Solar flares are powerful radiations occurring in the Sun’s atmosphere. They are powered by magnetic reconnection, a phenomenon that can convert magnetic energy into other forms of energy such as heat and kinetic energy, and which is believed to be ubiquitous in the universe. With the ever increasing spatial and temporal resolutions of solar observations, as well as numerical simulations benefiting from increasing computer power, we can now probe into the nature and the characteristics of magnetic reconnection in three dimensions to better understand the phenomenon’s consequences during eruptive flares in our star’s atmosphere. We review in the following the efforts made on different fronts to approach the problem of magnetic reconnection. In particular, we will see how understanding the magnetic topology in three dimensions helps in locating the most probable regions for reconnection to occur, how the current layer evolves in three dimensions and how reconnection leads to the formation of flux ropes, plasmoids and flaring loops.

Comparisons are made of two different particle simulations: one for the study of plasma-based accelerators (Gueroult & Fisch, Phys. Plasmas, vol. 23, 2016, 032113) and the other for the study of shock formation in the interstellar medium (Yamauchi & Ohsawa, Phys. Plasmas, vol. 14, 2007, 053110). In the former, shock waves used for plasma density control create ion beams by reflection. In the latter, a fast and dense beam of exploding ions penetrates a surrounding plasma. In both simulations, magnetic bumps are generated from the motion of ion beams perpendicular to a magnetic field. Despite the apparent differences of their purposes, configurations and spatial scales, the two simulations show strong similarities in the generation processes and effects of the bumps, suggesting that these are not rare plasma phenomena. The bump created by the exploding ions develops into backward and forward magnetosonic pulses.

Subsequent to the recent rigorous derivation of an energetically consistent gyrokinetic collision operator in the so-called Landau representation, this paper investigates the possibility of finding a differential formulation of the gyrokinetic Landau collision operator. It is observed that, while a differential formulation is possible in the gyrokinetic phase space, reduction of the resulting system of partial differential equations to five dimensions via gyroaveraging poses a challenge. Based on the present work, it is likely that the gyrocentre analogues of the Rosenbluth–MacDonald–Judd potential functions must be kept gyroangle dependent.

Accurate models of X-ray absorption and re-emission in partly stripped ions are necessary to calculate the structure of stars, the performance of hohlraums for inertial confinement fusion and many other systems in high-energy-density plasma physics. Despite theoretical progress, a persistent discrepancy exists with recent experiments at the Sandia Z facility studying iron in conditions characteristic of the solar radiative–convective transition region. The increased iron opacity measured at Z could help resolve a longstanding issue with the standard solar model, but requires a radical departure for opacity theory. To replicate the Z measurements, an opacity experiment has been designed for the National Facility (NIF). The design uses established techniques scaled to NIF. A laser-heated hohlraum will produce X-ray-heated uniform iron plasmas in local thermodynamic equilibrium (LTE) at temperatures ${\geqslant}150$ eV and electron densities ${\geqslant}7\times 10^{21}~\text{cm}^{-3}$. The iron will be probed using continuum X-rays emitted in a ${\sim}200$ ps, ${\sim}200~\unicode[STIX]{x03BC}\text{m}$ diameter source from a 2 mm diameter polystyrene (CH) capsule implosion. In this design, $2/3$ of the NIF beams deliver 500 kJ to the ${\sim}6$ mm diameter hohlraum, and the remaining $1/3$ directly drive the CH capsule with 200 kJ. Calculations indicate this capsule backlighter should outshine the iron sample, delivering a point-projection transmission opacity measurement to a time-integrated X-ray spectrometer viewing down the hohlraum axis. Preliminary experiments to develop the backlighter and hohlraum are underway, informing simulated measurements to guide the final design.

Penetration of a magnetic field into plasma that is faster than resistive diffusion can be induced by the Hall electric field in a non-uniform plasma. This mechanism explained successfully the measured velocity of the magnetic field penetration into pulsed plasmas. Major related issues have not yet been resolved. Such is the theoretically predicted, but so far not verified experimentally, high magnetic energy dissipation, as well as the correlation between the directions of the density gradient and of the field penetration.

Aiming at a fusion reactor, two issues must be solved for the lower hybrid current drive (LHCD), namely good lower hybrid wave (LHW)–plasma coupling and effective current drive at high density. For this goal, efforts have been made to improve LHW–plasma coupling and current drive capability at high density in experimental advanced superconducting tokamak (EAST). LHW–plasma coupling is improved by means of local gas puffing and gas puffing from the electron side is taken as a routine way for EAST to operate with LHCD. Studies of high density experiments suggest that low recycling and high lower hybrid (LH) frequency are preferred for LHCD experiments at high density, consistent with previous results in other machines. With the combination of 2.45 GHz and 4.6 GHz LH waves, a repeatable high confinement mode plasma with maximum density up to $4.5\times 10^{19}~\text{m}^{-3}$ was obtained by LHCD in EAST. In addition, in the first stage of LHCD cyclic operation, an alternative candidate for more economical fusion reactors has been demonstrated in EAST and further work will be continued.

In traditional electron/ion laboratory plasmas, the system size $L$ is much larger than both the plasma skin depth $l_{s}$ and the Debye length $\unicode[STIX]{x1D706}_{D}$. In current and planned efforts to create electron/positron plasmas in the laboratory, this is not necessarily the case. A low-temperature, low-density system may have $\unicode[STIX]{x1D706}_{D}<L<l_{s}$; a high-density, thermally relativistic system may have $l_{s}<L<\unicode[STIX]{x1D706}_{D}$. Here we consider the question of what plasma physics phenomena are accessible (and/or diagnostically exploitable) in these different regimes and how this depends on magnetization. While particularly relevant to ongoing pair plasma creation experiments, the transition from single-particle behaviour to collective, ‘plasma’ effects – and how the criterion for that threshold is different for different phenomena – is an important but often neglected topic in electron/ion systems as well.

Ion angular current and energy distributions are important parameters for ion thrusters, which are typically measured at a few tens of centimetres to a few metres distance from the thruster exit. However, fully kinetic particle-in-cell (PIC) simulations are not able to simulate such domain sizes due to high computational costs. Therefore, a parallelisation strategy of the code is presented to reduce computational time. The calculated ion beam angular distributions in the plume region are quite sensitive to boundary conditions of the potential, possible additional source contributions (e.g. from secondary electron emission at vessel walls) and charge exchange collisions. Within this work a model for secondary electrons emitted from the vessel wall is included. In order to account for limits of the model due to its limited domain size, a correction of the simulated angular ion energy distribution by the potential boundary is presented to represent the conditions at the location of the experimental measurement in $1~\text{m}$ distance. In addition, a post-processing procedure is suggested to include charge exchange collisions in the plume region not covered by the original PIC simulation domain for the simulation of ion angular distributions measured at $1~\text{m}$ distance.

Based on the beating of two Laguerre–Gaussian laser beams in a rippled plasma medium, the effective factors such as plasma density, Gouy phase and orbital angular momentums of input lasers on the output twisted terahertz radiation are investigated. As a result, the amplitude of the generated vortex terahertz radiation is an increasing function of plasma density. The vortex terahertz intensity is strongly dependent on the orbital angular momentum of the input lasers. The terahertz output amplitude increases by decreasing the orbital angular momentum of the Laguerre–Gaussian input lasers. Here, by employing a suitably ripple wavenumber, the destroyer effect of the relative Gouy phase of the input lasers is removed, and perfect phase matching is satisfied.

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.

A large number of wave modes exist in a magnetized plasma. Their properties are determined by the interaction of particles and waves. In a simulation code, the correct treatment of field quantities and particle behaviour is essential to correctly reproduce the wave properties. Consequently, plasma waves provide test problems that cover a large fraction of the simulation code. The large number of possible wave modes and the freedom to choose parameters make the selection of test problems time consuming and comparison between different codes difficult. This paper therefore aims to provide a selection of test problems, based on different wave modes and with well-defined parameter values, that is accessible to a large number of simulation codes to allow for easy benchmarking and cross-validation. Example results are provided for a number of plasma models. For all plasma models and wave modes that are used in the test problems, a mathematical description is provided to clarify notation and avoid possible misunderstanding in naming.

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.

Explicitly covariant dispersion relations for a variety of plasma waves in unmagnetized and magnetized plasmas are derived in a systematic manner from a fully covariant plasma formulation. One needs to invoke relatively little known invariant combinations constructed from the ambient electromagnetic fields and the wave vector to accomplish the program. The implication of this work applied to the self-induced transparency effect is discussed. Some problems arising from the inconsistent use of relativity are pointed out.

We take advantage of previous research in the field of cyclotron auto resonance maser (CARM) and undulator-based free electron laser (U-FEL) sources to establish a common formalism for the relevant description of the underlying physical mechanisms. This strategy is aimed at stressing the deep analogies between the two devices and at providing a practical tool for their study based on the use of well-tested scaling formulae developed independently for the two systems.