Chaotic electromagnetic fields are common in many relativistic plasma environments, where they can be excited by instabilities on kinetic spatial scales. When strong electric fluctuations exist on sub-electron scales, they may lead to small angle, stochastic deflections of the electrons’ pitch angles. Under certain conditions, this closely resembles the effect of Coulomb collisions in collisional plasmas. The electric pitch-angle diffusion coefficient acts as an effective collision – or ‘quasi-collision’ – frequency. We show that quasi-collisions may radically alter the expected radiative transport properties of candidate plasmas. In particular, we consider the quasi-collisional generalization of the classical Faraday effect.

In this paper we revisit the paradigm of space science turbulent dissipation traditionally considered as myth (Coroniti, Space Sci. Rev., vol. 42, 1985, pp. 399–410). We demonstrate that due to approach introduced by Pitaevskii (Sov. J. Expl Theor. Phys., vol. 44, 1963, pp. 969–979; (in Russian)) (the effect of a finite Larmor radius on a classical collision integral) dissipation induced by effective interaction with microturbulence produces a significant effect on plasma dynamics, especially in the vicinity of the reconnection region. We estimate the multiplication factor of collision frequency in the collision integral for short wavelength perturbations. For waves propagating transverse to the background magnetic field, this factor is approximately $({\it\rho}_{e}k_{x})^{2}$ with ${\it\rho}_{e}$ an electron gyroradius and where $k_{x}$ is a transverse wavenumber. We consider recent spacecraft observations in the Earth’s magnetotail reconnection region to the estimate possible impact of this multiplication factor. For small-scale reconnection regions this factor can significantly increase the effective collision frequency produced both by lower-hybrid drift turbulence and by kinetic Alfvén waves. We discuss the possibility that the Pitaevskii’s effect may be responsible for the excitation of a resistive electron tearing mode in thin current sheets formed in the outflow region of the primary X-line.

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.

These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation and internal dynamics of stars and giant planets, the workings of jets and accretion discs around stars and black holes and the dynamics of the expanding Universe. Effects that can be important in astrophysical fluids include compressibility, self-gravitation and the dynamical influence of the magnetic field that is ‘frozen in’ to a highly conducting plasma. The basic models introduced and applied in this course are Newtonian gas dynamics and magnetohydrodynamics (MHD) for an ideal compressible fluid. The mathematical structure of the governing equations and the associated conservation laws are explored in some detail because of their importance for both analytical and numerical methods of solution, as well as for physical interpretation. Linear and nonlinear waves, including shocks and other discontinuities, are discussed. The spherical blast wave resulting from a supernova, and involving a strong shock, is a classic problem that can be solved analytically. Steady solutions with spherical or axial symmetry reveal the physics of winds and jets from stars and discs. The linearized equations determine the oscillation modes of astrophysical bodies, as well as their stability and their response to tidal forcing.

Challenges in plasma physics are wide. Investigation and advances are made in experiments but at the same time, to understand and to reach the experimental limits, accurate numerical simulations are required from systems of nonlinear equations. The numerical challenges of solving the associated fluid equations are discussed in this paper. Using the framework of the finite difference discretization, the most widely used methods for the problems linked to the diffusion or advection operators are presented.

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.

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.

In this paper a method is described that allows mapping of the forces acting on dust particles in a GEC reference cell. Monodisperse particles are dropped into the plasma environment and their trajectories are tracked using a high-speed camera system to determine local accelerations and respective forces. Collecting data from a large number of particle drops allows the identification of three-dimensional vector fields for the acting forces. The procedure is described and multiple examples in which the method has been applied are given. These examples include a simple plasma sheath, plasmas perturbed by a horizontal and vertical dipole magnet, an array of multiple magnets mimicking the fields found at a lunar swirl, and the fields inside a glass box used for particle confinement. Further applicability in other plasma environments will be discussed shortly.

We report on the experimental demonstration of a technique to generate steep density gradients in gas-jet targets of interest to laser–plasma ion acceleration. By using an intentional low-energy prepulse, we generated a hydrodynamic blast wave in the gas to shape the target prior to the arrival of an intense CO$_{2}$ (${\it\lambda}\approx 10~{\rm\mu}\text{m}$) drive pulse. This technique has been recently shown to facilitate the generation of ion beams by shockwave acceleration (Tresca et al., Phys. Rev. Lett., vol. 115 (9), 2015, 094802). Here, we discuss and introduce a model to understand the generation of these blast waves and discuss in depth the experimental realisation of the technique, supported by hydrodynamics simulations. With appropriate prepulse energy and timing, this blast wave can generate steepened density gradients as short as $l\approx 20~{\rm\mu}\text{m}$ ($1/e$), opening up new possibilities for laser–plasma studies with near-critical gaseous targets.

An explanation is provided for the disruptive instability in diverted tokamaks when the safety factor $q$ at the 95 % poloidal flux surface, $q_{95}$ , is driven below 2.0. The instability is a resistive kink counterpart to the current-driven ideal mode that traditionally explained the corresponding disruption in limited cross-sections (Shafranov, Sov. Phys. Tech. Phys., vol. 15, 1970, p. 175) when $q_{edge}$ , the safety factor at the outermost closed flux surface, lies just below a rational value $m/n$ . Experimentally, external kink modes are observed in limiter configurations as the current in a tokamak is ramped up and $q_{edge}$ decreases through successive rational surfaces. For $q_{edge}<2$ , the instability is always encountered and is highly disruptive. However, diverted plasmas, in which $q_{edge}$ is formally infinite in the magnetohydrodynamic (MHD) model, have presented a longstanding difficulty since the theory would predict stability, yet, the disruptive limit occurs in practice when $q_{95}$ , reaches 2. It is shown from numerical calculations that a resistive kink mode is linearly destabilized by the rapidly increasing resistivity at the plasma edge when $q_{95}<2$ , but $q_{edge}\gg 2$ . The resistive kink behaves much like the ideal kink with predominantly kink or interchange parity and no real sign of a tearing component. However, the growth rates scale with a fractional power of the resistivity near the $q=2$ surface. The results have a direct bearing on the conventional edge cutoff procedures used in most ideal MHD codes, as well as implications for ITER and for future reactor options.

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.

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.

Coaxially nested intense $E\times B$ sheared flow realized an upgraded stable mirror plasma regime. After such an external control of high vorticity formation due to electron cyclotron heating, significantly unstable plasmas appeared. Thereby, the associated cross-field transport caused a crash of plasmas. Its generalized physics and interpretation could prepare or extend to another possibility of stability in a field-reversed configuration (FRC), for instance. Such underlying physics bases of vorticity formation were essentially or partially performed in tokamaks and stellarators (solved problems). Nevertheless, it remains to be seen whether this mirror-based experimental evidence is applicable or not to open ended FRC devices. This open issue may give a solution of one of unsolved important problems, and possibly provide more generalized and externally controllable opportunities for not only FRC but wider plasma confinement improvements.

Numerical simulations have consistently shown that the reconnection rate in certain collisionless regimes can be fast, of the order of $0.1v_{A}B_{u}$ , where $v_{A}$ and $B_{u}$ are the Alfvén speed and the reconnecting magnetic field upstream of the ion diffusion region. This particular value has been reported in myriad numerical simulations under disparate conditions. However, despite decades of research, the reasons underpinning this specific value remain mysterious. Here, we present an overview of this problem and discuss the conditions under which the ‘0.1 value’ is attained. Furthermore, we explain why this problem should be interpreted in terms of the ion diffusion region length.

The influence of quantum tunnelling and shielding on the resonant electron transfer process in strongly coupled plasmas is investigated. The screened atomic states and energy eigenvalues are employed to obtain the resonant electron transfer cross-section in strongly coupled plasmas. It is found that the classical resonant electron transfer cross-section increases with an increase of the ion-sphere radius. However, the energy-dependent quantum tunnelling resonant electron transfer cross-section is shown to decrease with increasing ion-sphere radius. It is demonstrated that an increase of the nuclear charge decreases the screening effect on the electron transfer cross-section while the quantum tunnelling effect enhances the resonant electron transfer cross-section in strongly coupled plasmas. In addition, it is shown that the effect of quantum tunnelling on the resonant electron transfer process decreases when both the collision energy and ion-sphere radius increase. The variation of shielding effect on the resonant electron transfer process in strongly coupled plasmas is also discussed.

Two in situ experimental methods are presented in which dust particles are used to determine the extent of the sheath and gain information about the time-averaged electric force profile within a radio frequency (RF) plasma sheath. These methods are advantageous because they are not only simple and quick to carry out, but they also can be performed using standard dusty plasma experimental equipment. In the first method, dust particles are tracked as they fall through the plasma towards the lower electrode. These trajectories are then used to determine the electric force on the particle as a function of height as well as the extent of the sheath. In the second method, dust particle levitation height is measured across a wide range of RF voltages. Similarities were observed between the two experiments, but in order to understand the underlying physics behind these observations, the same conditions were replicated using a self-consistent fluid model. Through comparison of the fluid model and experimental results, it is shown that the particles exhibiting a levitation height that is independent of RF voltage indicate the sheath edge – the boundary between the quasineutral bulk plasma and the sheath. Therefore, both of these simple and inexpensive, yet effective, methods can be applied across a wide range of experimental parameters in any ground-based RF plasma chamber to gain useful information regarding the sheath, which is needed for interpretation of dusty plasma experiments.

The particle-in-cell (PIC) method was used to simulate heat flux mitigation experiments with partially ionised argon. The experiments demonstrate the possibility of reducing heat flux towards a target using magnetic fields. Modelling using the PIC method is able to reproduce the heat flux mitigation qualitatively. This is driven by modified electron transport. Electrons are magnetised and react directly to the external magnetic field. In addition, an increase of radial turbulent transport is also needed to explain the experimental observations in the model. Close to the target an increase of electron density is created. Due to quasi-neutrality, ions follow the electrons. Charge exchange collisions couple the dynamics of the neutrals to the ions and reduce the flow velocity of neutrals by radial momentum transport and subsequent losses. By this, the dominant heat-transport channel by neutrals gets reduced and a reduction of the heat deposition, similar to the experiment, is observed. Using the simulation a diagnostic module for optical emission is developed and its results are compared with spectroscopic measurements and photos from the experiment. The results of this study are in good agreement with the experiment. Experimental observations such as a shrank bright emission region close to the nozzle exit, an additional emission in front of the target and an overall change in colour to red are reproduced by the simulation.

In the single fluid, non-relativistic, ideal magnetohydrodynamic (MHD) plasma description, magnetic field lines play a fundamental role by defining dynamically preserved ‘magnetic connections’ between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MHD description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D magnetic connection hypersurfaces in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when $\boldsymbol{E}\boldsymbol{\cdot }\boldsymbol{B}=0$.