The dynamics of passage and capture into resonance of a distribution of particles driven by a chirped frequency perturbation is discussed. The resonant capture in this case involves crossing of the separatrix by individual particles and, therefore, the adiabatic theorem cannot be used in studying this problem no matter how slow the variation of the driving frequency is. It is shown that, if instead of analysing complicated single particle dynamics in passage through resonance, one considers the slow evolution of a whole distribution of initial conditions in phase space, the adiabaticity and phase space incompressibility arguments yield a solution to the resonant passage problem. This approach is illustrated in the case of an ensemble of electrons driven by a chirped frequency wave passing through Cherenkov resonances with the velocity distribution of electrons.

Reduced models are derived for a strongly magnetized collisionless plasma at scales which are large relative to the electron thermal gyroradius and in two asymptotic regimes. One corresponds to cold ions and the other to far sub-ion scales. By including the electron pressure dynamics, these models improve the Hall reduced magnetohydrodynamics (MHD) and the kinetic Alfvén wave model of Boldyrev et al. (2013 Astrophys. J., vol. 777, 2013, p. 41), respectively. We show that the two models can be obtained either within the gyrofluid formalism of Brizard (Phys. Fluids, vol. 4, 1992, pp. 1213–1228) or as suitable weakly nonlinear limits of the finite Larmor radius (FLR)–Landau fluid model of Sulem and Passot (J. Plasma Phys., vol 81, 2015, 325810103) which extends anisotropic Hall MHD by retaining low-frequency kinetic effects. It is noticeable that, at the far sub-ion scales, the simplifications originating from the gyroaveraging operators in the gyrofluid formalism and leading to subdominant ion velocity and temperature fluctuations, correspond, at the level of the FLR–Landau fluid, to cancellation between hydrodynamic contributions and ion finite Larmor radius corrections. Energy conservation properties of the models are discussed and an explicit example of a closure relation leading to a model with a Hamiltonian structure is provided.

We consider the relativistic ion-acoustic mode in a plasma composed by cold ions and an ultra-degenerate electron gas, described the relativistic Vlasov–Poisson system. A critical examination of popular fluid models for relativistic ion-acoustic waves is provided, comparing kinetic and hydrodynamic results. The kinetic linear dispersion relation is shown to be reproduced by the rigorous relativistic hydrodynamic equations with Chandrasekhar’s equation of state.

The Weibel instability, driven by a temperature anisotropy, is investigated within different kinetic descriptions based on the semi-Lagrangian full kinetic and relativistic Vlasov–Maxwell model, on the multi-stream approach, which is based on a Hamiltonian reduction technique, and finally, with the full pressure tensor fluid-type description. Dispersion relations of the Weibel instability are derived using the three different models. A qualitatively different regime is observed in Vlasov numerical experiments depending on the excitation of a longitudinal plasma electric field driven initially by the combined action of the stream symmetry breaking and weak relativistic effects, in contrast with the existing theories of the Weibel instability based on their purely transverse characters. The multi-stream model offers an alternate way to simulate easily the coupling with the longitudinal electric field and particularly the nonlinear regime of saturation, making numerical experiments more tractable, when only a few moments of the distribution are considered. Thus a numerical comparison between the reduced Hamiltonian model (the multi-stream model) and full kinetic (relativistic) Vlasov simulations has been investigated in that regime. Although nonlinear simulations of the fluid model, including the dynamics of the pressure tensor, have not been carried out here, the model is strongly relevant even in the three-dimensional case.

Turbulence plays a key role in the conversion of the energy of large-scale fields and flows to plasma heat, impacting the macroscopic evolution of the heliosphere and other astrophysical plasma systems. Although we have long been able to make direct spacecraft measurements of all aspects of the electromagnetic field and plasma fluctuations in near-Earth space, our understanding of the physical mechanisms responsible for the damping of the turbulent fluctuations in heliospheric plasmas remains incomplete. Here we propose an innovative field–particle correlation technique that can be used to measure directly the secular energy transfer from fields to particles associated with collisionless damping of the turbulent fluctuations. Furthermore, this novel procedure yields information about the collisionless energy transfer as a function of particle velocity, providing vital new information that can help to identify the dominant collisionless mechanism governing the damping of the turbulent fluctuations. Kinetic plasma theory is used to devise the appropriate correlation to diagnose Landau damping, and the field–particle correlation technique is thoroughly illustrated using the simplified case of the Landau damping of Langmuir waves in a 1D-1V (one dimension in physical space and one dimension in velocity space) Vlasov–Poisson plasma. Generalizations necessary to apply the field–particle correlation technique to diagnose the collisionless damping of turbulent fluctuations in the solar wind are discussed, highlighting several caveats. This novel field–particle correlation technique is intended to be used as a primary analysis tool for measurements from current, upcoming and proposed spacecraft missions that are focused on the kinetic microphysics of weakly collisional heliospheric plasmas, including the Magnetospheric Multiscale (MMS), Solar Probe Plus, Solar Orbiter and Turbulence Heating ObserveR (THOR) missions.

We discuss a fluid model with inclusion of the complete pressure tensor dynamics for the description of Weibel-type instabilities in a counterstreaming beam configuration. Differently from the case recently studied in Sarrat et al. (Europhys. Lett., vol. 115, 2016, 45001), where perturbations perpendicular to the beams were considered, here we focus only on modes propagating along the beams. Such a configuration is responsible for the growth of two kinds of instabilities, the two-stream instability and the Weibel instability, which in this geometry becomes ‘time resonant’, i.e. propagating. This fluid description agrees with the kinetic one and makes it possible e.g. to identify the transition between non-propagating and propagating Weibel modes, already evidenced by Lazar et al. (J. Plasma Phys., vol. 76 (1), 2010, p. 49) as a ‘slope breaking’ of the growth rate, in terms of a merger of two non-propagating Weibel modes.

Systems of multiple current sheets arise in various situations in natural plasmas, such as at the heliospheric current sheet in the solar wind and in the outer heliosphere in the heliosheath. Previous three-dimensional simulations have shown that such systems can develop turbulent-like fluctuations resulting from a forward and inverse cascade in wave vector space. We present a study of the transition to turbulence of such multiple current sheet systems, including the effects of adding a magnetic guide field and velocity shears across the current sheets. Three-dimensional hybrid simulations are performed of systems with eight narrow current sheets in a triply periodic geometry. We carry out a number of different analyses of the evolution of the fluctuations as the initially highly ordered state relaxes to one which resembles turbulence. Despite the evidence of a forward and inverse cascade in the fluctuation power spectra, we find that none of the simulated cases have evidence of intermittency after the initial period of fast reconnection associated with the ion tearing instability at the current sheets. Cancellation analysis confirms that the simulations have not evolved to a state which can be identified as fully developed turbulence. The addition of velocity shears across the current sheets slows the evolution in the properties of the fluctuations, but by the end of the simulation they are broadly similar. However, if the simulation is constrained to be two-dimensional, differences are found, indicating that fully three-dimensional simulations are important when studying the evolution of an ordered equilibrium towards a turbulent-like state.

Using two-dimensional hybrid expanding box simulations we study the competition between the continuously driven parallel proton temperature anisotropy and fire hose instabilities in collisionless homogeneous plasmas. For a quasi-radial ambient magnetic field the expansion drives $T_{p\Vert }>T_{p\bot }$ and the system becomes eventually unstable with respect to the dominant parallel fire hose instability. This instability is generally unable to counteract the induced anisotropization and the system typically becomes unstable with respect to the oblique fire hose instability later on. The oblique instability efficiently reduces the anisotropy and the system rapidly stabilizes, while a significant part of the generated electromagnetic fluctuations is damped to protons. As long as the magnetic field is in the quasi-radial direction, this evolution repeats itself and the electromagnetic fluctuations accumulate. For a sufficiently oblique magnetic field the expansion drives $T_{p\bot }>T_{p\Vert }$ and brings the system to the stable region with respect to the fire hose instabilities.

We discuss the self-consistent dynamics of plasmas by means of a Hamiltonian formalism for a system of $N$ near-resonant electrons interacting with a single Langmuir wave. The connection with the Vlasov description is revisited through the numerical calculation of the van Kampen-like eigenfrequencies of the linearized dynamics for many degrees of freedom. Both the exponential-like growth as well as damping of the Langmuir wave are shown to emerge from a phase mixing effect among beam modes, revealing unexpected similarities between the stable and unstable regimes.

The purpose of the current work is to find numerical solutions of the steady state inhomogeneous Vlasov equation. This problem has a wide range of applications in the kinetic simulation of non-thermal plasmas. However, the direct application of either time stepping schemes or iterative methods (such as Krylov-based methods such as the generalized minimal residual method (GMRES) or relaxation schemes) is computationally expensive. In the former case the slowest time scale in the system forces us to perform a long time integration while in the latter case a large number of iterations is required. In this paper we propose a preconditioner based on an alternating direction implicit type splitting method. This preconditioner is then combined with both GMRES and Richardson iteration. The resulting numerical schemes scale almost ideally (i.e. the computational effort is proportional to the number of grid points). Numerical simulations conducted show that this can result in a speed-up of close to two orders of magnitude (even for intermediate grid sizes) with respect to the unpreconditioned case. In addition, we discuss the characteristics of these numerical methods and show the results for a number of numerical simulations.

The analysis of the Parker–Moffatt problem, recently revisited in Pezzi et al. (Astrophys. J., vol. 834, 2017, p. 166), is here extended by including Hall magnetohydrodynamics and two hybrid kinetic Vlasov–Maxwell numerical models. The presence of dispersive and kinetic features is studied in detail and a comparison between the two kinetic codes is also reported. Focus on the presence of non-Maxwellian signatures shows that – during the collision – regions characterized by strong temperature anisotropy are recovered and the proton distribution function displays a beam along the direction of the magnetic field, similar to some recent observations of the solar wind.

The paper studies the influence of the background plasma density fluctuations on the dynamics of the Langmuir turbulence generated by electron beams, for parameters typical for solar type III beams and plasmas near 1 AU. A self-consistent Hamiltonian model based on the Zakharov and the Newton equations is used, which presents several advantages compared to the Vlasov approach. Beams generating Langmuir turbulence can be accelerated as a result of wave transformation effects or/and decay cascade processes; in both cases, the beam-driven Langmuir waves transfer part of their energy to waves of smaller wavenumbers, which can be reabsorbed later on by beam particles of higher velocities. As a consequence, beams can conserve a large part of their initial kinetic energy while propagating and radiating wave turbulence over long distances in inhomogeneous plasmas. Beam particles can also be accelerated in quasi-homogeneous plasmas due to the second cascade of wave decay, the wave transformation processes being very weak in this case. The net gains and losses of energy of a beam and the wave turbulence it radiates are calculated as a function of the average level of plasma density fluctuations and the beam parameters. The results obtained provide relevant information on the mechanism of energy reabsorption by beams radiating Langmuir turbulence in solar wind plasmas.

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-$\unicode[STIX]{x1D6FD}$.

The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov–Poisson equation. Since these methods are conservative, local in space and able to limit numerical diffusion, they are considered a promising alternative to more traditional semi-Lagrangian schemes. In this paper we study the conservation of important physical invariants and the long-time behaviour of the semi-Lagrangian discontinuous Galerkin method. To that end we conduct a theoretical analysis and perform a number of numerical simulations. In particular, we find that the entropy is non-decreasing for the discontinuous Galerkin scheme, while unphysical oscillations in the entropy are observed for the traditional method based on cubic spline interpolation.

We present a case study of the flank magnetosheath crossing by the Spektr-R satellite. High time resolution measurements of the ion flux value and its direction provided by the BMSW (Fast Solar Wind Monitor) instrument are examined at different distances from the magnetosheath boundaries – the bow shock and the magnetopause. The magnetosheath behind the quasi-perpendicular bow shock is analysed. The time resolution of these data – 31 ms – is sufficient for observing the frequency spectra of plasma fluctuations both at the magnetohydrodynamics (MHD) and ion kinetic scales. Generally, MHD scales are characterised by Kolmogorov-like spectra ${\sim}f^{-5/3}$ while spectra at kinetic scales are steeper with a break existing between the two scales. We examine evolution of spectral parameters such as power density and slopes, and the break frequency together with the evolution of properties of the probability distribution function. We find out that (i) power spectral densities of the two quantities change differently toward the magnetosheath (MSH) boundaries, (ii) the spectra slopes do not change significantly across the magnetosheath, (iii) the break frequency of the spectrum changes toward the magnetopause. In the middle MSH the spectra are affected by instabilities supposed to be ion cyclotron instabilities. We demonstrate that the plasma is low intermittent in the middle MSH and highly intermittent near its boundaries in the absence of large-scale variations.

The recently developed energy conserving semi-implicit method (ECsim) for particle-in-cell (PIC) simulation is applied to multiple-scale problems where the electron-scale physics needs to be only partially retained and the interest is on the macroscopic or ion-scale processes. Unlike hybrid methods, the ECsim is capable of providing kinetic electron information, such as wave–electron interaction (Landau damping or cyclotron resonance) and non-Maxwellian electron velocity distributions. However, like hybrid methods, the ECsim does not need to resolve all electron scales, allowing time steps and grid spacings orders of magnitude larger than in explicit PIC schemes. The additional advantage of the ECsim is that the stability at large scale is obtained while conserving energy exactly. Three examples are presented: ion acoustic waves, electron acoustic instability and reconnection processes.

Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of relativistic plasmas require accurate computations able to catch the full spatial and temporal dynamics of the system. Numerical simulations of ultra-relativistic plasmas face severe restrictions due to limitations in the maximum possible Lorentz factors that current algorithms can reproduce to good accuracy. In order to circumvent this flaw and repel the limit to $\unicode[STIX]{x1D6FE}\approx 10^{9}$, we design a new fully implicit scheme to solve the relativistic particle equation of motion in an external electromagnetic field using a three-dimensional Cartesian geometry. We show some examples of numerical integrations in constant electromagnetic fields to prove the efficiency of our algorithm. The code is also able to follow the electric drift motion for high Lorentz factors. In the most general case of spatially and temporally varying electromagnetic fields, the code performs extremely well, as shown by comparison with exact analytical solutions for the relativistic electrostatic Kepler problem as well as for linearly and circularly polarized plane waves.

While electron kinetic effects are well known to be of fundamental importance in several situations, the electron mean-flow inertia is often neglected when length scales below the electron skin depth become irrelevant. This has led to the formulation of different reduced models, where electron inertia terms are discarded while retaining some or all kinetic effects. Upon considering general full-orbit particle trajectories, this paper compares the dispersion relations emerging from such models in the case of the Weibel instability. As a result, the question of how length scales below the electron skin depth can be neglected in a kinetic treatment emerges as an unsolved problem, since all current theories suffer from drawbacks of different nature. Alternatively, we discuss fully kinetic theories that remove all these drawbacks by restricting to frequencies well below the plasma frequency of both ions and electrons. By giving up on the length scale restrictions appearing in previous works, these models are obtained by assuming quasi-neutrality in the full Vlasov–Maxwell system.

We propose a new semi-Lagrangian Vlasov–Poisson solver. It employs metric elements to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $\boldsymbol{Q}(\boldsymbol{P})$ of any test particle $\boldsymbol{P}$ , by expanding at second order the geometry of the motion in the vicinity of the closest element. It is thus possible to reconstruct accurately the phase-space distribution function at any time $t$ and position $\boldsymbol{P}$ by proper interpolation of initial conditions, following Liouville theorem. When distortion of the elements of metric becomes too large, it is necessary to create new initial conditions along with isotropic elements and repeat the procedure again until next resampling. To speed up the process, interpolation of the phase-space distribution is performed at second order during the transport phase, while third-order splines are used at the moments of remapping. We also show how to compute accurately the region of influence of each element of metric with the proper percolation scheme. The algorithm is tested here in the framework of one-dimensional gravitational dynamics but is implemented in such a way that it can be extended easily to four- or six-dimensional phase space. It can also be trivially generalised to plasmas.