Density functional theory (DFT) is a powerful theoretical tool widely used in such diverse fields as computational condensed-matter physics, atomic physics and quantum chemistry. DFT establishes that a system of $N$ interacting electrons can be described uniquely by its single-particle density $n(\boldsymbol{r})$, instead of the $N$-body wave function, yielding an enormous gain in terms of computational speed and memory storage space. Here, we use time-dependent DFT to show that a classical collisionless plasma can always, in principle, be described by a set of fluid equations for the single-particle density and current. The results of DFT guarantee that an exact closure relation, fully reproducing the Vlasov dynamics, necessarily exists, although it may be complicated (non-local in space and time, for instance) and difficult to obtain in practice. This goes against the common wisdom in plasma physics that the Vlasov and fluid descriptions are mutually incompatible, with the latter inevitably missing some ‘purely kinetic’ effects.

The evolution of a linearly polarized, long-wavelength Alfvén wave propagating in a collisionless magnetized plasma with a sheared parallel-directed velocity flow is here studied by means of two-dimensional hybrid Vlasov–Maxwell (HVM) simulations. The unperturbed sheared flow has been represented by an exact solution of the HVM set of equations of (Malara et al., Phys. Rev. E, vol. 97, 2018, 053212), thus avoiding spurious oscillations that would arise from the non-stationary initial state and inevitably affect the dynamics of the system. We have considered the evolution of both a small and a moderate amplitude Alfvén wave, in order to separate linear wave–shear flow couplings from kinetic effects, the latter being more relevant for larger wave amplitudes. The phase mixing generated by the shear flow modifies the initial perturbation, leading to the formation of small-scale transverse fluctuations at scales comparable with the proton inertial length/Larmor radius. By analysing both the polarization and group velocity of perturbations in the shear regions, we identify them as kinetic Alfvén waves (KAWs). In the moderate amplitude run, kinetic effects distort the proton distribution function in the shear region. This leads to the formation of a proton beam, at the Alfvén speed and parallel to the magnetic field. Such a feature, due to the parallel electric field associated with KAWs, positively compares with solar wind observations of suprathermal ion populations, suggesting that it may be related to the presence of ion-scale KAW-like fluctuations.

Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

The formation and control of strongly nonlinear standing plasma waves (SPWs) from a trivial equilibrium by a chirped frequency drive are discussed. If the drive amplitude exceeds a threshold, after passage through the linear resonance in this system, the excited wave preserves the phase locking with the drive, yielding a controlled growth of the wave amplitude. We illustrate these autoresonant waves via Vlasov–Poisson simulations, showing the formation of sharply peaked excitations with local electron density maxima significantly exceeding the unperturbed plasma density. The Whitham averaged variational approach applied to a simplified water bag model yields the weakly nonlinear evolution of the autoresonant SPWs and the autoresonance threshold. If the chirped driving frequency approaches some constant level, the driven SPW saturates at a target amplitude, avoiding the kinetic wave breaking.

We discuss a family of Vlasov–Maxwell equilibrium distribution functions for current sheet equilibria that are intermediate cases between the Harris sheet and the force-free (or modified) Harris sheet. These equilibrium distribution functions have potential applications to space and astrophysical plasmas. The existence of these distribution functions had been briefly discussed by Harrison & Neukirch (Phys. Rev. Lett., vol. 102, (2009a), 135003), but here it is shown that their approach runs into problems in the limit where the guide field goes to zero. The nature of this problem will be discussed and an alternative approach will be suggested that avoids the problem. This is achieved by considering a slight variation of the magnetic field profile, which allows a smooth transition between the Harris and force-free Harris sheet cases.

In this paper, we discuss the results of a new particle pusher in realistic ultra-strong electromagnetic fields such as those encountered around rotating neutron stars. After presenting the results of this algorithm in simple fields and comparing them to expected exact analytical solutions, we present new simulations for a rotating magnetic dipole in vacuum for a millisecond pulsar by using the Deutsch solution. Particles are injected within the magnetosphere, neglecting radiation reaction, interaction among them and their feedback on the fields. Our simulations are therefore not yet fully self-consistent because the Maxwell equations are not solved according to the current produced by these particles. The code highlights the symmetrical behaviour of particles of opposite charge to mass ratio, $q/m$, with respect to the north and south hemispheres. The relativistic Lorentz factor $\gamma$ of the accelerated particles is proportional to this ratio $q/m$: protons reach up to $\gamma _p \simeq 10^{10.7}$, whereas electrons reach up to $\gamma _e \simeq 10^{14}$. Our simulations show that particles could either be captured by the neutron star, trapped around it or ejected far from it, well outside the light cylinder. Actually, for a given charge to mass ratio, particles follow similar trajectories. These particle orbits show some depleted directions, especially at high magnetic inclination with respect to the rotation axis for positive charges and at low inclination for negative charges because of symmetry. Other directions are preferred and loaded with a high density of particles, some directions concentrating the highest or lowest acceleration efficiencies.

Kinetic plasma simulations are nowadays commonly used to study a wealth of nonlinear behaviours and properties in laboratory and space plasmas. In particular, in high-energy physics and astrophysics, the plasma usually evolves in ultra-strong electromagnetic fields produced by intense laser beams for the former or by rotating compact objects such as neutron stars and black holes for the latter. In these ultra-strong electromagnetic fields, the gyro-period is several orders of magnitude smaller than the time scale on which we desire to investigate the plasma evolution. Some approximations are required such as, for instance, artificially decreasing the electromagnetic field strength, which is certainly not satisfactory. The main flaw of this downscaling is that it cannot reproduce particle acceleration to ultra-relativistic speeds with a Lorentz factor above $\gamma \approx 10^3$–$10^4$. In this paper, we design a new algorithm able to catch particle motion and acceleration to a Lorentz factor of up to $10^{15}$ or even higher by using Lorentz boosts to special frames where the electric and magnetic field are parallel. Assuming that these fields are locally uniform in space and constant in time, we solve analytically the equation of motion in a tiny region smaller than the length scale of the spatial and temporal gradient of the field. This analytical integration of the orbit severely reduces the constraint on the time step, allowing us to use large time steps, avoiding resolving the ultra-high gyro-frequency. We performed simulations in ultra-strong spatially and time-dependent electromagnetic fields, showing that our particle pusher is able to follow accurately the exact analytical solution for very long times. This property is crucial to properly capture for instance lepton electrodynamics in electromagnetic waves produced by fast rotating neutron stars. We conclude with a simple implementation of our new pusher into a one-dimensional relativistic electromagnetic particle-in-cell code, testing it against plasma oscillations, two-stream instabilities and strongly magnetized relativistic shocks.

The purpose of this paper is to bridge kinetic plasma descriptions and low-frequency single-fluid models. More specifically, the asymptotics leading to magnetohydrodynamic regimes starting from the Vlasov–Maxwell system are investigated. The analogy with the derivation, from the Vlasov–Poisson system, of a fluid representation for ions coupled to the Boltzmann relation for electrons is also outlined. The aim is to identify asymptotic parameters explaining the transitions from one microscopic description to a macroscopic low-frequency model. These investigations provide groundwork for the derivation of multi-scale numerical methods, model coupling or physics-based preconditioning.

We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e. entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow and temperature as the local distribution. First, we consider a form previously employed by Kaufmann & Paterson (J. Geophys. Res., vol. 114, 2009, A00D04), assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.

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

We propose a numerical scheme to solve the semiclassical Vlasov–Maxwell equations for electrons with spin. The electron gas is described by a distribution function $f(t,{\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$ that evolves in an extended 9-dimensional phase space $({\boldsymbol x},{{{\boldsymbol p}}}, {\boldsymbol s})$, where $\boldsymbol s$ represents the spin vector. Using suitable approximations and symmetries, the extended phase space can be reduced to five dimensions: $(x,{{p_x}}, {\boldsymbol s})$. It can be shown that the spin Vlasov–Maxwell equations enjoy a Hamiltonian structure that motivates the use of the recently developed geometric particle-in-cell (PIC) methods. Here, the geometric PIC approach is generalized to the case of electrons with spin. Total energy conservation is very well satisfied, with a relative error below $0.05\,\%$. As a relevant example, we study the stimulated Raman scattering of an electromagnetic wave interacting with an underdense plasma, where the electrons are partially or fully spin polarized. It is shown that the Raman instability is very effective in destroying the electron polarization.