Search

Over the past decades, near-Earth spacecraft observations have provided insights into the physics of the bow shock, suggesting that solar wind intrinsic turbulence influences the bow shock dynamics. On the other hand, theoretical studies, based on global numerical simulations, have not yet investigated the global 3D interaction between a turbulent solar wind and a planetary magnetosphere. This paper addresses this gap for the first time by investigating the global dynamics of this interaction, providing new perspectives on the underlying physical processes. We examine how the turbulent nature of the solar wind influences the 3D structure and dynamics of magnetized planetary environments or magnetized Earth-like exoplanets, using the newly developed numerical code Menura. We use the hybrid PIC model Menura to conduct 3D simulations of the turbulent solar wind and its interaction with an Earth-like magnetized planet through global numerical simulations of the magnetosphere and its surroundings. We show that solar wind turbulence globally influences the shape and dynamics of the bow shock, the magnetosheath structures, and the ion foreshock dynamics. We show that a turbulent solar wind disrupts the coherence of foreshock fluctuations, induces large fluctuations on the quasi-perpendicular surface of the bow shock, facilitates the formation of bubble-like structures near the bow shock's nose, and modifies the properties of the magnetosheath region. None of these phenomena occur when comparing with the case in which the solar wind is laminar. The turbulent nature of the solar wind impacts the 3D shape and dynamics of the bow shock, magnetosheath, and ion foreshock region. This influence should be considered when studying solar wind-planet interactions in observations and simulations. We discuss the relevance of our findings for current and future missions launched into the heliosphere.

The ESA-JAXA BepiColombo mission will provide simultaneous measurements from two spacecraft, offering an unprecedented opportunity to investigate magnetospheric and exospheric dynamics at Mercury as well as their interactions with the solar wind, radiation, and interplanetary dust. Many scientific instruments onboard the two spacecraft will be completely, or partially devoted to study the near-space environment of Mercury as well as the complex processes that govern it. Many issues remain unsolved even after the MESSENGER mission that ended in 2015. The specific orbits of the two spacecraft, MPO and Mio, and the comprehensive scientific payload allow a wider range of scientific questions to be addressed than those that could be achieved by the individual instruments acting alone, or by previous missions. These joint observations are of key importance because many phenomena in Mercury's environment are highly temporally and spatially variable. Examples of possible coordinated observations are described in this article, analysing the required geometrical conditions, pointing, resolutions and operation timing of different BepiColombo instruments sensors., Comment: 78 pages, 14 figures, published

Density inhomogeneities are ubiquitous in space and astrophysical plasmas, in particular at contact boundaries between different media. They often correspond to regions that exhibits strong dynamics on a wide range of spatial and temporal scales. Indeed, density inhomogeneities are a source of free energy that can drive various instabilities such as, for instance, the lower-hybrid-drift instability which in turn transfers energy to the particles through wave-particle interactions and eventually heat the plasma. We aim at quantifying the efficiency of the lower-hybrid-drift instability to accelerate and/or heat electrons parallel to the ambient magnetic field. We combine two complementary methods: full-kinetic and quasilinear models. We report self-consistent evidence of electron acceleration driven by the development of the lower-hybrid-drift instability using 3D-3V full-kinetic numerical simulations. The efficiency of the observed acceleration cannot be explained by standard quasilinear theory. For this reason, we develop an extended quasilinear model able to quantitatively predict the interaction between lower-hybrid fluctuations and electrons on long time scales, now in agreement with full-kinetic simulations results. Finally, we apply this new, extended quasilinear model to a specific inhomogeneous space plasma boundary: the magnetopause of Mercury, and we discuss our quantitative predictions of electron acceleration in support to future BepiColombo observations., Comment: Paper under evaluation for publication on the journal "Astronomy and Astrophysics"

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 non-trivial 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 (HVM) 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 (CNN) 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., Comment: 16 pages, 9 figures and 5 tabels

This white paper submitted for 2020 Decadal Assessment of Plasma Science concerns the importance of multi-spacecraft missions to address fundamental questions concerning plasma turbulence. Plasma turbulence is ubiquitous in the universe, and it is responsible for the transport of mass, momentum, and energy in such diverse systems as the solar corona and wind, accretion discs, planet formation, and laboratory fusion devices. Turbulence is an inherently multi-scale and multi-process phenomenon, coupling the largest scales of a system to sub-electron scales via a cascade of energy, while simultaneously generating reconnecting current layers, shocks, and a myriad of instabilities and waves. The solar wind is humankind's best resource for studying the naturally occurring turbulent plasmas that permeate the universe. Since launching our first major scientific spacecraft mission, Explorer 1, in 1958, we have made significant progress characterizing solar wind turbulence. Yet, due to the severe limitations imposed by single point measurements, we are unable to characterize sufficiently the spatial and temporal properties of the solar wind, leaving many fundamental questions about plasma turbulence unanswered. Therefore, the time has now come wherein making significant additional progress to determine the dynamical nature of solar wind turbulence requires multi-spacecraft missions spanning a wide range of scales simultaneously. A dedicated multi-spacecraft mission concurrently covering a wide range of scales in the solar wind would not only allow us to directly determine the spatial and temporal structure of plasma turbulence, but it would also mitigate the limitations that current multi-spacecraft missions face, such as non-ideal orbits for observing solar wind turbulence. Some of the fundamentally important questions that can only be addressed by in situ multipoint measurements are discussed., Comment: 6 pages, submitted for the Plasma 2020 Decadal Survey

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., Comment: 20 pages, 8 figures; Accepted for publication

We present a three-dimensional study of the plasma dynamics at the flank magnetopause of the Earth's magnetosphere during mainly northward interplanetary magnetic field (IMF) periods. Two-fluid simulations show that the initial magnetic shear at the magnetopause and the field line bending caused by the dynamics itself (in a configuration taken as representative of the properties of the flank magnetopause) influence both the location where the Kelvin-Helmholtz (KH) instability and the induced magnetic reconnection take place and their nonlinear development. The KH vortices develop asymmetrically with respect to the Earth's equatorial plane where the local KH linear growth rate is maximal. Vortex driven reconnection processes take place at different latitudes, ranging from the equatorial plane to mid-latitude regions, but only in the hemisphere that turns out to be the less KH unstable. These results suggest that KH-induced reconnection is not limited to specific regions around the vortices (inside, below or above), but may be triggered over a broad and continuous range of locations in the vicinity of the vortices., Comment: 29 pages, 6 figures, 1 table; submitted

To explain energy dissipation via turbulence in collisionless, magnetized plasmas, the existence of a dual real- and velocity-space cascade of ion-entropy fluctuations below the ion gyroradius has been proposed. Such a dual cascade, predicted by the gyrokinetic theory, has previously been observed in gyrokinetic simulations of two-dimensional, electrostatic turbulence. For the first time we show evidence for a dual phase-space cascade of ion-entropy fluctuations in a three-dimensional simulation of hybrid-kinetic, electromagnetic turbulence. Some of the scalings observed in the energy spectra are consistent with a generalized theory for the cascade that accounts for the spectral anisotropy of critically balanced, intermittent, sub-ion-Larmor-scale fluctuations. The observed velocity-space cascade is also anisotropic with respect to the magnetic-field direction, with linear phase mixing along magnetic-field lines proceeding mainly at spatial scales above the ion gyroradius and nonlinear phase mixing across magnetic-field lines proceeding at perpendicular scales below the ion gyroradius. Such phase-space anisotropy could be sought in heliospheric and magnetospheric data of solar-wind turbulence and has far-reaching implications for the dissipation of turbulence in weakly collisional astrophysical plasmas., Comment: version accepted in ApJL

Understanding the nature of the turbulent fluctuations below the ion gyroradius in solar-wind turbulence is a great challenge. Recent studies have been mostly in favor of kinetic Alfv\'en wave (KAW) type of fluctuations, but other kinds of fluctuations with characteristics typical of magnetosonic, whistler and ion Bernstein modes, could also play a role depending on the plasma parameters. Here we investigate the properties of the sub-proton-scale cascade with high-resolution hybrid-kinetic simulations of freely-decaying turbulence in 3D3V phase space, including electron inertia effects. Two proton plasma beta are explored: the "intermediate" $\beta_p=1$ and "low" $\beta_p=0.2$ regimes, both typically observed in solar wind and corona. The magnetic energy spectum exhibits $k_\perp^{-8/3}$ and $k_\|^{-7/2}$ power laws at $\beta_p=1$, while they are slightly steeper at $\beta_p=0.2$. Nevertheless, both regimes develop a spectral anisotropy consistent with $k_\|\sim k_\perp^{2/3}$ at $k_\perp\rho_p>1$, and pronounced small-scale intermittency. In this context, we find that the kinetic-scale cascade is dominated by KAW-like fluctuations at $\beta_p=1$, whereas the low-$\beta$ case presents a more complex scenario suggesting the simultaneous presence of different types of fluctuations. In both regimes, however, a non-negligible role of ion Bernstein type of fluctuations at the smallest scales seems to emerge., Comment: 6 pages, 5 figures, final version published in The Astrophysical Journal Letters: Cerri, Servidio & Califano, ApJL 846, L18 (2017)

A new path for the generation of a sub-ion scale cascade in collisionless 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 evidences 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 ~-2.8, 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 towards a spectral index of -5/3 in the MHD range and of ~-3 at sub-ion scales., Comment: 6 pages, 5 figures

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 ($\beta_i$) regimes are considered: 0.1 and 0.5. For $\beta_i=0.5$, 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 Alfv\'en cascade scenario. In the same range, the HK model produces shallower spectral slopes, presumably due to the lack of electron Landau damping. For $\beta_i=0.1$, a detailed analysis of spectral ratios reveals a slight disagreement between the GK and FK descriptions at kinetic scales, even though kinetic Alfv\'en 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 fully-kinetic 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.

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 model 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 about two decades in wavenumber - from MHD inertial range to scales well below the ion gyroradius - with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell (HPIC) simulations of freely-decaying Alfv\'enic turbulence, whereas the other consists of Eulerian hybrid Vlasov-Maxwell (HVM) 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 $k_\perp\rho_i\gtrsim1$ are observed. 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. Small-scale turbulence has been found to be mainly populated by kinetic Alfv\'en wave (KAW) fluctuations for $\beta\geq1$, whereas KAW fluctuations are only sub-dominant for low-$\beta$., Comment: 18 pages, 4 figures, accepted for publication in J. Plasma Phys. (Collection: "The Vlasov equation: from space to laboratory plasma physics")

A long-lasting debate in space plasma physics concerns the nature of subproton-scale fluctuations in solar wind (SW) turbulence. Over the past decade, a series of theoretical and observational studies were presented in favor of either kinetic Alfv\'en wave (KAW) or whistler turbulence. Here, we investigate numerically the nature of the subproton-scale turbulent cascade for typical SW parameters by means of unprecedented high-resolution simulations of forced hybrid-kinetic turbulence in two real-space and three velocity-space dimensions. Our analysis suggests that small-scale turbulence in this model is dominated by KAWs at $\beta\gtrsim1$ and by magnetosonic/whistler fluctuations at lower $\beta$. The spectral properties of the turbulence appear to be in good agreement with theoretical predictions. A tentative interpretation of this result in terms of relative changes in the damping rates of the different waves is also presented. Overall, the results raise interesting new questions about the properties and variability of subproton-scale turbulence in the SW, including its possible dependence on the plasma $\beta$, and call for detailed and extensive parametric explorations of driven kinetic turbulence in three dimensions., Comment: 6 pages, 4 figures, accepted for publication in The Astrophysical Journal Letters

Magnetic fields pervade the entire Universe and affect the formation and evolution of astrophysical systems from cosmological to planetary scales. The generation and dynamical amplification of extragalactic magnetic fields through cosmic times, up to $\mu$Gauss levels reported in nearby galaxy clusters, near equipartition with kinetic energy of plasma motions and on scales of at least tens of kiloparsecs, is a major puzzle largely unconstrained by observations. A dynamo effect converting kinetic flow energy into magnetic energy is often invoked in that context, however extragalactic plasmas are weakly collisional (as opposed to magnetohydrodynamic fluids), and whether magnetic-field growth and sustainment through an efficient turbulent dynamo instability is possible in such plasmas is not established. Fully kinetic numerical simulations of the Vlasov equation in a six-dimensional phase space necessary to answer this question have until recently remained beyond computational capabilities. Here, we show by means of such simulations that magnetic-field amplification via a dynamo instability does occur in a stochastically-driven, non-relativistic subsonic flow of initially unmagnetized collisionless plasma. We also find that the dynamo self-accelerates and becomes entangled with kinetic instabilities as magnetization increases. The results suggest that such a plasma dynamo may be realizable in laboratory experiments, support the idea that intracluster medium (ICM) turbulence may have significantly contributed to the amplification of cluster magnetic fields up to near-equipartition levels on a timescale shorter than the Hubble time, and emphasize the crucial role of multiscale kinetic physics in high-energy astrophysical plasmas., Comment: revised version published in PNAS (doi: 10.1073/pnas.1525194113). Author's version pre-journal final editing, 4 pages, 4 figures, 2 movies (url links in manuscript)

The nonlinear evolution of the Kelvin Helmholtz instability in a magnetized plasma with a perpendicular flow close to, or in, the supermagnetosonic regime can produce a significant parallel-to-perpendicular pressure anisotropy. This anisotropy, localized inside the flow shear region, can make the configuration unstable either to the mirror or to the firehose instability and, in general, can affect the development of the KHI. The interface between the solar wind and the Earth's magnetospheric plasma at the magnetospheric equatorial flanks provides a relevant setting for the development of this complex nonlinear dynamics., Comment: 11 pages, 7 figures, submitted to Plasma Phys. Control. Fusion

Forty articles have been recently published in EPJD as contributions to the topical issue "Theory and applications of the Vlasov equation". The aim of this topical issue was to provide a forum for the presentation of a broad variety of scientific results involving the Vlasov equation. In this editorial, after some introductory notes, a brief account is given of the main points addressed in these papers and of the perspectives they open., Comment: Editorial

Observations and numerical simulations of laboratory and space plasmas in almost collisionless regimes reveal anisotropic and non-gyrotropic particle distribution functions. We investigate how such states can persist in the presence of a sheared flow. We focus our attention on the pressure tensor equation in a magnetized plasma and derive analytical self-consistent plasma equilibria which exhibit a novel asymmetry with respect to the magnetic field direction. These results are relevant for investigating, within fluid models that retain the full pressure tensor dynamics, plasma configurations where a background shear flow is present., Comment: 13 pages, 7 figures

The nonlinear evolution of collisionless plasmas is typically a multi-scale process where the energy is injected at large, fluid scales and dissipated at small, kinetic scales. Accurately modelling the global evolution requires to take into account the main micro-scale physical processes of interest. This is why comparison of different plasma models is today an imperative task aiming at understanding cross-scale processes in plasmas. We report here the first comparative study of the evolution of a magnetized shear flow, through a variety of different plasma models by using magnetohydrodynamic, Hall-MHD, two-fluid, hybrid kinetic and full kinetic codes. Kinetic relaxation effects are discussed to emphasize the need for kinetic equilibriums to study the dynamics of collisionless plasmas in non trivial configurations. Discrepancies between models are studied both in the linear and in the nonlinear regime of the magnetized Kelvin-Helmholtz instability, to highlight the effects of small scale processes on the nonlinear evolution of collisionless plasmas. We illustrate how the evolution of a magnetized shear flow depends on the relative orientation of the fluid vorticity with respect to the magnetic field direction during the linear evolution when kinetic effects are taken into account. Even if we found that small scale processes differ between the different models, we show that the feedback from small, kinetic scales to large, fluid scales is negligable in the nonlinear regime. This study show that the kinetic modeling validates the use of a fluid approach at large scales, which encourages the development and use of fluid codes to study the nonlinear evolution of magnetized fluid flows, even in the colisionless regime.

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., Comment: 12 pages, 3 figures

Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in \cite{valentini12}. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in \cite{comment}

Langmuir turbulence is an archetype of wave turbulence in plasma physics. By means of 1D-1V Vlasov-Poisson simulations, we show that coherent structures, called Langmuir cavitons, are generated by the long time evolution of Langmuir weak turbulence, thus illustrating the breakdown of a weak turbulence regime. These structures correspond to an equilibrium between the pressure forces and the ponderomotive force resulting from high frequency Langmuir oscillations. Langmuir cavitons are typical features of strong Langmuir turbulence expected to be generated at high energy and to saturate when Langmuir energy is of the order of the plasma thermal energy. Despite this wide-spread belief, here we observe that cavitons, emerging from weak Langmuir turbulence evolution, saturate at much lower energies. We show that these Langmuir coherent structures are characterized by a much larger length scale with respect to the Debye length. This gives evidence that "large" and "shallow" stable cavitons should be seen in space plasma observations. The transition toward strong turbulence is shown to be a consequence of an initial weak turbulent inverse cascade. Finally, the effective equation of state for ion acoustic oscillations is tested numerically from the kinetic model., Comment: 8 pages, 5 figures

The electrostatic decay enables energy transfer from a finite amplitude Langmuir to a backscattered daughter Langmuir wave and ion acoustic density fluctuations. This mechanism is thought to be a first step for the generation of type III solar radio emissions at twice the plasma frequency. The electrostatic decay is here investigated through Vlasov-Poisson simulations by considering Langmuir localized wave packets in the case Te = Tp. Simulation results are found to be in good agreement with recently reported observations from the STEREO mission of the electrostatic decay of beam-driven Langmuir waves during a type III burst., Comment: 4 pages, 4 figures, Solar Wind 12

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named {\it corner modes}. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the $(k,\omega_{_R})$ plane ($\omega_{_R}$ being the real part of the wave frequency and $k$ the wavenumber), away from the well-known `thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower $k$-values and chopping the tail shifts them toward higher $k$-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas., Comment: 11 pages, 10 figures

The transition between non resonant (Weibel-type) and resonant (whistler) instabilities is investigated numerically in plasma configurations with an ambient magnetic field of increasing amplitudes. The Vlasov-Maxwell system is solved in a configuration where the fields have three components but depend only on one coordinate and on time. The nonlinear evolution of these instabilities is shown to lead to the excitation of electromagnetic and electrostatic modes at the first few harmonics of the plasma frequency and, in the case of a large ambient magnetic field, to a long-wavelength, spatial modulation of the amplitude of the magnetic field generated by the whistler instability., Comment: 11 pages

The nonlinear evolution of the Weibel instability driven by the anisotropy of the electron distribution function in a collisionless plasma is investigated in a spatially one-dimensional configuration with a Vlasov code in a two-dimensional velocity space. It is found that the electromagnetic fields generated by this instability cause a strong deformation of the electron distribution function in phase space, corresponding to highly filamented magnetic vortices. Eventually, these deformations lead to the generation of short wavelength Langmuir modes that form highly localized electrostatic structures corresponding to jumps of the electrostatic potential., Comment: 12 pages

Kinetic numerical simulations of the evolution of the Weibel instability during the full nonlinear regime are presented. The formation of strong distortions in the electron distribution function resulting in formation of strong peaks in it and their influence on the resulting electrostatic waves are shown., Comment: 6 pages, 4 figures

The linear stability of a shear layer in a highly diffusive stably stratified atmosphere has been investigated. This study completes and extends previous works by Dudis (1974) and Jones (1977). We show that: (i) an asymptotic regime is reached in the limit of large thermal diffusivity, (ii) there exists two different types of unstable modes. The slowest growing modes correspond to predominantly horizontal motions and the fast growing ones to isotropic motions, (iii) the physical interpretation of the stability properties in this asymptotic regime is simple. Applications to the dynamics of stellar radiative zone are discussed., Comment: 11 pages, 8 figures, to be published in Astronomy and Astrophysics