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Alfv\'enic interactions which transfer energy from large to small spatial scales lie at the heart of magnetohydrodynamic turbulence. An important feature of the turbulence is the generation of negative residual energy -- excess energy in magnetic fluctuations compared to velocity fluctuations. By contrast, an MHD Alfv\'en wave has equal amounts of energy in fluctuations of each type. Alfv\'enic quasimodes that do not satisfy the Alfv\'en wave dispersion relation and exist only in the presence of a nonlinear term can contain either positive or negative residual energy, but until now an intuitive physical explanation for why negative residual energy is preferred has remained elusive. This paper shows that the equations of reduced MHD are symmetric in that they have no intrinsic preference for one sign of the residual energy over the other. An initial state that is not an exact solution to the equations can break this symmetry in a way that leads to net-negative residual energy generation. Such a state leads to a solution with three distinct parts: nonresonant Alfv\'enic quasimodes, normal modes produced to satisfy initial conditions, and resonant normal modes that grow in time. The latter two parts strongly depend on initial conditions; the resulting symmetry breaking leads to net-negative residual energy both in Alfv\'enic quasimodes and $\omega=k_\parallel{V_A}=0$ modes. These modes have net-positive residual energy in the equivalent boundary value problem, suggesting that the initial value setup is a better match for solar wind turbulence., Comment: 19 pages, 1 figure

We carry out a population study of magnetized radio filaments in the Galactic center using MeerKAT data by focusing on the spacing between the filaments that are grouped. The morphology of a sample of 43 groupings containing 174 magnetized radio filaments are presented. Many grouped filaments show harp-like, fragmented cometary tail-like, or loop-like structures in contrast to many straight filaments running mainly perpendicular to the Galactic plane. There are many striking examples of a single filament splitting into two prongs at a junction, suggestive of a flow of plasma along the filaments. Spatial variations in spectral index, brightness, bending and sharpening along the filaments indicate that they are evolving on a 10^{5-6}-year time scale. The mean spacings between parallel filaments in a given grouping peaks at $\sim16''$. We argue by modeling that the filaments in a grouping all lie on the same plane and that the groupings are isotropically oriented in 3D space. One candidate for the origin of filamentation is interaction with an obstacle, which could be a compact radio source, before a filament splits and bends into multiple filaments. In this picture, the obstacle or sets the length scale of the separation between the filaments. Another possibility is synchrotron cooling instability occurring in cometary tails formed as a result of the interaction of cosmic-ray driven Galactic center outflow with obstacles such as stellar winds. In this picture, the mean spacing and the mean width of the filaments are expected to be a fraction of a parsec, consistent with observed spacing., Comment: 53 pages, 32 figures, MNRS (in press)

This white paper submitted for 2020 Decadal Assessment of Plasma Science concerns the importance of multi-spacecraft missions to address fundamental questions concerning plasma turbulence. Plasma turbulence is ubiquitous in the universe, and it is responsible for the transport of mass, momentum, and energy in such diverse systems as the solar corona and wind, accretion discs, planet formation, and laboratory fusion devices. Turbulence is an inherently multi-scale and multi-process phenomenon, coupling the largest scales of a system to sub-electron scales via a cascade of energy, while simultaneously generating reconnecting current layers, shocks, and a myriad of instabilities and waves. The solar wind is humankind's best resource for studying the naturally occurring turbulent plasmas that permeate the universe. Since launching our first major scientific spacecraft mission, Explorer 1, in 1958, we have made significant progress characterizing solar wind turbulence. Yet, due to the severe limitations imposed by single point measurements, we are unable to characterize sufficiently the spatial and temporal properties of the solar wind, leaving many fundamental questions about plasma turbulence unanswered. Therefore, the time has now come wherein making significant additional progress to determine the dynamical nature of solar wind turbulence requires multi-spacecraft missions spanning a wide range of scales simultaneously. A dedicated multi-spacecraft mission concurrently covering a wide range of scales in the solar wind would not only allow us to directly determine the spatial and temporal structure of plasma turbulence, but it would also mitigate the limitations that current multi-spacecraft missions face, such as non-ideal orbits for observing solar wind turbulence. Some of the fundamentally important questions that can only be addressed by in situ multipoint measurements are discussed., Comment: 6 pages, submitted for the Plasma 2020 Decadal Survey

This is a science white paper submitted to the Astro-2020 and Plasma-2020 Decadal Surveys. The paper describes the present status and emerging opportunities in Extreme Plasma Astrophysics -- a study of astrophysically-relevant plasma processes taking place under extreme conditions that necessitate taking into account relativistic, radiation, and QED effects., Comment: A science white paper submitted to the Astro-2020 and Plasma-2020 Decadal Surveys. 7 pages including cover page and references. Paper updated in late March 2019 to include a several additional co-authors and references, and a few small changes

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

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 $E(k)dk\propto k^{-3}dk$., Comment: submitted for publication

We present a combined observational and theoretical analysis to investigate the nature of plasma turbulence at kinetic scales in the Earth's magnetosheath. In the first decade of the kinetic range, just below the ion gyroscale, the turbulence was found to be similar to that in the upstream solar wind: predominantly anisotropic, low-frequency and kinetic Alfv\'en in nature. A key difference, however, is that the magnetosheath ions are typically much hotter than the electrons, $T_\mathrm{i}\gg T_\mathrm{e}$, which, together with $\beta_\mathrm{i}\sim 1$, leads to a change in behaviour in the second decade, close to electron scales. The turbulence here is characterised by an increased magnetic compressibility, following a mode we term the inertial kinetic Alfv\'en wave, and a steeper spectrum of magnetic fluctuations, consistent with the prediction $E_B(k_\perp)\propto k_\perp^{-11/3}$ that we obtain from a set of nonlinear equations. This regime of plasma turbulence may also be relevant for other astrophysical environments with $T_\mathrm{i}\gg T_\mathrm{e}$, such as the solar corona, hot accretion flows, and regions downstream of collisionless shocks.

The current understanding of 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-sheet-like structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $\lambda\sim L S_L^{-4/7}$, where $S_L$ is the outer-scale ($L$) Lundquist number and $\lambda$ 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 sub-inertial, reconnection interval of MHD turbulence, with the Fourier energy spectrum $E(k_\perp)\propto k_\perp^{-5/2}$, where $k_\perp$ 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 $\lambda/L\sim S_L^{-4/7}Pm^{-2/7}$., Comment: submitted for publication

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., Comment: 6 pages, 4 figures

The inertial-interval energy spectrum of strong magnetohydrodynamic (MHD) turbulence with a uniform background magnetic field was observed numerically to be close to $k^{-3/2}$ by a number of independent groups. A dissenting opinion has been voiced by Beresnyak, A. 2011, PRL, 106, 075001-. 2012, MNRAS, 422, 3495-. 2014, ApJ, 784, L20 that the spectral scaling is close to $k^{-5/3}$. The conclusions of these papers are however incorrect as they are based on numerical simulations that are drastically unresolved, so that the discrete numerical scheme does not approximate the physical solution at the scales where the measurements are performed. These results have been rebutted in our more detailed papers Perez, J. C., Mason, J., Boldyrev, S., & Cattaneo, F. 2012, PRX, 2, 041005-. 2014, ApJL, 793, L13; here, by popular demand, we present a brief and simple explanation of our major criticism of Beresnyak's work., Comment: An extended discussion of the results presented in this comment can be found in Perez et.al., ApJL, 793, L13 (2014)

Magnetohydrodynamic (MHD) turbulence in the majority of natural systems, including the interstellar medium, the solar corona, and the solar wind, has Reynolds numbers far exceeding the Reynolds numbers achievable in numerical experiments. Much attention is therefore drawn to the universal scaling properties of small-scale fluctuations, which can be reliably measured in the simulations and then extrapolated to astrophysical scales. However, in contrast with hydrodynamic turbulence, where the universal structure of the inertial and dissipation intervals is described by the Kolmogorov self-similarity, the scaling for MHD turbulence cannot be established based solely on dimensional arguments due to the presence of an intrinsic velocity scale -- the Alfven velocity. In this Letter, we demonstrate that the Kolmogorov first self-similarity hypothesis cannot be formulated for MHD turbulence in the same way it is formulated for the hydrodynamic case. Besides profound consequences for the analytical consideration, this also imposes stringent conditions on numerical studies of MHD turbulence. In contrast with the hydrodynamic case, the discretization scale in numerical simulations of MHD turbulence should decrease faster than the dissipation scale, in order for the simulations to remain resolved as the Reynolds number increases., Comment: Accepted and published in ApJL

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 Alfven turbulence and whistler turbulence. These two possibilities, however, have one key qualitative difference: whistler turbulence, unlike kinetic Alfven 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. The results show, for the first time, that the fluctuations well below the proton scale are predominantly kinetic Alfven turbulence, and, if present at all, the whistler fluctuations make up only a small fraction of the total energy.

A combination of observation, theory, modeling, and laboratory plasma experiments provides a multifaceted approach to develop a much greater understanding of how magnetic fields arise in galactic settings and how these magnetic fields mediate important processes that affect the dynamics, distribution, and composition of galactic plasmas. An important emphasis below is the opportunity to connect laboratory experiments to astrophysics. This approach is especially compelling for the galactic neighborhood, where the distribution and character of magnetic fields can be observed with greater detail than what is possible elsewhere in the universe. The ability to produce laboratory plasmas with unparalleled accessibility permits an even greater level of detail to be assessed and exposed. Theory and modeling provide fundamental ways to understand important processes, and they act as the bridge to connect experimental validation to astronomical observations. In many cases the studies that utilize this approach can make use of existing laboratory facilities, resulting in a cost that is quite small compared to the cost of measurements in dedicated space missions., Comment: 8 pages, white paper submitted to the Galactic Neighborhood (GAN) Panel

We consider the one-dimensional Burgers equation randomly stirred at large scales by a Gaussian short-time correlated force. Using the method of dissipative anomalies, we obtain velocity and velocity-difference probability density functions and confirm the results with high-resolution numerical simulations., Comment: 4 pages, 3 figures, improved numerics, matches the published version

We develop a model of thin turbulent accretion discs supported by magnetic pressure of turbulent magnetic fields. This applies when the turbulent kinetic and magnetic energy densities are greater than the thermal energy density in the disc. Whether such discs survive in nature or not remains to be determined, but here we simply demonstrate that self-consistent solutions exist when the alpha-prescription for the viscous stress, similar to that of the original Shakura-Sunyaev model, is used. We show that \alpha \sim 1 for the strongly magnetized case and we calculate the radial structure and emission spectra from the disc in the regime when it is optically thick. Strongly magnetized optically thick discs can apply to the full range of disc radii for objects < 10^{-2} of the Eddington luminosity or for the outer parts of discs in higher luminosity sources. In the limit that the magnetic pressure is equal to the thermal or radiation pressure, our strongly magnetized disc model transforms into the Shakura-Sunyaev model with \alpha=1. Our model produces spectra quite similar to those of standard Shakura-Sunyaev models. In our comparative study, we also discovered a small discrepancy in the spectral calculations of Shakura and Sunyaev (1973)., Comment: 27 pages, 11 figures, Astron. Astroph. in press; shortened version accepted by A&A, all calculations and conclusions are unchanged

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

We reduce the problem of integer quantum Hall transition to a random rotation of an N-dimensional vector by an su(N) algebra, where only N specially selected generators of the algebra are nonzero. The group-theoretical structure revealed in this way allows us to obtain a new series of conservation laws for the equation describing the electron density evolution in the lowest Landau level. The resulting formalism is particularly well suited to numerical simulations, allowing us to obtain the critical exponent \nu numerically in a very simple way. We also suggest that if the number of nonzero generators is much less than N, the same model, in a certain intermediate time interval, describes percolating properties of a random incompressible steady two-dimensional flow. In other words, quantum Hall transition in a very smooth random potential inherits certain properties of percolation., Comment: 4 pages, 1 figure

The Batchelor passive advection is an advection by a smooth velocity field. If the velocity field is a delta-correlated in time random Gaussian process, then the problem is reduced to quantum mechanics of fluctuating velocity gradient u'(t). For the finite-time correlated velocity field, such a reduction does not exist. To illustrate this point, the second moment of a passively advected magnetic field is considered, and the stochastic calculus is used to find finite-time corrections to its growth rate. The growth rate depends on large scale properties of the velocity field. Moreover, the problem is not universal with respect to the short-time regularization: different regularizations give different answers for the growth rate., Comment: 4 pages, 1 figure

We study geometric properties of a random Gaussian short-time correlated velocity field by considering statistics of a passively advected metric tensor. That describes universal properties of fluctuations of tensor objects frozen into the fluid and passively advected by it. The problem of one-point statistics of co- and contravariant tensors is solved exactly, provided the advected fields do not reach dissipative scales, which would break the symmetry of the problem. Asymptotic in time duality of the problem is established, which in the three-dimensional case relates the probabilities of the volume deformations into "tubes" and into "sheets"., Comment: latex, 8 pages

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., Comment: latex, 5 pages, revised and enlarged

Magnetosonic waves are intensively studied due to their importance in space plasmas and also in fusion plasmas where they are used in particle acceleration and heating experiments. In the present paper we investigate the magnetosonic waves propagating in a multi-ion-species plasma perpendicular to an external magnetic field. Due to the presence of several ion species, this mode splits into two branches: high- and low-frequency modes. This opens a new channel of nonlinear interactions (between these two modes), and qualitatively changes the picture of turbulence in the long-wave region. Using the exact kinetic approach, we derive a general system describing the propagation of nonlinearly coupled high- and low-frequency waves. This system includes the KdV, Boussinesq, and Zakharov equations as limiting cases. Solitary solutions of the system of coupled equations are obtained., Comment: 15 pages, Latex

The randomly driven Burgers equation with pressure is considered as a 1D model of strong turbulence of compressible fluid. It is shown that infinitely small pressure provides a finite effect on the velocity and density statistics and this case therefore is qualitatively different from turbulence without pressure. We establish the corresponding operator product expansion and predict the intermittent velocity- difference and mass-difference PDFs. We then apply the developed methods to the statistics of a passive scalar advected by the Burgers field., Comment: 4 pages, revtex

In this note the Polyakov equation [Phys. Rev. E {\bf 52} (1995) 6183] for the velocity-difference PDF, with the exciting force correlation function $\kappa (y)\sim1-y^{\alpha}$ is analyzed. Several solvable cases are considered, which are in a good agreement with available numerical results. Then it is shown how the method developed by A. Polyakov can be applied to turbulence with short-scale-correlated forces, a situation considered in models of self-organized criticality., Comment: 11 pages, Latex