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 the proper 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 anisotropy T⊥/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 by T⊥/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

We present a study of magnetic field fluctuations, in a slow solar wind stream, close to ion scales, where an increase of the level of magnetic compressibility is observed. Here, the nature of these compressive fluctuations is found to be characterized by coherent structures. Although previous studies have shown that current sheets can be considered as the principal cause of intermittency at ion scales, here we show for the first time that, in the case of the slow solar wind, a large variety of coherent structures contributes to intermittency at proton scales, and current sheets are not the most common. Specifically, we find compressive (δb ≫ δb ⊥ ), linearly polarized structures in the form of magnetic holes, solitons and shock waves. Examples of Alfvénic structures (δb ⊥ > δb ) are identified as current sheets and vortex-like structures. Some of these vortices have δb ⊥ ≫ δb , as in the case of Alfvén vortices, but the majority of them are characterized by δb ⊥ δb . Thanks to multipoint measurements by Cluster spacecraft, for about 100 structures, we could determine the normal, the propagation velocity and the spatial scale along this normal. Independently of the nature of the structures, the normal is always perpendicular to the local magnetic field, meaning that k ⊥ ≫ k . The spatial scales of the studied structures are found to be between 2 and 8 times the proton gyroradius. Most of them are simply convected by the wind, but 25% propagate in the plasma frame. Possible interpretations of the observed structures and the connection with plasma heating are discussed.

Plasma turbulence is investigated using high-resolution ion velocity distributions measured by the Magnetospheric Multiscale Mission (MMS) in the Earth's magnetosheath. The particle distribution is highly structured, suggesting a cascade-like process in velocity space. This complex velocity space structure is investigated using a three-dimensional Hermite transform that reveals a power law distribution of moments. In analogy to hydrodynamics, a Kolmogorov approach leads directly to a range of predictions for this phase-space cascade. The scaling theory is in agreement with observations, suggesting a new path for the study of plasma turbulence in weakly collisional space and astrophysical plasmas.Turbulence in fluids is characterized by nonlinear interactions that transfer energy from large to small scales, eventually producing heat. For a collisional medium, whether an ordinary gas or a plasma, turbulence leads to complex real space structure, but the velocity space, constrained by collisions, remains smooth and close to local thermodynamic equilibrium (as, e.g., in ChapmanEnskog theory [1].) However, in a weakly collisional plasma, spatial fluctuations are accompanied by fluctuations in velocity space, representing another essential facet of plasma dynamics. The characterization of the velocity space is challenging in computations and in experiments, although Vlasov simulation has revealed complexity in the velocity space, often near coherent magnetic and flow structures [2][3][4]. Here we make use of powerful new spacecraft observations in the terrestrial magnetosheath that reveal this structure with sufficient accuracy to quantify the velocity cascade for the first time in a space plasma.The observations reported here are enabled by the Magnetospheric Multiscale Mission (MMS), launched in 2015 to explore magnetic reconnection. The MMS/FPI instrument measures ion and electron velocity distributions (VDFs) at high time cadence, and with high resolution in angle and energy. High resolution magnetic field measurements are available and four-point observation is available for all instruments. MMS provides characterization of plasma turbulence with unprecedented resolution and accuracy. The spacecraft orbit repeatedly crosses the Earth's magnetosheath, enabling new and important characterizations of plasma dynamics (see e.g. Burch et al. [5]). Here we focus on one traversal of the magnetosheath, and specifically on a quantitative description of the ion velocity space cascade.

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 ⊥ /T on the parallel plasma beta β , 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 ⊥ /T and β , 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. PACS numbers: 52.35.Ra, 96.50.Ci, 94.05.Lk, 52.65.Ff

We investigate the nature of magnetic turbulent fluctuations, around ion characteristic scales, in a fast solar wind stream, by using Cluster data. Contrarily to slow solar wind, where both Alfvénic (δb ⊥ ≫ δb ) and compressive (δb ≫ δb ⊥ ) coherent structures are observed (Perrone et al. 2016), the turbulent cascade of fast solar wind is dominated by Alfvénic structures, namely Alfvén vortices, with small and/or finite compressive part, with the presence also of several current sheets aligned with the local magnetic field. Several examples of vortex chains are also recognized. Although an increase of magnetic compressibility around ion scales is observed also for fast solar wind, no strongly compressive structures are found, meaning that the nature of the slow and fast winds is intrinsically different. Multi-spacecraft analysis applied to this interval of fast wind indicate that the coherent structures are almost convected by the flow and aligned with the local magnetic field, i.e. their normal is perpendicular to B, that is consistent with a two dimensional turbulence picture. Understanding intermittency and the related generation of coherent structures could provide a key insight into the nonlinear energy transfer and dissipation processes in magnetized and collisionless plasmas.

The solar wind plasma is a fully ionized and turbulent gas ejected by the outer layers of the solar corona at very high speed, mainly composed by protons and electrons, with a small percentage of helium nuclei and a significantly lower abundance of heavier ions. Since particle collisions are practically negligible, the solar wind is typically not in a state of thermodynamic equilibrium. Such a complex system must be described through self-consistent and fully nonlinear models, taking into account its multi-species composition and turbulence. We use a kinetic hybrid Vlasov-Maxwell numerical code to reproduce the turbulent energy cascade down to ion kinetic scales, in typical conditions of the uncontaminated solar wind plasma, with the aim of exploring the differential kinetic dynamics of the dominant ion species, namely protons and alpha particles. We show that the response of different species to the fluctuating electromagnetic fields is different. In particular, a significant differential heating of alphas with respect to protons is observed. Interestingly, the preferential heating process occurs in spatial regions nearby the peaks of ion vorticity and where strong deviations from thermodynamic equilibrium are recovered. Moreover, by feeding a simulator of a top-hat ion spectrometer with the output of the kinetic simulations, we show that measurements by such spectrometer planned on board the Turbulence Heating ObserveR (THOR mission), a candidate for the next M4 space mission of the European Space Agency, can provide detailed three-dimensional ion velocity distributions, highlighting important non-Maxwellian features. These results support the idea that future space missions will allow a deeper understanding of the physics of the interplanetary medium.

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

Hybrid Vlasov-Maxwell simulations are employed to investigate the role of kinetic effects in a twodimensional 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.