Showing papers by "William H. Matthaeus published in 2010"

Statistics of magnetic reconnection in two-dimensional magnetohydrodynamic turbulence

Abstract: The nonlinear dynamics of magnetic reconnection in turbulence is investigated through direct numerical simulations of decaying, incompressible, two-dimensional magnetohydrodynamics. Recently, it was shown by Servidio et al. [Phys. Rev. Lett. 102, 115003 (2009)] that in fully developed turbulence complex processes of reconnection occur locally. Here, the main statistical features of these multiscale reconnection events are further described, providing details on the methodology. It is found that is possible to describe the reconnection process in turbulence as a generalized local Sweet–Parker process in which the parameters are locally controlled by the turbulence cascade, thus providing a step toward reconciling classical turbulence analysis with reconnection theory. This general description of reconnection may be useful for laboratory and space plasmas, where the presence of turbulence plays a crucial role.

Turbulent heating of the distant solar wind by interstellar pickup protons in a decelerating flow

Abstract: Previous models of solar wind heating by interstellar pickup proton-driven turbulence have assumed that the wind speed is a constant in heliocentric radial position. However, the same pickup process, which is taken to provide the turbulent energy, must also decelerate the wind. In this paper, we extend our phenomenological turbulence model to include variable wind speed, and then incorporate the deceleration due to interstellar pickup protons into the model. We compare the model results with plasma and field data from Voyager 2, taking this opportunity to present an extended and improved data set of proton core temperature, magnetic field fluctuation intensity, and correlation length along the Voyager trajectory. A particular motivation for including the solar wind deceleration in this model is the expectation that a slower wind would reduce the resulting proton core temperature in the region beyond ~60 AU, where the previous model predictions were higher than the observed values. However, we find instead that the deceleration of the steady-state wind increases the energy input to the turbulence, causing even higher temperatures in that region. The increased heating is shown to result from the larger values of the ratio of Alfven speed to solar wind speed that develop in the decelerating wind.

On the accuracy of simulations of turbulence

Abstract: The widely recognized issue of adequate spatial resolution in numerical simulations of turbulence is studied in the context of two-dimensional magnetohydrodynamics. The familiar criterion that the dissipation scale should be resolved enables accurate computation of the spectrum, but fails for precise determination of higher-order statistical quantities. Examination of two straightforward diagnostics, the maximum of the kurtosis and the scale-dependent kurtosis, enables the development of simple tests for assessing adequacy of spatial resolution. The efficacy of the tests is confirmed by examining a sample problem, the distribution of magnetic reconnection rates in turbulence. Oversampling the Kolmogorov dissipation scale by a factor of 3 allows accurate computation of the kurtosis, the scale-dependent kurtosis, and the reconnection rates. These tests may provide useful guidance for resolution requirements in many plasma computations involving turbulence and reconnection.

Kinetic driven turbulence: Structure in space and time

Abstract: The structure in space and time of a driven turbulent magnetoplasma is analyzed using kinetic simulations. For a two dimensional case with a strong uniform out-of-plane magnetic field, large scale driving produces a turbulent state that spans fluid scales to kinetic proton scales. There are fluid electrons in this hybrid representation. In near steady conditions, spectral analysis shows an almost complete absence of discrete point spectral features that would be associated with a dispersion relation and wave activity. While there is indication of a low level of wave activity, the results show that the dynamics are dominated by nonlinear activity. Implications for understanding plasma cascade, dissipation, and heating are discussed.

Cosmic ray diffusion tensor throughout the heliosphere

Abstract: [1] We calculate the cosmic ray diffusion tensor based on a recently developed model of magnetohydrodynamic (MHD) turbulence in the expanding solar wind. Parameters of this MHD model are tuned by using published observations from Helios, Voyager 2, and Ulysses. We present solutions of two turbulence parameter sets and derive the characteristics of the cosmic ray diffusion tensor for each. We determine the parallel diffusion coefficient of the cosmic rays following the method presented by Bieber et al. (1995). We use the nonlinear guiding center theory to obtain the perpendicular diffusion coefficient of the cosmic rays. We find that (1) the radial mean free path decreases from 1 to 30 AU for both turbulence scenarios; (2) after 30 AU the radial mean free path is nearly constant; (3) the radial mean free path is dominated by the parallel component before 30 AU, after which the perpendicular component becomes important; (4) the rigidity dependence of the parallel mean free path is proportional to P.404 for one turbulence scenario and P.374 for the other at 1 AU from 0.1 to 10 GV, but in the outer heliosphere its dependence steepens above 4 GV; and (5) the rigidity dependence of the perpendicular mean free path is very weak.

The third-order law for magnetohydrodynamic turbulence with shear: Numerical investigation

Abstract: The scaling laws of third-order structure functions for isotropic, homogeneous, and incompressible magnetohydrodynamic (MHD) turbulence relate the observable structure function with the energy dissipation rate. Recently [Wan et al. Phys. Plasmas 16, 090703 (2009)], the theory was extended to the case in which a constant velocity shear is present, motivated by the application of the third-order law to the solar wind. We use direct numerical simulations of two-dimensional MHD with shear to confirm this new generalization of the theory. The presence of the shear effect broadens the circumstances in which the law can be applied. Important implications for laboratory and space plasmas are discussed.

Dropouts in solar energetic particles: associated with local trapping boundaries or current sheets?

Abstract: In recent observations by the Advanced Composition Explorer, the intensity of solar energetic particles exhibits sudden, large changes known as dropouts. These have been explained in terms of turbulence or a flux tube structure in the solar wind. Dropouts are believed to indicate filamentary magnetic connection to a localized particle source near the solar surface, and computer simulations of a random-phase model of magnetic turbulence have indicated a spatial association between dropout features and local trapping boundaries (LTBs) defined for a two-dimensional (2D) + slab model of turbulence. Previous observations have shown that dropout features are not well associated with sharp magnetic field changes, as might be expected in the flux tube model. Random-phase turbulence models do not properly treat sharp changes in the magnetic field, such as current sheets, and thus cannot be tested in this way. Here, we explore the properties of a more realistic magnetohydrodynamic (MHD) turbulence model (2D MHD), in which current sheets develop and the current and magnetic field have characteristic non-Gaussian statistical properties. For this model, computer simulations that trace field lines to determine magnetic connection from a localized particle source indicate that sharp particle gradients should frequently be associated with LTBs, sometimes with strong 2D magnetic fluctuations, and infrequently with current sheets. Thus, the 2D MHD + slab model of turbulent fluctuations includes some realistic features of the flux tube view and is consistent with the lack of an observed association between dropouts and intense magnetic fields or currents.

Eulerian decorrelation of fluctuations in the interplanetary magnetic field

Abstract: A method is devised for estimating the two-time correlation function and the associated Eulerian decorrelation timescale in turbulence. With the assumptions of a single decorrelation time and a frozen-in flow approximation for the single-point analysis, the method compares two-point correlation measurements with single-point correlation measurements at the corresponding spatial lag. This method is applied to interplanetary magnetic field measurements from the Advanced Composition Explorer and Wind spacecraft. An average Eulerian decorrelation time of 2.9 hr is found. This measures the total rate of distortion of turbulent fluid elements—including sweeping, nonlinear distortion, and wave propagation.

Local relaxation and maximum entropy in two-dimensional turbulence

Abstract: The phenomenon of vortex merging in two-dimensional hydrodynamics has been investigated through direct numerical simulations. The fast and local processes that occur during the turbulent relaxation of a randomly initialized system in periodic geometry have been examined. The analysis reveals that many of the coherent structures can be described by a local principle of maximization of entropy. The validity of this entropy principle has been further confirmed by time-dependent statistics using a contour-tracking technique. Implications for the description of persistent coherent vortices commonly observed in nature are suggested, including growing evidence for the wide applicability of maximum entropy-based relaxation principles.

Anisotropy of the Taylor scale and the correlation scale in plasma sheet magnetic field fluctuations as a function of auroral electrojet activity

Abstract: [1] Magnetic field data from the Cluster spacecraft in the magnetospheric plasma sheet are employed to determine the correlation scale and the magnetic Taylor microscale from simultaneous multiple-point measurements for multiple intervals over a range of mean magnetic field directions for three different levels of geomagnetic activity. We have determined that in the plasma sheet the correlation scale along the mean magnetic field direction decreases from 19,500 ± 2200 to 13,100 ± 700 km as the auroral electrojet activity increases from quiet ( 200 nT). The reverse occurs for the correlation scale perpendicular to the magnetic field, which increases from 8200 ± 600 km to 13,000 ± 2100 km as the auroral electrojet activity increases from quiet to active conditions. This variation of the correlation scale with geomagnetic activity may mean either a change in the scale size of the turbulence driver or may mean a change in the predominance of one over another type of turbulence driving mechanism. Unlike the correlation scale, the Taylor scale does not show any clear variation with geomagnetic activity. We find that the Taylor scale is longer parallel to the magnetic field than perpendicular to it for all levels of geomagnetic activity. The correlation and Taylor scales may be used to estimate the effective magnetic Reynolds numbers separately for each angular channel. Reynolds numbers were found to be approximately independent of the angle relative to the mean magnetic field. These results may be useful in magnetohydrodynamic modeling of the magnetosphere and can contribute to our understanding of energetic particle diffusion in the magnetosphere.

Solar Wind Speed And Temperature Relationship

Abstract: Previous studies of solar wind proton temperature and speed have found a break in the curve between 400 and 550 km/s. Examining all the OMNI 2 data from 1965 to 2009, we create plots binned in both temperature and speed in order to identify where the majority of the points lie. Using yearly color plots to evaluate the curve shape we find most of the data is well represented by a single linear fit even though the slope varies significantly from year to year. A clear break in the temperature speed curve occurs in 2003 coincident with a large polar coronal hole extension which produced faster wind speeds than expected at low latitudes based on the Ulysses speed‐latitude polar coronal hole relationship. Although the slope does not change in a systematic way for each individual solar cycle, there seems to be an overall decrease in the slope since 1972.

Heating of the solar wind with electron and proton effects

Abstract: 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.

The Interaction of Turbulence with Shock Waves

Abstract: The heliosheath was expected to be turbulent, the result of upstream turbulence and disturbances (shock waves, pressure and density enhancements, structures, etc.) being transmitted across and interacting with the heliospheric termination shock (HTS). A turbulent heliosheath has indeed been observed downstream of the HTS, but the character of the turbulence is significantly different from that of the solar wind. Here, we discuss the transmission of waves and turbulence across the HTS, both analytically and numerically, in the large plasma beta approximation, and we investigate both small amplitude and large‐amplitude cases. We find that the linear theory is a reasonable approximation for small amplitude waves incident on the shock. In the case of large amplitude entropy fluctuations incident on the shock, the downstream state is initially one of coherent wave forms, but this rapidly devolves to a highly disturbed state that evolves eventually to a state dominated by vortical structures. Of particular impo...

Dispersive Effects of Hall Electric Field in Turbulence

Abstract: A familiar feature of turbulence in a low collisionality turbulence is an increase in the electric field spectrum, relative to the magnetic field spectrum, at wavenumbers near the reciprocal of the ion inertial scale. This effect is commonly observed in the solar wind. Here we examine this feature numerically, using a variety of simulations, including compressible Hall MHD, incompressible Hall MHD, and one‐, two‐, and three‐dimensional cases. A feature of this type is even found in a statistical Hall MHD model with no dissipation. This leads to the conclusion that the only requirement for obtaining this dispersive effect is the Hall term in the generalized Ohm’s law. Therefore this observation does not distinguish between whistler and kinetic Alfven waves, between waves and turbulence, nor even between fluid and kinetic plasma models.

Similarity decay of enstrophy in an electron fluid.

Abstract: A similarity decay law is proposed for enstrophy of a one-signed-vorticity fluid in a circular free-slip domain. It excludes the metastable equilibrium enstrophy which cannot drive turbulence, and approaches Batchelor's t{sup -2} law for strong turbulence. Measurements of the decay of a turbulent electron fluid agree well with the predictions of the decay law for a variety of initial conditions.

Anisotropy of the magnetic correlation function in the inner heliosphere

Abstract: For over four decades, low frequency plasma and electromagnetic fluctuations have been observed in the solar wind (SW), making it the most completely studied case of magnetohydrodynamic turbulence in astrophysics, and the only one extensively and directly studied using in situ observations. Magnetohydrodynamic scale fluctuations in the SW are usually anisotropic with respect to the local mean magnetic field (B0). In this work, we present a study of turbulent properties in the inner heliosphere (solar wind between 0.3 and 1 AU) based on modeling in situ plasma and magnetic observations collected by Helios 1 and Helios 2 spacecraft throughout a solar minimum. We present preliminary results on the evolution of the spatial structure of the magnetic self‐correlation function in the inner heliosphere. In particular we focus on the evolution of the integral length scale (λ) for magnetic fluctuations and on its anisotropy in the inertial range. As previously known from different studies, we confirm that near Eart...

Statistical properties of solar wind discontinuities, intermittent turbulence, and rapid emergence of non‐Gaussian distributions

Abstract: Recent studies have compared properties of the magnetic field in simulations of Hall MHD turbulence with spacecraft data, focusing on methods used to identify classical discontinuities and intermittency statistics. Comparison of ACE solar wind data and simulations of 2D and 3D turbulence shows good agreement in waiting‐time analysis of magnetic discontinuities, and in the related distribution of magnetic field increments. This supports the idea that the magnetic structures in the solar wind may emerge fast and locally from nonlinear dynamics that can be understood in the framework of nonlinear MHD theory. The analysis suggests that small scale current sheets form spontaneously and rapidly enough that some of the observed solar wind discontinuities may be locally generated, representing boundaries between interacting flux tubes.

The third‐order law for magnetohydrodynamic turbulence with constant shear

Abstract: The scaling laws of mixed third‐order structure functions for isotropic, homogeneous, and incompressible magnetohydrodynamic (MHD) turbulence have been recently applied in solar wind studies, even though there is recognition that isotropy is not well satisfied. Other studies have taken account of the anisotropy induced by a constant mean magnetic field. However, large‐scale shear can also cause departures from isotropy. Here we examine shear effects in the simplest case, and derive the third‐order laws for MHD turbulence with constant shear, where homogeneity is still assumed. This generalized scaling law has been checked by data from direct numerical simulations (DNS) of two‐dimensional (2D) MHD and is found to hold across the inertial range. These results suggest that third‐order structure function analysis and interpretation in the solar wind should be undertaken with some caution, since, when present, shear can change the meaning of the third‐order relations.

A Two‐component Transport Model for Solar Wind Fluctuations: Waves plus Quasi‐2D Turbulence

Abstract: 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.

Properties of magnetic reconnection in MHD turbulence

Abstract: Numerical simulations of two‐dimensional Magnetohydrodynamic (2D MHD) turbulence reveal the presence of a huge number of sites where magnetic reconnection locally occurs. The properties of this ensemble of reconnection events, that are spontaneously generated by turbulence, have been studied. The associated reconnection rates, computed as the electric field at the neutral points, are broadly distributed and the statistics of these events are presented. This new description of reconnection is relevant for space and laboratory plasmas, where generally turbulence is present.

Solar Wind Turbulent Heating by Interstellar Pickup Protons: 2‐Component Model

Abstract: 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.

Emergence of intermittent structures and reconnection in MHD turbulence

Abstract: In recent analyses of numerical simulation and solar wind dataset, the idea that the magnetic discontinuities may be related to intermittent structures that appear spontaneously in MHD turbulence has been explored in details These studies are consistent with the hypothesis that discontinuity events founds in the solar wind might be of local origin as well, ie a by-product of the turbulent evolution of magnetic fluctuationsUsing simulations of 2D MHD turbulence, we are exploring a possible link between tangential discontinuities and magnetic reconnection The goal is to develop numerical algorithms that may be useful for solar wind applications

Ultraviolet Coronagraph Spectroscopy: A Key Capability for Understanding the Physics of Solar Wind Acceleration

Abstract: Understanding the physical processes responsible for acce lerating the solar wind requires detailed measurements of the collisionless plasma in the extended solar corona. Some key clues about these processes have come from instruments that combine the power of an ultraviolet (UV) spectrometer with an occulted telescope. This combination enables measurements of ion emission lines far from the bright solar disk, where most of the solar wind acceleration occurs. Although the UVCS instrument on SOHO made several key discoveries, many questions remain unanswered because its capabilities were limited. This white paper summarizes these past achievements and also describes what can be accomplished with next-generation instrumentation of this kind. 1. Background and Motivation The hot, ionized outer atmosphere of the Sun is a unique testbed for the study of magnetohydrodynamics (MHD) and plasma physics, with ranges of parameters that are inaccessible on Earth. Although considerable progress has been made during the last few decades, we still do not know the basic physical processes responsible for heating the million-degree solar corona an d accelerating the solar wind. Identifying these processes is important not only for understanding the origi ns and impacts of space weather (e.g., Schwenn 2006; Eastwood 2008), but also for establishing a baseline of knowledge about a well-resolved star that is directly relevant to other astrophysical systems. In order to construct and test theoretical models, a wide ran ge of measurements of relevant plasma parameters must be available. In the low-density, open-field r egions that reach into interplanetary space, more parameters need to be measured (in comparison to collision-dominated regions) because the plasma becomes collisionless. In other words, individual particle species—e.g., protons , electrons, helium, and minor ions— can exhibit different properties from one another. Such dif ferences in particle velocity distributions are valuable probes of “microscopic” processes of heating and acceleration. In interplanetary space, such kinetic properties have been measured for decades by in situ particle instruments (e.g., Marsch 1999, 2006; Kasper et al. 2008). However, measurements in the near-Sun regions that are being actively heated and accelerated have been more limited in scope. Remote-sensing measurements of plasma properties in the so-called “extended solar corona” (above about 1.5 R⊙ measured from Sun-center) are difficult to make because the p hoton emission at large heights is fainter by many orders of magnitude than the emission from the solar disk. Standard telescopes, that do not explicitly block out the solar disk, typically contai n enough scattered light from the disk to totally mask the faint off-limb emission. Because the corona is highly ionized, the dominant spectral features are at wavelengths accessible only from space. For these reasons, a series of Ultraviolet Coronagraph Spectrometer (UVCS) instruments have been built and flown on rockets, on a S huttle-deployed Spartan payload, and as an instrument on the Solar and Heliospheric Observatory(SOHO) spacecraft; see, e.g., Kohl et al. (1978,

Are statistical equilibria good predictors of large-scale behavior for dissipative fluids? The case of rotating turbulence

Abstract: We examine long-time properties of the ideal dynamics of three-dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases the results agree with the isotropic predictions stemming from statistical mechanics with no accumulation of excitation in the large scales, even though in the dissipative rotating case anisotropy and accumulation, in the form of an inverse cascade of energy, are known to occur. We attribute this latter discrepancy to the linearity of the term responsible for the emergence of inertial waves. At intermediate times, inertial energy spectra emerge that differ somewhat from classical wave-turbulence expectations, and with a trace of large-scale excitation that goes away for long times. These results are discussed in the context of partial two-dimensionalization of the flow undergoing strong rotation as advocated by several authors.