating and solar wind acceleration, in which effects of the order of the Alfven speed are retained while disregarding the solar wind velocity. We consider the general properties of the transport equations as well as some solutions of interest.

Models based upon anisotropic magnetohydrodynamic (MHD) cascade offer promising explanations for observations of both interplanetary and coronal turbulence and heating, which are reviewed here. In the standard picture the cascade proceeds by driving at the energy‐containing scales, transfers through the inertial range, and into small scales where it drives small‐scale random turbulent reconnection events. In order to understand more fully the heating and dissipation processes, one also needs to understand how small‐scale MHD‐driven reconnection — involving current sheets and filaments — induces kinetic plasma processes that thermalize the fluid energy. Here we suggest that in these reconnection sites MHD electric fields drive ion beam instabilities and nonlinear electron dynamics involving electron solitary wave structures, in analogy with the kinetic physics observed near parallel electric field auroral regions by the FAST spacecraft.

The heating of the lower solar corona is examined using numerical simulations and theoretical models of magnetohydrodynamic turbulence in open magnetic regions. A turbulent energy cascade to small length scales perpendicular to the mean magnetic field can be sustained by driving with low-frequency Alfven waves reflected from mean density and magnetic field gradients. This mechanism deposits energy efficiently in the lower corona, and we show that the spatial distribution of the heating is determined by the mean density through the Alfven speed profile. This provides a robust heating mechanism that can explain observed high coronal temperatures and accounts for the significant heating (per unit volume) distribution below two solar radius needed in models of the origin of the solar wind. The obtained heating per unit mass on the other hand is much more extended indicating that the heating on a per particle basis persists throughout all the lower coronal region considered here., 19 pages, 5 figures. Accepted for publication in ApJ

The application of linear kinetic treatments to plasma waves, damping, and instability requires favorable inequalities between the associated linear timescales and timescales for nonlinear (e.g., turbulence) evolution. In the solar wind these two types of timescales may be directly compared using standard Kolmogorov-style analysis and observational data. The estimated local nonlinear magnetohydrodynamic cascade times, evaluated as relevant kinetic scales are approached, remain slower than the cyclotron period, but comparable to, or faster than, the typical timescales of instabilities, anisotropic waves, and wave damping. The variation with length scale of the turbulence timescales is supported by observations and simulations. On this basis the use of linear theory - which assumes constant parameters to calculate the associated kinetic rates - may be questioned. It is suggested that the product of proton gyrofrequency and nonlinear time at the ion gyroscales provides a simple measure of turbulence influence on proton kinetic behavior., 9 pages, 4 figures, submitted to the Astrophysical Journal

We present a candidate mechanism for heating of the solar corona, via the interaction of (chromospherically-generated) Alfven waves, their reflections, and quasi-two dimensional (relative to the mean magnetic field) MHD turbulence. The non-propagating nature of the latter means that the restrictive Alfven timescale constraints associated with high frequency wave heating models are avoided. A phenomenology for this mechanism is described here, and “proof of concept” support from reduced MHD (RHMD) simulations is also discussed. Estimates of the achievable heating efficiency based on turbulence models are favorable, and encourage further investigation of the model’s quantitative feasibility.

Mechanisms for the deposition of heat in the lower coronal plasma are discussed, emphasizing recent attempts to reconcile the fluid and kinetic perspectives. Structures at the MHD scales are believed to act as reservoirs for fluctuation energy, which in turn drive a nonlinear cascade process. Kinetic processes act at smaller spatial scales and more rapid time scales. Cascade-driven processes are contrasted with direct cyclotron absorption, and this distinction is echoed in the contrast between frequency and wavenumber spectra of the fluctuations. Observational constraints are also discussed, along with estimates of the relative efficiency of cascade and cyclotron processes.

Anisotropies in the spectra of magnetohydrodynamic (MHD) scale fluctuations are observed or inferred in many plasmas, e.g.,laboratory fusion machines, the solar wind and corona, and the interstellar medium (see [1, 2] for references). Anisotropy is expected since a mean magnetic field B 0 (unlike a mean flow), cannot be transformed away and thus provides a preferred direction. Understanding the evolution and development of this spectral anisotropy is a major theoretical challenge as nonlinear effects play a crucial role. Nonetheless, some progress has been made. Using numerical simulations and a reduced MHD (RMHD) approach, we have developed a relatively simple model of the process [1, 2], which we present below.

Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic field than along it. This occurs both globally and locally, and has significant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensified in more localized estimates of the mean field. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in specific cases, illustrate the connection to higher order statistics by showing the sensitivity of local anisotropy to phase randomization, and thus establish that the local structure function is not a measure of the energy spectrum. Evidently the local enhancement of correlation anisotropy is of substantial fundamental interest, and this phenomenon must be understood in terms of higher order correlations, fourth-order and above., 5 pages, 1 figure, submitted to ApJ

The behavior of scale-dependent (or filtered) kurtosis is studied in the solar wind using magnetic field measurements from the ACE and Cluster spacecraft at 1 AU. It is also analyzed numerically with high-resolution magnetohydrodynamic spectral simulations. In each case the filtered kurtosis increases with wavenumber, implying the presence of coherent structures at the smallest scales. This phase coupling is related to intermittency in solar wind turbulence and the emergence of non-Gaussian statistics. However, it is inhibited by the presence of upstream waves and other phase-randomizing structures, which act to reduce the growth of kurtosis.

The magnetic and velocity field fluctuations in magnetohydrodynamic turbulence can be characterized by their directional alignment and induced electric field. These manifest as coherent spatial correlations which are measures of Alfvenicity and turbulence cascade strength, respectively. Solar wind observations and direct numerical simulations find that these distinctive correlations, caused by rapid relaxation processes that act to suppress nonlinearity, occur in localized spatial patches. This cellularization of magnetofluid turbulence is inconsistent with a superposition of Gaussian fields and could be related to spatial intermittency or other non-Gaussian statistics.

We present various numerical and analytical solutions for the transport of solar wind turbulence. The model used takes into account the effects of convection, expansion, and wave propagation, as well as the recently illuminated effects of (non-WKB) 'mixing' terms. The radial evolution of the fluctuating kinetic energy, magnetic energy, and normalized cross helicity is computed, and, it is demonstrated that in appropriate limits the solutions converge to the WKB forms. In the general case, solutions which differ substantially from those predicted by WKB theory are obtained. The degree of turbulent 'mixing' shows considerable dependence on the nature of the turbulence, giving rise to varying levels, at 1 AU, of the ratio of 'inward' and 'outward' fluctuation energies and the ratio of kinetic to magnetic energies in the fluctuations. The transport properties described here may provide at least a partial explanation for the observed mixing of cross helicities with increasing heliocentric distance in the solar wind.

An evaluation is conducted of recent theories of small-scale MHD turbulence transport in an inhomogeneous background that are pertinent to the evolution of solar wind turbulence. Attention is given to the WKB formalism that has been used in many solar wind-related physics applications, with a view to its shortcomings. Also discussed are the structure of two-scale transport theories, and their relationship to WKB theory in light of multiple-scales analysis.

Numerical solutions for the linear transport of solar wind fluctuations are presented. The model used takes into account the effects of advection, expansion, and wave propagation, as well as the recently illuminated effects of (non-WKB) “mixing” terms. The radial evolution of the fluctuating kinetic and magnetic energies and of the cross helicity is computed, and it is demonstrated that in appropriate limits the solutions converge to the WKB forms. In more general cases, however, where the fluctuations consist of a superposition of various types of turbulence, mixing leads to solutions which differ substantially from those predicted by WKB theory. The degree of mixing shows considerable dependence on the nature of the turbulence, giving rise to varying levels, at 1 ∼ AU, of the ratio of “inward” and “outward” fluctuation energies and the ratio of kinetic and magnetic fluctuation energies. The transport properties described here may provide a partial explanation for the observed decrease of cross helicity with increasing heliocentric distance in the solar wind.

Previous theoretical treatments of fluid-scale turbulence in the solar wind have concentrated on describing the state and dynamical evolution of fluctuations in the inertial range, which are characterized by power law energy spectra. In the present paper a model for the evolution of somewhat larger, more energetic magnetohydrodynamic (MHD) fluctuations is developed by analogy with classical hydrodynamic turbulence in the quasi-equilibrium range. The model is constructed by assembling and extending existing phenomenologies of homogeneous MHD turbulence, as well as simple two-length-scale models for transport of MHD turbulence in a weekly inhomogeneous medium. A set of equations is presented for the evolution of the turbulence, including the transport and nonlinear evolution of magnetic and kinetic energy, cross helicity, and their correlation scales. Two versions of the model are derived, depending on whether the fluctuations are distributed isotropically in three dimensions or restricted to the two-dimensional plane perpendicular to the mean magnetic field. This model includes a number of potentially important physical effects that have been neglected in previous discussions of transport of solar wind turbulence.