Relativistic magnetic reconnection has been proposed as an important non-thermal particle acceleration (NTPA) mechanism that generates power-law spectra and high-energy emissions. Power-law particle spectra are in general characterised by three parameters: the power-law index, the high-energy cutoff and the low-energy cutoff (i.e. the injection energy). Particle injection into the non-thermal power law, despite also being a critical step in the NTPA chain, has received considerably less attention than the subsequent acceleration to high energies. Open questions on particle injection that are important for both physical understanding and astronomical observations include how the upstream magnetisation $\sigma$ influences the injection energy and the contributions of the known injection mechanisms (i.e. direct acceleration by the reconnection electric field, Fermi kicks and pickup acceleration) to the injected particle population. Using fully kinetic particle-in-cell simulations, we uncover these relationships by systematically measuring the injection energy and calculating the contributions of each acceleration mechanism to the total injected particle population. We also present a theoretical model to explain these results. Additionally, we compare two- and three-dimensional simulations to assess the impact of the flux-rope kink and drift-kink instability on particle injection. We conclude with comparisons with previous work and outlook for future work.

The presence of multi-component protons with their distinct features is confirmed by various space missions in the Earth’s outer magnetosphere regions. Isotropic cold protons and anisotropic hot protons significantly influence/modify the dispersion behaviour of various modes and instabilities and regulate the magnetospheric dynamics effectively. Our present study pays attention to the left-hand-polarised proton cyclotron mode, which gets unstable in the large proton temperature anisotropy condition, i.e. $T_{\perp p}\gt T_{\parallel p}$. Such favourable thermal conditions for protons are extensively observed during the compression of the solar wind against the Earth’s magnetic field. To reveal the wave dynamics in more detail, i.e. time-scale variations in the cold and hot proton temperatures and resulting wave-energy density, we further allow the time evolution of our model bi-Maxwellian distribution function in response to the proton cyclotron instability. Based on velocity-moment techniques, we formulated a set of equations comprising an instantaneous dispersion relation, dynamical perpendicular and parallel temperature relations and a wave-energy density equation. For the graphical illustrations of our mathematical results, we choose initial conditions that are relevant to magnetospheric space environments and reported in various experimental studies. Our exact numerical analysis shows the notable impact of hot proton temperature anisotropy and relative density on the real frequency, growth rate, evolution of initial distributions and wave-energy density of the proton cyclotron instability. Such detailed outcomes will be quite helpful for global/local magnetospheric experimental and simulation studies.

We revisit the double-adiabatic evolution equations and extend them to the relativistic and ultrarelativistic regimes. We analytically solve the relativistic, time-dependent drift kinetic equation for a homogeneous, magnetised, collisionless plasma and obtain a solution explicitly dependent on the magnetic field and density variations. In the case of an initial relativistic Maxwellian distribution, a natural extension to an anisotropic Maxwell–Jüttner distribution is obtained. We calculate the moments of this time-dependent solution and obtain analytical expressions for the evolution of the perpendicular and parallel pressures in the ultrarelativistic case. We numerically solve the moment equations in the relativistic case and obtain general expressions for the double-adiabatic equations in this regime. We confirm our results using fully kinetic particle-in-cell simulations of shearing and compressing boxes. Our findings can be readily applied to relativistic species including cosmic rays and electron–positron pairs, present in astrophysical plasmas like pulsar wind nebulae, astrophysical jets, black hole accretion flows and Van Allen radiation belts.

Magnetic reconnection can develop spontaneously via the tearing instability, often invoked to explain disruptive instabilities in fusion devices, solar flares, the generation of periodic density disturbances at the tip of helmet streamers and flux transfer events at the Earth’s dayside magnetopause. However, in many such environments the presence of gravity, magnetic field curvature or other forms of acceleration often result in situations of a heavy-over-light plasma in an effective gravitational field with an embedded current sheet. This paper studies the linear stability of a slab current sheet with respect to reconnecting modes in the presence of a density gradient under the effect of a constant gravitational acceleration. We show that the presence of stratification and gravity modify the properties of the tearing-mode instability in the case of both favourable and unfavourable stratification. Favourable stratification suppresses reconnection while unfavourable stratification strongly destabilises the tearing mode. Furthermore, we show that the classical constant-$\psi$ regime effectively does not exist, even for weak unfavourable stratification, for $S \gg 1$. Instead, the gravity-modified tearing progressively transitions into the G-mode, which is a gravity-driven reconnecting mode with a growth rate scaling as $S^{-1/3}$. As a consequence, unfavourable stratification only permits rapidly reconnecting modes.

The influence of the heat source through the fractional time-derivative, with the impact of dynamic and static slips on transient magnetohydrodynamic (MHD) free convective rotating flow in a vertical channel/duct under invariable isoflux and isothermal heating, has been determined. Chemical reaction and heat source consequences are considered. The presentation of the Laplace transformations of Caputo–Fabrizio (CF) and Atangana–Baleanu (AB) fractional time-derivative models is used to transform the governing equations from the time domain into the Laplace domain. The semi-analytical resolutions are obtained for the velocity, temperature and concentration over the transformed solutions with the numerical application of ‘Riemann sum approximation’. Using the MATHEMATICA programme, the impacts of the governing parameters on the velocity, temperature and concentration are graphically demonstrated, and numerical computations for skin friction, Nusselt and Sherwood numbers are presented in tabular format. Remarkably, the static slip and relaxation parameters supported the convective movement of the fluids and the spreading of heat and concentration, while the fractional order parameters and dynamic slip did otherwise. Also, the circulation of heat and the movement of the fluid are considerably enhanced with the heat source compared with the chemical reaction. Additionally, the CF model produced higher temperature, velocity and skin friction compared with the AB model. Notably, it is observable that the heat source amplified the heat, while the fractional time parameter reduced the temperature.

In plasmas and in astrophysical systems, particle diffusion faster than normal, namely superdiffusion, has been detected, calling for a generalisation of Fick’s law and of the transport equation. Formally, superdiffusive transport is often described by fractional diffusion equations, where the second-order spatial derivative is changed into a spatial derivative of fractional order less than two, usually in the form of the so-called Riesz derivative. Fractional operators are non-local, so that this involves the contribution of very distant points (far from the particle source) to the particle flux at a given position in the system. To consider the property of non-locality in the case of anomalous transport, we give a simple analytical derivation of the fractional Fick’s law, where the contribution to the flux of distant points is weighted by an inverse power law, and show that this is consistent with use of the Riesz derivative in the transport equation. A numerical procedure for the computation of the non-local flux is presented and applied to both a simple Gaussian density profile and also to density profiles coming from test particle simulations of one-dimensional collisionless shocks. In these simulations, energetic particles can move diffusively or superdiffusively. The latter case naturally gives rise to the emergence of uphill transport in the downstream region, which means a flux of particles in the same direction of the density gradient. This analysis contributes to the interpretation of energetic particle fluxes accelerated at collisionless shock waves in the interplanetary medium.

A novel large-scale dynamo mechanism, the magnetic shear-current effect, is discussed and explored. The effect relies on the interaction of magnetic fluctuations with a mean shear flow, meaning the saturated state of the small-scale dynamo can drive a large-scale dynamo – in some sense the inverse of dynamo quenching. The dynamo is non-helical, with the mean field ${\it\alpha}$ coefficient zero, and is caused by the interaction between an off-diagonal component of the turbulent resistivity and the stretching of the large-scale field by shear flow. Following up on previous numerical and analytic work, this paper presents further details of the numerical evidence for the effect, as well as an heuristic description of how magnetic fluctuations can interact with shear flow to produce the required electromotive force. The pressure response of the fluid is fundamental to this mechanism, which helps explain why the magnetic effect is stronger than its kinematic cousin, and the basic idea is related to the well-known lack of turbulent resistivity quenching by magnetic fluctuations. As well as being interesting for its applications to general high Reynolds number astrophysical turbulence, where strong small-scale magnetic fluctuations are expected to be prevalent, the magnetic shear-current effect is a likely candidate for large-scale dynamo in the unstratified regions of ionized accretion disks. Evidence for this is discussed, as well as future research directions and the challenges involved with understanding details of the effect in astrophysically relevant regimes.

The most massive baryonic component of galaxy clusters is the ‘intracluster medium’ (ICM), a diffuse, hot, weakly magnetized plasma that is most easily observed in the X-ray band. Despite being observed for decades, the macroscopic transport properties of the ICM are still not well constrained. A path to determine macroscopic ICM properties opened up with the discovery of ‘cold fronts’. These were observed as sharp discontinuities in surface brightness and temperature in the ICM, with the property that the denser side of the discontinuity is the colder one. The high spatial resolution of the Chandra X-ray Observatory revealed two puzzles about cold fronts. First, they should be subject to Kelvin–Helmholtz instabilities, yet in many cases they appear relatively smooth and undisturbed. Second, the width of the interface between the two gas phases is typically narrower than the mean free path of the particles in the plasma, indicating negligible thermal conduction. It was thus realized that these special characteristics of cold fronts may be used to probe the properties of the cluster plasma. In this review, we will discuss the recent simulations of cold fronts in galaxy clusters, focusing on those which have attempted to use these features to constrain ICM physics. In particular, we will examine the effects of magnetic fields, viscosity, and thermal conductivity on the stability properties and long-term evolution of cold fronts. We conclude with a discussion on what important questions remain unanswered, and the future role of simulations and the next generation of X-ray observatories.

Magnetic reconnection can occur in current sheets separating magnetic fields sheared by any angle and of arbitrarily different amplitudes. In such asymmetric and non-coplanar systems, it is not yet understood what the orientation of the X-line will be. Studying how this orientation is determined locally by the reconnection process is important to understand systems such as the Earth magnetopause, where reconnection occurs in regions with large differences in upstream plasma and field properties. This study aims at determining what the local X-line orientation is for different upstream magnetic shear angles in an asymmetric set-up relevant to the Earth’s magnetopause. We use two-dimensional hybrid simulations and vary the simulation plane orientation with regard to the fixed magnetic field profile and search for the plane maximizing the reconnection rate. We find that the plane defined by the bisector of upstream fields maximizes the reconnection rate and this appears not to depend on the magnetic shear angle, domain size or upstream plasma and asymmetries.

Magnetic reconnection is thought to be the dynamical mechanism underlying many explosive phenomena observed both in space and in the laboratory, although the question of how fast magnetic reconnection is triggered in such high Lundquist ( $S$ ) number plasmas has remained elusive. It has been well established that reconnection can develop over time scales faster than those predicted traditionally once kinetic scales are reached. It has also been shown that, within the framework of resistive magnetohydrodynamics (MHD), fast reconnection is achieved for thin enough sheets via the onset of the so-called plasmoid instability. The latter was discovered in studies specifically devoted to the Sweet–Parker current sheet, either as an initial condition or an apparent transient state developing in nonlinear studies. On the other hand, a fast tearing instability can grow on an ideal, i.e. $S$ -independent, time scale (dubbed ‘ideal’ tearing) within current sheets whose aspect ratio scales with the macroscopic Lundquist number as $L/a\sim S^{1/3}$ – much smaller than the Sweet–Parker one – suggesting a new way to approach to the initiation of fast reconnection in collapsing current configurations. Here we present an overview of what we have called ‘ideal’ tearing in resistive MHD, and discuss how the same reasoning can be extended to other plasma models commonly used that include electron inertia and kinetic effects. We then discuss a scenario for the onset of ‘ideal’ fast reconnection via collapsing current sheets and describe a quantitative model for the interpretation of the nonlinear evolution of ‘ideally’ unstable sheets in two dimensions.

Magnetic fields play an important role in astrophysical accretion discs and in the interstellar and intergalactic medium. They drive jets, suppress fragmentation in star-forming clouds and can have a significant impact on the accretion rate of stars. However, the exact amplification mechanisms of cosmic magnetic fields remain relatively poorly understood. Here, I start by reviewing recent advances in the numerical and theoretical modelling of the turbulent dynamo, which may explain the origin of galactic and intergalactic magnetic fields. While dynamo action was previously investigated in great detail for incompressible plasmas, I here place particular emphasis on highly compressible astrophysical plasmas, which are characterised by strong density fluctuations and shocks, such as the interstellar medium. I find that dynamo action works not only in subsonic plasmas, but also in highly supersonic, compressible plasmas, as well as for low and high magnetic Prandtl numbers. I further present new numerical simulations from which I determine the growth of the turbulent (un-ordered) magnetic field component ( $B_{turb}$ ) in the presence of weak and strong guide fields ( $B_{0}$ ). I vary $B_{0}$ over five orders of magnitude and find that the dependence of $B_{turb}$ on $B_{0}$ is relatively weak, and can be explained with a simple theoretical model in which the turbulence provides the energy to amplify $B_{turb}$ . Finally, I discuss some important implications of magnetic fields for the structure of accretion discs, the launching of jets and the star-formation rate of interstellar clouds.

This paper summarises some of the recent progress that has been made in understanding astrophysical plasma turbulence in the solar wind, from in situ spacecraft observations. At large scales, where the turbulence is predominantly Alfvénic, measurements of critical balance, residual energy and three-dimensional structure are discussed, along with comparison to recent models of strong Alfvénic turbulence. At these scales, a few per cent of the energy is also in compressive fluctuations, and their nature, anisotropy and relation to the Alfvénic component is described. In the small-scale kinetic range, below the ion gyroscale, the turbulence becomes predominantly kinetic Alfvén in nature, and measurements of the spectra, anisotropy and intermittency of this turbulence are discussed with respect to recent cascade models. One of the major remaining questions is how the turbulent energy is dissipated, and some recent work on this question, in addition to future space missions which will help to answer it, are briefly discussed.

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.

We compare, in an extensive and systematic way, linear theory results obtained with the hybrid (ion kinetic and electron fluid), the gyrokinetic and the fully kinetic plasma models. We present a test case with parameters that are relevant for solar wind turbulence at small scales, which is a topic now recognized to need a kinetic treatment, to a certain extent. We comment on the comparison of low-frequency single modes (Alfvén/ion-cyclotron, ion-acoustic and fast modes) for a wide range of propagation angles, and on the overall spectral properties of the linear operators, for quasi-perpendicular propagation. The methodology and the results presented in this paper will be valuable when choosing which model should be used in regimes where the assumptions of each model are not trivially satisfied.

Determining the physical mechanisms that extract energy from turbulent fluctuations in weakly collisional magnetized plasmas is necessary for a more complete characterization of the behaviour of a variety of space and astrophysical plasmas. Such a determination is complicated by the complex nature of the turbulence as well as observational constraints, chiefly that in situ measurements of such plasmas are typically only available at a single point in space. Recent work has shown that correlations between electric fields and particle velocity distributions constructed from single-point measurements produce a velocity-dependent signature of the collisionless damping mechanism. We extend this work by constructing field–particle correlations using data sets drawn from single points in strongly driven, turbulent, electromagnetic gyrokinetic simulations to demonstrate that this technique can identify the collisionless mechanisms operating in such systems. The velocity-space structure of the correlation between proton distributions and parallel electric fields agrees with expectations of resonant mechanisms transferring energy collisionlessly in turbulent systems. This work motivates the eventual application of field–particle correlations to spacecraft measurements in the solar wind, with the ultimate goal to determine the physical mechanisms that dissipate magnetized plasma turbulence.

The Kelvin–Helmholtz instability, proposed a long time ago for its role in and impact on the transport properties at magnetospheric flanks, has been widely investigated in the Earth’s magnetosphere context. This review covers more than fifty years of theoretical and numerical efforts in investigating the evolution of Kelvin–Helmholtz vortices and how the rich nonlinear dynamics they drive allow solar wind plasma bubbles to enter into the magnetosphere. Special care is devoted to pointing out the main advantages and weak points of the different plasma models that can be adopted for describing the collisionless magnetospheric medium and in underlying the important role of the three-dimensional geometry of the system.

We study the longitudinal stability of beam–plasma systems in the presence of a density inhomogeneity in the background plasma. Previous works have focused on the non-relativistic regime where hydrodynamical models are used to evolve pre-existing Langmuir waves within inhomogeneous background plasmas. Here, for the first time we study the problem with kinetic equations in a fully relativistic way. We do not assume the existence of Langmuir waves, and we focus on the rate and the mechanism by which waves are excited in such systems from an initial perturbation. We derive the structure of the unstable modes and compute an analytical approximation for their growth rates. Our computation is limited to dilute and cold beams, and shows an excellent agreement with particle-in-cell simulations performed using the SHARP code. We show that, due to such an inhomogeneity, the virulent beam–plasma instabilities in the intergalactic medium are not suppressed but their counterparts in the solar wind can be suppressed as evidenced by propagating type-III solar radio bursts.

We report on an analytical and numerical study of the dynamics of a three-dimensional array of identical magnetic flux tubes in the reduced-magnetohydrodynamic description of the plasma. We propose that the long-time evolution of this system is dictated by flux-tube mergers, and that such mergers are dynamically constrained by the conservation of the pertinent (ideal) invariants, viz. the magnetic potential and axial fluxes of each tube. We also propose that in the direction perpendicular to the merging plane, flux tubes evolve in a critically balanced fashion. These notions allow us to construct an analytical model for how quantities such as the magnetic energy and the energy-containing scale evolve as functions of time. Of particular importance is the conclusion that, like its two-dimensional counterpart, this system exhibits an inverse transfer of magnetic energy that terminates only at the system scale. We perform direct numerical simulations that confirm these predictions and reveal other interesting aspects of the evolution of the system. We find, for example, that the early time evolution is characterized by a sharp decay of the initial magnetic energy, which we attribute to the ubiquitous formation of current sheets. We also show that a quantitatively similar inverse transfer of magnetic energy is observed when the initial condition is a random, small-scale magnetic seed field.

The onset of magnetic reconnection in space, astrophysical and laboratory plasmas is reviewed discussing results from theory, numerical simulations and observations. After a brief introduction on magnetic reconnection and approach to the question of onset, we first discuss recent theoretical models and numerical simulations, followed by observations of reconnection and its effects in space and astrophysical plasmas from satellites and ground-based detectors, as well as measurements of reconnection in laboratory plasma experiments. Mechanisms allowing reconnection spanning from collisional resistivity to kinetic effects as well as partial ionization are described, providing a description valid over a wide range of plasma parameters, and therefore applicable in principle to many different astrophysical and laboratory environments. Finally, we summarize the implications of reconnection onset physics for plasma dynamics throughout the Universe and illustrate how capturing the dynamics correctly is important to understanding particle acceleration. The goal of this review is to give a view on the present status of this topic and future interesting investigations, offering a unified approach.

The zeroth law of turbulence states that, for fixed energy input into large-scale motions, the statistical steady state of a turbulent system is independent of microphysical dissipation properties. This behaviour, which is fundamental to nearly all fluid-like systems from industrial processes to galaxies, occurs because nonlinear processes generate smaller and smaller scales in the flow, until the dissipation – no matter how small – can thermalise the energy input. Using direct numerical simulations and theoretical arguments, we show that in strongly magnetised plasma turbulence such as that recently observed by the Parker Solar Probe spacecraft, the zeroth law is routinely violated. Namely, when such turbulence is ‘imbalanced’ – when the large-scale energy input is dominated by Alfvénic perturbations propagating in one direction (the most common situation in space plasmas) – nonlinear conservation laws imply the existence of a ‘barrier’ at scales near the ion gyroradius. This causes energy to build up over time at large scales. The resulting magnetic-energy spectra bear a strong resemblance to those observed in situ, exhibiting a sharp, steep kinetic transition range above and around the ion-Larmor scale, with flattening at yet smaller scales. The effect thus offers a possible solution to the decade-long puzzle of the position and variability of ion-kinetic spectral breaks in plasma turbulence. The existence of the ‘barrier’ also suggests that, how a plasma is forced at large scales (the imbalance) may have a crucial influence on thermodynamic properties such as the ion-to-electron heating ratio.