Turbulence In Astrophysical Plasmas Research Articles

Long-lived Equilibria in Kinetic Astrophysical Plasma Turbulence

Turbulence in classical fluids is characterized by persistent structures that emerge from the chaotic landscape. We investigate the analogous process in fully kinetic plasma turbulence by using high-resolution, direct numerical simulations in two spatial dimensions. We observe the formation of long-lived vortices with a profile typical of macroscopic, magnetically dominated force-free states. Inspired by the Harris pinch model for inhomogeneous equilibria, we describe these metastable solutions with a self-consistent kinetic model in a cylindrical coordinate system centered on a representative vortex, starting from an explicit form of the particle velocity distribution function. Such new equilibria can be simplified to a Gold–Hoyle solution of the modified force-free state. Turbulence is mediated by the long-lived structures, accompanied by transients in which such vortices merge and form self-similarly new metastable equilibria. This process can be relevant to the comprehension of various astrophysical phenomena, going from the formation of plasmoids in the vicinity of massive compact objects to the emergence of coherent structures in the heliosphere.

Enhanced Energy Conversion by Turbulence in Collisionless Magnetic Reconnection

Abstract Magnetic reconnection and turbulence are two of the most significant mechanisms for energy dissipation in collisionless plasma. The role of turbulence in magnetic reconnection poses an outstanding problem in astrophysics and plasma physics. It is still unclear whether turbulence can modify the reconnection process by enhancing the reconnection rate or energy conversion rate. In this study, utilizing unprecedented high-resolution data obtained from the Magnetospheric Multiscale spacecraft, we provide direct evidence that turbulence plays a vital role in promoting energy conversion during reconnection. We reached this conclusion by comparing magnetotail reconnection events with similar inflow Alfvén speed and plasma β but varying amplitudes of turbulence. The disparity in energy conversion was attributed to the strength of turbulence. Stronger turbulence generates more coherent structures with smaller spatial scales, which are pivotal contributors to energy conversion during reconnection. However, we find that turbulence has negligible impact on particle heating, but it does affect the ion bulk kinetic energy in these two events. These findings significantly advance our understanding of the relationship between turbulence and reconnection in astrophysical plasmas.

Turbulent Reconnection Acceleration

The ubiquitous turbulence in astrophysical plasmas is important for both magnetic reconnection and reconnection acceleration. We study the particle acceleration during fast 3D turbulent reconnection with reconnection-driven turbulence. Particles bounce back and forth between the reconnection-driven inflows due to the mirror reflection and convergence of strong magnetic fields. Via successive head-on collisions, the kinetic energy of the inflows is converted into accelerated particles. Turbulence not only regulates the inflow speed but also introduces various inflow obliquities with respect to the local turbulent magnetic fields. As both the energy gain and probability of the escape of particles depend on the inflow speed, the spectral index of particle energy spectrum is not universal. We find it in the range of ≈2.5–4, with the steepest spectrum expected at a strong guide field, i.e., a small angle between the total incoming magnetic field and the guide field. Without scattering diffusion needed for confining particles, the reconnection acceleration can be very efficient at a large inflow speed and a weak guide field.

Tracking of magnetic helicity evolution in the inner heliosphere

Context. Magnetic helicity is one of the invariants in ideal magnetohydrodynamics, and its spectral evolution has a substantial amount of information to reveal the mechanism that are behind turbulence in space and astrophysical plasmas. Aims. The goal of our study is to observationally characterize the magnetic helicity evolution in the inner heliosphere by resolving the helicity transport in a scale-wise fashion in the spectral domain. Methods. The evolution of the magnetic helicity spectrum in the inner heliosphere was tracked using a radial alignment event achieved by Parker Solar Probe at a distance of 0.17 astronomical units (AU) from the Sun and BepiColombo at 0.58 AU with a delay of about 3.5 days. Results. The reduced magnetic helicity resolved in the frequency domain shows three main features: (1) a coherent major peak of a highly helical component at the lowest frequency at about 5 × 10−4 Hz, (2) a damping of helicity oscillation at the intermediate frequencies from 10−3 to 10−2 Hz when observed at 0.58 AU, and (3) a coherent nonhelical component in the ion-kinetic range at frequencies of about 0.1 − 1 Hz. Conclusions. Though limited in the frequency range, the main message from this work is that the solar wind develops into turbulence by convecting large-scale helicity components on the one hand and creating and annihilating helical wave components on the other hand. Excitation of waves can overwrite the helicity profile in the inner heliosphere. By comparing this with the typical helicity spectra at a distance of 1 AU (that is, a randomly oscillating helicity sign in the intermediate frequency range up to about 1 Hz), the helicity evolution reaches a nearly asymptotic state at the Venus orbit (about 0.7 AU) and beyond.

On the Variation of Intermittency of Fast and Slow Solar Wind With Radial Distance, Heliospheric Latitude, and Solar Cycle

Intermittency, an important property of astrophysical plasma turbulence, is studied extensively during last decades from in-situ measurements of the solar wind plasma and magnetic field in the ecliptic plane and at higher latitudes, and heliocentric distances between 0.3 and 5 Astronomical Units. In this paper, we review the main findings on intermittency derived from investigation of solar wind turbulence for the inertial range of scales. It turns out that our current knowledge on the evolution of intermittency in the heliosphere is based on two missions, Helios two and Ulysses. We discuss the importance of data selection methodologies and applications for heliospheric spacecraft, the different data analysis techniques (the anomalous scaling of the structure function, the non-Gaussianity of the probability distribution functions, the local intermittency measure estimated from a wavelet representation and the multifractal spectrum). Studies show that Alvénic solar wind is less intermittent but reveals increase with the radial distance. Moreover, intermittency is stronger for the magnetic than for velocity fluctuations and is considered to be responsible for the increase with the radial distance of the anisotropy of magnetic fluctuations. The intermittency of fast solar wind at solar minimum decreases with latitude. Finally, the level of intermittency in the solar wind depends on solar cycle phase, reflecting the changes of the state of solar wind and suggesting that the deeper study of origin of fast and slow wind can further improve our understanding of the intermittency.

Proton–Proton Collisions in the Turbulent Solar Wind: Hybrid Boltzmann–Maxwell Simulations

Abstract The mechanism of heating for hot, dilute, and turbulent plasmas represents a long-standing problem in space physics, whose implications concern both near-Earth environments and astrophysical systems. In order to explore the possible role of interparticle collisions, simulations of plasma turbulence—in both collisionless and weakly collisional regimes—have been compared by adopting Eulerian Hybrid Boltzmann–Maxwell simulations, being proton–proton collisions explicitly introduced through the nonlinear Dougherty operator. Although collisions do not significantly influence the statistical characteristics of the turbulence, they dissipate nonthermal features in the proton distribution function and suppress the enstrophy/entropy cascade in the velocity space, damping the spectral transfer toward large Hermite modes. This enstrophy dissipation is particularly effective in regions where the plasma distribution function is strongly distorted, suggesting that collisional effects are enhanced by fine velocity–space structures. A qualitative connection between the turbulent energy cascade in fluids and the enstrophy cascade in plasmas has been established, opening a new path to the understanding of astrophysical plasma turbulence.

Kinetic Turbulence in Astrophysical Plasmas: Waves and/or Structures?

The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize high-resolution observational and simulation data to investigate the nature of waves and structures emerging in a weakly collisional, turbulent kinetic plasma. Observational results are based on in situ solar wind measurements from the Cluster and Magnetospheric Multiscale (MMS) spacecraft, and the simulation results are obtained from an externally driven, three-dimensional fully kinetic simulation. Using a set of novel diagnostic measures, we show that both the large-amplitude structures and the lower-amplitude background fluctuations preserve linear features of kinetic Alfvén waves to order unity. This quantitative evidence suggests that the kinetic turbulence cannot be described as a mixture of mutually exclusive waves and structures but may instead be pictured as an ensemble of localized, anisotropic wave packets or “eddies” of varying amplitudes, which preserve certain linear wave properties during their nonlinear evolution.1 MoreReceived 14 June 2018Revised 3 June 2019DOI:https://doi.org/10.1103/PhysRevX.9.031037Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasElectromagnetic waves & oscillationsPlasma turbulencePhysical SystemsSpace & astrophysical plasmaTechniquesParticle-in-cell methodsSatellite data analysisPlasma PhysicsGravitation, Cosmology & AstrophysicsParticles & Fields

Scale dependence of energy transfer in turbulent plasma

In the context of space and astrophysical plasma turbulence and particle heating, several vocabularies emerge for estimating turbulent energy dissipation rate, including Kolmogorov-Yaglom third-order law and, in its various forms, $\boldsymbol{j}\cdot\boldsymbol{E}$ (work done by the electromagnetic field on particles), and $-\left( \boldsymbol{P} \cdot \nabla \right) \cdot \boldsymbol{u}$ (pressure-strain interaction), to name a couple. It is now understood that these energy transfer channels, to some extent, are correlated with coherent structures. In particular, we find that different energy dissipation proxies, although not point-wise correlated, are concentrated in proximity to each other, for which they decorrelate in a few $d_i$(s). However, the energy dissipation proxies dominate at different scales. For example, there is an inertial range over which the third-order law is meaningful. Contributions from scale bands stemming from scale-dependent spatial filtering show that, the energy exchange through $\boldsymbol{j}\cdot\boldsymbol{E}$ mainly results from large scales, while the energy conversion from fluid flow to internal through $-\left( \boldsymbol{P} \cdot \nabla \right) \cdot \boldsymbol{u}$ dominates at small scales.

Coexistence of Weak and Strong Wave Turbulence in Incompressible Hall Magnetohydrodynamics

We report a numerical investigation of three dimensional, incompressible, Hall magnetohydrodynamic turbulence with a relatively strong mean magnetic field. Using helicity decomposition and cross-bicoherence analysis, we observe that the resonant three--wave coupling is substantial among ion cyclotron and whistler waves. A detailed study of the degree of non-linearity of these two populations shows that the ion cyclotron component experiences a transition from weak to strong wave turbulence going from large to small scales, while the whistler fluctuations display a weak wave turbulence character for all scales. This non-trivial coexistence of the two regimes with the two populations of waves gives rise to anomalous anisotropy and scaling properties. The weak and strong wave turbulence components can be distinguished rather efficiently using spatio-temporal Fourier transforms. The analysis shows that while resonant triadic interactions survive the highly non-linear bath of ion cyclotron fluctuations at large scales for which the degree of non-linearity is low for both populations of waves, whistler waves tend to be killed by the non-linear cross-coupling at smaller scales where the ion cyclotron component is in the strong wave turbulent regime. Such situation may have far-reaching implications for the physics of magnetized turbulence in many astrophysical and space plasmas where different waves coexist and compete to transfer non-linearly energy across scales.

Spatially localized particle energization by Landau damping in current sheets produced by strong Alfvén wave collisions

Understanding the removal of energy from turbulent fluctuations in a magnetized plasma and the consequent energization of the constituent plasma particles is a major goal of heliophysics and astrophysics. Previous work has shown that nonlinear interactions among counterpropagating Alfvén waves – or Alfvén wave collisions – are the fundamental building block of astrophysical plasma turbulence and naturally generate current sheets in the strongly nonlinear limit. A nonlinear gyrokinetic simulation of a strong Alfvén wave collision is used to examine the damping of the electromagnetic fluctuations and the associated energization of particles that occurs in self-consistently generated current sheets. A simple model explains the flow of energy due to the collisionless damping and the associated particle energization, as well as the subsequent thermalization of the particle energy by collisions. The net particle energization by the parallel electric field is shown to be spatially localized, and the nonlinear evolution is essential in enabling spatial non-uniformity. Using the recently developed field–particle correlation technique, we show that particles resonant with the Alfvén waves in the simulation dominate the energy transfer, demonstrating conclusively that Landau damping plays a key role in the spatially localized damping of the electromagnetic fluctuations and consequent energization of the particles in this strongly nonlinear simulation.

Magnetic Reconnection as a Driver for a Sub-ion-scale Cascade in Plasma Turbulence

Abstract A new path for the generation of a sub-ion-scale cascade in collisionless space and astrophysical plasma turbulence, triggered by magnetic reconnection, is uncovered by means of high-resolution two-dimensional hybrid-kinetic simulations employing two complementary approaches, Lagrangian and Eulerian, and different driving mechanisms. The simulation results provide clear numerical evidence that the development of power-law energy spectra below the so-called ion break occurs as soon as the first magnetic reconnection events take place, regardless of the actual state of the turbulent cascade at MHD scales. In both simulations, the reconnection-mediated small-scale energy spectrum of parallel magnetic fluctuations exhibits a very stable spectral slope of , whether or not a large-scale turbulent cascade has already fully developed. Once a quasi-stationary turbulent state is achieved, the spectrum of the total magnetic fluctuations settles toward a spectral index of in the MHD range and of at sub-ion scales.

The development of magnetic field line wander by plasma turbulence

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

A basic plasma test for gyrokinetics: GDC turbulence in LAPD

Providing an important step towards validating gyrokinetics under comparatively little-explored conditions, simulations of pressure-gradient-driven plasma turbulence in the Large Plasma Device (LAPD) are compared with experimental observations. The corresponding signatures confirm the existence of a novel regime of turbulence, based on the recently-discovered gradient-driven drift coupling (GDC) instability, which is thus confirmed as a candidate mechanism for turbulence in basic, space and astrophysical plasmas. Despite the limitations of flux-tube gyrokinetics for this scenario, when accounting for box size scaling by applying a scalar factor , agreement between simulations and experiment improves to within a factor of two for key observables: compressional magnetic, density, and temperature fluctuations, both in amplitude and structure. Thus, a first, strong indication is presented that the GDC instability seen in gyrokinetics appears to operate in the experiment and that the essential instability physics is present in the numerical model. Overall, the gyrokinetic framework and its numerical implementation in the Gene code therefore perform well for LAPD plasmas very different from their brethren in fusion experiments.

Recent progress in astrophysical plasma turbulence from solar wind observations

This paper summarises some of the recent progress that has been made in understanding astrophysical plasma turbulence in the solar wind, fromin situspacecraft observations. At large scales, where the turbulence is predominantly Alfvénic, measurements of critical balance, residual energy and three-dimensional structure are discussed, along with comparison to recent models of strong Alfvénic turbulence. At these scales, a few per cent of the energy is also in compressive fluctuations, and their nature, anisotropy and relation to the Alfvénic component is described. In the small-scale kinetic range, below the ion gyroscale, the turbulence becomes predominantly kinetic Alfvén in nature, and measurements of the spectra, anisotropy and intermittency of this turbulence are discussed with respect to recent cascade models. One of the major remaining questions is how the turbulent energy is dissipated, and some recent work on this question, in addition to future space missions which will help to answer it, are briefly discussed.

On the role of ion-scale whistler waves in space and astrophysical plasma turbulence

Abstract. Competition of linear mode waves is studied numerically to understand the energy cascade mechanism in plasma turbulence on ion-kinetic scales. Hybrid plasma simulations are performed in a 3-D simulation box by pumping large-scale Alfvén waves on the fluid scale. The result is compared with that from our earlier 2-D simulations. We find that the whistler mode is persistently present both in the 2-D and 3-D simulations irrespective of the initial setup, e.g., the amplitude of the initial pumping waves, while all the other modes are excited and damped such that the energy is efficiently transported to thermal energy over non-whistler mode. The simulation results suggest that the whistler mode could transfer the fluctuation energy smoothly from the fluid scale down to the electron-kinetic scale, and justifies the notion of whistler turbulence.

COLLISIONLESS ISOTROPIZATION OF THE SOLAR-WIND PROTONS BY COMPRESSIVE FLUCTUATIONS AND PLASMA INSTABILITIES

ABSTRACT Compressive fluctuations are a minor yet significant component of astrophysical plasma turbulence. In the solar wind, long-wavelength compressive slow-mode fluctuations lead to changes in and in , where and are the perpendicular and parallel temperatures of the protons, B is the magnetic field strength, and is the proton density. If the amplitude of the compressive fluctuations is large enough, crosses one or more instability thresholds for anisotropy-driven microinstabilities. The enhanced field fluctuations from these microinstabilities scatter the protons so as to reduce the anisotropy of the pressure tensor. We propose that this scattering drives the average value of away from the marginal stability boundary until the fluctuating value of stops crossing the boundary. We model this “fluctuating-anisotropy effect” using linear Vlasov–Maxwell theory to describe the large-scale compressive fluctuations. We argue that this effect can explain why, in the nearly collisionless solar wind, the average value of is close to unity.

Nonlinear magnetic field enhancement and turbulence in laboratory and astrophysical plasmas

The transient response of nonlinear coupling between relatively high frequency magnetosonic wave (HMSW) and low frequency magnetosonic wave (LMSW) in the overdense plasma has been presented in this paper. Along with this, the adiabatic response of HMSW also has been studied for low value of magnetic field in the underdense plasma. The ponderomotive force of relatively high frequency and high power pump magnetosonic wave is expected to excite the low frequency magnetosonic wave. The dynamical equation of LMSW in the presence of ponderomotive force of HMSW (pump wave) has been derived for this purpose. Using this coupled system of dynamical equations, the nonlinear behavior of the pump HMSW was studied, and the resulting turbulent spectrum has been presented. Numerical simulation has been carried out for dimensionless nonlinear coupled equations of HMSW and LMSW, and the results show quite complex localized structures that grow with time. The ensemble averaged power spectrum has also been studied which shows that the spectral index follows an approximate scaling of the order of ∼k−1.67 at larger scales and scaling of the order of ∼k−3.4 at smaller scales. The results indicate considerable randomness in the spatial structure of the magnetic field profile which gives sufficient indication of turbulence. In this context, filamentation of high frequency magnetosonic wave has been considered to be responsible for magnetic turbulence during the laser plasma interaction. The results of the present paper are found relevant with two different experimental observations. Such a nonlinear interaction is quite important in understanding turbulence in the astrophysical phenomenon.

Analysis of Magnetic Fields in Inertial Alfvén Wave Collisions

Turbulence in astrophysical and space plasmas is dominated by the nonlinear interaction of counter propagating Alfvén waves. Most Alfvén wave turbulence theories have been based on ideal plasma models for Alfvén waves at large scales. However, in the inertial Alfvén wave regime, relevant to magnetospheric plasmas, how the turbulent nonlinear interactions are modified by the dispersive nature of the waves remains to be explored. Here, we present the first laboratory evidence of the nonlinear interaction in the inertial regime. A comparison is made with the theory for MHD Alfvén waves.

Collision-dependent power law scalings in two dimensional gyrokinetic turbulence

Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely decaying two dimensional electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.

Towards optimal explicit time-stepping schemes for the gyrokinetic equations

The nonlinear gyrokinetic equations describe plasma turbulence in laboratory and astrophysical plasmas. To solve these equations, massively parallel codes have been developed and run on present-day supercomputers. This paper describes measures to improve the efficiency of such computations, thereby making them more realistic. Explicit Runge–Kutta schemes are considered to be well suited for time-stepping. Although the numerical algorithms are often highly optimized, performance can still be improved by a suitable choice of the time-stepping scheme, based on the spectral analysis of the underlying operator. Here, an operator splitting technique is introduced to combine first-order Runge–Kutta–Chebychev schemes for the collision term with fourth-order schemes for the remaining terms. In the nonlinear regime, based on the observation of eigenvalue shifts due to the (generalized) E×B advection term, an accurate and robust estimate for the nonlinear timestep is developed. The presented techniques can reduce simulation times by factors of up to three in realistic cases. This substantial speedup encourages the use of similar timestep optimized explicit schemes not only for the gyrokinetic equation, but also for other applications with comparable properties.