A new approach to target development for laboratory astrophysics experiments at high-power laser facilities is presented. With the dawn of high-power lasers, laboratory astrophysics has emerged as a field, bringing insight into physical processes in astrophysical objects, such as the formation of stars. An important factor for success in these experiments is targetry. To date, targets have mainly relied on expensive and challenging microfabrication methods. The design presented incorporates replaceable machined parts that assemble into a structure that defines the experimental geometry. This can make targets cheaper and faster to manufacture, while maintaining robustness and reproducibility. The platform is intended for experiments on plasma flows, but it is flexible and may be adapted to the constraints of other experimental setups. Examples of targets used in experimental campaigns are shown, including a design for insertion in a high magnetic field coil. Experimental results are included, demonstrating the performance of the targets.

We develop a model of gamma-ray flares of the Crab Nebula resulting from the magnetic reconnection events in a highly magnetised relativistic plasma. We first discuss physical parameters of the Crab Nebula and review the theory of pulsar winds and termination shocks. We also review the principle points of particle acceleration in explosive reconnection events [Lyutikov et al., J. Plasma Phys., vol. 83(6), p. 635830601 (2017a); J. Plasma Phys., vol. 83(6), p. 635830602 (2017b)]. It is required that particles producing flares are accelerated in highly magnetised regions of the nebula. Flares originate from the poleward regions at the base of the Crab’s polar outflow, where both the magnetisation and the magnetic field strength are sufficiently high. The post-termination shock flow develops macroscopic (not related to the plasma properties on the skin-depth scale) kink-type instabilities. The resulting large-scale magnetic stresses drive explosive reconnection events on the light-crossing time of the reconnection region. Flares are produced at the initial stage of the current sheet development, during the X-point collapse. The model has all the ingredients needed for Crab flares: natural formation of highly magnetised regions, explosive dynamics on the light travel time, development of high electric fields on macroscopic scales and acceleration of particles to energies well exceeding the average magnetic energy per particle.

Using analytical and numerical methods (fluid and particle-in-cell simulations) we study a number of model problems involving merger of magnetic flux tubes in relativistic magnetically dominated plasma. Mergers of current-carrying flux tubes (exemplified by the two-dimensional ‘ABC’ structures) and zero-total-current magnetic flux tubes are considered. In all cases regimes of spontaneous and driven evolution are investigated. We identify two stages of particle acceleration during flux mergers: (i) fast explosive prompt X-point collapse and (ii) ensuing island merger. The fastest acceleration occurs during the initial catastrophic X-point collapse, with the reconnection electric field of the order of the magnetic field. During the X-point collapse, particles are accelerated by charge-starved electric fields, which can reach (and even exceed) values of the local magnetic field. The explosive stage of reconnection produces non-thermal power-law tails with slopes that depend on the average magnetization $\unicode[STIX]{x1D70E}$. For plasma magnetization $\unicode[STIX]{x1D70E}\leqslant 10^{2}$ the spectrum power-law index is $p>2$; in this case the maximal energy depends linearly on the size of the reconnecting islands. For higher magnetization, $\unicode[STIX]{x1D70E}\geqslant 10^{2}$, the spectra are hard, $p<2$, yet the maximal energy $\unicode[STIX]{x1D6FE}_{\text{max}}$ can still exceed the average magnetic energy per particle, ${\sim}\unicode[STIX]{x1D70E}$, by orders of magnitude (if $p$ is not too close to unity). The X-point collapse stage is followed by magnetic island merger that dissipates a large fraction of the initial magnetic energy in a regime of forced magnetic reconnection, further accelerating the particles, but proceeds at a slower reconnection rate.

The extreme properties of the gamma-ray flares in the Crab nebula present a clear challenge to our ideas on the nature of particle acceleration in relativistic astrophysical plasma. It seems highly unlikely that standard mechanisms of stochastic type are at work here and hence the attention of theorists has switched to linear acceleration in magnetic reconnection events. In this series of papers, we attempt to develop a theory of explosive magnetic reconnection in highly magnetized relativistic plasma which can explain the extreme parameters of the Crab flares. In the first paper, we focus on the properties of the X-point collapse. Using analytical and numerical methods (fluid and particle-in-cell simulations) we extend Syrovatsky’s classical model of such collapse to the relativistic regime. We find that the collapse can lead to the reconnection rate approaching the speed of light on macroscopic scales. During the collapse, the plasma particles are accelerated by charge-starved electric fields, which can reach (and even exceed) values of the local magnetic field. The explosive stage of reconnection produces non-thermal power-law tails with slopes that depend on the average magnetization $\unicode[STIX]{x1D70E}$. For sufficiently high magnetizations and vanishing guide field, the non-thermal particle spectrum consists of two components: a low-energy population with soft spectrum that dominates the number census; and a high-energy population with hard spectrum that possesses all the properties needed to explain the Crab flares.

The influence of finite Larmor radius correction, tensor viscosity and uniform rotation on self-gravitational and firehose instabilities is discussed in the framework of the quantum magnetohydrodynamic and Chew–Goldberger–Low (CGL) fluid models. The general dispersion relation is obtained for transverse and longitudinal modes of propagation. In both the modes of propagation the dispersion relation is further analysed with respect to the direction of the rotational axis. In the analytical discussion the axis of rotation is considered in parallel and in the perpendicular direction to the magnetic field. (i) In the transverse mode of propagation, when rotation is parallel to the direction of the magnetic field, the Jeans instability criterion is affected by the rotation, finite Larmor radius (FLR) and quantum parameter but remains unaffected due to the presence of tensor viscosity. The calculated critical Jeans masses for rotating and non-rotating dense degenerate plasma systems are $3.5M_{\odot }$ and $2.1M_{\odot }$ respectively. It is clear that the presence of rotation enhances the threshold mass of the considered system. (ii) In the case of longitudinal mode of propagation when rotation is parallel to the direction of the magnetic field, Alfvén and viscous self-gravitating modes are obtained. The Alfvén mode is modified by FLR corrections and rotation. The analytical as well as graphical results show that the presence of FLR and rotation play significant roles in stabilizing the growth rate of the firehose instability by suppressing the parallel anisotropic pressure. The viscous self-gravitating mode is significantly affected by tensor viscosity, anisotropic pressure and the quantum parameter while it remains free from rotation and FLR corrections. When the direction of rotation is perpendicular to the magnetic field, the rotation of the considered system coupled the Alfvén and viscous self-gravitating modes to each other. The finding of the present work is applicable to strongly magnetized dense degenerate plasma.

The basic physics of the processes playing the most important role in divertor plasma detachment is reviewed. The models used in the two-dimensional edge plasma transport codes that are widely used to address different issues of the edge plasma physics and to simulate the experimental data, as well as the numerical schemes and convergence issues, are described. The processes leading to ultimate divertor plasma detachment, the transition to and the stability of the detached regime, as well as the impact of the magnetic configuration and divertor geometry on detachment, are considered. A consistent, integral physical picture of ultimate detachment of a tokamak divertor plasma is developed.

We present a fast and spectrally accurate numerical scheme for the evaluation of the gyroaveraged electrostatic potential in non-periodic gyrokinetic-Poisson simulations. Our method relies on a reformulation of the gyrokinetic-Poisson system in which the gyroaverage in Poisson’s equation is computed for the compactly supported charge density instead of the non-periodic, non-compactly supported potential itself. We calculate this gyroaverage with a combination of two Fourier transforms and a Hankel transform, which has the near optimal run-time complexity $O(N_{\unicode[STIX]{x1D70C}}(P+\hat{P})\log (P+\hat{P}))$, where $P$ is the number of spatial grid points, $\hat{P}$ the number of grid points in Fourier space and $N_{\unicode[STIX]{x1D70C}}$ the number of grid points in velocity space. We present numerical examples illustrating the performance of our code and demonstrating geometric convergence of the error.

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.

Upgraded heating and current drive (H/CD) systems have been equipped on the Experimental Advanced Superconducting Tokamak (EAST). With the upgraded H/CD systems, the operation space of EAST is extended, and the ability to achieve higher performance is improved. In this paper, a 0.5 dimension transport code named Minute Embedded Tokamak Integrated Simulator (METIS) is applied to predict the EAST operation space and to assess the current drive capability of the 4.6 GHz lower hybrid current drive system. Predictive simulation of several EAST scenarios, including steady-state high confinement mode (H-mode), advanced regime, high normalized beta and high electron temperature, are also performed with the available H/CD systems. The simulation results provide a guidance for forthcoming advanced EAST experiments.

In this article, self-focusing of an intense circularly polarized laser pulse in the presence of an external oblique magnetic field in hot magnetized plasma, using Maxwell’s equations and the relativistic fluid momentum equation, is studied. An envelope equation governing the spot size of the laser beam for both of left- and right-hand polarizations has been derived and the effects of the plasma temperature and oblique magnetic field on the electron density distribution of hot plasma with respect to variation of the normalized laser spot size has been investigated. Numerical results depict that in right-hand polarization, self-focusing of the laser pulse along the propagation direction in hot magnetized plasma becomes better and more compressed with increasing $\unicode[STIX]{x1D703}$. Inversely, in left-hand polarization, increase of $\unicode[STIX]{x1D703}$ in an oblique magnetic field leads to enhancement of the spot size and reduction self-focusing. Besides, in the plasma density profile, self-focusing of the laser pulse improves in comparison with no oblique magnetic field. Also it is shown that plasma temperature has a key role in the laser spot size, normalized laser output power and the variation of plasma density.

The energy budget of a collisionless plasma subject to electrostatic fluctuations is considered, and the excess of thermal energy over the minimum accessible to it under various constraints that limit the possible forms of plasma motion is calculated. This excess measures how much thermal energy is ‘available’ for conversion into plasma instabilities, and therefore constitutes a nonlinear measure of plasma stability. A distribution function with zero available energy defines a ‘ground state’ in the sense that its energy cannot decrease by any linear or nonlinear plasma motion. In a Vlasov plasma with small density and temperature fluctuations, the available energy is proportional to the mean square of these quantities, and exceeds the corresponding energy in ideal or resistive magnetohydrodynamics. If the first or second adiabatic invariant is conserved, ground states generally have inhomogeneous density and temperature. Magnetically confined plasmas are usually not in any ground state, but certain types of stellarator plasmas are so with respect to fluctuations that conserve both these adiabatic invariants, making the plasma linearly and nonlinearly stable to such fluctuations. Similar stability properties can also be enjoyed by plasmas confined by a dipole magnetic field.

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.

The collisionless axisymmetric zonal flow residual calculation for a tokamak plasma is generalized to include electromagnetic perturbations. We formulate and solve the complete initial value zonal flow problem by retaining the fully self-consistent axisymmetric spatial perturbations in the electric and magnetic fields. Simple expressions for the electrostatic, shear and compressional magnetic residual responses are derived that provide a fully electromagnetic test of the zonal flow residual in gyrokinetic codes. Unlike the electrostatic potential, the parallel vector potential and the parallel magnetic field perturbations need not relax to flux functions for all possible initial conditions.

The paper investigates the dynamics of magnetized non-neutral (electron) plasmas subjected to external electric field perturbations. A two-dimensional (2-D) particle-in-cell code is effectively exploited to model this system with a special attention to the role that non-axisymmetric, multipolar radio frequency (RF) drives applied to the cylindrical (circular) boundary play on the insurgence of azimuthal instabilities and the subsequent formation of coherent structures preventing the relaxation to a fully developed turbulent state, when the RF fields are chosen in the frequency range of the low-order fluid modes themselves. The isomorphism of such system with a 2-D inviscid incompressible fluid offers an insight into the details of forced 2-D fluid turbulence. The choice of different initial density (i.e. fluid vorticity) distributions allows for a selection of conditions where different levels of turbulence and intermittency are expected and a range of final states is achieved. Integral and spectral quantities of interest are computed along the flow using a multiresolution analysis based on a wavelet decomposition of both enstrophy and energy 2-D maps. The analysis of a variety of cases shows that the qualitative features of turbulent relaxation are similar in conditions of both free and forced evolution; at the same time, fine details of the flow beyond the self-similarity turbulence properties are highlighted in particular in the formation of structures and their timing, where the influence of the initial conditions and the effect of the external forcing can be distinguished.

Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of relativistic plasmas require accurate computations able to catch the full spatial and temporal dynamics of the system. Numerical simulations of ultra-relativistic plasmas face severe restrictions due to limitations in the maximum possible Lorentz factors that current algorithms can reproduce to good accuracy. In order to circumvent this flaw and repel the limit to $\unicode[STIX]{x1D6FE}\approx 10^{9}$, we design a new fully implicit scheme to solve the relativistic particle equation of motion in an external electromagnetic field using a three-dimensional Cartesian geometry. We show some examples of numerical integrations in constant electromagnetic fields to prove the efficiency of our algorithm. The code is also able to follow the electric drift motion for high Lorentz factors. In the most general case of spatially and temporally varying electromagnetic fields, the code performs extremely well, as shown by comparison with exact analytical solutions for the relativistic electrostatic Kepler problem as well as for linearly and circularly polarized plane waves.

According to magnetohydrodynamics (MHD), the encounter of two collisional magnetized plasmas at high velocity gives rise to shock waves. Investigations conducted so far have found that the same conclusion still holds in the case of collisionless plasmas. For the case of a flow-aligned field, MHD stipulates that the field and the fluid are disconnected, so that the shock produced is independent of the field. We present a violation of this MHD prediction when considering the encounter of two cold pair plasmas along a flow-aligned magnetic field. As the guiding magnetic field grows, isotropization is progressively suppressed, resulting in a strong influence of the field on the resulting structure. A micro-physics analysis allows us to understand the mechanisms at work. Particle-in-cell simulations also support our conclusions and show that the results are not restricted to a strictly parallel field.

The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker–Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function (e.g. the INMDF (Izacard, O. 2016b Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas. Phys. Plasmas 23, 082504) that stands for interpreted non-Maxwellian distribution function). One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. The results shown here could provide the insights to break some of the unsolved puzzles of turbulence.

Kinetic-range turbulence in magnetized plasmas and, in particular, in the context of solar wind turbulence has been extensively investigated over the past decades via numerical simulations. Among others, one of the widely adopted reduced plasma models is the so-called hybrid-kinetic model, where the ions are fully kinetic and the electrons are treated as a neutralizing (inertial or massless) fluid. Within the same model, different numerical methods and/or approaches to turbulence development have been employed. In the present work, we present a comparison between two-dimensional hybrid-kinetic simulations of plasma turbulence obtained with two complementary approaches spanning approximately two decades in wavenumber – from the magnetohydrodynamics inertial range to scales well below the ion gyroradius – with a state-of-the-art accuracy. One approach employs hybrid particle-in-cell simulations of freely decaying Alfvénic turbulence, whereas the other consists of Eulerian hybrid Vlasov–Maxwell simulations of turbulence continuously driven with partially compressible large-scale fluctuations. Despite the completely different initialization and injection/drive at large scales, the same properties of turbulent fluctuations at $k_{\bot }\unicode[STIX]{x1D70C}_{i}\gtrsim 1$ are observed, where $k_{\bot }$ is the fluctuations’ wavenumber perpendicular to the background magnetic field and $\unicode[STIX]{x1D70C}_{i}$ is the ion Larmor radius. The system indeed self-consistently ‘reprocesses’ the turbulent fluctuations while they are cascading towards smaller and smaller scales, in a way which actually depends on the plasma beta parameter ($\unicode[STIX]{x1D6FD}$ is the ratio between the thermal and the magnetic pressures). Small-scale turbulence has been found to be mainly populated by kinetic Alfvén wave (KAW) fluctuations for $\unicode[STIX]{x1D6FD}\geqslant 1$, whereas KAW fluctuations are only sub-dominant for low-$\unicode[STIX]{x1D6FD}$.

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.

The Jeans instability is examined in quantum dusty magnetoplasmas due to low-frequency magnetosonic perturbations. The fluid model consisting of the momentum balance equation for quantum plasmas, Poisson’s equation for the gravitational potential and Maxwell’s equations for electromagnetic magnetosonic perturbations is solved. The numerical analysis elaborates the significant contribution of magnetic field, electron number density and variable dust mass to the Jeans instability.