Space plasma physics, pushed by the impressive recent technological developments, is undergoing a period of intense progress. This progress is achieved first at the level of observations, including both remote and in situ measurements, but also on the theoretical side, mainly by means of large scale numerical simulations made possible by the dramatic increase of computational resources. In particular, three-dimensional mainly hybrid but also fully kinetic simulations are today feasible, and large intervals in spatial and time scales can at last be accessed by fluid simulations. Addressing fundamental problems such as, e.g. magnetic reconnection, nonlinear dynamics or turbulence development in the kinetic range, are no longer just a heart's desire today.

The long-term evolution of large-amplitude Alfvén waves propagating in the solar wind is investigated by performing two-dimensional MHD simulations within the expanding box model. The linear and nonlinear phases of the parametric decay instability are studied for both circularly polarized waves in parallel propagation and for arc-polarized waves in oblique propagation. The non-monochromatic case is also considered. In the oblique case, the direct excitation of daughter modes transverse to the local background field is found for the first time in an expanding environment, and this transverse cascade seems to be favored for monochromatic mother waves. The expansion effect reduces the instability growth rate, and it can even suppress its onset for the lowest frequency modes considered here, possibly explaining the persistence of these outgoing waves in the solar wind.

With the aim to develop a tool for simulating turbulence in collisionless magnetized plasmas, fluid models retaining low-frequency kinetic effects such as Landau damping and finite Larmor radius (FLR) corrections are discussed. It turns out that, in the absence of ion-cyclotron resonance, the dispersion and damping of kinetic Alfvén waves at scales as small as a fraction of the ion Larmor radius are accurately reproduced when using fluid estimates of the non-gyrotropic moments, at leading-order within a large-scale asymptotics. Differently, evaluations based on the low-frequency linear kinetic theory are necessary in regimes of large temperature anisotropies, and in particular in the presence of the mirror instability. Combining both descriptions leads to a new Landau fluid model retaining large-scale FLR nonlinearities, while reproducing the linear dynamics of low-frequency modes at the sub-ionic scales.

It is shown that two circularly polarized Alfvén waves that propagate along the ambient magnetic field in an uniform plasma trigger non oscillating electromagnetic field components when they cross each other. The non-oscilliating field components can accelerate ions and electrons with great efficiency. This work is based on particle-in-cell (PIC) numerical simulations and on analytical non-linear computations. The analytical computations are done for two counter-propagating monochromatic waves. The simulations are done with monochromatic waves and with wave packets. The simulations show parallel electromagnetic fields consistent with the theory, and they show that the particle acceleration results in plasma cavities and, if the waves amplitudes are high enough, in ion beams. These acceleration processes could be relevant in space plasmas. For instance, they could be at work in the auroral zone and in the radiation belts of the Earth magnetosphere. In particular, they may explain the origin of the deep plasma cavities observed in the Earth auroral zone.

A widely accepted scenario of magnetic reconnection in collisionless space plasmas is the breakage of magnetic field lines in X-points. In laboratory, reconnection is commonly studied in pinches, current channels embedded into twisted magnetic fields. No model of magnetic reconnection in space plasmas considers both null-points and pinches as peers. We have performed a particle-in-cell simulation of magnetic reconnection in a three-dimensional configuration where null-points are present initially, and Z-pinches are formed during the simulation along the lines of spiral null-points. The non-spiral null-points are more stable than spiral ones, and no substantial energy dissipation is associated with them. On the contrary, turbulent magnetic reconnection in the pinches causes the magnetic energy to decay at a rate of ~1.5% per ion gyro period. Dissipation in similar structures is a likely scenario in space plasmas with large fraction of spiral null-points.

The role of magnetic helicity is investigated in kinetic Alfvén wave and oblique whistler turbulence in presence of a relatively intense external magnetic field b0e∥. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall magnetohydrodynamics (MHD). We use the asymptotic equations derived by Galtier and Bhattacharjee (2003 Phys. Plasmas10, 3065–3076) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, n + ñ = −6, where n and ñ are the power law indices of the perpendicular (to b0) wave number magnetic energy and helicity spectra, respectively. Therefore, the spectra derived in the past from the energy equation only, namely n = −2.5 and ñ = −3.5, are not the unique solutions to this problem but rather characterize the direct energy cascade. The solution ñ = −3 is a limit imposed by the locality condition; it is also the constant helicity flux solution obtained heuristically. The results obtained offer a new paradigm to understand solar wind turbulence at sub-ion scales where it is often observed that −3 < n < −2.5.

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.

Non-diffusive transport, for which the particle mean free path grows nonlinearly in time, is envisaged for many space and laboratory plasmas. In particular, superdiffusion, i.e. 〈Δx2〉 ∝ tα with α > 1, can be described in terms of a Lévy random walk, in which case the probability of free-path lengths has power-law tails. Here, we develop a direct numerical simulation to reproduce the Lévy random walk, as distinct from the Lévy flights. This implies that in the free-path probability distribution Ψ(x, t) there is a space-time coupling, that is, the free-path length is proportional to the free-path duration. A power-law probability distribution for the free-path duration is assumed, so that the numerical model depends on the power-law slope μ and on the scale distance x0. The numerical model is able to reproduce the expected mean square deviation, which grows in a superdiffusive way, and the expected propagator P(x, t), which exhibits power-law tails, too. The difference in the power-law slope between the Lévy flights propagator and the Lévy walks propagator is also estimated.

Magnetic reconnection is one of the key processes in astrophysical and laboratory plasmas: it is the opposite of a dynamo. Looking at energy, a dynamo transforms kinetic energy in magnetic energy while reconnection takes magnetic energy and returns it to its kinetic form. Most plasma processes at their core involve first storing magnetic energy accumulated over time and then releasing it suddenly. We focus here on this release. A key concept in analysing reconnection is that of the separatrix, a surface (line in 2D) that separates the fresh unperturbed plasma embedded in magnetic field lines not yet reconnected with the hotter exhaust embedded in reconnected field lines. In kinetic physics, the separatrices become a layer where many key processes develop. We present here new results relative to the processes at the separatrices that regulate the plasma flow, the energization of the species, the electromagnetic fields and the instabilities developing at the separatrices.

Narrow-band linearly polarized waves, having a resonant structure and a peak frequency between the local cyclotron frequency of protons and heavy ions, have been detected in the magnetospheres of Earth and of Mercury. Some of these wave events have been suggested to be driven by linear mode conversion (MC) of the fast magnetosonic waves (FWs) at the ion–ion hybrid (IIH) resonances. Since the resonant IIH frequency is linked to the plasma composition, solving the inverse problem allows one to infer the concentration of the heavy ions from the measured frequency spectra. In this paper, we identify the conditions when the MC efficiency is maximized in the magnetospheric plasmas and discuss how this can be applied for estimating the heavy ion concentration in the magnetospheres of Earth and Mercury.

We carried out a 3D fully kinetic simulation of Earth's magnetotail magnetic reconnection to study the dynamics of energetic particles. We developed and implemented a new relativistic particle mover in iPIC3D, an implicit Particle-in-Cell code, to correctly model the dynamics of energetic particles. Before the onset of magnetic reconnection, energetic electrons are found localized close to current sheet and accelerated by lower hybrid drift instability. During magnetic reconnection, energetic particles are found in the reconnection region along the x-line and in the separatrices region. The energetic electrons are first present in localized stripes of the separatrices and finally cover all the separatrix surfaces. Along the separatrices, regions with strong electron deceleration are found. In the reconnection region, two categories of electron trajectory are identified. First, part of the electrons are trapped in the reconnection region, bouncing a few times between the outflow jets. Second, part of the electrons pass the reconnection region without being trapped. Different from electrons, energetic ions are localized on the reconnection fronts of the outflow jets.

It is often asserted or implicitly assumed, without justification, that the results of two-dimensional investigations of plasma turbulence are applicable to the three-dimensional plasma environments of interest. A projection method is applied to derive two scalar equations that govern the nonlinear evolution of the Alfvénic and pseudo-Alfvénic components of ideal incompressible magnetohydrodynamic (MHD) plasma turbulence. The mathematical form of these equations makes clear the inherently three-dimensional nature of plasma turbulence, enabling an analysis of the nonlinear properties of two-dimensional limits often used to study plasma turbulence. In the anisotropic limit, k⊥ ≫ k∥, that naturally arises in magnetized plasma systems, the perpendicular 2D limit retains the dominant nonlinearities that are mediated only by the Alfvénic fluctuations but lacks the wave physics associated with the linear term that is necessary to capture the anisotropic cascade of turbulent energy. In the in-plane 2D limit, the nonlinear energy transfer is controlled instead by the pseudo-Alfvén waves, with the Alfvén waves relegated to a passive role. In the oblique 2D limit, an unavoidable azimuthal dependence connecting the wavevector components will likely cause artificial azimuthal asymmetries in the resulting turbulent dynamics. Therefore, none of these 2D limits is sufficient to capture fully the rich three-dimensional nonlinear dynamics critical to the evolution of plasma turbulence.

All the bodies of the solar system are embedded in the supersonic flux of energetic particles emitted by the Sun. Since the advent of the space age, the models to describe the interaction of this plasma flow with the planets, asteroids, comets etc. have drastically progressed. The possibilities of in situ measurements of the particle distributions and electromagnetic fields have enabled the plasma theories to be tested under astrophysical conditions. Energy transfer from the Sun to the outermost regions of the heliosphere as well as the processes leading to the dissipation of this energy are central questions for heliophysicists. Understanding the dynamics of the particles is thus critical. It is a particularly complicated subject since the medium is (almost) non-collisional. Thus, next to the description of the particles, the development of waves must be considered. Indeed, they participate to the exchange of energy between different species that would not interact otherwise. In other words, waves may play the role of collisions. This paper concentrates on Langmuir waves for their strong links with the electron dynamics. The basic processes of growth and saturation of the Langmuir waves are reviewed to stress their diagnostic capabilities. Then, the characteristics of the waves are described in the several heliophysical contexts: the planetary environments (in particular the ionosphere, the magnetotail and the foreshock) and in the interplanetary medium (in quiescent conditions of the solar wind or during transient events). A particular emphasis is given to results obtained in the last 15 years.

Plasmas are ubiquitous in nature, surround our local geospace environment, and permeate the universe. Plasma phenomena in space give rise to energetic particles, the aurora, solar flares and coronal mass ejections, as well as many energetic phenomena in interstellar space. Although plasmas can be studied in laboratory settings, it is often difficult, if not impossible, to replicate the conditions (density, temperature, magnetic and electric fields, etc.) of space. Single-point space missions too numerous to list have described many properties of near-Earth and heliospheric plasmas as measured both in situ and remotely (see http://www.nasa.gov/missions/#.U1mcVmeweRY for a list of NASA-related missions). However, a full description of our plasma environment requires three-dimensional spatial measurements. Cluster is the first, and until data begin flowing from the Magnetospheric Multiscale Mission (MMS), the only mission designed to describe the three-dimensional spatial structure of plasma phenomena in geospace. In this paper, we concentrate on some of the many plasma phenomena that have been studied using data from Cluster. To date, there have been more than 2000 refereed papers published using Cluster data but in this paper we will, of necessity, refer to only a small fraction of the published work. We have focused on a few basic plasma phenomena, but, for example, have not dealt with most of the vast body of work describing dynamical phenomena in Earth's magnetosphere, including the dynamics of current sheets in Earth's magnetotail and the morphology of the dayside high latitude cusp. Several review articles and special publications are available that describe aspects of that research in detail and interested readers are referred to them (see for example, Escoubet et al. 2005Multiscale Coupling of Sun-Earth Processes, p. 459, Keith et al. 2005Sur. Geophys.26, 307–339, Paschmann et al. 2005Outer Magnetospheric Boundaries: Cluster Results, Space Sciences Series of ISSI. Berlin: Springer, Goldstein et al. 2006Adv. Space Res.38, 21–36, Taylor et al. 2010The Cluster Mission: Space Plasma in Three Dimensions, Springer, pp. 309–330 and Escoubet et al. 2013Ann. Geophys.31, 1045–1059).

A theoretical framework for low-frequency electromagnetic (drift-)kinetic turbulence in a collisionless, multi-species plasma is presented. The result generalises reduced magnetohydrodynamics (RMHD) and kinetic RMHD (Schekochihin et al., Astrophys. J. Suppl. Ser., vol. 182, 2009, pp. 310–377) to the case where the mean distribution function of the plasma is pressure-anisotropic and different ion species are allowed to drift with respect to each other – a situation routinely encountered in the solar wind and presumably ubiquitous in hot dilute astrophysical plasmas such as the intracluster medium. Two main objectives are achieved. First, in a non-Maxwellian plasma, the relationships between fluctuating fields (e.g. the Alfvén ratio) are order-unity modified compared to the more commonly considered Maxwellian case, and so a quantitative theory is developed to support quantitative measurements now possible in the solar wind. Beyond these order-unity corrections, the main physical feature of low-frequency plasma turbulence survives the generalisation to non-Maxwellian distributions: Alfvénic and compressive fluctuations are energetically decoupled, with the latter passively advected by the former; the Alfvénic cascade is fluid, satisfying RMHD equations (with the Alfvén speed modified by pressure anisotropy and species drifts), whereas the compressive cascade is kinetic and subject to collisionless damping (and for a bi-Maxwellian plasma splits into three independent collisionless cascades). Secondly, the organising principle of this turbulence is elucidated in the form of a conservation law for the appropriately generalised kinetic free energy. It is shown that non-Maxwellian features in the distribution function reduce the rate of phase mixing and the efficacy of magnetic stresses, and that these changes influence the partitioning of free energy amongst the various cascade channels. As the firehose or mirror instability thresholds are approached, the dynamics of the plasma are modified so as to reduce the energetic cost of bending magnetic-field lines or of compressing/rarefying them. Finally, it is shown that this theory can be derived as a long-wavelength limit of non-Maxwellian slab gyrokinetics.

We want to study the connections between the magnetic field generated inside the Sun and the solar wind impacting Earth, especially the influence of north–south asymmetry on the magnetic and velocity fields. We study a solar-like 11-year cycle in a quasi-static way: an asymmetric dynamo field is generated through a 2.5-dimensional (2.5-D) flux-transport model with the Babcock–Leighton mechanism, and then is used as bottom boundary condition for compressible 2.5-D simulations of the solar wind. We recover solar values for the mass loss rate, the spin-down time scale and the Alfvén radius, and are able to reproduce the observed delay in latitudinal variations of the wind and the general wind structure observed for the Sun. We show that the phase lag between the energy of the dipole component and the total surface magnetic energy has a strong influence on the amplitude of the variations of global quantities. We show in particular that the magnetic torque variations can be linked to topological variations during a magnetic cycle, while variations in the mass loss rate appear to be driven by variations of the magnetic energy.

Spacecraft measurements of propagating interplanetary shocks are often interpreted using the ideal magnetohydrodynamic (MHD) model of a planar shock wave travelling with constant velocity $\boldsymbol{V}_{\text{sh}}$ through a spatially uniform plasma. In particular, measurements of the plasma variables upstream and downstream have long been used in conjunction with the Rankine–Hugoniot conditions, also known as the MHD jump conditions, to determine shock velocities and other physical parameters of interplanetary shocks. This procedure is justified only if the shock velocity determined by the MHD jump conditions is unique. In this study the important property of uniqueness is demonstrated for non-perpendicular shocks in MHD media characterized by an isotropic pressure tensor. The primary conclusion is that the shock velocity is uniquely determined by the jump conditions regardless of the type of shock (slow, intermediate or fast). Several new formulas for the shock speed are also derived including one that is independent of the shock normal $\hat{\boldsymbol{n}}$. In principle, the solution technique developed here can be applied to estimate $\boldsymbol{V}_{\text{sh}}$ using solar wind data provided the measurements obey the MHD shock model with sufficient accuracy. That is not its intended purpose, however, and such applications are beyond the scope of this work.

Boundary layers in space and astrophysical plasmas are the location of complex dynamics where different mechanisms coexist and compete, eventually leading to plasma mixing. In this work, we present fully kinetic particle-in-cell simulations of different boundary layers characterized by the following main ingredients: a velocity shear, a density gradient and a magnetic gradient localized at the same position. In particular, the presence of a density gradient drives the development of the lower-hybrid drift instability (LHDI), which competes with the Kelvin–Helmholtz instability (KHI) in the development of the boundary layer. Depending on the density gradient, the LHDI can even dominate the dynamics of the layer. Because these two instabilities grow on different spatial and temporal scales, when the LHDI develops faster than the KHI an inverse cascade is generated, at least in two dimensions. This inverse cascade, starting at the LHDI kinetic scales, generates structures at scale lengths at which the KHI would typically develop. When that is the case, those structures can suppress the KHI itself because they significantly affect the underlying velocity shear gradient. We conclude that, depending on the density gradient, the velocity jump and the width of the boundary layer, the LHDI in its nonlinear phase can become the primary instability for plasma mixing. These numerical simulations show that the LHDI is likely to be a dominant process at the magnetopause of Mercury. These results are expected to be of direct impact to the interpretation of the forthcoming BepiColombo observations.

Turbulent space and astrophysical plasmas exhibit a complex dynamics, which involves nonlinear coupling across different temporal and spatial scales. There is growing evidence that impulsive events, such as magnetic reconnection instabilities, lead to a spatially localized enhancement of energy dissipation, thus speeding up the energy transfer at small scales. Capturing such a diverse dynamics is challenging. Here, we employ the Multidimensional Iterative Filtering (MIF) method, a novel technique for the analysis of non-stationary multidimensional signals. Unlike other traditional methods (e.g. based on Fourier or wavelet decomposition), MIF does not require any previous assumption on the functional form of the signal to be identified. Using MIF, we carry out a multiscale analysis of Hall-magnetohydrodynamic (HMHD) and hybrid particle-in-cell (HPIC) numerical simulations of decaying plasma turbulence. The results assess the ability of MIF to spatially identify and separate the different scales (the MHD inertial range, the sub-ion kinetic and the dissipation scales) of the plasma dynamics. Furthermore, MIF decomposition allows localized current structures to be detected and their contribution to the statistical and spectral properties of turbulence to be characterized. Overall, MIF arises as a very promising technique for the study of turbulent plasma environments.