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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 present a kinetic stability analysis of the solar wind electron distribution function consisting of the Maxwellian core and the magnetic-field aligned strahl, a superthermal electron beam propagating away from the sun. We use an electron strahl distribution function obtained as a solution of a weakly collisional drift-kinetic equation, representative of a strahl affected by Coulomb collisions but unadulterated by possible broadening from turbulence. This distribution function is essentially non-Maxwellian and varies with the heliospheric distance. The stability analysis is performed with the Vlasov-Maxwell linear solver LEOPARD. We find that depending on the heliospheric distance, the core-strahl electron distribution becomes unstable with respect to sunward-propagating kinetic-Alfv\'en, magnetosonic, and whistler modes, in a broad range of propagation angles. The wavenumbers of the unstable modes are close to the ion inertial scales, and the radial distances at which the instabilities first appear are on the order of 1 AU. However, we have not detected any instabilities driven by resonant wave interactions with the superthermal strahl electrons. Instead, the observed instabilities are triggered by a relative drift between the electron and ion cores necessary to maintain zero electric current in the solar wind frame (ion frame). Contrary to strahl distributions modeled by shifted Maxwellians, the electron strahl obtained as a solution of the kinetic equation is stable. Our results are consistent with the previous studies based on a more restricted solution for the electron strahl., Comment: 8 pages, 6 figures. Accepted by Monthly Notices of the Royal Astronomical Society. Removed references from abstract, added references in body. Other minor editorial changes

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

In weakly collisional plasma environments with sufficiently low electron beta, Alfv\'enic turbulence transforms into inertial Alfv\'enic turbulence at scales below the electron skin depth, ${k}_{\ensuremath{\perp}}{d}_{e}\ensuremath{\gtrsim}1$. We argue that, in inertial Alfv\'enic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as $\mathrm{cos}{\ensuremath{\alpha}}_{k}\ensuremath{\propto}{k}_{\ensuremath{\perp}}^{\ensuremath{-}1}$. The kinetic and magnetic energy spectra scale as $\ensuremath{\propto}{k}_{\ensuremath{\perp}}^{\ensuremath{-}5/3}$ and $\ensuremath{\propto}{k}_{\ensuremath{\perp}}^{\ensuremath{-}11/3}$, respectively. As a result of the dual direct cascade, the generalized helicity spectrum scales as $\ensuremath{\propto}{k}_{\ensuremath{\perp}}^{\ensuremath{-}5/3}$, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the ${k}_{\ensuremath{\perp}}{d}_{e}\ensuremath{\gg}1$ range. Turbulent eddies exhibit a phase-space anisotropy ${k}_{\ensuremath{\parallel}}\ensuremath{\propto}{k}_{\ensuremath{\perp}}^{5/3}$, consistent with critically balanced inertial Alfv\'en fluctuations. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, and nonrelativistic pair plasmas, as well as to strongly rotating nonionized fluids.

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

For velocity and magnetic fields, the turbulent pressure and, more generally, the squared fields such as the components of the turbulent stress tensor, play important roles in astrophysics. For both one and three dimensions, we derive the equations relating the energy spectra of the fields to the spectra of their squares. We solve the resulting integrals numerically and show that for turbulent energy spectra of Kolmogorov type, the spectral slope of the stress spectrum is also of Kolmogorov type. For shallower turbulence spectra, the slope of the stress spectrum quickly approaches that of white noise, regardless of how blue the spectrum of the field is. For fully helical fields, the stress spectrum is elevated by about a factor of two in the subinertial range, while that in the inertial range remains unchanged. We discuss possible implications for understanding the spectrum of primordial gravitational waves from causally generated magnetic fields during cosmological phase transitions in the early universe. We also discuss potential diagnostic applications to the interstellar medium, where polarization and scintillation measurements characterize the square of the magnetic field., 7 pages, 9 figures, ApJ, in press

Recently, it has been realized that magnetic plasma turbulence and magnetic field reconnection are inherently related phenomena. Turbulent fluctuations generate regions of a sheared magnetic field that become unstable to the tearing instability and reconnection, thus modifying turbulence at the corresponding scales. In this contribution, we give a brief discussion of some recent results on tearing-mediated magnetic turbulence. We illustrate the main ideas of this rapidly developing field of study by concentrating on two important examples -- magnetohydrodynamic Alfv\'en turbulence and small-scale kinetic-Alfv\'en turbulence. Due to various potential applications of these phenomena in space physics and astrophysics, we specifically try not to overload the text by heavy analytical derivations, but rather present a qualitative discussion accessible to a non-expert in the theories of turbulence and reconnection., Comment: A book chapter in AGU Book "Solar and Heliospheric Plasma Structures" (to appear)

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

Alfv\'enic-type turbulence in strongly magnetized, low-beta pair plasmas is investigated. A coupled set of equations for the evolution of the magnetic and flow potentials are derived, covering both fluid and kinetic scales. In the fluid (MHD) range those equations are the same as for electron-ion plasmas, so turbulence at those scales is expected to be of the Alfv\'enic nature, exhibiting critical balance, dynamic alignment, and transition to a tearing mediated regime at small scales. The critical scale at which a transition to a tearing-mediated range occurs is derived, and the spectral slope in that range is predicted to be $k_\perp^{-8/3}$ (or $k_\perp^{-3}$, depending on details of the reconnecting configuration assumed). At scales below the electron (and positron) skin depth, it is argued that turbulence is dictated by a cascade of the inertial Alfv\'en wave, which we show to result in the magnetic energy spectrum $\propto k_\perp^{-11/3}$., Comment: submitted for publication

In this work, we analyze the kinetic stability of a solar wind electron distribution composed of core and strahl subpopulations. The core is modeled by a drifting Maxwellian distribution, while the strahl is modeled by an analytic function recently derived in (Horaites et al. 2018) from the collisional kinetic equation. We perform a numerical linear stability analysis using the LEOPARD solver (Astfalk & Jenko 2017), which allows for arbitrary gyrotropic distribution functions in a magnetized plasma. We find that for typical solar wind conditions, the core-strahl distribution is unstable to the kinetic Alfv��n and magnetosonic modes. The maximum growth rates for these instabilities occur at wavenumbers $k d_i \lesssim 1$, at moderately oblique angles of propagation, thus providing a potential source of kinetic-scale turbulence. In contrast with previous reports, we however do not find evidence for a whistler instability directly associated with the electron strahl. This may be related to the more realistic shape of the electron strahl distribution function adopted in our work. We therefore suggest that the whistler modes often invoked to explain anomalous scattering of strahl particles could appear as a result of nonlinear mode coupling and turbulent cascade originating at scales $k d_i \lesssim 1$., 7 pages, 7 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

The intermittent small-scale structure of turbulence governs energy dissipation in many astrophysical plasmas and is often believed to have universal properties for sufficiently large systems. In this work, we argue that small-scale turbulence in accretion disks is universal in the sense that it is insensitive to the magnetorotational instability (MRI) and background shear, and therefore indistinguishable from standard homogeneous magnetohydrodynamic (MHD) turbulence at small scales. We investigate the intermittency of current density, vorticity, and energy dissipation in numerical simulations of incompressible MHD turbulence driven by the MRI in a shearing box. We find that the simulations exhibit a similar degree of intermittency as in standard MHD turbulence. We perform a statistical analysis of intermittent dissipative structures and find that energy dissipation is concentrated in thin sheet-like structures that span a wide range of scales up to the box size. We show that these structures exhibit strikingly similar statistical properties to those in standard MHD turbulence. Additionally, the structures are oriented in the toroidal direction with a characteristic tilt of approximately 17.5 degrees, implying an effective guide field in that direction., Comment: 9 pages, 11 figures, to appear in Monthly Notices of the Royal Astronomical Society

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)

Energy dissipation is highly intermittent in turbulent plasmas, being localized in coherent structures such as current sheets. The statistical analysis of spatial dissipative structures is an effective approach to studying turbulence. In this paper, we generalize this methodology to investigate four-dimensional spatiotemporal structures, i.e., dissipative processes representing sets of interacting coherent structures, which correspond to flares in astrophysical systems. We develop methods for identifying and characterizing these processes, and then perform a statistical analysis of dissipative processes in numerical simulations of driven magnetohydrodynamic turbulence. We find that processes are often highly complex, long-lived, and weakly asymmetric in time. They exhibit robust power-law probability distributions and scaling relations, including a distribution of dissipated energy with power-law index near -1.75, indicating that intense dissipative events dominate the overall energy dissipation. We compare our results with the previously observed statistical properties of solar flares., Submitted to the Astrophysical Journal. 48 pages, 18 figures

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