Two signatures of quantum effects on radiation reaction in the collision of a ${\sim}$ GeV electron beam with a high intensity ( ${>}3\times 10^{20}~\text{W}~\text{cm}^{-2}$ ) laser pulse have been considered. We show that the decrease in the average energy of the electron beam may be used to measure the Gaunt factor $g$ for synchrotron emission. We derive an equation for the evolution of the variance in the energy of the electron beam in the quantum regime, i.e. quantum efficiency parameter $\unicode[STIX]{x1D702}\not \ll 1$ . We show that the evolution of the variance may be used as a direct measure of the quantum stochasticity of the radiation reaction and determine the parameter regime where this is observable. For example, stochastic emission results in a 25 % increase in the standard deviation of the energy spectrum of a GeV electron beam, 1 fs after it collides with a laser pulse of intensity $10^{21}~\text{W}~\text{cm}^{-2}$ . This effect should therefore be measurable using current high-intensity laser systems.

A brief critique is presented of some different classes of magnetohydrodynamic equilibrium solutions based on their continuity properties and whether the magnetic field is integrable or not. A generalized energy functional is introduced that is comprised of alternating ideal regions, with nested flux surfaces with an irrational rotational transform, and Taylor-relaxed regions, possibly with magnetic islands and chaos. The equilibrium states have globally continuous magnetic fields, and may be constructed for arbitrary three-dimensional plasma boundaries and appropriately prescribed pressure and rotational-transform profiles.

A one-dimensional electrostatic filtered Vlasov–Poisson simulation study is discussed. The transition from persisting to arrested Landau damping that is produced by increasing the strength of a sinusoidal perturbation on a background Vlasov–Poisson equilibrium is explored. Emphasis is placed on observed features of the electron phase-space distribution when the perturbation strength is near the transition value. A single ubiquitous waveform is found perturbing the space-averaged phase-space distribution at almost any time in all of the simulations; the sole exception is the saturation stage that can occur at the end of the arrested damping scenario. This waveform contains relatively strong, very narrow structures in velocity bracketing $\pm v_{\text{res}}$ – the velocities at which electrons must move to traverse the dominant field mode wavelength in one of its oscillation periods – and propagating with $\pm v_{\text{res}}$ respectively. Local streams of electrons are found in these structures crossing the resonant velocities from low speed to high speed during Landau damping and from high speed to low speed during Landau growth. At the arrest time, when the field strength is briefly constant, these streams vanish. It is conjectured that the expected transfer of energy between electrons and field during Landau growth or damping has been visualized for the first time. No evidence is found in the phase-space distribution to support recent well-established discoveries of a second-order phase transition in the electric field evolution. While trapping is known to play a role for larger perturbation strengths, it is shown that trapping plays no role at any time in any of the simulations near the transition perturbation strength.

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.

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov–Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss’ law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

We experimentally study the excitation and propagation of acoustic solitary waves in a one-dimensional dusty plasma (i.e. a Yukawa chain) with $n=65$ particles interacting through a screened Coulomb potential. The lattice constant $a=1.02\pm 0.02$  mm. Waves are launched by applying a 100 mW laser pulse to one end of the chain for laser pulse durations from 0.10 to 2.0 s. We observe damped solitary waves which propagate for distances ${\gtrsim}30a$ with an acoustic speed $c_{s}=11.5\pm 0.2~\text{mm}~\text{s}^{-1}$ . The maximum velocity perturbation increases with laser pulse duration for durations ${\leqslant}0.5$ s and then saturates at ${\approx}15\,\%$ . The wave speed is found to be independent of the maximum amplitude, indicating that the formation of nonlinear solitons is prevented by neutral-gas damping.

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.

The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified framework. The current, semiclassical methods to describe the dynamics of quantum particles in strong classical fields also provide the theoretical framework for fundamental questions in gravity and hadron–hadron collisions, including Hawking radiation, cosmological particle production and thermalization of particles created in heavy-ion collisions. However, as we show, these methods break down for highly relativistic particles propagating in strong fields. They must therefore be improved and adapted for the description of laser–plasma experiments that typically involve the acceleration of electrons. Theory developed from quantum electrodynamics, together with dedicated experimental efforts, offer the best controllable context to establish a robust, experimentally validated foundation for the fundamental theory of quantum effects in strong classical potentials.

Five-dimensional gyrokinetic continuum simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using a full- $f$ discontinuous-Galerkin approach implemented in the Gkeyll code. While various simplifications have been used for now, such as long-wavelength approximations in the gyrokinetic Poisson equation and the Hamiltonian, these simulations include the basic elements of a fusion-device scrape-off layer: localised sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath-model boundary conditions. The set of sheath-model boundary conditions used in the model allows currents to flow through the walls. In addition to details of the numerical approach, results from numerical simulations of turbulence in the Large Plasma Device, a linear device featuring straight magnetic field lines, are presented.

To properly describe heating in weakly collisional turbulent plasmas such as the solar wind, interparticle collisions should be taken into account. Collisions can convert ordered energy into heat by means of irreversible relaxation towards the thermal equilibrium. Recently, Pezzi et al. (Phys. Rev. Lett., vol. 116, 2016a, 145001) showed that the plasma collisionality is enhanced by the presence of fine structures in velocity space. Here, the analysis is extended by directly comparing the effects of the fully nonlinear Landau operator and a linearized Landau operator. By focusing on the relaxation towards the equilibrium of an out of equilibrium distribution function in a homogeneous force-free plasma, here it is pointed out that it is significant to retain nonlinearities in the collisional operator to quantify the importance of collisional effects. Although the presence of several characteristic times associated with the dissipation of different phase space structures is recovered in both the cases of the nonlinear and the linearized operators, the influence of these times is different in the two cases. In the linearized operator case, the recovered characteristic times are systematically larger than in the fully nonlinear operator case, this suggesting that fine velocity structures are dissipated more slowly if nonlinearities are neglected in the collisional operator.

Although, for current laser pulse energies, the weakly nonlinear regime of laser wakefield acceleration is known to be the optimal for reaching the highest possible electron energies, the capabilities of upcoming large laser systems will provide the possibility of running highly nonlinear regimes of laser pulse propagation in underdense or near-critical plasmas. Using an extended particle-in-cell (PIC) model that takes into account all the relevant physics, we show that such regimes can be implemented with external guiding for a relatively long distance of propagation and allow for the stable transformation of laser energy into other types of energy, including the kinetic energy of a large number of high energy electrons and their incoherent emission of photons. This is despite the fact that the high intensity of the laser pulse triggers a number of new mechanisms of energy depletion, which we investigate systematically.

Relativistic electron beam transport through a high-density, magnetized plasma is studied numerically and theoretically. An electron beam injected into a cold plasma excites Weibel and two-stream instabilities that heat the beam and saturate. In the absence of an applied magnetic field, the heated beam continues to propagate. However, when a magnetic field of particular strength is applied along the direction of beam propagation, a secondary instability of off-angle whistler modes is excited. These modes then couple nonlinearly creating a large amplitude parallel-propagating whistler that stops the beam. Here, we will show these phenomena in detail and explain the mechanism of whistler mediated beam stagnation.

The multiple colliding laser pulse concept formulated by Bulanov et al. (Phys. Rev. Lett., vol. 104, 2010b, 220404) is beneficial for achieving an extremely high amplitude of coherent electromagnetic field. Since the topology of electric and magnetic fields of multiple colliding laser pulses oscillating in time is far from trivial and the radiation friction effects are significant in the high field limit, the dynamics of charged particles interacting with the multiple colliding laser pulses demonstrates remarkable features corresponding to random walk trajectories, limit circles, attractors, regular patterns and Lévy flights. Under extremely high intensity conditions the nonlinear dissipation mechanism stabilizes the particle motion resulting in the charged particle trajectory being located within narrow regions and in the occurrence of a new class of regular patterns made by the particle ensembles.

High-frequency photons travelling in plasma exhibit a linear polarizability that can influence the dispersion of linear plasma waves. We present a detailed calculation of this effect for Langmuir waves as a characteristic example. Two alternative formulations are given. In the first formulation, we calculate the modified dispersion of Langmuir waves by solving the governing equations for the electron fluid, where the photon contribution enters as a ponderomotive force. In the second formulation, we provide a derivation based on the photon polarizability. Then, the calculation of ponderomotive forces is not needed, and the result is more general.

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.

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.

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.

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.

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.

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.