Collisionless Plasma Turbulence Research Articles

Spectral properties and energy transfer at kinetic scales in collisionless plasma turbulence

Context. Recent satellite observations in the solar wind and in the Earth’s magnetosheath have shown that the turbulent magnetic field spectrum, which is know to steepen around ion scales, has another break at electron scales where it becomes even steeper. The origin of this second spectral break is not yet fully understood, and the shape of the magnetic field spectrum below electron scales is still under debate. Aims. By means of a fully kinetic simulation of freely decaying plasma turbulence, we study the spectral properties and the energy exchanges characterizing the turbulent cascade in the kinetic range. Methods. We started by analyzing the magnetic field, electron velocity, and ion velocity spectra at fully developed turbulence. We then investigated the dynamics responsible for the development of the kinetic scale cascade by analyzing the ion and electron filtered energy conversion channels, represented by the electromagnetic work J ⋅ E, pressure–strain interaction −P : ∇ u, and the cross-scale fluxes of electromagnetic (e.m.) energy and fluid flow energy, accounting for the nonlinear scale-to-scale transfer of energy from large to small scales. Results. We find that the magnetic field spectrum follows the k−α exp(−λ k) law at kinetic scales with α ≃ 2.73 and λ ≃ ρe (where ρe is the electron gyroradius). The same law with α ≃ 0.94 and λ ≃ 0.87ρe is observed in the electron velocity spectrum, but not in the ion velocity spectrum that drops as a steep power law ∼k−3.25 before reaching electron scales. By analyzing the filtered energy conversion channels, we find that electrons play a major role with respect to the ions in driving the magnetic field dynamics at kinetic scales. Our analysis reveals the presence of an indirect electron-driven mechanism that channels the e.m. energy from large to sub-ion scales more efficiently than the direct nonlinear scale-to-scale transfer of e.m. energy. This mechanism consists of three steps. In the first step the e.m. energy is converted into electron fluid flow energy at large scales; in the second step the electron fluid flow energy is nonlinearly transferred toward sub-ion scales; in the final step the electron fluid flow energy is converted back into e.m. energy at sub-ion scales. This electron-driven transfer drives the magnetic field cascade up to fully developed turbulence, after which dissipation becomes dominant and the electrons start to subtract energy from the magnetic field and dissipate it via the pressure–strain interaction at sub-ion scales.

Balancing turbulent heating with radiative cooling in blazars

ABSTRACT Recently, particle-in-cell (PIC) simulations have shown that relativistic turbulence in collisionless plasmas can result in an equilibrium particle distribution function where turbulent heating is balanced by radiative cooling of electrons. Strongly magnetized plasmas are characterized by higher energy peaks and broader particle distributions. In relativistically moving astrophysical jets, it is believed that the flow is launched Poynting flux dominated and that the resulting magnetic instabilities may create a turbulent environment inside the jet, i.e. the regime of relativistic turbulence. In this paper, we extend previous PIC simulation results to larger values of plasma magnetization by linearly extrapolating the diffusion and advection coefficients relevant for the turbulent plasmas under consideration. We use these results to build a single-zone turbulent jet model that is based on the global parameters of the blazar emission region, and consistently calculate the particle distribution and the resulting emission spectra. We then test our model by comparing its predictions with the broad-band quiescent emission spectra of a dozen blazars. Our results show good agreement with observations of low synchrotron peaked (LSP) sources and find that LSPs are moderately Poynting flux dominated with magnetization 1 ≲ σ ≲ 5, have bulk Lorentz factor Γj ∼ 10–30, and that the turbulent region is located at the edge, or just beyond the broad-line region (BLR). The turbulence is found to be driven at an area comparable to the jet cross-section.

Importance of accurate consideration of the electron inertia in hybrid-kinetic simulations of collisionless plasma turbulence: The 2D limit

The dissipation mechanism of the magnetic energy in turbulent collisionless space and astrophysical plasmas is still not well understood. Its investigation requires efficient kinetic simulations of the energy transfer in collisionless plasma turbulence. In this respect, hybrid-kinetic simulations, in which ions are treated as particles and electrons as an inertial fluid, have begun to attract a significant interest recently. Hybrid-kinetic models describe both ion- and electron scale processes by ignoring electron kinetic effects so that they are computationally much less demanding compared to fully kinetic plasma models. Hybrid-kinetic codes solve either the Vlasov equation for the ions (Eulerian Vlasov-hybrid codes) or the equations of motion of the ions as macro-particles [Lagrangian particle-in-cell (PIC)-hybrid codes]. They consider the inertia of the electron fluid using different approximations. We check the validity of these approximations by employing our recently massively parallelized three-dimensional PIC-hybrid code Code Hybrid with Inertial Electron Fluid (CHIEF), which considers the electron inertia without any of the common approximations. In particular, we report the results of simulations of two-dimensional collisionless plasma turbulence. We conclude that the simulation results obtained using hybrid-kinetic codes, which use approximations to describe the electron inertia, need to be interpreted with caution. We also discuss the parallel scalability of CHIEF, to the best of our knowledge, the first PIC-hybrid code, which without approximations describes the inertial electron fluid.

Coexistence of Plasmoid and Kelvin–Helmholtz Instabilities in Collisionless Plasma Turbulence

The plasmoid formation in collisionless plasmas, where magnetic reconnection within turbulence may take place driven by the electron inertia, is analyzed. We find a complex situation in which, due to the presence of strong velocity shears, the typical plasmoid formation, observed to influence the energy cascade in the magnetohydrodynamic context, has to coexist with the Kelvin–Helmholtz (KH) instability. We find that the current density layers may undergo the plasmoid or the KH instability depending on the local values of the magnetic and velocity fields. The competition among these instabilities affects not only the evolution of the current sheets, that may generate plasmoid chains or KH-driven vortices, but also the energy cascade, that is different for the magnetic and kinetic spectra.

Free Energy Sources in Current Sheets Formed in Collisionless Plasma Turbulence

Abstract Collisionless dissipation of macroscopic energy into heat is an unsolved problem of space and astrophysical plasmas, e.g., solar wind and Earth’s magnetosheath. The most viable process under consideration is the turbulent cascade of macroscopic energy to kinetic scales where collisionless plasma processes dissipate the energy. Space observations and numerical simulations show the formation of kinetic scale current sheets in turbulent plasmas. Instabilities in these current sheets (CS) can provide collisionless dissipation and influence the turbulence. Spatial gradients of physical quantities and non-Maxwellian velocity distribution functions provide the free energy sources for CS plasma instabilities. To determine the free energy sources provided by the spatial gradients of plasma density and electron/ion bulk velocities in CS formed in collisionless turbulent plasmas with an external magnetic field B 0, we carried out two-dimensional particle-in-cell-hybrid simulations and interpret the results within the limitations of the simulation model. We found that ion-scale CS in a collisionless turbulent plasma are formed primarily by electron shear flows, i.e., electron bulk velocity inside CS is much larger than ion bulk velocity while the density variations through the CS are relatively small (<10%). The electron bulk velocity and, thus, the current density inside the sheets are directed mainly parallel to B 0. The shear in the perpendicular electron and ion bulk velocities generates parallel electron and ion flow vorticities. Inside CS, parallel electron flow vorticity exceeds the parallel ion flow vorticity, changes sign around the CS centers, and peaks near the CS edges. An ion temperature anisotropy develops near CS during the CS formation. It has a positive correlation with the parallel ion and electron flow vorticities. Theoretical estimates support the simulation results.

Identification and characterization of current sheets in collisionless plasma turbulence

Current sheets forming in an ion-kinetic turbulent collisionless plasma are characterized by utilizing the results of two-dimensional hybrid-kinetic numerical simulations (ions treated as kinetic species using particle-in-cell method and electrons treated as mass-less fluid). For this sake, the algorithm, proposed by Zhdankin et al. [Astrophys. J. 771, 124 (2013)] for the identification and characterization of current sheets forming in magnetohydrodynamic plasma turbulence, is extended to current sheets forming in a much noisier kinetic plasma turbulence. Effects of the algorithm parameters on the identification of current sheets in plasma turbulence are analyzed. Based on this analysis, appropriate values of algorithm parameters for the current sheet identification are chosen. Current sheets are statistically characterized in terms of their main properties—the peak current density, the peak current carrier velocity (mainly electrons), the thickness, the length, and also the aspect ratio (length/thickness). Results of the characterization show that the current sheets have a tendency to thin down to below ion inertial length scale until numerical (grid-resolution based) dissipation stops any further thinning. Simulations that include the physics at the electron inertial scales, e.g., hybrid simulations with electron inertia, are required to fully address the current sheet thinning processes and determination of the final thicknesses of current sheets.

Identifying Magnetic Reconnection in 2D Hybrid Vlasov Maxwell Simulations with Convolutional Neural Networks

Abstract Magnetic reconnection is a fundamental process that quickly releases magnetic energy stored in a plasma. Identifying from simulation outputs where reconnection is taking place is nontrivial and, in general, has to be performed by human experts. Hence, it would be valuable if such an identification process could be automated. Here, we demonstrate that a machine-learning algorithm can help to identify reconnection in 2D simulations of collisionless plasma turbulence. Using a Hybrid Vlasov Maxwell model, a data set containing over 2000 potential reconnection events was generated and subsequently labeled by human experts. We test and compare two machine-learning approaches with different configurations on this data set. The best results are obtained with a convolutional neural network combined with an “image cropping” step that zooms in on potential reconnection sites. With this method, more than 70% of reconnection events can be identified correctly. The importance of different physical variables is evaluated by studying how they affect the accuracy of predictions. Finally, we also discuss various possible causes for wrong predictions from the proposed model.

Uncovering Magnetic Turbulence in Young Supernova Remnants with Polarized X-Ray Imaging

Abstract Observations of young supernova remnants (SNRs) in X-rays and γ-rays have provided conclusive evidence for particle acceleration to at least TeV energies. Analysis of high-spatial-resolution X-ray maps of young SNRs has indicated that the particle acceleration process is accompanied by strong nonadiabatic amplification of magnetic fields. If Fermi acceleration is the mechanism producing the energetic cosmic rays (CRs), the amplified magnetic field must be turbulent, and CR-driven instabilities are among the most probable mechanisms for converting the shock ram pressure into magnetic turbulence. The development and evolution of strong magnetic turbulence in collisionless plasmas forming SNR shells are complicated phenomena which include the amplification of magnetic modes, anisotropic mode transformations at shocks, as well as the nonlinear physics of turbulent cascades. Polarized X-ray synchrotron radiation from ultrarelativistic electrons accelerated in the SNR shock is produced in a thin layer immediately behind the shock and is not subject to the Faraday depolarization effect. These factors open up possibilities to study some properties of magnetic turbulence, and here we present polarized X-ray synchrotron maps of SNR shells assuming different models of magnetic turbulence cascades. It is shown that different models of anisotropic turbulence can be distinguished by measuring the predominant polarization angle direction. We discuss the detection of these features in Tycho’s SNR with the coming generation of X-ray polarimeters such as the Imaging X-ray Polarimetry Explorer.

Interplay between intermittency and dissipation in collisionless plasma turbulence

We study the damping of collisionless Alfvénic turbulence in a strongly magnetised plasma by two mechanisms: stochastic heating (whose efficiency depends on the local turbulence amplitude $\unicode[STIX]{x1D6FF}z_{\unicode[STIX]{x1D706}}$ ) and linear Landau damping (whose efficiency is independent of $\unicode[STIX]{x1D6FF}z_{\unicode[STIX]{x1D706}}$ ), describing in detail how they affect and are affected by intermittency. The overall efficiency of linear Landau damping is not affected by intermittency in critically balanced turbulence, while stochastic heating is much more efficient in the presence of intermittent turbulence. Moreover, stochastic heating leads to a drop in the scale-dependent kurtosis over a narrow range of scales around the ion gyroscale.

Fluidization of collisionless plasma turbulence

In a collisionless, magnetized plasma, particles may stream freely along magnetic field lines, leading to "phase mixing" of their distribution function and consequently, to smoothing out of any "compressive" fluctuations (of density, pressure, etc.). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma-one of the most fundamental physical phenomena that makes plasma different from a conventional fluid. Nevertheless, broad power law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditions conducive to strong Landau damping. Elsewhere in nature, such spectra are normally associated with fluid turbulence, where energy cannot be dissipated in the inertial-scale range and is, therefore, cascaded from large scales to small. By direct numerical simulations and theoretical arguments, it is shown here that turbulence of compressive fluctuations in collisionless plasmas strongly resembles one in a collisional fluid and does have broad power law spectra. This "fluidization" of collisionless plasmas occurs, because phase mixing is strongly suppressed on average by "stochastic echoes," arising due to nonlinear advection of the particle distribution by turbulent motions. Other than resolving the long-standing puzzle of observed compressive fluctuations in the solar wind, our results suggest a conceptual shift for understanding kinetic plasma turbulence generally: rather than being a system where Landau damping plays the role of dissipation, a collisionless plasma is effectively dissipationless, except at very small scales. The universality of "fluid" turbulence physics is thus reaffirmed even for a kinetic, collisionless system.

Thermal disequilibration of ions and electrons by collisionless plasma turbulence

Does overall thermal equilibrium exist between ions and electrons in a weakly collisional, magnetized, turbulent plasma? And, if not, how is thermal energy partitioned between ions and electrons? This is a fundamental question in plasma physics, the answer to which is also crucial for predicting the properties of far-distant astronomical objects such as accretion disks around black holes. In the context of disks, this question was posed nearly two decades ago and has since generated a sizeable literature. Here we provide the answer for the case in which energy is injected into the plasma via Alfvénic turbulence: Collisionless turbulent heating typically acts to disequilibrate the ion and electron temperatures. Numerical simulations using a hybrid fluid-gyrokinetic model indicate that the ion-electron heating-rate ratio is an increasing function of the thermal-to-magnetic energy ratio, [Formula: see text]: It ranges from [Formula: see text] at [Formula: see text] to at least 30 for [Formula: see text] This energy partition is approximately insensitive to the ion-to-electron temperature ratio [Formula: see text] Thus, in the absence of other equilibrating mechanisms, a collisionless plasma system heated via Alfvénic turbulence will tend toward a nonequilibrium state in which one of the species is significantly hotter than the other, i.e., hotter ions at high [Formula: see text] and hotter electrons at low [Formula: see text] Spectra of electromagnetic fields and the ion distribution function in 5D phase space exhibit an interesting new magnetically dominated regime at high [Formula: see text] and a tendency for the ion heating to be mediated by nonlinear phase mixing ("entropy cascade") when [Formula: see text] and by linear phase mixing (Landau damping) when [Formula: see text].

Fully Kinetic versus Reduced-kinetic Modeling of Collisionless Plasma Turbulence

Abstract We report the results of a direct comparison between different kinetic models of collisionless plasma turbulence in two spatial dimensions. The models considered include a first-principles fully kinetic (FK) description, two widely used reduced models (gyrokinetic (GK) and hybrid-kinetic (HK) with fluid electrons), and a novel reduced gyrokinetic approach (KREHM). Two different ion beta ( ) regimes are considered: 0.1 and 0.5. For , good agreement between the GK and FK models is found at scales ranging from the ion to the electron gyroradius, thus providing firm evidence for a kinetic Alfvén cascade scenario. In the same range, the HK model produces shallower spectral slopes, presumably due to the lack of electron Landau damping. For , a detailed analysis of spectral ratios reveals a slight disagreement between the GK and FK descriptions at kinetic scales, even though kinetic Alfvén fluctuations likely still play a significant role. The discrepancy can be traced back to scales above the ion gyroradius, where the FK and HK results seem to suggest the presence of fast magnetosonic and ion Bernstein modes in both plasma beta regimes, but with a more notable deviation from GK in the low-beta case. The identified practical limits and strengths of reduced-kinetic approximations, compared here against the FK model on a case-by-case basis, may provide valuable insight into the main kinetic effects at play in turbulent collisionless plasmas, such as the solar wind.

Reconnection and small-scale fields in 2D-3V hybrid-kinetic driven turbulence simulations

The understanding of the fundamental properties of turbulence in collisionless plasmas, such as the solar wind, is a frontier problem in plasma physics. In particular, the occurrence of magnetic reconnection in turbulent plasmas and its interplay with a fully-developed turbulent state is still a matter of great debate. Here we investigate the properties of small-scale electromagnetic fluctuations and the role of fast magnetic reconnection in the development of a quasi-steady turbulent state by means of 2D-3V high-resolution Vlasov–Maxwell simulations. At the largest scales turbulence is fed by external random forcing. We show that large-scale turbulent motions establish a spectrum at and, at the same time, feed the formation of current sheets where magnetic reconnection occurs. As a result coherent magnetic structures are generated which, together with the rise of the associated small-scale non-ideal electric field, mediate the transition between the inertial and the subproton-scale spectrum. A mechanism that boosts the magnetic reconnection process is identified, making the generation of coherent structures rapid enough to be competitive with wave mode interactions and leading to the formation of a fully-developed turbulent spectrum across the so-called ion break.

Features of collisionless turbulence in the intracluster medium from simulated Faraday Rotation maps

Observations of the intracluster medium (ICM) in galaxy clusters suggest for the presence of turbulence and the magnetic fields existence has been proved through observations of Faraday Rotation and synchrotron emission. The ICM is also known to be filled by a rarefied weakly collisional plasma. In this work we study the possible signatures left on Faraday Rotation maps by collisionless instabilities. For this purpose we use a numerical approach to investigate the dynamics of the turbulence in collisionless plasmas based on an magnetohydrodynamical (MHD) formalism taking into account different levels of pressure anisotropy. We consider models covering the sub/super-Alfv\'enic and trans/supersonic regimes, one of them representing the fiducial conditions corresponding to the ICM. From the simulated models we compute Faraday Rotation maps and analyze several statistical indicators in order to characterize the magnetic field structure and compare the results obtained with the collisionless model to those obtained using standard collisional MHD framework. We find that important imprints of the pressure anisotropy prevails in the magnetic field and also manifest in the associated Faraday Rotation maps which evidence smaller correlation lengths in the collisionless MHD case. These points are remarkably noticeable for the case mimicking the conditions prevailing in ICM. Nevertheless, in this study we have neglected the decrease of pressure anisotropy due to the feedback of the instabilities that naturally arise in collisionless plasmas at small scales. This decrease may not affect the statistical imprint differences described above, but should be examined elsewhere.

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.

Fluid simulations of ion scale plasmas with weakly distorted magnetic fields

Three-dimensional simulations of turbulence in collisionless plasmas are presented, using a fluid model that extends the anisotropic MHD to scales of the order of the ion gyroradius and below in directions perpendicular to the ambient magnetic field. This model, which includes linear Landau damping and finite Larmor radius corrections to all the retained moments, provides an efficient tool to describe Alfvénic turbulence in the absence of cyclotron resonance. When sufficiently small scales are retained, no artificial damping nor collisional effects is required. Simulations with large-scale Alfvenic driving show the development of perpendicular power-law spectra (taken at zero parallel wavenumber) with an exponent close to –2.8 for the perpendicular magnetic field at scales smaller than the ion inertial length. The electric field spectrum displays a break at intermediate scales, consistent with Solar Wind observations. These spectra appear in a quasi-stationary state after early-formed sheet-like density and current structures have evolved into filaments. In the presence of temperature anisotropy, the nonlinear development of the mirror instability leads to pressure-balanced magnetic structures surrounded by significant ion velocity fields perpendicular to the ambient field. At later time, the system becomes turbulent, with the disruption of the magnetic structures into parallel filaments.

On apparent temperature in low-frequency Alfvénic turbulence

Low-frequency, parallel propagating Alfvénic turbulence in collisionless plasmas is theoretically studied. Alfvénic turbulence is derived as an equilibrium state (Beltrami field) in the magnetohydrodynamic equations with the pressure anisotropy and multi-species of ions. It is shown that the conservation of the total “apparent temperature” corresponds to the Bernoulli law. A simple model of the radially expanding solar wind including Alfvénic turbulence is also discussed. The conversion of the wave energy in the “apparent temperature” into the “real temperature” is facilitated with increasing radial distance.

Particle-in-cell simulations of particle energization from low Mach number fast mode shocks

Astrophysical shocks are often studied in the high Mach number limit but weakly compressive fast shocks can occur in magnetic reconnection outflows and are considered to be a site of particle energization in solar flares. Here we study the microphysics of such perpendicular, low Mach number collisionless shocks using two-dimensional particle-in-cell simulations with a reduced ion/electron mass ratio and employ a moving wall boundary method for initial generation of the shock. This moving wall method allows for more control of the shock speed, smaller simulation box sizes, and longer simulation times than the commonly used fixed wall, reflection method of shock formation. Our results, which are independent of the shock formation method, reveal the prevalence shock drift acceleration (SDA) of both electron and ions in a purely perpendicular shock with Alfvén Mach number MA=6.8 and ratio of thermal to magnetic pressure β=8. We determine the respective minimum energies required for electrons and ions to incur SDA. We derive a theoretical electron distribution via SDA that compares to the simulation results. We also show that a modified two-stream instability due to the incoming and reflecting ions in the shock transition region acts as the mechanism to generate collisionless plasma turbulence that sustains the shock.

Turbulence in collisionless plasmas: statistical analysis from numerical simulations with pressure anisotropy

In recent years, we have experienced increasing interest in the understanding of the physical properties of collisionless plasmas, mostly because of the large number of astrophysical environments (e.g. the intracluster medium (ICM)) containing magnetic fields that are strong enough to be coupled with the ionized gas and characterized by densities sufficiently low to prevent the pressure isotropization with respect to the magnetic line direction. Under these conditions, a new class of kinetic instabilities arises, such as firehose and mirror instabilities, which have been studied extensively in the literature. Their role in the turbulence evolution and cascade process in the presence of pressure anisotropy, however, is still unclear. In this work, we present the first statistical analysis of turbulence in collisionless plasmas using three-dimensional numerical simulations and solving double-isothermal magnetohydrodynamic equations with the Chew–Goldberger–Low laws closure (CGL-MHD). We study models with different initial conditions to account for the firehose and mirror instabilities and to obtain different turbulent regimes. We found that the CGL-MHD subsonic and supersonic turbulences show small differences compared to the MHD models in most cases. However, in the regimes of strong kinetic instabilities, the statistics, i.e. the probability distribution functions (PDFs) of density and velocity, are very different. In subsonic models, the instabilities cause an increase in the dispersion of density, while the dispersion of velocity is increased by a large factor in some cases. Moreover, the spectra of density and velocity show increased power at small scales explained by the high growth rate of the instabilities. Finally, we calculated the structure functions of velocity and density fluctuations in the local reference frame defined by the direction of magnetic lines. The results indicate that in some cases the instabilities significantly increase the anisotropy of fluctuations. These results, even though preliminary and restricted to very specific conditions, show that the physical properties of turbulence in collisionless plasmas, as those found in the ICM, may be very different from what has been largely believed. Implications can range from interchange of energies to cosmic ray acceleration.

Global Scale-Invariant Dissipation in Collisionless Plasma Turbulence

A higher-order multiscale analysis of the dissipation range of collisionless plasma turbulence is presented using in situ high-frequency magnetic field measurements from the Cluster spacecraft in a stationary interval of fast ambient solar wind. The observations, spanning five decades in temporal scales, show a crossover from multifractal intermittent turbulence in the inertial range to non-Gaussian monoscaling in the dissipation range. This presents a strong observational constraint on theories of dissipation mechanisms in turbulent collisionless plasmas.