We investigate two-dimensional (2-D) axisymmetric flow in toroidal geometry, with a focus on a transition between 2-D three-component flow and 2-D two-component flow. This latter flow state allows a self-organization of the system to a quiescent dynamics, characterized by long-living coherent structures. When these large-scale structures orient in the azimuthal direction, the radial transport is reduced. Such a transition, if it can be triggered in toroidally confined fusion plasmas, is beneficial for the generation of zonal flows and should consequently result in a flow field beneficial for confinement.

The Richtmyer–Meshkov instability (RMI) results from the impulsive acceleration of a density interface where either it or the acceleration is perturbed. Density interfaces may arise due to a change in gas species, isotope, temperature or a combination of these. We computationally investigate the effect of interface type on the plasma RMI, which is relevant for a range of applications, including inertial confinement fusion. We simulate the evolution of single-mode perturbed thermal, species and isotope interfaces in an ideal ion–electron plasma using the multi-fluid plasma (MFP) model. We find that, in the MFP model, the evolution of different types of interface differs significantly, in contrast to single-fluid models where they behave similarly if the Atwood number is matched. The thermal and species interfaces produce the most severe response to shock acceleration, experiencing the secondary instabilities and enhanced primary mode growth. The isotope interface evolution is restrained in comparison with the former cases, resembling the response predicted by single-fluid models. The determining factor in the severity of the MFP RMI is the density ratio across the initial interface in the electron fluid, which is unity for an isotope interface. We observe that, as the density ratio across the electron interface decreases, so do the magnitudes of the self-generated fields and consequently the severity of the growth amplification. Generally, the evolution of the RMI with different types of interface becomes more similar as the level of coupling between the ion and electron fluids is increased, characterised by reducing the plasma non-dimensional skin depth.

We investigate the linear stability of a sinusoidal shear flow with an initially uniform streamwise magnetic field in the framework of incompressible magnetohydrodynamics (MHD) with finite resistivity and viscosity. This flow is known to be unstable to the Kelvin–Helmholtz instability in the hydrodynamic case. The same is true in ideal MHD, where dissipation is neglected, provided the magnetic field strength does not exceed a critical threshold beyond which magnetic tension stabilizes the flow. Here, we demonstrate that including viscosity and resistivity introduces two new modes of instability. One of these modes, which we refer to as an Alfvénic Dubrulle–Frisch instability, exists for any non-zero magnetic field strength as long as the magnetic Prandtl number ${{{Pm}}} < 1$. We present a reduced model for this instability that reveals its excitation mechanism to be the negative eddy viscosity of periodic shear flows described by Dubrulle & Frisch (Phys. Rev. A, vol. 43, 1991, pp. 5355–5364). Finally, we demonstrate numerically that this mode saturates in a quasi-stationary state dominated by counter-propagating solitons.

Shock tubes are a crucial source of experimental data for the aerothermodynamic modelling of atmospheric entry vehicles. Notably, many chemical-kinetic and radiative models are validated directly against optical measurements from these facilities. Typically, the incident shock speed at the location of the experimental measurement is taken to be representative of the test slug; however, the shock velocity can vary substantially upstream of this location. These variations have been long posited as a source of disagreement with computational predictions, although a definitive link has proved elusive. This work describes a series of experiments which aim to isolate and confirm the importance of the shock deceleration effect. This is achieved by generating different shock trajectories and comparing the post-shock trends in atomic oxygen emission and electron density. These trends are shown to be directly linked to the upstream shock speed variations using a recently developed numerical tool (LASTA). The close agreement of the comparisons confirms the importance of shock speed variation for shock tube experiments; these findings have direct and potentially critical relevance for all such studies, both past and present.

The Naval Research Laboratory ‘Mag Noh problem’, described in this paper, is a self-similar magnetized implosion flow, which contains a fast magnetohydrodynamic (MHD) outward propagating shock of constant velocity. We generalize the classic Noh (OSTI Tech. Rep. 577058, 1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimuthal field and rotation. While the classic Noh problem must have a supersonic implosion velocity to create a shock, our solutions have an interesting three-parametric special case with zero initial velocity in which magnetic tension, instead of implosion flow, creates the shock at $t=0+$. Our self-similar solutions are indeed realized when we solve the initial value MHD problem with the finite volume MHD code Athena. We numerically investigated the stability of these solutions and found both stable and unstable regions in parameter space. Stable solutions can be used to test the accuracy of numerical codes. Unstable solutions have also been widely used to test how codes reproduce linear growth, transition to turbulence and the practically important effects of mixing. Now we offer a family of unstable solutions featuring all three elements relevant to magnetically driven implosions: convergent flow, magnetic field and a shock wave.

A three-dimensional fully kinetic particle-in-cell (PIC) simulation strategy has been implemented to simulate the acceleration stage of a magnetically enhanced plasma thruster (MEPT). The study has been performed with the open-source code Spacecraft Plasma Interaction Software (SPIS). The tool has been copiously modified to simulate properly the dynamics of a magnetized plasma plume. A cross-validation of the methodology has been done with Starfish, a two-dimensional open-source PIC software. Two configurations have been compared: (i) in the absence of a magnetic field and (ii) in the presence of a magnetic field generated by a coil with maximum intensity of 300 G at the thruster outlet. The results show a reduction of the plume divergence angle, an increase of ion speed and an increase of the specific impulse in the presence of the magnetic nozzle. The simulations presented in this study are representative of the operative conditions of a 50 W MEPT. Nonetheless, the methodology adopted can be extended to handle the magnetized plasma plume of several other types of thrusters such as electron cyclotron resonance and applied field magnetoplasmadynamic thrusters.

Recently, the energization of superthermal electrons at the Earth's bow shock was found to be consistent with a new magnetic pumping model derived in the limit where the electron transit time is much shorter than any time scale governing the evolution of the magnetic fields. The new model breaks with the common approach of integrating the kinetic equations along unperturbed orbits. Rather, the fast transit-time limit allows the electron dynamics to be characterized by adiabatic invariants (action variables) accurately capturing the nonlinear effects of electrons becoming trapped in magnetic perturbations. Without trapping, fast parallel streaming along magnetic field lines causes the electron pressure to be isotropized and homogeneous along the magnetic field lines. In contrast, trapping permits spatially varying pressure anisotropy to form along the magnetic field lines, and through a Fermi process this pressure anisotropy in turn becomes the main ingredient that renders magnetic pumping efficient for energizing superthermal electrons. We here present a detailed mathematical derivation of the model.

An equilibrium statistical mechanics theory for the Hasegawa–Mima equations of toroidal plasmas, with canonical constraint on energy and microcanonical constraint on potential enstrophy, is solved exactly as a spherical model. The use of a canonical energy constraint instead of a fixed-energy microcanonical approach is justified by the preference for viewing real plasmas as an open system. A significant consequence of the results obtained from the partition function, free energy and critical temperature, is the condensation into a ground state exhibiting a blob-hole-like structure observed in real plasmas.

We study the influence of the shape of the plasma container on the dynamics of the reversed-field pinch (RFP). The geometries we consider are periodic cylinders with elliptical and circular-shaped cross-sections. Numerical simulations of fully nonlinear viscoresistive magnetohydrodynamics are carried out to illustrate how the plasma dynamics is affected by shaping. It is shown that independent of the plasma shape, the quantity $\beta$, comparing the hydrodynamic pressure to the magnetic pressure, decreases for increasing values of the Lundquist number, but the pressure gradient fluctuations remain roughly constant, when compared to the Lorentz force. Different elliptical shapes of the cross-section of the domain lead to the excitation of different toroidal (or axial) magnetic and dynamic modes. Furthermore, it is found that in a geometry with circular cross-section, a significant local poloidal angular momentum is observed, absent in the geometries with elliptical cross-section. Because the confinement is dominantly determined by plasma movement, and the dynamics of the velocity and magnetic field are modified by the modification of the geometry, shaping can thus affect the performance of RFP devices.

The GENE-3D code, the global stellarator version of the established GENE framework, has been extended to an electromagnetic gyrokinetic code. This paper outlines the basic structure of the algorithm, highlighting the treatment of the electromagnetic terms. The numerical implementation is verified against the radially global GENE code in linear and nonlinear tokamak simulations, recovering excellent agreement between both codes. As a first application to stellarator plasmas, linear and nonlinear global simulations with kinetic electrons of ion temperature gradient (ITG) turbulence in Wendelstein 7-X were performed, showing a decrease of ITG activity through the introduction of electromagnetic effects via a finite plasma-$\beta$. The upgrade makes it possible to study a large variety of new physical scenarios, including kinetic electron and electromagnetic effects, reducing the gap between gyrokinetic models and physically realistic systems.

Steady plasma flows have been studied almost exclusively in systems with continuous symmetry or in open domains. In the absence of continuous symmetry, the lack of a conserved quantity makes the study of flows intrinsically challenging. In a toroidal domain, the requirement of double periodicity for physical quantities adds to the complications. In particular, the magnetohydrodynamics (MHD) model of plasma steady state with the flow in a non-symmetric toroidal domain allows the development of singularities when the rotational transform of the magnetic field is rational, much like the equilibrium MHD model. In this work, we show that steady flows can still be maintained provided the rotational transform is close to rational and the magnetic shear is weak. We extend the techniques developed in carrying out perturbation methods to all orders for static MHD equilibrium by Weitzner (Phys. Plasmas, vol. 21, 2014, p. 022515) to MHD equilibrium with flows. We construct perturbative MHD equilibrium in a doubly periodic domain with nearly parallel flows by systematically eliminating magnetic resonances order by order. We then utilize an additional symmetry of the flow problem, first discussed by Hameiri (J. Math. Phys., vol. 22, 1981, pp. 2080–2088, § III), to obtain a generalized Grad–Shafranov equation for a class of non-symmetric three-dimensional MHD equilibrium with flows both parallel and perpendicular to the magnetic field. For this class of flows, we can obtain non-symmetric generalizations of integrals of motion, such as Bernoulli's function and angular momentum. Finally, we obtain the generalized Hamada conditions, which are necessary to suppress singular currents in such a system when the magnetic field lines are closed. We do not attempt to address the question of neoclassical damping of flows.

The quantum effects in plasmas can be described by the hydrodynamics containing the continuity and Euler equations. However, novel quantum phenomena are found via the extended set of hydrodynamic equations, where the pressure evolution equation and the pressure flux third-rank tensor evolution equation are included. These give the quantum corrections to the Coulomb interaction. The spectra of the Langmuir waves and the spin-electron acoustic waves are calculated. The application of the pressure evolution equation ensures that the contribution of pressure in the Langmuir wave spectrum is proportional to $(3/5)v_{\textrm {Fe}}^{2}$ rather than $(1/3)v_{\textrm {Fe}}^{2}$, where $v_{\textrm {Fe}}$ is the Fermi velocity.

The self-focusing condition of a charged particle beam in a resistive plasma has been studied. When plasma heating is weak, the beam focusing is intensified by increasing the beam density or velocity. However, when plasma heating is strong, the beam focusing is only determined by the beam velocity. Especially, in weak heating conditions, the beam trends to be focused into the centre as a whole, and in strong heating conditions, a double-peak structure with a hollow centre is predicted to appear. Furthermore, it is found that the beam radius has a significant effect on focusing distance: a larger the beam radius will result in a longer focusing distance. Simulation results also show that when the beam radius is large enough, filamentation of the beam appears. Our results will serve as a reference for relevant beam–plasma experiments and theoretical analyses, such as heavy ion fusion and ion-beam-driven high energy density physics.

Fusion energy research is delivering impressive new results emerging from different infrastructures and industrial devices evolving rapidly from ideas to proof-of-principle demonstration and aiming at the conceptual design of reactors for the production of electricity. A major milestone has recently been announced in laser fusion by the Lawrence Livermore National Laboratory and is giving new thrust to laser-fusion energy research worldwide. Here we discuss how these circumstances strongly suggest the need for a European intermediate-energy facility dedicated to the physics and technology of laser-fusion ignition, the physics of fusion materials and advanced technologies for high-repetition-rate, high-average-power broadband lasers. We believe that the participation of the broader scientific community and the increased engagement of industry, in partnership with research and academic institutions, make most timely the construction of this infrastructure of extreme scientific attractiveness.

The Epoch of Reionisation (EoR) is the period within which the neutral universe transitioned to an ionised one. This period remains unobserved using low-frequency radio interferometers, which target the 21 cm signal of neutral hydrogen emitted in this era. The Murchison Widefield Array (MWA) radio telescope was built with the detection of this signal as one of its major science goals. One of the most significant challenges towards a successful detection is that of calibration, especially in the presence of the Earth’s ionosphere. By introducing refractive source shifts, distorting source shapes, and scintillating flux densities, the ionosphere is a major nuisance in low-frequency radio astronomy. We introduce sivio, a software tool developed for simulating observations of the MWA through different ionospheric conditions, which is estimated using thin screen approximation models and propagated into the visibilities. This enables us to directly assess the impact of the ionosphere on observed EoR data and the resulting power spectra. We show that the simulated data captures the dispersive behaviour of ionospheric effects. We show that the spatial structure of the simulated ionospheric media is accurately reconstructed either from the resultant source positional offsets or from parameters evaluated during the data calibration procedure. In turn, this will inform on the best strategies of identifying and efficiently eliminating ionospheric contamination in EoR data moving into the Square Kilometre Array era.

This paper describes a computational investigation of multimode instability growth and multimaterial mixing induced by multiple shock waves in a high-energy-density (HED) environment, where pressures exceed 1 Mbar. The simulations are based on a series of experiments performed at the National Ignition Facility (NIF) and designed as an HED analogue of non-HED shock-tube studies of the Richtmyer–Meshkov instability and turbulent mixing. A three-dimensional computational modelling framework is presented. It treats many complications absent from canonical non-HED shock-tube flows, including distinct ion and free-electron internal energies, non-ideal equations of state, radiation transport and plasma-state mass diffusivities, viscosities and thermal conductivities. The simulations are tuned to the available NIF data, and traditional statistical quantities of turbulence are analysed. Integrated measures of turbulent kinetic energy and enstrophy both increase by over an order of magnitude due to reshock. Large contributions to enstrophy production during reshock are seen from both the baroclinic source and enstrophy–dilatation terms, highlighting the significance of fluid compressibility in the HED regime. Dimensional analysis reveals that Reynolds numbers and diffusive Péclet numbers in the HED flow are similar to those in a canonical non-HED analogue, but conductive Péclet numbers are much smaller in the HED flow due to efficient thermal conduction by free electrons. It is shown that the mechanism of electron thermal conduction significantly softens local spanwise gradients of both temperature and density, which causes a minor but non-negligible decrease in enstrophy production and small-scale mixing relative to a flow without this mechanism.

We report a knot cascade of magnetic field lines through the stepwise reconnection of a pair of orthogonal helical flux tubes with opposite chirality. The magnetic-surface field is developed to identify the evolution of flux tubes and pinpoint the reconnection region. We find that the incipient X-type magnetic reconnection generates antiparallel U-shaped field lines moving in opposite directions away from the plasmoid. This reconnection is characterized by the decay of the magnetic flux through the diagonal symmetric planes. Subsequently, overhand magnetic knots are tied via the secondary reconnection, coinciding with the notable conversion from magnetic energy to kinetic energy. The knotted field lines are then rotated and stretched in the plasmoid by the vortical-like local motion induced by the magnetic knots themselves via the Lorentz force. This nonlinear evolution triggers the tertiary reconnection to form double overhand knots, and then further reconnections to produce more complex knots. From field lines extracted at different times, the knot cascade via the sequence of reconnections in a finite time period is quantified by the increment of the minimum crossing number and the migration of the probability density function of the Alexander–Briggs notation. Finally, the knot cascade slows down and then terminates due to resistive and viscous dissipations.

A new methodology to accurately and efficiently examine the radio frequency blackout phenomenon during the hypersonic reentry process is introduced and validated. The current state-of-the-art thermochemical modelling of $\textrm {CO}_2$ flows is reviewed and one-dimensional stagnation line studies are performed in order to determine a suitable chemical mechanism for the electron density modelling. Hypersonic computational fluid dynamics (CFD) simulations are performed with a simplified chemical model including only neutral species, in order to calculate the flow field surrounding the ExoMars Schiapparelli module in flight conditions. A novel decoupled CFD approach is then applied where the calculation of the electron density is performed separately using a computationally inexpensive Lagrangian approach. Subsequently, a ray tracing algorithm is applied in order to model the propagation of electromagnetic waves in the wake flow past the ExoMars vehicle accounting for collisions between electrons and gas particles. The numerical results of the proposed novel approach for blackout analysis consisting of CFD, Lagrangian and ray tracing algorithms are in good agreement with the flight data.

We investigate the effects of magnetisation on the two-fluid plasma Richtmyer–Meshkov instability of a single-mode thermal interface using a computational approach. The initial magnetic field is normal to the mean interface location. Results are presented for a magnetic interaction parameter of 0.1 and plasma skin depths ranging from 0.1 to 10 perturbation wavelengths. These are compared to initially unmagnetised and neutral fluid cases. The electron flow is found to be constrained to lie along the magnetic field lines resulting in significant longitudinal flow features that interact strongly with the ion fluid. The presence of an initial magnetic field is shown to suppress the growth of the initial interface perturbation with effectiveness determined by plasma length scale. Suppression of the instability is attributed to the magnetic field's contribution to the Lorentz force. This acts to rotate the vorticity vector in each fluid about the local magnetic-field vector leading to cyclic inversion and transport of the out-of-plane vorticity that drives perturbation growth. The transport of vorticity along field lines increases with decreasing plasma length scales and the wave packets responsible for vorticity transport begin to coalesce. In general, the two-fluid plasma Richtmyer–Meshkov instability is found to be suppressed through the action of the imposed magnetic field with increasing effectiveness as plasma length scale is decreased. For the conditions investigated, a critical skin depth for instability suppression is estimated.

We argue that measurements of X-ray polarization using the recently launched Imaging X-ray Polarimetry Explorer will answer many open questions about magnetars in particular the physical state of their surfaces, whether vacuum birefringence exists, and the nature of the hard X-ray emission from these objects. We outline the capabilities of the instrument, specific models and the results of simulations for the magnetar 4U 0142+61.