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Solar wind provides an example of a weakly collisional plasma expanding from a thermal source in the presence of spatially diverging magnetic-field lines. Observations show that in the inner heliosphere, the electron temperature declines with the distance approximately as T e ( r ) ∼ r − 0.3 … r − 0.7 , which is significantly slower than the adiabatic expansion law ∼ r − 4 / 3 . Motivated by such observations, we propose a kinetic theory that addresses the nonadiabatic evolution of a nearly collisionless plasma expanding from a central thermal source. We concentrate on the dynamics of energetic electrons propagating along a radially diverging magnetic-flux tube. Due to conservation of their magnetic moments, the electrons form a beam collimated along the magnetic-field lines. Due to weak energy exchange with the background plasma, the beam population slowly loses its energy and heats the background plasma. We propose that no matter how weak the collisions are, at large enough distances from the source a universal regime of expansion is established where the electron temperature declines as T e ( r ) ∝ r − 2 / 5 . This is close to the observed scaling of the electron temperature in the inner heliosphere. Our first-principle kinetic derivation may thus provide an explanation for the slower-than-adiabatic temperature decline in the solar wind. More broadly, it may be useful for describing magnetized collisionless winds from G-type stars.

We provide evidence that the sunward-propagating half of the solar wind electron halo distribution evolves without scattering in the inner heliosphere. We assume the particles conserve their total energy and magnetic moment, and perform a ‘Liouville mapping’ on electron pitch angle distributions measured by the Parker Solar Probe SPAN-E instrument. Namely, we show that the distributions are consistent with Liouville’s theorem if an appropriate interplanetary potential is chosen. This potential, an outcome of our fitting method, is compared against the radial profiles of proton bulk flow energy. We find that the inferred potential is responsible for nearly 100 per cent of the proton acceleration in the solar wind at heliocentric distances 0.18-0.79 AU. These observations combine to form a coherent physical picture: the same interplanetary potential accounts for the acceleration of the solar wind protons as well as the evolution of the electron halo. In this picture the halo is formed from a sunward-propagating population that originates somewhere in the outer heliosphere by a yet-unknown mechanism.

We present a drift kinetic model for the free expansion of a thermal plasma out of a magnetic nozzle. This problem relates to plasma space propulsion systems, natural environments such as the solar wind, and end losses from the expander region of mirror magnetically confined fusion concepts such as the Gas Dynamic Trap. The model incorporates trapped and passing orbit types encountered in the mirror expander geometry and maps to an upstream thermal distribution. This boundary condition and quasineutrality require the generation of an ambipolar potential drop of $\sim5 T_e/e$, forming a thermal barrier for the electrons. The model for the electron and ion velocity distributions and fluid moments is confirmed with data from a fully kinetic simulation. Finally, the model is extended to account for a population of fast sloshing ions arising from neutral beam heating within a magnetic mirror, again resulting in good agreement with a corresponding kinetic simulation., Comment: 27 pages, 10 figures

In Navier-Stokes turbulence, energy and helicity injected at large scales are subject to a joint direct cascade, with both quantities exhibiting a spectral scaling $\propto k^{-5/3}$. We demonstrate via direct numerical simulations that the two cascades are compatible due to the existence of a strong scale-dependent phase alignment between velocity and vorticity fluctuations, with the phase alignment angle scaling as $\cos\alpha_k\propto k^{-1}$.

In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a non-thermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter $\sigma \gg 1$) quickly evolves into a state with ultra-relativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent $\alpha$ in the power-law particle energy distribution function, $f(\gamma)d\gamma\propto \gamma^{-\alpha}d\gamma$, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent $\alpha$ is in good agreement with the numerical results., Comment: 8 pages, 3 figures. Accepted for publication at ApJL

We develop a model for the strahl population in the solar wind -- a narrow, low-density and high-energy electron beam centered on the magnetic field direction. Our model is based on the solution of the electron drift-kinetic equation at heliospheric distances where the plasma density, temperature, and the magnetic field strength decline as power-laws of the distance along a magnetic flux tube. Our solution for the strahl depends on a number of parameters that, in the absence of the analytic solution for the full electron velocity distribution function (eVDF), cannot be derived from the theory. We however demonstrate that these parameters can be efficiently found from matching our solution with observations of the eVDF made by the Wind satellite's SWE strahl detector. The model is successful at predicting the angular width (FWHM) of the strahl for the Wind data at 1 AU, in particular by predicting how this width scales with particle energy and background density. We find the strahl distribution is largely determined by the local temperature Knudsen number $\gamma \sim |T dT/dx|/n$, which parametrizes solar wind collisionality. We compute averaged strahl distributions for typical Knudsen numbers observed in the solar wind, and fit our model to these data. The model can be matched quite closely to the eVDFs at 1 AU, however, it then overestimates the strahl amplitude at larger heliocentric distances. This indicates that our model may be improved through the inclusion of additional physics, possibly through the introduction of "anomalous diffusion" of the strahl electrons.

In magnetohydrodynamic (MHD) turbulence, the large-scale magnetic field sets a preferred local direction for the small-scale dynamics, altering the statistics of turbulence from the isotropic case. This happens even in the absence of a total magnetic flux, since MHD turbulence forms randomly oriented large-scale domains of strong magnetic field. It is therefore customary to study small-scale magnetic plasma turbulence by assuming a strong background magnetic field relative to the turbulent fluctuations. This is done, for example, in reduced models of plasmas, such as reduced MHD, reduced-dimension kinetic models, gyrokinetics, etc., which make theoretical calculations easier and numerical computations cheaper. Recently, however, it has become clear that the turbulent energy dissipation is concentrated in the regions of strong magnetic field variations. A significant fraction of the energy dissipation may be localized in very small volumes corresponding to the boundaries between strongly magnetized domains. In these regions the reduced models are not applicable. This has important implications for studies of particle heating and acceleration in magnetic plasma turbulence. The goal of this work is to systematically investigate the relationship between local magnetic field variations and magnetic energy dissipation, and to understand its implications for modeling energy dissipation in realistic turbulent plasmas., 6 pages, 5 figures, to appear in Monthly Notices of the Royal Astronomical Society

In a weakly collisional, low-electron-beta plasma, large-scale Alfv\'en turbulence transforms into inertial kinetic-Alfv\'en turbulence at scales smaller than the ion microscale (gyroscale or inertial scale). We propose that at such kinetic scales, the nonlinear dynamics tend to organize turbulent eddies into thin current sheets, consistent with the existence of two conserved integrals of the ideal equations, energy and helicity. The formation of strongly anisotropic structures is arrested by the tearing instability that sets a critical aspect ratio of the eddies at each scale $a$ in the plane perpendicular to the guide field. This aspect ratio is defined by the balance of the eddy turnover rate and the tearing rate, and varies from $(d_e/a)^{1/2}$ to $d_e/a$ depending on the assumed profile of the current sheets. The energy spectrum of the resulting turbulence varies from $k^{-8/3}$ to $k^{-3}$, and the corresponding spectral anisotropy with respect to the strong background magnetic field from $k_z\lesssim k_\perp^{2/3}$ to $k_z\lesssim k_\perp$., Comment: published version

We propose a new approach to study the long time dynamics of the wave kinetic equation in the statistical description of acoustic turbulence. The approach is based on rewriting the discrete version of the wave kinetic equation in the form of a chemical reaction network, then employing techniques used to study the Global Attractor Conjecture to investigate the long time dynamics of the newly obtained chemical system. We show that the solution of the chemical system converges to an equilibrium exponentially in time. In addition, a resonance broadening modification of the acoustic wave kinetic equation is also studied with the same technique. For the near-resonance equation, if the resonance broadening frequency is larger than a threshold, the solution of the system goes to infinity as time evolves., Comment: arXiv admin note: text overlap with arXiv:1608.05438

Recent analytical works on strong magnetized plasma turbulence have hypothesized the existence of a range of scales where the tearing instability may govern the energy cascade. In this paper, we estimate the conditions under which such tearing may give rise to full nonlinear magnetic reconnection in the turbulent eddies, thereby enabling significant energy conversion and dissipation. When those conditions are met, a new turbulence regime is accessed where reconnection-driven energy dissipation becomes common, rather than the rare feature that it must be when they are not., Comment: Submitted to Astrophysical Journal

We investigate the intermittency of energy dissipation in Alfvenic turbulence by considering the statistics of the coarse-grained energy dissipation rate, using direct measurements from numerical simulations of magnetohydrodynamic turbulence and surrogate measurements from the solar wind. We compare the results to the predictions of the log-normal and log-Poisson random cascade models. We find that, to a very good approximation, the log-normal model describes the probability density function for the energy dissipation over a broad range of scales, but does not accurately describe the scaling exponents of the moments. The log-Poisson model better describes the scaling exponents of the moments, while the comparison with the probability density function is not straightforward., To appear in MNRAS Letters. 5 pages, 4 figures

We study numerically small-scale reconnection events in kinetic, low-frequency, quasi-2D turbulence (termed kinetic-Alfv\'en turbulence). Using 2D particle-in-cell simulations, we demonstrate that such turbulence generates reconnection structures where the electron dynamics do not couple to the ions, similarly to the electron-only reconnection events recently detected in the Earth's magnetosheath by Phan et al. (2018). Electron-only reconnection is thus an inherent property of kinetic-Alfv\'en turbulence, where the electron current sheets have limited anisotropy and, as a result, their sizes are smaller than the ion inertial scale. The reconnection rate of such electron-only events is found to be close to $0.1$., Comment: 8 pages, 3 figures

We propose a kinetic model describing the formation of the strahl and halo electron populations in the solar wind. We demonstrate that the suprathermal electrons propagating from the sun along the Parker-spiral magnetic field lines are progressively focused into a narrow strahl at heliospheric distances $r\lesssim 1$ AU, while at $r\gtrsim 1$ AU the width of the strahl saturates due to Coulomb collisions and becomes independent of the distance. Our theory of the strahl broadening does not contain free parameters and it agrees with the Wind observations at 1 AU to within $15-20\%$. This indicates that Coulomb scattering, rather than anomalous turbulent diffusion, plays a dominant role in strahl formation in these observations. We further propose that the nearly isotropic halo electron population may be composed of electrons that ran away from the sun as an electron strahl, but later ended up on magnetic field lines leading them back to the sun. Through the effects of magnetic defocusing and Coulomb pitch-angle scattering, a narrow source distribution at large heliocentric distances appears nearly isotropic at distances $\sim$1 AU. The halo electrons are, therefore, not produced locally; rather, they are the fast electrons trapped by magnetic field lines on global heliospheric scales. At the electron energies $K \lesssim 200\,\, {\rm eV}$, our theory is quite insensitive to the particular mechanism that produces a population of sunward-streaming suprathermal particles. At larger energies, however, our theory indicates that the scattering provided by Coulomb collisions alone is not sufficient to isotropize a narrow sunward-propagating electron beam., Comment: 9 pages, 3 figures

Recent studies have suggested that the tearing instability may play a significant role in magnetic turbulence. In this work, we review the theory of the magnetohydrodynamic tearing instability in the general case of an arbitrary tearing parameter, which is relevant for applications in turbulence. We discuss a detailed derivation of the results for the standard Harris profile and accompany it by the derivation of the results for a lesser known sine-shaped profile. We devote special attention to the exact solution of the inner equation, which is the central result in the theory of tearing instability. We also briefly discuss the influence of shear flows on tearing instability in magnetic structures. Our presentation is self-contained; we expect it to be accessible to researchers in plasma turbulence who are not experts in magnetic reconnection., Comment: Proceedings of the 17th Annual International Astrophysics Conference (2018)

In this work we study the process of energy dissipation triggered by a slow large scale motion of a magnetized conducting fluid. Our consideration is motivated by the problem of heating the solar corona, which is believed to be governed by fast reconnection events set off by the slow motion of magnetic field lines anchored in the photospheric plasma. To elucidate the physics governing the disruption of the imposed laminar motion and the energy transfer to small scales, we propose a simplified model where the large-scale motion of magnetic field lines is prescribed not at the footpoints but rather imposed volumetrically. As a result, the problem can be treated numerically with an efficient, highly-accurate spectral method, allowing us to use a resolution and statistical ensemble exceeding those of the previous work. We find that, even though the large-scale deformations are slow, they eventually lead to reconnection events that drive a turbulent state at smaller scales. The small-scale turbulence displays many of the universal features of field-guided MHD turbulence like a well developed inertial range spectrum. Based on these observations, we construct a phenomenological model that gives the scalings of the amplitude of the fluctuations and the energy dissipation rate as functions of the input parameters. We find a good agreement between the numerical results and the predictions of the model., 6 pages, 4 figures

The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $\ensuremath{\lambda}\ensuremath{\sim}L{S}_{L}^{\ensuremath{-}4/7}$, where ${S}_{L}$ is the outer-scale ($L$) Lundquist number and $\ensuremath{\lambda}$ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum $E({k}_{\ensuremath{\perp}})\ensuremath{\propto}{k}_{\ensuremath{\perp}}^{\ensuremath{-}5/2}$, where ${k}_{\ensuremath{\perp}}$ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas ($Pm$), where the reconnection scale is found to be $\ensuremath{\lambda}/L\ensuremath{\sim}{S}_{L}^{\ensuremath{-}4/7}P{m}^{\ensuremath{-}2/7}$.

Magnetic field fluctuations in MHD turbulence can be viewed as current sheets that are progressively more anisotropic at smaller scales. As suggested by Loureiro & Boldyrev (2017) and Mallet et al (2017), below a certain critical thickness $\lambda_c$ such current sheets become tearing-unstable. We propose that the tearing instability changes the effective alignment of the magnetic field lines in such a way as to balance the eddy turnover rate at all scales smaller than $\lambda_c$. As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as $\theta \sim (\lambda/\lambda_*)^{-4/5+\beta}$, where $\lambda_*\sim L_0 S_0^{-3/4}$ is the resistive dissipation scale. Here $L_0$ is the outer scale of the turbulence, $S_0$ is the corresponding Lundquist number, and {$0\leq \beta, Comment: submitted for publication

Magnetic dynamo action caused by the magnetorotational instability is studied in the shearing-box approximation with no imposed net magnetic flux. Consistent with recent studies, the dynamo action is found to be sensitive to the aspect ratio of the box: it is much easier to obtain in tall boxes (stretched in the direction normal to the disk plane) than in long boxes (stretched in the radial direction). Our direct numerical simulations indicate that the dynamo is possible in both cases, given a large enough magnetic Reynolds number. To explain the relatively larger effort required to obtain the dynamo action in a long box, we propose that the turbulent eddies caused by the instability most efficiently fold and mix the magnetic field lines in the radial direction. As a result, in the long box the scale of the generated strong azimuthal (stream-wise directed) magnetic field is always comparable to the scale of the turbulent eddies. In contrast, in the tall box the azimuthal magnetic flux spreads in the vertical direction over a distance exceeding the scale of the turbulent eddies. As a result, different vertical sections of the tall box are permeated by large-scale nonzero azimuthal magnetic fluxes, facilitating the instability. In agreement with this picture, the cases when the dynamo is efficient are characterized by a strong intermittency of the local azimuthal magnetic fluxes., Comment: 7 pages, 9 figures, 1 table

This paper summarizes the outcomes from the Turbulent Flow Simulation at the Exascale: Opportunities and Challenges Workshop, which was held 4-5 August 2015, and was sponsored by the U.S. Department of Energy Office of Advanced Scientific Computing Research. The workshop objective was to define and describe the challenges and opportunities that computing at the exascale will bring to turbulent-flow simulations in applied science and technology. The need for accurate simulation of turbulent flows is evident across the U.S. Department of Energy applied-science and engineering portfolios, including combustion, plasma physics, nuclear-reactor physics, wind energy, and atmospheric science. The workshop brought together experts in turbulent-flow simulation, computational mathematics, and high-performance computing. Building upon previous ASCR workshops on exascale computing, participants defined a research agenda and path forward that will enable scientists and engineers to continually leverage, engage, and direct advances in computational systems on the path to exascale computing.

Turbulence is ubiquitous in plasmas, leading to rich dynamics characterized by irregularity, irreversibility, energy fluctuations across many scales, and energy transfer across many scales. Another fundamental and generic feature of turbulence, although sometimes overlooked, is the inhomogeneous dissipation of energy in space and in time. This is a consequence of intermittency, the scale-dependent inhomogeneity of dynamics caused by fluctuations in the turbulent cascade. Intermittency causes turbulent plasmas to self-organize into coherent dissipative structures, which may govern heating, diffusion, particle acceleration, and radiation emissions. In this paper, we present recent progress on understanding intermittency in incompressible magnetohydrodynamic turbulence with a strong guide field. We focus on the statistical analysis of intermittent dissipative structures, which occupy a small fraction of the volume but arguably account for the majority of energy dissipation. We show that, in our numerical simulations, intermittent structures in the current density, vorticity, and Els\"{a}sser vorticities all have nearly identical statistical properties. We propose phenomenological explanations for the scalings based on general considerations of Els\"{a}sser vorticity structures. Finally, we examine the broader implications of intermittency for astrophysical systems., Comment: 24 pages, 6 figures, to appear in Physics of Plasmas

Magnetohydrodynamic (MHD) turbulence is pervasive in astrophysical systems. Recent high-resolution numerical simulations suggest that the energy spectrum of strong incompressible MHD turbulence is $E(k_{\perp})\propto k_{\perp}^{-3/2}$. So far, there has been no phenomenological theory that simultaneously explains this spectrum and satisfies the exact analytic relations for MHD turbulence due to Politano & Pouquet. Indeed, the Politano-Pouquet relations are often invoked to suggest that the spectrum of MHD turbulence instead has the Kolmogorov scaling -5/3. Using geometrical arguments and numerical tests, here we analyze this seeming contradiction and demonstrate that the -3/2 scaling and the Politano-Pouquet relations are reconciled by the phenomenon of scale-dependent dynamic alignment that was recently discovered in MHD turbulence.

We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model. We present the numerical solution of the model for the practically important case of Kolmogorov distribution of velocity fluctuations, with a large magnetic Reynolds number. We find that in contrast to the nonhelical case where growing magnetic fields are described by a few bound eigenmodes concentrated inside the inertial interval of the velocity field, in the helical case the number of bound eigenmodes considerably increases; moreover, new unbound eigenmodes appear. Both bound and unbound eigenmodes contribute to the large-scale magnetic field. This indicates a limited applicability of the conventional alpha model of a large-scale dynamo action, which captures only unbound modes., Comment: 10 pages, 1 figure (with minor changes to match published version)

Interactions of plasma motion with magnetic fields occur in nature and in the laboratory in an impressively broad range of scales, from megaparsecs in astrophysical systems to centimeters in fusion devices. The fact that such an enormous array of phenomena can be effectively studied lies in the existence of fundamental scaling laws in plasma turbulence, which allow one to scale the results of analytic and numerical modeling to the sized of galaxies, velocities of supernovae explosions, or magnetic fields in fusion devices. Magnetohydrodynamics (MHD) provides the simplest framework for describing magnetic plasma turbulence. Recently, a number of new features of MHD turbulence have been discovered and an impressive array of thought-provoking phenomenological theories have been put forward. However, these theories have conflicting predictions, and the currently available numerical simulations are not able to resolve the contradictions. MHD turbulence exhibits a variety of regimes unusual in regular hydrodynamic turbulence. Depending on the strength of the guide magnetic field it can be dominated by weakly interacting Alfv\'en waves or strongly interacting wave packets. At small scales such turbulence is locally anisotropic and imbalanced (cross-helical). In a stark contrast with hydrodynamic turbulence, which tends to ``forget'' global constrains and become uniform and isotropicmore » at small scales, MHD turbulence becomes progressively more anisotropic and unbalanced at small scales. Magnetic field plays a fundamental role in turbulent dynamics. Even when such a field is not imposed by external sources, it is self-consistently generated by the magnetic dynamo action. This project aims at a comprehensive study of universal regimes of magnetic plasma turbulence, combining the modern analytic approaches with the state of the art numerical simulations. The proposed study focuses on the three topics: weak MHD turbulence, which is relevant for laboratory devices, the solar wind, solar corona heating, and planetary magnetospheres; strong MHD turbulence, which is relevant for fusion devices, star formation, cosmic rays acceleration, scattering and trapping in galaxies, as well as many aspects of dynamics, distribution and composition of space plasmas, and the process of magnetic dynamo action, which explains the generation and the structure of magnetic fields in turbulent plasmas. The planned work will aim at developing new analytic approaches, conducting new numerical simulations with currently unmatched resolution, and training students in the methods of the modern theory of plasma turbulence. The work will be performed at the University of Wisconsin--Madison.« less

We propose a self-similar kinetic theory of thermal conductivity in a magnetized plasma, and discuss its application to the solar wind. We study a collisional kinetic equation in a spatially expanding magnetic flux tube, assuming that the magnetic field strength, the plasma density, and the plasma temperature decline as power laws of distance along the tube. We demonstrate that the electron kinetic equation has a family of scale-invariant solutions for a particular relation among the magnetic-, density-, and temperature-scaling exponents. These solutions describe the heat flux as a function of the temperature Knudsen number $\ensuremath{\gamma}$, which we require to be constant along the flux tube. We observe that self-similarity may be realized in the solar wind; for the Helios data $0.3--1\text{ }\text{ }\mathrm{AU}$ we find that the scaling exponents for density, temperature, and heat flux are close to those dictated by scale invariance. We find steady-state solutions of the self-similar kinetic equation numerically, and show that these solutions accurately reproduce the electron strahl population seen in the solar wind, as well as the measured heat flux.

The local properties of turbulence driven by the magnetorotational instability (MRI) in rotating, shearing flows are studied in the framework of a shearing-box model. Based on numerical simulations, we propose that the MRI-driven turbulence comprises two components: the large-scale shear-aligned strong magnetic field and the small-scale fluctuations resembling magnetohydrodynamic (MHD) turbulence. The energy spectrum of the large-scale component is close to $k^{-2}$, whereas the spectrum of the small-scale component agrees with the spectrum of strong MHD turbulence $k^{-3/2}$. While the spectrum of the fluctuations is universal, the outer-scale characteristics of the turbulence are not; they depend on the parameters of the system, such as the net magnetic flux. However, there is remarkable universality among the allowed turbulent states -- their intensity $v_0$ and their outer scale $\lambda_0$ satisfy the balance condition $v_0/\lambda_0\sim \mathrm d\Omega/\mathrm d\ln r$, where $\mathrm d\Omega/\mathrm d\ln r$ is the local orbital shearing rate of the flow. Finally, we find no sustained dynamo action in the $\mathrm{Pm}=1$ zero net-flux case for Reynolds numbers as high as $45\,000$, casting doubts on the existence of an MRI dynamo in the $\mathrm{Pm}\leq 1$ regime., Comment: 5 pages, 6 figures, 1 table

We sought to determine the scale of scintillation in the interstellar plasma of PSR J0437-4715. We used the Very Long Baseline Array to obtain scintillation amplitude and phase data, from dynamic spectra at 327 MHz. We observe two scales of scintillation of pulsar PSR J0437-4715, differing by more than an order of magnitude in scintillation bandwidth. The wider-bandwidth scale of scintillation that we observe indicates less scattering for this pulsar than for other nearby pulsars, except for PSR B0950+08., Comment: 7 pages, 4 figures, submitted to Astronomy & Astrophysics

Radio waves propagating from distant pulsars in the interstellar medium (ISM), are refracted by electron density inhomogeneities, so that the intensity of observed pulses fluctuates with time. The theory relating the observed pulse time-shapes to the electron-density correlation function has developed for 30 years, however, two puzzles have remained. First, observational scaling of pulse broadening with the pulsar distance is anomalously strong; it is consistent with the standard model only when non-uniform statistics of electron fluctuations along the line of sight are assumed. Second, the observed pulse shapes are consistent with the standard model only when the scattering material is concentrated in a narrow slab between the pulsar and the Earth. We propose that both paradoxes are resolved at once if one assumes stationary and uniform, but non-Gaussian statistics of the electron-density distribution. Such statistics must be of Levy type, and the propagating ray should exhibit a Levy flight. We propose that a natural realization of such statistics may be provided by the interstellar medium with random electron-density discontinuities. We develop a theory of wave propagation in such a non-Gaussian random medium, and demonstrate its good agreement with observations. The qualitative introduction of the approach and the resolution of the anomalous-scaling paradox was presented earlier in [PRL 91, 131101 (2003); ApJ 584, 791 (2003)]., Comment: 27 pages, changes to match published version

We discuss a model for driven supersonic, super-Alfvenic MHD turbulence that is believed to govern the structure of molecular clouds. Such turbulence is highly intermittent; we describe its statistical properties by obtaining scaling of velocity-difference structure functions. This scaling was analytically predicted in Boldyrev (2002), confirmed in numerical simulations by Boldyrev et al. (2002), and discovered in observations by Padoan et al. (2003).

We present the new model for interstellar scintillations, which assumes that the electron density fluctuations causing the scintillations obey Levy statistics rather than Gaussian statistics, as was thought previously. Our model explains the observed anomalous scaling of the signal time-width with respect to the pulsar distance, which remained a puzzle for more than 30 years.

We compute the structure function scaling of the integrated intensity images of two J=1-0 13CO maps of Taurus and Perseus. The scaling exponents of the structure functions follow the velocity scaling of supersonic turbulence, suggesting that turbulence plays an important role in the fragmentation of cold interstellar clouds. The data also allows to verify the validity of the two basic assumptions of the hierarchical symmetry model, originally proposed for the derivation of the velocity structure function scaling. This shows that the same hierarchical symmetry holds for the projected density field of cold interstellar clouds., submitted to ApJ

We present a direct numerical and analytical study of driven supersonic MHD turbulence that is believed to govern the dynamics of star-forming molecular clouds. We describe statistical properties of the turbulence by measuring the velocity difference structure functions up to the fifth order. In particular, the velocity power spectrum in the inertial range is found to be close to E(k) \~ k^{-1.74}, and the velocity difference scales as ~ L^{0.42}. The results agree well with the Kolmogorov--Burgers analytical model suggested for supersonic turbulence in [astro-ph/0108300]. We then generalize the model to more realistic, fractal structure of molecular clouds, and show that depending on the fractal dimension of a given molecular cloud, the theoretical value for the velocity spectrum spans the interval [-1.74 ... -1.89], while the corresponding window for the velocity difference scaling exponent is [0.42 ... 0.78]., Comment: 17 pages, 6 figures included

It has recently been proposed (Loureiro & Boldyrev 2017; Mallet et al. 2017) that the inertial interval in magnetohydrodynamic (MHD) turbulence is terminated at small scales not by a Kolmogorov-like dissipation region, but rather by a new sub-inertial interval mediated by tearing instability. However, many astrophysical plasmas are nearly collisionless so that the MHD approximation is not applicable to turbulence at small scales. In this Letter, we propose the extension of the theory of reconnection-mediated turbulence to plasmas which are so weakly collisional that the reconnection occurring in the turbulent eddies is caused by electron inertia rather than by resistivity. We find that the transition scale to reconnection-mediated turbulence depends on the plasma beta and on the assumptions of the plasma turbulence model. However, in all cases analyzed, the energy spectra in the reconnection-mediated interval range from $E(k)dk\propto k^{-8/3}dk$ to $E(k)dk\propto k^{-3}dk$., submitted for publication

Energy dissipation in magnetohydrodynamic (MHD) turbulence is known to be highly intermittent in space, being concentrated in sheet-like coherent structures. Much less is known about intermittency in time, another fundamental aspect of turbulence which has great importance for observations of solar flares and other space/astrophysical phenomena. In this Letter, we investigate the temporal intermittency of energy dissipation in numerical simulations of MHD turbulence. We consider four-dimensional spatiotemporal structures, "flare events", responsible for a large fraction of the energy dissipation. We find that although the flare events are often highly complex, they exhibit robust power-law distributions and scaling relations. We find that the probability distribution of dissipated energy has a power law index close to -1.75, similar to observations of solar flares, indicating that intense dissipative events dominate the heating of the system. We also discuss the temporal asymmetry of flare events as a signature of the turbulent cascade., Comment: To appear in Physical Review Letters. 6 pages, 4 figures

The randomly driven Navier-Stokes equation without pressure in d-dimensional space is considered as a model of strong turbulence in a compressible fluid. We derive a closed equation for the velocity-gradient probability density function. We find the asymptotics of this function for the case of the gradient velocity field (Burgers turbulence), and provide a numerical solution for the two-dimensional case. Application of these results to the velocity-difference probability density function is discussed., latex, 5 pages, revised and enlarged

In this paper the Polyakov equation [Phys. Rev. E {bold 52}, 6183 (1995)] for the velocity-difference probability density functions, with the random Gaussian external force, with the correlation function {kappa}(y){approximately}1{minus}y{sup {alpha}}, is analyzed. Solutions for the cases {alpha}={l_brace}2,1/2,1{r_brace} are found, which agree very well with available numerical results. It is also argued that the stationary regime of Burgers turbulence can depend not only on the distribution of the external force, but also on the dissipative regularization. {copyright} {ital 1997} {ital The American Physical Society}

The complete project had two major goals — investigate MHD turbulence generated by counterpropagating Alfven modes, and study such processes in the LAPD device. In order to study MHD turbulence in numerical simulations, two codes have been used: full MHD, and reduced MHD developed specialy for this project. Quantitative numerical results are obtained through high-resolution simulations of strong MHD turbulence, performed through the 2010 DOE INCITE allocation. We addressed the questions of the spectrum of turbulence, its universality, and the value of the so-called Kolmogorov constant (the normalization coefficient of the spectrum). In these simulations we measured with unprecedented accuracy the energy spectra of magnetic and velocity fluctuations. We also studied the so-called residual energy, that is, the difference between kinetic and magnetic energies in turbulent fluctuations. In our analytic work we explained generation of residual energy in weak MHD turbulence, in the process of random collisions of counterpropagating Alfven waves. We then generalized these results for the case of strong MHD turbulence. The developed model explained generation of residual energy is strong MHD turbulence, and verified the results in numerical simulations. We then analyzed the imbalanced case, where more Alfven waves propagate in one direction. We found that spectralmore » properties of the residual energy are similar for both balanced and imbalanced cases. We then compared strong MHD turbulence observed in the solar wind with turbulence generated in numerical simulations. Nonlinear interaction of Alfv´en waves has been studied in the upgraded Large Plasma Device (LAPD). We have simulated the collision of the Alfven modes in the settings close to the experiment. We have created a train of wave packets with the apltitudes closed to those observed n the experiment, and allowed them to collide. We then saw the generation of the second harmonic, resembling that observed in the experiment.« less

The goal of the project was to develop a theory of turbulence in magnetized plasmas at large scales, that is, scales larger than the characteristic plasma microscales (ion gyroscale, ion inertial scale, etc.). Collisions of counter-propagating Alfven packets govern the turbulent cascade of energy toward small scales. It has been established that such an energy cascade is intrinsically anisotropic, in that it predominantly supplies energy to the modes with mostly field-perpendicular wave numbers. The resulting energy spectrum of MHD turbulence, and the structure of the fluctuations were studied both analytically and numerically. A new parallel numerical code was developed for simulating reduced MHD equations driven by an external force. The numerical setting was proposed, where the spectral properties of the force could be varied in order to simulate either strong or weak turbulent regimes. It has been found both analytically and numerically that weak MHD turbulence spontaneously generates a “condensate”, that is, concentration of magnetic and kinetic energy at small k{sub {parallel}}. A related topic that was addressed in the project is turbulent dynamo action, that is, generation of magnetic field in a turbulent flow. We were specifically concentrated on the generation of large-scale magnetic field compared to the scalesmore » of the turbulent velocity field. We investigate magnetic field amplification in a turbulent velocity field with nonzero helicity, in the framework of the kinematic Kazantsev-Kraichnan model.« less

Magnetic plasma turbulence is observed over a broad range of scales in the solar wind. We discuss the results of high-resolution numerical simulations of magnetohydrodynamic (MHD) turbulence that models plasma motion at large scales and the results of numerical simulations of kinetic-Alfven turbulence that models plasma motion at small, sub-proton scales. The simulations, with numerical resolutions up to 20483 mesh points in the MHD case and 5123 points in kinetic-Alfven case and statistics accumulated over 30 to 150 eddy turnover times, constitute, to the best of our knowledge, the largest statistical sample of steadily driven three dimensional MHD and kinetic-Alfven turbulence to date.

The nature of subproton scale fluctuations in the solar wind is an open question, partly because two similar types of electromagnetic turbulence can occur: kinetic Alfvén turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfvén turbulence, has negligible power in density fluctuations. In this Letter, we present new observational data, as well as analytical and numerical results, to investigate this difference. These results show, for the first time, that the fluctuations well below the proton scale are predominantly kinetic Alfvén turbulence, and, if present at all, the whistler fluctuations make up only a small fraction of the total energy.

Two-dimensional weak turbulence of magnetosonic waves, propagating perpendicular to an external magnetic field in multi-ion and dusty plasmas, is considered. Kolmogorov spectra of the turbulence in a long-wave region are obtained. They are determined by decay interactions of the magnetosonic mode with an additional wave mode existing in the low-frequency region in such plasmas.

Recent observations indicate that kinetic and magnetic energies are not in equipartition in the solar wind turbulence. Rather, magnetic fluctuations are more energetic and have somewhat steeper energy spectrum compared to the velocity fluctuations. This leads to the presence of the so-called residual energy Er = Ev – Eb in the inertial interval of turbulence. This puzzling effect is addressed in the present paper in the framework of weak turbulence theory. Using a simple model of weakly colliding Alfven waves, we demonstrate that the kinetic-magnetic equipartition indeed gets broken as a result of nonlinear interaction of Alfven waves. We establish that magnetic energy is indeed generated more efficiently as a result of these interactions, which proposes an explanation for the solar wind observations.

In a collisionless “dusty” plasma, where both ion-sound and dust-sound waves exist, the local spectra of isotropic sound turbulence are obtained. They are determined by decays of ion-sound waves into ion-sound and dust-sound waves and by scattering of dust-sound waves on dust particles.

There is mounting evidence in solar wind observations and in numerical simulations that kinetic and magnetic energies are not in equipartition in magnetohydrodynamic turbulence. The origin of their mismatch, the residual energy E_r=E_v-E_b, is not well understood. In the present work this effect is studied analytically in the regime of weak magnetohydrodynamic turbulence. We find that residual energy is spontaneously generated by turbulent dynamics, and it has a negative sign, in good agreement with the observations. We obtain that the residual energy condenses around k_||=0 with its k_||-spectrum broadening linearly with k_perp, where k_|| and k_perp are the wavenumbers parallel and perpendicular to the background magnetic field, and the field-perpendicular spectrum of the residual energy has the scaling E_r(k_perp)\propto k_perp^{-1} in the inertial interval. These results are found to be in agreement with numerical simulations. We propose that residual energy plays a fundamental role in Alfvenic turbulence and it should be taken into account for correct interpretation of observational and numerical data., Comment: To match the version accepted to Astrophys. J. Letters; KITP Preprint

Amplification of magnetic field due to kinematic turbulent dynamo action is studied in the regime of small magnetic Prandtl numbers. Such a regime is relevant for planets and stars interiors, as well as for liquid metal laboratory experiments. A comprehensive analysis based on the Kazantsev-Kraichnan model is reported, which establishes the dynamo threshold and the dynamo growth rates for varying kinetic helicity of turbulent fluctuations. It is proposed that in contrast with the case of large magnetic Prandtl numbers, the kinematic dynamo action at small magnetic Prandtl numbers is significantly affected by kinetic helicity, and it can be made quite efficient with an appropriate choice of the helicity spectrum., 4 pages, 3 figures, accepted to Physical Review Letters

We report the results of an extensive set of direct numerical simulations of forced, incompressible, magnetohydrodynamic turbulence with a strong guide field. The aim is to resolve the controversy regarding the power law exponent (\alpha, say) of the field perpendicular energy spectrum E(k_\perp) \propto k_\perp ^ {\alpha}. The two main theoretical predictions, \alpha=-3/2 and \alpha=-5/3, have both received some support from numerical simulations carried out by different groups. Our simulations have a resolution of 512^3 mesh points, a strong guide field, an anisotropic simulation domain, and implement a broad range of large-scale forcing routines, including those previously reported in the literature. Our findings indicate that the spectrum of well developed, strong incompressible MHD turbulence with a strong guide field is E(k_{\perp})\propto k_{\perp}^{-3/2}., Comment: 4 pages, 2 figures

Strong incompressible three-dimensional magnetohydrodynamic turbulence is investigated by means of high resolution direct numerical simulations. The simulations show that the configuration space is characterized by regions of positive and negative cross-helicity, corresponding to highly aligned or anti-aligned velocity and magnetic field fluctuations, even when the average cross-helicity is zero. To elucidate the role of cross-helicity, the spectra and structure of turbulence are obtained in imbalanced regions where cross-helicity is non-zero. When averaged over regions of positive and negative cross-helicity, the result is consistent with the simulations of balanced turbulence. An analytical explanation for the obtained results is proposed., Comment: 4 pages, 4 figures

Recent numerical and observational studies contain conflicting reports on the spectrum of magnetohydrodynamic turbulence. In an attempt to clarify the issue we investigate anisotropic incompressible magnetohydrodynamic turbulence with a strong guide field $B_0$. We perform numerical simulations of the reduced MHD equations in a special setting that allows us to elucidate the transition between weak and strong turbulent regimes. Denote $k_{\|}$, $k_\perp$ characteristic field-parallel and field-perpendicular wavenumbers of the fluctuations, and $b_{\lambda}$ the fluctuating field at the scale $\lambda\sim 1/k_{\perp}$. We find that when the critical balance condition, $k_{\|}B_0\sim k_{\perp} b_{\lambda}$, is satisfied, the turbulence is strong, and the energy spectrum is $E(k_{\perp})\propto k^{-3/2}_{\perp}$. As the $k_{\|}$ width of the spectrum increases, the turbulence rapidly becomes weaker, and in the limit $k_{\|}B_0\gg k_{\perp} b_{\lambda}$, the spectrum approaches $E(k_{\perp})\propto k_{\perp}^{-2}$. The observed sensitivity of the spectrum to the balance of linear and nonlinear interactions may explain the conflicting numerical and observational findings where this balance condition is not well controlled., Comment: 4 pages, 2 figures

Recent observations reveal that magnetic turbulence in the nearly colisionless solar wind plasma extends to scales smaller than the plasma microscales, such as ion gyroradius and ion inertial length. Measured breaks in the spectra of magnetic and density fluctuations at high frequencies are thought to be related to the transition from large-scale hydromagnetic to small-scale kinetic turbulence. The scales of such transitions and the responsible physical mechanisms are not well understood however. In the present work we emphasize the crucial role of the plasma parameters in the transition to kinetic turbulence, such as the ion and electron plasma beta, the electron to ion temperature ratio, the degree of obliquity of turbulent fluctuations. We then propose an explanation for the spectral breaks reported in recent observations., 9 pages, 7 figures. A few typos found in the published version are corrected

Motivated by recent analytic predictions, we report numerical evidence showing that in driven incompressible magnetohydrodynamic turbulence the magnetic- and velocity-field fluctuations locally tend to align the directions of their polarizations. This dynamic alignment is stronger at smaller scales with the angular mismatch between the polarizations decreasing with the scale \lambda approximately as \theta_\lambda ~ \lambda^{1/4}. This can naturally lead to a weakening of the nonlinear interactions and provide an explanation for the energy spectrum E(k) ~ k^{-3/2} that is observed in numerical experiments of strongly magnetized turbulence., Comment: 4 pages, 2 figures, minor changes to match published version