Hybrid Vlasov-Maxwell Simulations Research Articles

On the fractal pattern of the current structure at ion scales in turbulent space plasmas

The recent ability to investigate the features of magnetic field fluctuations at ion/sub-ion scales employing both measurements and simulations has clearly demonstrated how, at these scales, the current has a filamentary structure, i.e., it is not a compact structure. This points toward the idea that the current and the dissipation field may have a fractal structure. An intriguing question immediately arises: is there a relationship between the fractal topology of currents at ion/sub-ion scales and the observed spectral features at the same scales? The goal of this work is to investigate the fractal topology of currents at the Low-end of MHD inertial domain and at ion scales using Hall-MagnetoHydroDynamics and Hybrid Vlasov-Maxwell simulations. The results show a clear relationship between the fractal dimension of the current pattern and the spectral features at ion scales. The relevance of this link is discussed in connection with the dynamics of coherent plasma structures at these scales.

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.

Local and global properties of energy transfer in models of plasma turbulence

The nature of the turbulent energy transfer rate is studied using direct numerical simulations of weakly collisional space plasmas. This is done comparing results obtained from hybrid Vlasov–Maxwell simulations of collisionless plasmas, Hall magnetohydrodynamics and Landau fluid models reproducing low-frequency kinetic effects, such as the Landau damping. In this turbulent scenario, estimates of the local and global scaling properties of different energy channels are obtained using a proxy of the local energy transfer. This approach provides information on the structure of energy fluxes, under the assumption that the turbulent cascade transfers most of the energy that is then dissipated at small scales by various kinetic processes in these kinds of plasmas.

Statistical properties of turbulent fluctuations associated with electron-only magnetic reconnection

Context. Recent satellite measurements in the turbulent magnetosheath of Earth have given evidence of an unusual reconnection mechanism that is driven exclusively by electrons. This newly observed process was called electron-only reconnection, and its interplay with plasma turbulence is a matter of great debate. Aims. By using 2D-3V hybrid Vlasov–Maxwell simulations of freely decaying plasma turbulence, we study the role of electron-only reconnection in the development of plasma turbulence. In particular, we search for possible differences with respect to the turbulence associated with standard ion-coupled reconnection. Methods. We analyzed the structure functions of the turbulent magnetic field and ion fluid velocity fluctuations to characterize the structure and the intermittency properties of the turbulent energy cascade. Results. We find that the statistical properties of turbulent fluctuations associated with electron-only reconnection are consistent with those of turbulent fluctuations associated with standard ion-coupled reconnection, and no peculiar signature related to electron-only reconnection is found in the turbulence statistics. This result suggests that the turbulent energy cascade in a collisionless magnetized plasma does not depend on the specific mechanism associated with magnetic reconnection. The properties of the dissipation range are discussed as well, and we claim that only electrons contribute to the dissipation of magnetic field energy at sub-ion scales.

Electron-Only Reconnection in Plasma Turbulence

Hybrid-Vlasov–Maxwell simulations of magnetized plasma turbulence including non-linear electron-inertia effects in a generalized Ohm's law are presented. When fluctuation energy is injected on scales sufficiently close to ion-kinetic scales, the ions efficiently become de-magnetized and electron-scale current sheets largely dominate the distribution of the emerging current structures, in contrast to the usual picture, where a full hierarchy of structure sizes is generally observed. These current sheets are shown to be the sites of electron-only reconnection (e-rec), in which the usual electron exhausts are unaccompanied by ion outflows and which are in qualitative agreement with those recently observed by MMS in the Earth's turbulent magnetosheath, downstream of the bow shock. Some features of the e-rec phenomenology are shown to be consistent with an electron magnetohydrodynamic description. Simulations suggest that this regime of collisionless reconnection may be found in turbulent systems where plasma processes, such as micro-instabilities and/or shocks, overpower the more customary turbulent cascade by directly injecting energy close to the ion-kinetic scales.

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.

Kelvin–Helmholtz Instability at Proton Scales with an Exact Kinetic Equilibrium

Abstract The Kelvin–Helmholtz instability (KHI) is a ubiquitous physical process in ordinary fluids and plasmas, frequently observed also in space environments. In this paper, kinetic effects at proton scales in the nonlinear and turbulent stage of the KHI have been studied in magnetized collisionless plasmas by means of hybrid Vlasov–Maxwell simulations. The main goal of this work is to point out the back-reaction on particles triggered by the evolution of such instability, as energy reaches kinetic scales along the turbulent cascade. Interestingly, turbulence is inhibited when KHI develops over an initial state that is not an exact equilibrium state. On the other hand, when an initial equilibrium condition is considered, energy can be efficiently transferred toward short scales, reaches the typical proton wavelengths, and drives the dynamics of particles. As a consequence of the interaction of particles with the turbulent fluctuating fields, the proton velocity distribution deviates significantly from the local thermodynamic equilibrium, the degree of deviation increasing with the level of turbulence in the system and being located near regions of strong magnetic stresses. These numerical results support recent space observations from the Magnetospheric MultiScale mission of ion kinetic effects driven by the turbulent dynamics at Earth’s magnetosheath and by the KHI in Earth’s magnetosphere.

Plasma turbulence at ion scales: a comparison between particle in cell and Eulerian hybrid-kinetic approaches

Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma models is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic simulations of plasma turbulence obtained with two complementary approaches spanning approximately two decades in wavenumber – from the magnetohydrodynamics inertial range to scales well below the ion gyroradius – with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell simulations of freely decaying Alfvénic turbulence, whereas the other consists of Eulerian hybrid Vlasov–Maxwell simulations of turbulence continuously driven with partially compressible large-scale fluctuations. Despite the completely different initialization and injection/drive at large scales, the same properties of turbulent fluctuations at $k_{\bot }\unicode[STIX]{x1D70C}_{i}\gtrsim 1$ are observed, where $k_{\bot }$ is the fluctuations’ wavenumber perpendicular to the background magnetic field and $\unicode[STIX]{x1D70C}_{i}$ is the ion Larmor radius. The system indeed self-consistently ‘reprocesses’ the turbulent fluctuations while they are cascading towards smaller and smaller scales, in a way which actually depends on the plasma beta parameter ($\unicode[STIX]{x1D6FD}$ is the ratio between the thermal and the magnetic pressures). Small-scale turbulence has been found to be mainly populated by kinetic Alfvén wave (KAW) fluctuations for $\unicode[STIX]{x1D6FD}\geqslant 1$, whereas KAW fluctuations are only sub-dominant for low-$\unicode[STIX]{x1D6FD}$.

Erratum: “Multifractal scaling and intermittency in hybrid Vlasov-Maxwell simulations of plasma turbulence” [Phys. Plasmas 23, 022307 (2016)

Erratum: “Multifractal scaling and intermittency in hybrid Vlasov-Maxwell simulations of plasma turbulence” [Phys. Plasmas <b>23</b>, 022307 (2016)

Multifractal scaling and intermittency in hybrid Vlasov-Maxwell simulations of plasma turbulence

By employing Hybrid Vlasov-Maxwell simulations in 2D-3V phase space configuration (2D in physical space and 3D in velocity space) of plasma turbulence, the statistical properties of the energy cascade at kinetic scales have been investigated. High-order moments of the magnetic field fluctuations have been inspected in order to quantify the intermittency phenomenon. At scales l larger than the ion skin depth di, fluctuations exhibit anomalous scaling, suggesting the presence of a multifractal intermittent turbulent cascade. For l&amp;lt;di, fluctuations show monoscaling, indicating Gaussian statistics. This scenario is consistent with the statistics of the dissipation fields J·E and J2, suggesting that the processes of dissipation, intended as a conversion of energy from electromagnetic fluctuations to electron Ohmic heating and non-thermal proton effects, occur non-homogeneously in space.

KINETIC ALFVÉN WAVE GENERATION BY LARGE-SCALE PHASE MIXING

One view of the solar-wind turbulence is that the observed highly anisotropic fluctuations at spatial scales near the proton inertial length $d_p$ may be considered as Kinetic Alfv\'en waves (KAWs). In the present paper, we show how phase-mixing of large-scale parallel propagating Alfv\'en waves is an efficient mechanism for the production of KAWs at wavelengths close to $d_p$ and at large propagation angle with respect to the magnetic field. Magnetohydrodynamic (MHD), Hall-Magnetohydrodynamic (HMHD), and hybrid Vlasov-Maxwell (HVM) simulations modeling the propagation of Alfv\'en waves in inhomogeneous plasmas are performed. In linear regime, the role of dispersive effects is singled out by comparing MHD and HMHD results. Fluctuations produced by phase-mixing are identified as KAWs through a comparison of polarization of magnetic fluctuations and wave group velocity with analytical linear predictions. In the nonlinear regime, comparison of HMHD and HVM simulations allows to point out the role of kinetic effects in shaping the proton distribution function. We observe generation of temperature anisotropy with respect to the local magnetic field and production of field-aligned beams. The regions where the proton distribution function highly departs from thermal equilibrium are located inside the shear layers, where the KAWs are excited, this suggesting that the distortions of the proton distribution are driven by a resonant interaction of protons with KAW fluctuations. Our results are relevant in configurations where magnetic field inhomogeneities are present, as, for example, in the solar corona where the presence of Alfv\'en waves has been ascertained.

Vlasov simulations of kinetic Alfvén waves at proton kinetic scales

Kinetic Alfvén waves represent an important subject in space plasma physics, since they are thought to play a crucial role in the development of the turbulent energy cascade in the solar wind plasma at short wavelengths (of the order of the proton gyro radius ρp and/or inertial length dp and beyond). A full understanding of the physical mechanisms which govern the kinetic plasma dynamics at these scales can provide important clues on the problem of the turbulent dissipation and heating in collisionless systems. In this paper, hybrid Vlasov-Maxwell simulations are employed to analyze in detail the features of the kinetic Alfvén waves at proton kinetic scales, in typical conditions of the solar wind environment (proton plasma beta βp = 1). In particular, linear and nonlinear regimes of propagation of these fluctuations have been investigated in a single-wave situation, focusing on the physical processes of collisionless Landau damping and wave-particle resonant interaction. Interestingly, since for wavelengths close to dp and βp ≃ 1 (for which ρp ≃ dp) the kinetic Alfvén waves have small phase speed compared to the proton thermal velocity, wave-particle interaction processes produce significant deformations in the core of the particle velocity distribution, appearing as phase space vortices and resulting in flat-top velocity profiles. Moreover, as the Eulerian hybrid Vlasov-Maxwell algorithm allows for a clean almost noise-free description of the velocity space, three-dimensional plots of the proton velocity distribution help to emphasize how the plasma departs from the Maxwellian configuration of thermodynamic equilibrium due to nonlinear kinetic effects.

A kinetic model of plasma turbulence

A Hybrid Vlasov–Maxwell (HVM) model is presented and recent results about the link between kinetic effects and turbulence are reviewed. Using five-dimensional (2D in space and 3D in the velocity space) simulations of plasma turbulence, it is found that kinetic effects (or non-fluid effects) manifest through the deformation of the proton velocity distribution function (DF), with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The direction of theproper temperature anisotropy, calculated in the main reference frame of the distribution itself, has a finite probability of being along or across the ambient magnetic field, in general agreement with the classical definition of anisotropyT⊥/T∥(where subscripts refer to the magnetic field direction). Adopting the latter conventional definition, by varying the global plasma beta (β) and fluctuation level, simulations explore distinct regions of the space given byT⊥/T∥and β∥, recovering solar wind observations. Moreover, as in the solar wind, HVM simulations suggest that proton anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. The role of alpha particles is reviewed using multi-ion kinetic simulations, revealing a similarity between proton and helium non-Maxwellian effects. The techniques presented here are applied to 1D spacecraft-like analysis, establishing a link between non-fluid phenomena and solar wind magnetic discontinuities. Finally, the dimensionality of turbulence is investigated, for the first time, via 6D HVM simulations (3D in both spaces). These preliminary results provide support for several previously reported studies based on 2.5D simulations, confirming several basic conclusions. This connection between kinetic features and turbulence open a new path on the study of processes such as heating, particle acceleration, and temperature-anisotropy, commonly observed in space plasmas.

Hybrid Vlasov-Maxwell simulations of two-dimensional turbulence in plasmas

Turbulence in plasmas is a very challenging problem since it involves wave-particle interactions, which are responsible for phenomena such as plasma dissipation, acceleration mechanisms, heating, temperature anisotropy, and so on. In this work, a hybrid Vlasov-Maxwell numerical code is employed to study local kinetic processes in a two-dimensional turbulent regime. In the present model, ions are treated as a kinetic species, while electrons are considered as a fluid. As recently reported in [S. Servidio, Phys. Rev. Lett. 108, 045001 (2012)], nearby regions of strong magnetic activity, kinetic effects manifest through a deformation of the ion velocity distribution function that consequently departs from the equilibrium Maxwellian configuration. Here, the structure of turbulence is investigated in detail in phase space, by evaluating the high-order moments of the particle velocity distribution, i.e., temperature, skewness, and kurtosis. This analysis provides quantitative information about the non-Maxwellian character of the system dynamics. This departure from local thermodynamic equilibrium triggers several processes commonly observed in many astrophysical and laboratory plasmas.

Analysis of intermittent heating in a multi-component turbulent plasma

Kinetic effects and turbulence are two phenomena that characterize the solar wind, and, therefore, kinetic models represent the best tool of investigation for this collisionless plasma. In this work, hybrid Vlasov-Maxwell simulations are performed to investigate the intermittent heating of the solar wind, in a two-dimensional multi-ion plasma composed by protons, alpha particles and fluid electrons. The numerical results show that particle distribution functions depart from the typical Maxwellian configuration under the effect of the turbulence. Both ion species develop temperature anisotropy, with respect to the local magnetic field, that increases during the development of the turbulent cascade. During the nonlinear evolution of the system, coherent structures (vortices and current sheets) appear in physical space, related to the intermittent nature of the magnetic field. Conditioned ion temperature distributions suggest that enhancements of ion temperatures are associated with stronger coherent structures, in agreement with recent solar wind data analyses.

PROTON KINETIC EFFECTS IN VLASOV AND SOLAR WIND TURBULENCE

Kinetic plasma processes have been investigated in the framework of solar wind turbulence, employing Hybrid Vlasov-Maxwell (HVM) simulations. The dependency of proton temperature anisotropy T_{\perp}/T_{\parallel} on the parallel plasma beta \beta_{\parallel}, commonly observed in spacecraft data, has been recovered using an ensemble of HVM simulations. By varying plasma parameters, such as plasma beta and fluctuation level, the simulations explore distinct regions of the parameter space given by T_{\perp}/T_{\parallel} and \beta_{\parallel}, similar to solar wind sub-datasets. Moreover, both simulation and solar wind data suggest that temperature anisotropy is not only associated with magnetic intermittent events, but also with gradient-type structures in the flow and in the density. This connection between non-Maxwellian kinetic effects and various types of intermittency may be a key point for understanding the complex nature of plasma turbulence.

VLASOV SIMULATIONS OF MULTI-ION PLASMA TURBULENCE IN THE SOLAR WIND

Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a two-dimensional turbulent multi-ion plasma, composed of protons, alpha particles and fluid electrons. In the typical conditions of the solar-wind environment, and in situations of decaying turbulence, the numerical results show that the velocity distribution functions of both ion species depart from the typical configuration of thermal equilibrium. These non-Maxwellian features are quantified through the statistical analysis of the temperature anisotropy, for both protons and alpha particles, in the reference frame given by the local magnetic field. Anisotropy is found to be higher in regions of high magnetic stress. Both ion species manifest a preferentially perpendicular heating, although the anisotropy is more pronounced for the alpha particles, according with solar wind observations. Anisotropy of the alpha particle, moreover, is correlated to the proton anisotropy, and also depends on the local differential flow between the two species. Evident distortions of the particle distribution functions are present, with the production of bumps along the direction of the local magnetic field. The physical phenomenology recovered in these numerical simulations reproduces very common measurements in the turbulent solar wind, suggesting that the multi-ion Vlasov model constitutes a valid approach to the understanding of the nature of complex kinetic effects in astrophysical plasmas.

Excitation of nonlinear electrostatic waves with phase velocity close to the ion-thermal speed

Recent hybrid Vlasov–Maxwell simulations predicted the presence of a significant level of electrostatic activity, consisting of ion-acoustic waves and of a new branch of waves (called ion-bulk (IBk) waves), at short spatial scalelengths in the tail of the solar-wind turbulent cascade along the direction of the ambient magnetic field. These waves, driven by particle trapping processes, have phase speed comparable to the ion-thermal speed and acoustic dispersion. In this paper, the hybrid Vlasov–Maxwell code redesigned in the electrostatic configuration is used to reproduce the excitation of the IBk waves. An external driver electric field is applied to the plasma ions in order to create a population of trapped particles. This inhibits Landau damping that would otherwise suppress these low phase speed oscillations. The aim of this work is to show that the IBk waves, like ordinary linear modes, can be excited by general type drivers (even of low amplitude) applied to the plasma. Finally, Vlasov–Poisson simulations, with kinetic ions and Boltzmann electrons, are used to point out the limitations of the quasi-neutrality assumption, on which the hybrid model is based.

SHORT-WAVELENGTH ELECTROSTATIC FLUCTUATIONS IN THE SOLAR WIND

Hybrid Vlasov-Maxwell simulations have been used recently to investigate the dynamics of the solar-wind plasma in the tail at short wavelengths of the energy cascade. These simulations have shown that a significant level of electrostatic activity is detected at wavelengths smaller than the proton inertial scale in the longitudinal direction with respect to the ambient magnetic field. In this paper, we describe the results of a new series of hybrid Vlasov-Maxwell simulations that allow us to investigate in more detail the generation process of these electrostatic fluctuations in terms of the electron-to-proton temperature ratio Te /Tp . This analysis gives evidence for the first time that even in the case of cold electrons, Te Tp (the appropriate condition for solar-wind plasmas), the resonant interaction of protons with large-scale left-hand polarized ion-cyclotron waves is responsible for the excitation of short-scale electrostatic fluctuations with an acoustic dispersion relation. Moreover, through our numerical results we propose a physical mechanism to explain the generation of longitudinal proton-beam distributions in typical conditions of the solar-wind environment.

The kinetic nature of turbulence at short scales in the solar wind

The analysis of the transition from the large-scale fluid regime to the short-scale kinetic range of wavelengths in the development of the turbulent cascade of energy is nowadays subject of fervent discussion in the space plasmas scientific community. We make use of Hybrid Vlasov–Maxwell simulations where the full kinetic dynamics of ions is taken into account, while electrons are treated as a fluid. We investigate the development of turbulence in the solar wind, in 1D–3V phase space configuration and in the frequency range across the ion cyclotron frequency. These simulations allow for the analysis of the role of kinetic effects in the short-scale region of the energy spectra in the direction parallel to the background magnetic field. Our numerical results show the presence of a significant electrostatic activity at small wavelengths, triggered by the resonant interaction of ions with longitudinal waves. Our model does not allow to take into account the evolution of the turbulent spectra in the plane perpendicular to the ambient field, due to limited dimensionality in phase space. On the other hand, this model permits to isolate and study the possibility of transferring the electromagnetic large-scale energy on the small-scale kinetic electrostatic component of the spectrum. Peculiar features observed in the spacecraft data in the solar wind are qualitatively reproduced within the hybrid-Vlasov model, such as the generation of perpendicular temperature anisotropy and accelerated longitudinal beams of ions in the distribution of particle velocities as well as the appearance of a marked peak of electrostatic activity in the short-scale termination of the turbulent spectra.