Intermittent dissipation at kinetic scales in collisionless plasma 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.

Three-Dimensional Energy Transfer in Space Plasma Turbulence from Multipoint Measurement

A novel multispacecraft technique applied to Magnetospheric Multiscale Mission data in the Earth's magnetosheath enables evaluation of the energy cascade rate from the full Yaglom's equation. The method differs from existing approaches in that it (i) is inherently three-dimensional, (ii) provides a statistically significant number of estimates from a single data stream, and (iii) allows visualization of energy flux in turbulent plasmas. This new "lag polyhedral derivative ensemble" technique exploits ensembles of tetrahedra in lag space and established curlometerlike algorithms.

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.

Kinetic Heating by Alfvén Waves in Magnetic Shears

With first-principles kinetic simulations, we show that a large-scale Alfvén wave (AW) propagating in an inhomogeneous background decays into kinetic Alfvén waves (KAWs), triggering ion and electron energization. We demonstrate that the two species can access unequal amounts of the initial AW energy, experiencing differential heating. During the decay process, the electric field carried by KAWs produces non-Maxwellian features in the particle velocity distribution functions, in accordance with space observations. The process we present solely requires the interaction of a large-scale AW with a magnetic shear and may be relevant for several astrophysical and laboratory plasmas.

Properties of Hall-MHD Turbulence at Sub-Ion Scales: Spectral Transfer Analysis

We present results of a multiscale study of Hall-magnetohydrodynamic (MHD) turbulence, carried out on a dataset of compressible nonlinear 2D Hall-MHD numerical simulations of decaying Alfvénic turbulence. For the first time, we identify two distinct regimes of fully developed turbulence. In the first one, the power spectrum of the turbulent magnetic fluctuations at sub-ion scales exhibits a power law with a slope of ∼−2.9, typically observed both in solar wind and in magnetosheath turbulence. The second regime, instead, shows a slope of −7/3, in agreement with classical theoretical models of Hall-MHD turbulence. A spectral-transfer analysis reveals that the latter regime occurs when the energy transfer rate at sub-ion scales is dominated by the Hall term, whereas in the former regime, the governing process is the dissipation (and the system exhibits large intermittency). Results of this work are relevant to the space plasma community, as they may potentially reconcile predictions from theoretical models with results from numerical simulations and spacecraft observations.

Magnetic Topology of Actively Evolving and Passively Convecting Structures in the Turbulent Solar Wind

Multipoint in situ observations of the solar wind are used to identify the magnetic topology and current density of turbulent structures. We find that at least 35% of all structures are both actively evolving and carrying the strongest currents, actively dissipating, and heating the plasma. These structures are comprised of ∼1/5 3D plasmoids, ∼3/5 flux ropes, and ∼1/5 3D X points consistent with magnetic reconnection. Actively evolving and passively advecting structures are both close to log-normally distributed. This provides direct evidence for the significant role of strong turbulence, evolving via magnetic shearing and reconnection, in mediating dissipation and solar wind heating.

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.

Evidence for electron Landau damping in space plasma turbulence

How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth's magnetosheath, the region of solar wind downstream of the Earth's bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the predicted resonant velocity, similar to that seen in kinetic Alfven turbulence simulations, and disappears under phase randomisation. This suggests that electron Landau damping could play a significant role in turbulent plasma heating, and that the technique is a valuable tool for determining the particle energisation processes operating in space and astrophysical plasmas.

Particle Acceleration in Relativistic Plasma Turbulence

Due to its ubiquitous presence, turbulence is often invoked to explain the origin of nonthermal particles in astrophysical sources of high-energy emission. With particle-in-cell simulations, we study decaying turbulence in magnetically dominated (or, equivalently, "relativistic") pair plasmas. We find that the generation of a power-law particle energy spectrum is a generic by-product of relativistic turbulence. The power-law slope is harder for higher magnetizations and stronger turbulence levels. In large systems, the slope attains an asymptotic, system-size-independent value, while the high-energy spectral cutoff increases linearly with system size; both the slope and the cutoff do not depend on the dimensionality of our domain. By following a large sample of particles, we show that particle injection happens at reconnecting current sheets; the injected particles are then further accelerated by stochastic interactions with turbulent fluctuations. Our results have important implications for the origin of nonthermal particles in high-energy astrophysical sources.

Energy transfer channels and turbulence cascade in Vlasov-Maxwell turbulence

Analysis of the Vlasov-Maxwell equations from the perspective of turbulence cascade clarifies the role of electromagnetic work, and reveals the importance of the pressure-strain relation in generating internal energy. Particle-in-cell simulation demonstrates the relative importance of the several energy exchange terms, indicating that the traceless pressure-strain interaction "Pi-D" is of particular importance for both electrons and protons. The Pi-D interaction and the second tensor invariants of the strain are highly localized in similar spatial regions, indicating that energy transfer occurs preferentially in coherent structures. The collisionless turbulence cascade may be fruitfully explored by study of these energy transfer channels, in addition to examining transfer across spatial scales.

Structure of Plasma Heating in Gyrokinetic Alfvénic Turbulence

We analyze plasma heating in weakly collisional kinetic Alfvén wave turbulence using high resolution gyrokinetic simulations spanning the range of scales between the ion and the electron gyroradii. Real space structures that have a higher than average heating rate are shown not to be confined to current sheets. This novel result is at odds with previous studies, which use the electromagnetic work in the local electron fluid frame, i.e., J·(E+v_{e}×B), as a proxy for turbulent dissipation to argue that heating follows the intermittent spatial structure of the electric current. Furthermore, we show that electrons are dominated by parallel heating while the ions prefer the perpendicular heating route. We comment on the implications of the results presented here.

Small-scale behavior of Hall magnetohydrodynamic turbulence

Decaying Hall magnetohydrodynamic (HMHD) turbulence is studied using three-dimensional (3D) direct numerical simulations with grids up to 768(3) points and two different types of initial conditions. Results are compared to analogous magnetohydrodynamic (MHD) runs and both Laplacian and Laplacian-squared dissipative operators are examined. At scales below the ion inertial length, the ratio of magnetic to kinetic energy as a function of wave number transitions to a magnetically dominated state. The transition in behavior is associated with the advection term in the momentum equation becoming subdominant to dissipation. Examination of autocorrelation functions reveals that, while current and vorticity structures are similarly sized in MHD, HMHD current structures are narrower and vorticity structures are wider. The electric field autocorrelation function is significantly narrower in HMHD than in MHD and is similar to the HMHD current autocorrelation function at small separations. HMHD current structures are found to be significantly more intense than in MHD and appear to have an enhanced association with strong alignment between the current and magnetic field, which may be important in collisionless plasmas where field-aligned currents can be unstable. When hyperdiffusivity is used, a longer region consistent with a k(-7/3) scaling is present for right-polarized fluctuations when compared to Laplacian dissipation runs.

A dynamical model of plasma turbulence in the solar wind

A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.

Intermittency, nonlinear dynamics and dissipation in the solar wind and astrophysical plasmas

An overview is given of important properties of spatial and temporal intermittency, including evidence of its appearance in fluids, magnetofluids and plasmas, and its implications for understanding of heliospheric plasmas. Spatial intermittency is generally associated with formation of sharp gradients and coherent structures. The basic physics of structure generation is ideal, but when dissipation is present it is usually concentrated in regions of strong gradients. This essential feature of spatial intermittency in fluids has been shown recently to carry over to the realm of kinetic plasma, where the dissipation function is not known from first principles. Spatial structures produced in intermittent plasma influence dissipation, heating, and transport and acceleration of charged particles. Temporal intermittency can give rise to very long time correlations or a delayed approach to steady-state conditions, and has been associated with inverse cascade or quasi-inverse cascade systems, with possible implications for heliospheric prediction.

Generation of magnetic holes in fully kinetic simulations of collisionless turbulence

The results of three-dimensional fully kinetic simulations of decaying turbulence with the amplitude of the fluctuating magnetic field comparable to that of the mean field are presented. Coherent structures in the form of localized depressions in the magnitude of the magnetic field are observed to form self-consistently in the simulations. These depressions bear considerable resemblance to the so-called magnetic holes frequently reported in spacecraft observations. The structures are pressure-balanced and tend to be aligned with the local magnetic field. In the smallest structures observed, the decrease in the magnetic field strength is compensated by an increase in the electron perpendicular pressure, such that the transverse size of these structures is comparable to the electron gyroradius inside the depression. It is suggested that the structures evolve self-consistently out of the depressions in the fluctuating magnetic field, rather than being the consequence of instability growth and saturation. This is confirmed by additional, small-scale simulations, including those with realistic mass ratio between protons and electrons.

Intermittent Dissipation and Heating in 3D Kinetic Plasma Turbulence

High resolution, fully kinetic, three dimensional (3D) simulation of collisionless plasma turbulence shows the development of turbulence characterized by sheetlike current density structures spanning a range of scales. The nonlinear evolution is initialized with a long wavelength isotropic spectrum of fluctuations having polarizations transverse to an imposed mean magnetic field. We present evidence that these current sheet structures are sites for heating and dissipation, and that stronger currents signify higher dissipation rates. The analyses focus on quantities such as J·E, electron, and proton temperatures, and conditional averages of these quantities based on local electric current density. Evidently, kinetic scale plasma, like magnetohydrodynamics, becomes intermittent due to current sheet formation, leading to the expectation that heating and dissipation in astrophysical and space plasmas may be highly nonuniform. Comparison with previous results from 2D kinetic simulations, as well as high frequency solar wind observational data, are discussed.

Proton kinetic effects and turbulent energy cascade rate in the solar wind

The first observed connection between kinetic instabilities driven by proton temperature anisotropy and estimated energy cascade rates in the turbulent solar wind is reported using measurements from the Wind spacecraft at 1 AU. We find enhanced cascade rates are concentrated along the boundaries of the (β∥, T⊥/T∥) plane, which includes regions theoretically unstable to the mirror and firehose instabilities. A strong correlation is observed between the estimated cascade rate and kinetic effects such as temperature anisotropy and plasma heating, resulting in protons 5-6 times hotter and 70%-90% more anisotropic than under typical isotropic plasma conditions. These results offer new insights into kinetic processes in a turbulent regime.

Von Kármán energy decay and heating of protons and electrons in a kinetic turbulent plasma

Decay in time of undriven weakly collisional kinetic plasma turbulence in systems large compared to the ion kinetic scales is investigated using fully electromagnetic particle-in-cell simulations initiated with transverse flow and magnetic disturbances, constant density, and a strong guide field. The observed energy decay is consistent with the von Kármán hypothesis of similarity decay, in a formulation adapted to magnetohydrodyamics. Kinetic dissipation occurs at small scales, but the overall rate is apparently controlled by large scale dynamics. At small turbulence amplitudes the electrons are preferentially heated. At larger amplitudes proton heating is the dominant effect. In the solar wind and corona the protons are typically hotter, suggesting that these natural systems are in the large amplitude turbulence regime.

Energetics of kinetic reconnection in a three-dimensional null-point cluster

We perform three-dimensional particle-in-cell simulations of magnetic reconnection with multiple magnetic null points. Magnetic field energy conversion into kinetic energy is about five times higher than in traditional Harris sheet configuration. More than 85% of initial magnetic field energy is transferred to particle energy during 25 reversed ion cyclofrequencies. Magnetic reconnection in the cluster of null points evolves in three phases. During the first phase, ion beams are excited, then give part of their energy back to the magnetic field in the second phase. In the third phase, magnetic reconnection occurs in many small patches around the current channels formed along the stripes of a low magnetic field. Magnetic reconnection in null points essentially presents three-dimensional features, with no two-dimensional symmetries or current sheets.