Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence

Higher-order nonequilibrium term: Effective power density quantifying evolution towards or away from local thermodynamic equilibrium

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A leading research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here we introduce the "higher-order nonequilibrium term" (HORNET) effective power density, which quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, Pi-D, and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8% and 35% for electrons and ions, respectively, for reconnection; up to 67% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed.

Extended Magnetic Reconnection in Kinetic Plasma Turbulence

Magnetic reconnection and plasma turbulence are ubiquitous processes important for laboratory, space, and astrophysical plasmas. Reconnection has been suggested to play an important role in the energetics and dynamics of turbulence by observations, simulations, and theory for two decades. The fundamental properties of reconnection at kinetic scales, essential to understanding the general problem of reconnection in magnetized turbulence, remain largely unknown at present. Here, we present an application of the magnetic flux transport method that can accurately identify reconnection in turbulence to a three-dimensional simulation. Contrary to ideas that reconnection in turbulence would be patchy and unpredictable, highly extended reconnection X lines, on the same order of magnitude as the system size, form at kinetic scales. Extended X lines develop through bidirectional reconnection spreading. They satisfy critical balance characteristic of turbulence, which predicts the X-line extent at a given scale. These results present a picture of fundamentally extended reconnection in kinetic-scale turbulence.

Subion-Scale Turbulence Driven by Magnetic Reconnection

The interplay between plasma turbulence and magnetic reconnection remains an unsettled question in astrophysical and laboratory plasmas. Here, we report the first observational evidence that magnetic reconnection drives subion-scale turbulence in magnetospheric plasmas by transferring energy to small scales. We employ a spatial "coarse-grained" model of Hall magnetohydrodynamics, enabling us to measure the nonlinear energy transfer rate across scale ℓ at position x. Its application to Magnetospheric Multiscale mission data shows that magnetic reconnection drives intense energy transfer to subion-scales. This observational evidence is remarkably supported by the results from Hybrid Vlasov-Maxwell simulations of turbulence to which the coarse-grained model is also applied. These results can potentially answer some open questions on plasma turbulence in planetary environments.

Magnetic Field Annihilation in a Magnetotail Electron Diffusion Region With Electron-Scale Magnetic Island

We present observations in Earth's magnetotail by the Magnetospheric Multiscale spacecraft that are consistent with magnetic field annihilation, rather than magnetic topology change, causing fast magnetic-to-electron energy conversion in an electron-scale current sheet. Multi-spacecraft analysis for the magnetic field reconstruction shows that an electron-scale magnetic island was embedded in the observed electron diffusion region (EDR), suggesting an elongated shape of the EDR. Evidence for the annihilation was revealed in the form of the island growing at a rate much lower than expected for the standard X-type geometry of the EDR, which indicates that magnetic flux injected into the EDR was not ejected from the X-point or accumulated in the island, but was dissipated in the EDR. This energy conversion process is in contrast to that in the standard EDR of a reconnecting current sheet where the energy of antiparallel magnetic fields is mostly converted to electron bulk-flow energy. Fully kinetic simulation also demonstrates that an elongated EDR is subject to the formation of electron-scale magnetic islands in which fast but transient annihilation can occur. Consistent with the observations and simulation, theoretical analysis shows that fast magnetic diffusion can occur in an elongated EDR in the presence of nongyrotropic electron effects. We suggest that the annihilation in elongated EDRs may contribute to the dissipation of magnetic energy in a turbulent collisionless plasma.

Energy transfer in reconnection and turbulence

Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady energy transfer rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection dynamics fundamentally involves turbulence-like energy transfer.

Faster Form of Electron Magnetic Reconnection with a Finite Length X-Line

Observations in Earth's turbulent magnetosheath downstream of a quasiparallel bow shock reveal a prevalence of electron-scale current sheets favorable for electron-only reconnection where ions are not coupled to the reconnecting magnetic fields. In small-scale turbulence, magnetic structures associated with intense current sheets are limited in all dimensions. And since the coupling of ions are constrained by a minimum length scale, the dynamics of electron reconnection is likely to be 3D. Here, both 2D and 3D kinetic particle-in-cell simulations are used to investigate electron-only reconnection, focusing on the reconnection rate and associated electron flows. A new form of 3D electron-only reconnection spontaneously develops where the magnetic X-line is localized in the out-of-plane (z) direction. The consequence is an enhancement of the reconnection rate compared with two dimensions, which results from differential mass flux out of the diffusion region along z, enabling a faster inflow velocity and thus a larger reconnection rate. This outflow along z is due to the magnetic tension force in z just as the conventional exhaust tension force, allowing particles to leave the diffusion region efficiently along z unlike the 2D configuration.

Onset of inverse magnetic energy transfer in collisionless turbulent plasmas

Inverse magnetic energy transfer from small to large scales is a key physical process for the origin of large-scale strong magnetic fields in the universe. However, so far, from the magnetohydrodynamic perspective, the onset of inverse transfer is still not fully understood, especially the underlying dynamics. Here, we use both two-dimensional and three-dimensional particle-in-cell simulations to show the self-consistent dynamics of inverse transfer in collisionless decaying turbulent plasmas. Using the space filtering technique in theory and numerical analyses, we identify magnetic reconnection as the onset and fundamental drive for inverse transfer, where, specifically, the subscale electromotive force driven by magnetic reconnection do work on the large-scale magnetic field, resulting in energy transfer from small to large scales. The mechanism is also verified by the strong correlations in locations and characteristic scales between inverse transfer and magnetic reconnection.

A Case for Electron-Astrophysics

The smallest characteristic scales, at which electron dynamics determines the plasma behaviour, are the next frontier in space and astrophysical plasma research. The analysis of astrophysical processes at these scales lies at the heart of the research theme of electron-astrophysics. Electron scales are the ultimate bottleneck for dissipation of plasma turbulence, which is a fundamental process not understood in the electron-kinetic regime. In addition, plasma electrons often play an important role for the spatial transfer of thermal energy due to the high heat flux associated with their velocity distribution. The regulation of this electron heat flux is likewise not understood. By focussing on these and other fundamental electron processes, the research theme of electron-astrophysics links outstanding science questions of great importance to the fields of space physics, astrophysics, and laboratory plasma physics. In this White Paper, submitted to ESA in response to the Voyage 2050 call, we review a selection of these outstanding questions, discuss their importance, and present a roadmap for answering them through novel space-mission concepts.

Phase space transport in the interaction between shocks and plasma turbulence

The interaction of collisionless shocks with fully developed plasma turbulence is numerically investigated. Hybrid kinetic simulations, where a turbulent jet is slammed against an oblique shock, are employed to address the role of upstream turbulence on plasma transport. A technique, using coarse graining of the Vlasov equation, is proposed, showing that the particle transport strongly depends on upstream turbulence properties, such as strength and coherency. These results might be relevant for the understanding of acceleration and heating processes in space plasmas.

The multi-scale nature of the solar wind

The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free paths of all species, their inertial lengths, their gyration radii, and their Debye lengths. The characteristic timescales include the expansion time, the collision times, and the periods associated with gyration, waves, and oscillations. We review the past and present research into the multi-scale nature of the solar wind based on in-situ spacecraft measurements and plasma theory. We emphasize that couplings of processes across scales are important for the global dynamics and thermodynamics of the solar wind. We describe methods to measure in-situ properties of particles and fields. We then discuss the role of expansion effects, non-equilibrium distribution functions, collisions, waves, turbulence, and kinetic microinstabilities for the multi-scale plasma evolution.

Sources of solar energetic particles

Solar energetic particles are an integral part of the physical processes related with space weather. We present a review for the acceleration mechanisms related to the explosive phenomena (flares and/or coronal mass ejections, CMEs) inside the solar corona. For more than 40 years, the main two-dimensional cartoon representing our understanding of the explosive phenomena inside the solar corona remained almost unchanged. The acceleration mechanisms related to solar flares and CMEs also remained unchanged and were part of the same cartoon. In this review, we revise the standard cartoon and present evidence from recent global magnetohydrodynamic simulations that support the argument that explosive phenomena will lead to the spontaneous formation of current sheets in different parts of the erupting magnetic structure. The evolution of the large-scale current sheets and their fragmentation will lead to strong turbulence and turbulent reconnection during solar flares and turbulent shocks. In other words, the acceleration mechanism in flares and CME-driven shocks may be the same, and their difference will be the overall magnetic topology, the ambient plasma parameters, and the duration of the unstable driver. This article is part of the theme issue 'Solar eruptions and their space weather impact'.

Extended Magnetohydrodynamic Simulations of Decaying, Homogeneous, Approximately-Isotropic and Incompressible Turbulence

Incompressible magnetohydrodynamic (MHD) turbulence under influences of the Hall and the gyro-viscous terms was studied by means of direct numerical simulations of freely decaying, homogeneous and approximately isotropic turbulence. Numerical results were compared among MHD, Hall MHD, and extended MHD models focusing on differences of Hall and extended MHD turbulence from MHD turbulence at a fully relaxed state. Magnetic and kinetic energies, energy spectra, energy transfer, vorticity and current structures were studied. The Hall and gyro-viscous terms change the energy transfer in the equations of motions to be forward-transfer-dominant while the magnetic energy transfer remains backward-transfer-dominant. The gyro-viscosity works as a kind of hyper-diffusivity, attenuating the kinetic energy spectrum sharply at a high wave-number region. However, this term also induces high-vorticity events more frequently than MHD turbulence, making the turbulent field more intermittent. Vortices and currents were found to be transformed from sheet to tubular structures under the influences of the Hall and/or the gyro-viscous terms. These observations highlight features of fluid-dynamic aspect of turbulence in sub-ion-scales where turbulence is governed by the ion skin depth and ion Larmor radius.

Role of the Plasmoid Instability in Magnetohydrodynamic Turbulence

The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic (MHD) turbulence by means of high-resolution direct numerical simulations. At a sufficiently large magnetic Reynolds number (R_{m}=10^{6}), the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets. The disruption of current sheet structures facilitates the energy cascade towards small scales, leading to the breaking and steepening of the energy spectrum. In the plasmoid-mediated regime, the energy spectrum displays a scaling that is close to the spectral index -2.2 as proposed by recent analytic theories. We also demonstrate that the scale-dependent dynamic alignment exists in 2D MHD turbulence and the corresponding slope of the alignment angle is close to 0.25.

Electron magnetic reconnection without ion coupling in Earth's turbulent magnetosheath

Magnetic reconnection in current sheets is a magnetic-to-particle energy conversion process that is fundamental to many space and laboratory plasma systems. In the standard model of reconnection, this process occurs in a minuscule electron-scale diffusion region^1,2. On larger scales, ions couple to the newly reconnected magnetic-field lines and are ejected away from the diffusion region in the form of bi-directional ion jets at the ion Alfvén speed^3-5. Much of the energy conversion occurs in spatially extended ion exhausts downstream of the diffusion region ⁶ . In turbulent plasmas, which contain a large number of small-scale current sheets, reconnection has long been suggested to have a major role in the dissipation of turbulent energy at kinetic scales^7-11. However, evidence for reconnection plasma jetting in small-scale turbulent plasmas has so far been lacking. Here we report observations made in Earth's turbulent magnetosheath region (downstream of the bow shock) of an electron-scale current sheet in which diverging bi-directional super-ion-Alfvénic electron jets, parallel electric fields and enhanced magnetic-to-particle energy conversion were detected. Contrary to the standard model of reconnection, the thin reconnecting current sheet was not embedded in a wider ion-scale current layer and no ion jets were detected. Observations of this and other similar, but unidirectional, electron jet events without signatures of ion reconnection reveal a form of reconnection that can drive turbulent energy transfer and dissipation in electron-scale current sheets without ion coupling.

On the Collisionless Asymmetric Magnetic Reconnection Rate

A prediction of the steady state reconnection electric field in asymmetric reconnection is obtained by maximizing the reconnection rate as a function of the opening angle made by the upstream magnetic field on the weak magnetic field (magnetosheath) side. The prediction is within a factor of 2 of the widely examined asymmetric reconnection model (Cassak & Shay, 2007, https://doi.org/10.1063/1.2795630) in the collisionless limit, and they scale the same over a wide parameter regime. The previous model had the effective aspect ratio of the diffusion region as a free parameter, which simulations and observations suggest is on the order of 0.1, but the present model has no free parameters. In conjunction with the symmetric case (Liu et al., 2017, https://doi.org/10.1103/PhysRevLett.118.085101), this work further suggests that this nearly universal number 0.1, essentially the normalized fast-reconnection rate, is a geometrical factor arising from maximizing the reconnection rate within magnetohydrodynamic-scale constraints.

PLAIN LANGUAGE SUMMARY

To understand the evolution of many space and astrophysical plasmas, it is imperative to know how fast magnetic reconnection processes the magnetic flux. Researchers found that reconnection in both symmetric and asymmetric geometries exhibits a normalized reconnection rate of order 0.1. In this work, we show that this nearly universal value in asymmetric geometry is also the maximal rate allowed in the magnetohydrodynamic scale. This result has applications to the transport process at plasma boundary layers like Earth's magnetopause.

Low Altitude Solar Magnetic Reconnection, Type III Solar Radio Bursts, and X-ray Emissions

Type III solar radio bursts are the Sun's most intense and frequent nonthermal radio emissions. They involve two critical problems in astrophysics, plasma physics, and space physics: how collective processes produce nonthermal radiation and how magnetic reconnection occurs and changes magnetic energy into kinetic energy. Here magnetic reconnection events are identified definitively in Solar Dynamics Observatory UV-EUV data, with strong upward and downward pairs of jets, current sheets, and cusp-like geometries on top of time-varying magnetic loops, and strong outflows along pairs of open magnetic field lines. Type III bursts imaged by the Murchison Widefield Array and detected by the Learmonth radiospectrograph and STEREO B spacecraft are demonstrated to be in very good temporal and spatial coincidence with specific reconnection events and with bursts of X-rays detected by the RHESSI spacecraft. The reconnection sites are low, near heights of 5-10 Mm. These images and event timings provide the long-desired direct evidence that semi-relativistic electrons energized in magnetic reconnection regions produce type III radio bursts. Not all the observed reconnection events produce X-ray events or coronal or interplanetary type III bursts; thus different special conditions exist for electrons leaving reconnection regions to produce observable radio, EUV, UV, and X-ray bursts.

Coherent Structure Formation through nonlinear interactions in 2D Magnetohydrodynamic Turbulence

Using high resolution 2D magnetohydrodynamic (MHD) simulations we analyze the formation of coherent structures induced by nonlinear interactions in turbulent flows. The properties of these coherent structures, which at the smallest scales are identified through a spatial intermittent behavior, turn out to be guided by the conservation of ideal quadratic (rugged) invariants of the 2D incompressible MHD equations. Different spatial regions can be identified, where the correlations predicted using the variational principles associated to the rugged invariants are locally displayed. These local correlated structures are produced rapidly, as soon as the turbulence is fully developed. It is worth speculating that the small scale structures under our investigation could give rise to singular weak solutions when letting the dissipative coefficients go to zero. In this case their properties could furnish a key to understand which mathematical conditions characterize singularity emergency in weak solutions of the MHD ideal case.

Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence

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 λ∼LS_{L}^{-4/7}, where S_{L} is the outer-scale (L) Lundquist number and λ 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_{⊥})∝k_{⊥}^{-5/2}, where k_{⊥} 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 λ/L∼S_{L}^{-4/7}Pm^{-2/7}.

Kinetic Turbulence in Relativistic Plasma: From Thermal Bath to Nonthermal Continuum

We present results from particle-in-cell simulations of driven turbulence in magnetized, collisionless, and relativistic pair plasmas. We find that the fluctuations are consistent with the classical k_{⊥}^{-5/3} magnetic energy spectrum at fluid scales and a steeper k_{⊥}^{-4} spectrum at sub-Larmor scales, where k_{⊥} is the wave vector perpendicular to the mean field. We demonstrate the development of a nonthermal, power-law particle energy distribution f(E)∼E^{-α}, with an index α that decreases with increasing magnetization and increases with an increasing system size (relative to the characteristic Larmor radius). Our simulations indicate that turbulence can be a viable source of energetic particles in high-energy astrophysical systems, such as pulsar wind nebulae, if scalings asymptotically become insensitive to the system size.

Depletion of nonlinearity in magnetohydrodynamic turbulence: Insights from analysis and simulations

It is shown how suitably scaled, order-m moments, D_{m}^{±}, of the Elsässer vorticity fields in three-dimensional magnetohydrodynamics (MHD) can be used to identify three possible regimes for solutions of the MHD equations with magnetic Prandtl number P_{M}=1. These vorticity fields are defined by ω^{±}=curlz^{±}=ω±j, where z^{±} are Elsässer variables, and where ω and j are, respectively, the fluid vorticity and current density. This study follows recent developments in the study of three-dimensional Navier-Stokes fluid turbulence [Gibbon et al., Nonlinearity 27, 2605 (2014)NONLE50951-771510.1088/0951-7715/27/10/2605]. Our mathematical results are then compared with those from a variety of direct numerical simulations, which demonstrate that all solutions that have been investigated remain in only one of these regimes which has depleted nonlinearity. The exponents q^{±} that characterize the inertial range power-law dependencies of the z^{±} energy spectra, E^{±}(k), are then examined, and bounds are obtained. Comments are also made on  (a) the generalization of our results to the case P_{M}≠1 and (b) the relation between D_{m}^{±} and the order-m moments of gradients of magnetohydrodynamic fields, which are used to characterize intermittency in turbulent flows.

Temporal intermittency of energy dissipation in magnetohydrodynamic turbulence

Energy dissipation in magnetohydrodynamic (MHD) turbulence is known to be highly intermittent in space, being concentrated in sheetlike 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 or 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 α≈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.

Explosive turbulent magnetic reconnection

We report simulation results for turbulent magnetic reconnection obtained using a newly developed Reynolds-averaged magnetohydrodynamics model. We find that the initial Harris current sheet develops in three ways, depending on the strength of turbulence: laminar reconnection, turbulent reconnection, and turbulent diffusion. The turbulent reconnection explosively converts the magnetic field energy into both kinetic and thermal energy of plasmas, and generates open fast reconnection jets. This fast turbulent reconnection is achieved by the localization of turbulent diffusion. Additionally, localized structure forms through the interaction of the mean field and turbulence.

Vortex merger and topological changes in two-dimensional turbulence

On the basis of the critical point analysis, we study the reconnection process of vorticity contours associated with coherent vortices in two-dimensional turbulence. After checking topological integrity by the Euler index theorem, we make use of the critical points and their connectivity (so-called surface networks) to characterize topological changes of vorticity contours. We quantify vortex merger by computing the number of centers and saddles of the vorticity field systematically. Surface networks are topological graphs consisting of the critical points and edges connecting them. They can tell in particular which vortices are going to merge in near future. Moreover, we show how this method can remarkably distinguish the dynamics of the vorticity field in the Navier-Stokes equations and that of the Charney-Hasegawa-Mima equation. The relationship between the number of the critical points and hyperpalinstrophy is discussed by deriving the so-called generalized Rice theorem in the spirit of S. Goto and J. C. Vassilicos [Phys. Fluids 21, 035104-1 (2009)]. The Okubo-Weiss' conditional sampling is used to compare reconnection in elliptic and hyperbolic regions. A comparison has been made between topological changes of the vorticity and that of a passive scalar. A study in inviscid flows with different resolutions is also given.

Local kinetic effects in two-dimensional plasma turbulence

Using direct numerical simulations of a hybrid Vlasov-Maxwell model, kinetic processes are investigated in a two-dimensional turbulent plasma. In the turbulent regime, kinetic effects manifest through a deformation of the ion distribution function. These patterns of non-Maxwellian features are concentrated in space nearby regions of strong magnetic activity: the distribution function is modulated by the magnetic topology, and can elongate along or across the local magnetic field. These results open a new path on the study of kinetic processes such as heating, particle acceleration, and temperature anisotropy, commonly observed in astrophysical and laboratory plasmas.

Jet deflection by very weak guide fields during magnetic reconnection

Previous 2D simulations of reconnection using a standard model of initially antiparallel magnetic fields have detected electron jets outflowing from the x point into the ion outflow exhausts. Associated with these jets are extended "outer electron diffusion regions." New PIC simulations with an ion to electron mass ratio as large as 1836 (an H(+) plasma) now show that the jets are strongly deflected and the outer electron diffusion region is broken up by a very weak out-of-plane magnetic guide field, even though the diffusion rate itself is unchanged. Jet outflow and deflection are interpreted in terms of electron dynamics and are compared to recent measurements of jets in the presence of a small guide field in Earth's magnetosheath.

Structures in magnetohydrodynamic turbulence: detection and scaling

We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stem from numerical simulations of decaying three-dimensional magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536³ points and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X -point configuration embedded in three dimensions, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic-field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with magnetohydrodynamics. We suggest that this range can be governed by turbulence dynamics as opposed to criticality and propose an interpretation of intermittency in terms of propagation of local instabilities.

Hall-magnetohydrodynamic small-scale dynamos

Magnetic field generation by dynamo action is often studied within the theoretical framework of magnetohydrodynamics (MHD). However, for sufficiently diffuse media, the Hall effect may become non-negligible. We present results from three-dimensional simulations of the Hall-MHD equations subjected to random nonhelical forcing. We study the role of the Hall effect in the dynamo efficiency for different values of the Hall parameter. For small values of the Hall parameter, the small-scale dynamo is more efficient, displaying faster growth and saturating at larger amplitudes of the magnetic field. For larger values of the Hall parameter, saturation of the magnetic field is reached at smaller amplitudes than in the MHD case. We also study energy transfer rates among spatial scales and show that the Hall effect produces a reduction of the direct energy cascade at scales larger than the Hall scale, therefore leading to smaller energy dissipation rates. Finally, we present results stemming from simulations at large magnetic Prandtl numbers, which is the relevant regime in the hot and diffuse interstellar medium. In the range of magnetic Prandtl numbers considered, the Hall effect moves the peak of the magnetic energy spectrum as well as other relevant magnetic length scales toward the Hall scale.

Quantification of topological changes of vorticity contours in two-dimensional Navier-Stokes flow

A characterization of reconnection of vorticity contours is made by direct numerical simulations of the two-dimensional Navier-Stokes flow at a relatively low Reynolds number. We identify all the critical points of the vorticity field and classify them by solving an eigenvalue problem of its Hessian matrix on the basis of critical-point theory. The numbers of hyperbolic (saddles) and elliptic (minima and maxima) points are confirmed to satisfy Euler's index theorem numerically. Time evolution of these indices is studied for a simple initial condition. Generally speaking, we have found that the indices are found to decrease in number with time. This result is discussed in connection with related works on streamline topology, in particular, the relationship between stagnation points and the dissipation. Associated elementary procedures in physical space, the merging of vortices, are studied in detail for a number of snapshots. A similar analysis is also done using the stream function.

Waiting-time distributions of magnetic discontinuities: clustering or Poisson process?

Using solar wind data from the Advanced Composition Explorer spacecraft, with the support of Hall magnetohydrodynamic simulations, the waiting-time distributions of magnetic discontinuities have been analyzed. A possible phenomenon of clusterization of these discontinuities is studied in detail. We perform a local Poisson's analysis in order to establish if these intermittent events are randomly distributed or not. Possible implications about the nature of solar wind discontinuities are discussed.