We study in detail the strong-field QED process of nonlinear Compton scattering in short intense plane wave laser pulses of circular polarization. Our main focus is placed on how the spectrum of the backscattered laser light depends on the shape and duration of the initial short intense pulse. Although this pulse shape dependence is very complicated and highly nonlinear, and has never been addressed explicitly, our analysis reveals that all the dependence on the laser pulse shape is contained in a class of three-parameter master integrals. Here we present completely analytical expressions for the nonlinear Compton spectrum in terms of these master integrals. Moreover, we analyse the universal behaviour of the shape of the spectrum for very high harmonic lines.

The Universe is permeated by hot, turbulent, magnetized plasmas. Turbulent plasma is a major constituent of active galactic nuclei, supernova remnants, the intergalactic and interstellar medium, the solar corona, the solar wind and the Earth’s magnetosphere, just to mention a few examples. Energy dissipation of turbulent fluctuations plays a key role in plasma heating and energization, yet we still do not understand the underlying physical mechanisms involved. THOR is a mission designed to answer the questions of how turbulent plasma is heated and particles accelerated, how the dissipated energy is partitioned and how dissipation operates in different regimes of turbulence. THOR is a single-spacecraft mission with an orbit tuned to maximize data return from regions in near-Earth space – magnetosheath, shock, foreshock and pristine solar wind – featuring different kinds of turbulence. Here we summarize the THOR proposal submitted on 15 January 2015 to the ‘Call for a Medium-size mission opportunity in ESAs Science Programme for a launch in 2025 (M4)’. THOR has been selected by European Space Agency (ESA) for the study phase.

A critical revision of the essential principles of the physics of relativistic flows of cold plasma is given. We prove that the approximation of ideal magnetic hydrodynamics of the cold plasma is equivalent to the drift approximation of motion of charged particles in an electromagnetic field. The equations of magnetohydrodynamics are obtained from equations for the drift motion of the charged particles. The conditions of application of the equations of ideal magnetohydrodynamics are obtained. In the case of the Crab pulsar the violation of the frozen-in condition can happen at a distance that well exceeds the distance to the termination shock. One fluid MHD can be incorrect at the light cylinder provided that the Lorentz factor of the plasma exceeds $10^{4}$ and the curvature radius of the flow line is comparable with the light cylinder. It is shown that the electric currents in the cold plasma are the result of the inertial drift motion of the charged particles in the crossed electric and magnetic fields.

Upper bounds are derived on the amount of magnetic energy that can be generated by dynamo action in collisional and collisionless plasmas with and without external forcing. A hierarchy of mathematical descriptions is considered for the plasma dynamics: ideal magnetohydrodynamics (MHD), visco-resistive MHD, the double-adiabatic theory of Chew, Goldberger and Low (CGL), kinetic MHD and other kinetic models. It is found that dynamo action is greatly constrained in models where the magnetic moment of any particle species is conserved. In the absence of external forcing, the magnetic energy then remains small at all times if it is small in the initial state. In other words, a small ‘seed’ magnetic field cannot be amplified significantly, regardless of the nature of flow, as long as the collision frequency and gyroradius are small enough to be negligible. A similar conclusion also holds if the system is subject to external forcing as long as this forcing conserves the magnetic moment of at least one plasma species and does not greatly increase the total energy of the plasma (i.e. in practice, is subsonic). Dynamo action therefore always requires collisions or some small-scale kinetic mechanism for breaking the adiabatic invariance of the magnetic moment.

In this paper, an Airy-like electron plasma wave is investigated in an unmagnetized collisionless plasma consisting of inertial electrons and static ions. Just like the optical Airy beam, the Airy-like electron plasma wave also has two interesting propagation characteristics: it has transverse acceleration and is diffraction-free, which display that the Airy-like electron plasma wave propagates along a curved trajectory and retains the basic structure for longer distances in the propagation direction, respectively. We give a numerical simulation for the electrostatic potential of the Airy-like electron plasma wave and show that, with the increase of the propagation distance, the electrostatic potential decreases in the propagation direction but increases in the transverse direction.

This article presents a mini-tutorial aimed at a wide readership not familiar with the field of solar plasma physics. The exposition is centred around the issue of excess/free magnetic energy stored in the solar corona. A general consideration is followed with a particular example of coronal magnetic arcade, where free magnetic energy builds up by photospheric convective flows. In the context of solar physics the major task is to explain how this free energy can be released quickly enough to match what is observed in coronal explosive events such as solar flares. Therefore, in the last section of the paper we discuss briefly a possible role of magnetic reconnection in these processes. This is done in quite simple qualitative physical terms, so that an interested reader can follow it up in more detail with help of the provided references.

Dust acoustic (or dust density) waves have been observed in many laboratory dusty plasmas. These low-frequency waves involve the dynamics of highly charged and massive dust grains, and can be excited by the flow of ions relative to dust. In this paper, we consider the nonlinear development of the dust acoustic instability, excited by thermal ion flow, in a collisional plasma containing dust with high kinetic temperature (warm dust). It is shown that under certain conditions there may be a long-wavelength secondary instability in the nonlinear stage as dust gets heated by the waves. The characteristics of the nonlinear development are considered as a function of the relative charge density of the dust. Application to possible experimental parameters is discussed.

In the present work there is presented a model describing transfer of the Crab pulsar’s spin-down energy into the powerful synchrotron emission of the nebula. The process of the energy transfer consists of several consecutive stages. The physical processes underlying the theoretical model provide us with the synchrotron emission spectrum, which fits well with the observed one.

A new class of exact electrostatic solutions of the Vlasov–Maxwell equations based on the Jeans’s theorem is proposed for studying the evolution and properties of two-dimensional anisotropic plasmas that are far from thermodynamic equilibrium. In particular, the free expansion of a slab of electron–ion plasma into vacuum is investigated.

The modulational instability of dust-ion acoustic (DIA) waves in an unmagnetized dusty plasma is investigated in the presence of weak dissipations arising due to the low rates (compared to the ion oscillation frequency) of ionization recombination and ion loss. Based on the multiple space and time scales perturbation, a new modified nonlinear Schrödinger equation governing the evolution of modulated DIA waves is derived with a linear damping term. It is shown that the combined action of all dissipative mechanisms due to collisions between particles reveals the permitted maximum time for the occurrence of the modulational instability. The influence on the modulational instability regions of relevant physical parameters such as ion temperature, dust concentration, ionization, recombination and ion loss is numerically examined. It is also found that the recombination frequency controls the instability growth rate, whereas recombination and ion loss make the instability regions wider.

In this model of a dusty plasma, we have investigated dust acoustic waves consisting of electrons with weak relativistic effects, Cairns distributed cold ions and negatively charged mobile dust. Dust acoustic (DA) compressive and rarefactive solitons of various amplitudes are established. The parameter ${\it\beta}$ involved in Cairns distribution is related to the non-thermal parameter ${\it\alpha}$. However, the increase of ${\it\beta}$, which is independent of temperature, becomes instrumental for complete linear increase or decrease of the amplitudes of both the compressive and rarefactive relativistic solitons. Hence it is worthwhile to note that the increase of ${\it\beta}$ is solely due to the rest energy and not due to kinetic energy in this relativistic plasma. This is one of the most significant results of our investigation. Also, the flux of negative charges from the dust particles, together with the effect of the relativistic electrons, appears to balance the positive charges of Cairns distributed ions for nearly constant growth of amplitudes.

The large number of ${\it\gamma}$ -ray pulsars discovered by the Fermi Gamma-Ray Space Telescope since its launch in 2008 dwarfs the handful that were previously known. The variety of observed light curves makes possible a tomography of both the ensemble-averaged field structure and the high-energy emission regions of a pulsar magnetosphere. Fitting the ${\it\gamma}$ -ray pulsar light curves with model magnetospheres and emission models has revealed that most of the high-energy emission, and the particles acceleration, takes place near or beyond the light cylinder, near the current sheet. As pulsar magnetosphere models become more sophisticated, it is possible to probe magnetic field structure and emission that are self-consistently determined. Light curve modelling will continue to be a powerful tool for constraining the pulsar magnetosphere physics.

Global, first-principles study of the kinetic ballooning mode (KBM) is crucial to understand tokamak edge physics in high-confinement mode (H-mode). In contrast to the ion temperature gradient mode and trapped electron mode, the KBM is found to be very sensitive to the equilibrium implementations in gyrokinetic codes. In this paper, we show that a second-order difference in Shafranov shift or geometric coordinates, or a difference between local and global profile implementations can bring a factor of two or more discrepancy in real frequency and growth rate. This suggests that an accurate global equilibrium is required for validation of gyrokinetic KBM simulations.

Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for stability. Known soliton results are recovered as special cases. A historical overview of the problem concludes the paper.

The SIESTA magnetohydrodynamic (MHD) equilibrium code has been used to compute a sequence of ideally stable equilibria resulting from numerical variation of the helical resonant magnetic perturbation (RMP) applied to an axisymmetric DIII-D plasma equilibrium. Increasing the perturbation strength at the dominant $m=2$, $n=-1$ resonant surface leads to lower MHD energies and increases in the equilibrium island widths at the $m=2$ (and sidebands) surfaces, in agreement with theoretical expectations. Island overlap at large perturbation strengths leads to stochastic magnetic fields which correlate well with the experimentally inferred field structure. The magnitude and spatial phase (around the dominant rational surfaces) of the resonant (shielding) component of the parallel current are shown to change qualitatively with the magnetic island topology.

The output power and the temperature profile of a copper vapour laser were investigated versus frequency with various kinds of back mirror in its resonator cavity. A semi-experimental method was used for measuring the plasma temperature and obtaining the temperature profile with various back mirrors. The obtained plasma temperature through this method has good agreement with the operational temperature of the laser.

The effects of ionization, ion loss and ion-neutral collisions on ion acoustic wave modulations in a dusty plasma are investigated. It is found that the dynamics of the modulated wave is governed by a nonlinear Schrödinger equation with a linear dissipative (damping or growth) term. This linear dissipative term arises due to the combined influence of ionization, ion loss and ion-neutral collisions. Analytical and numerical investigations predict the formation of envelope (bright) soliton with growing or decaying amplitude with time. The ionization instability causes the amplitude amplification, whereas, ion loss and ion-neutral collisions are responsible for the amplitude decay. Results are discussed in the context of dusty plasma experiments.

Counter-propagating and suitably polarized light (laser) beams can provide conditions for pair production. Here, we consider in more detail the following two situations: (i) in the homogeneity regions of anti-nodes of linearly polarized ultra-high intensity laser beams, the Schwinger process is dynamically assisted by a second high-frequency field, e.g. by an XFEL beam; and (ii) a high-energy probe photon beam colliding with a superposition of co-propagating intense laser and XFEL beams gives rise to the laser-assisted Breit–Wheeler process. The prospects of such bi-frequent field constellations with respect to the feasibility of conversion of light into matter are discussed.

A crude first assessment of how waves behave is commonly made relying on decoupled dispersion equation roots. In the low density, low temperature region behind the last closed flux surface in a tokamak – where the density decays exponentially and where the lower hybrid resonance is crossed but where the thermal velocity is small enough to justify dropping kinetic (hot plasma) effects – the study of the wave behaviour requires the roots of the full cold plasma dispersion equation. The IShTAR (Ion cyclotron Sheath Test ARrangement) device will be adopted in the coming years to shed light on the dynamics of wave–plasma interactions close to radio frequency (RF) launchers and in particular on the impact of the waves on the density and their role in the formation of RF sheaths close to metallic objects. As IShTAR is incapable of mimicking the actual conditions reigning close to launchers in tokamaks; a parameter range needs to be identified for the test stand to permit highlighting of the relevant wave physics. Studying the coupled dispersion equation roots allowed us to find a suitable operation domain for performing experiments.

Previous theoretical considerations of electron beam relaxation in inhomogeneous plasmas have indicated that the effects of the irregular solar wind may account for the poor agreement of homogeneous modelling with the observations. Quasi-linear theory and Hamiltonian models based on Zakharov’s equations have indicated that when the level of density fluctuations is above a given threshold, density irregularities act to de-resonate the beam–plasma interaction, restricting Langmuir wave growth on the expense of beam energy. This work presents the first fully kinetic particle-in-cell (PIC) simulations of beam relaxation under the influence of density irregularities. We aim to independently determine the influence of background inhomogeneity on the beam–plasma system, and to test theoretical predictions and alternative models using a fully kinetic treatment. We carry out one-dimensional (1-D) PIC simulations of a bump-on-tail unstable electron beam in the presence of increasing levels of background inhomogeneity using the fully electromagnetic, relativistic EPOCH PIC code. We find that in the case of homogeneous background plasma density, Langmuir wave packets are generated at the resonant condition and then quasi-linear relaxation leads to a dynamic increase of wavenumbers generated. No electron acceleration is seen – unlike in the inhomogeneous experiments, all of which produce high-energy electrons. For the inhomogeneous experiments we also observe the generation of backwards-propagating Langmuir waves, which is shown directly to be due to the refraction of the packets off the density gradients. In the case of higher-amplitude density fluctuations, similar features to the weaker cases are found, but also packets can also deviate from the expected dispersion curve in $(k,\unicode[STIX]{x1D714})$ -space due to nonlinearity. Our fully kinetic PIC simulations broadly confirm the findings of quasi-linear theory and the Hamiltonian model based on Zakharov’s equations. Strong density fluctuations modify properties of excited Langmuir waves altering their dispersion properties.