We describe a new parallel, non-orthogonal-grid, three-dimensional electromagnetic particle-in-cell (EMPIC) code based on a finite-volume formulation. This code uses a logically Cartesian grid of deformable hexahedral cells, a discrete surface integral (DSI) algorithm to calculate the electromagnetic field, and a hybrid logical–physical space algorithm to push particles. We investigate the numerical instability of the DSI algorithm for non-orthogonal grids, analyse the accuracy for EMPIC simulations on non-orthogonal grids, and present performance benchmarks of this code on a parallel supercomputer. While the hybrid particle push algorithm has a second-order accuracy in space, the accuracy of the DSI field solve algorithm is between first and second order for non-orthogonal grids. The parallel implementation of this code, which is almost identical to that of a Cartesian-grid EMPIC code using domain decomposition, achieved a high parallel efficiency of over 96% for large-scale simulations.

We investigate the Kelvin–Helmholtz instability occurring at the interface of a shear-flow configuration in 2D compressible magnetohydrodynamics (MHD). The linear growth and the subsequent nonlinear saturation of the instability are studied numerically. We consider an initial magnetic field aligned with the shear flow, and analyse the differences between cases where the initial field is unidirectional everywhere (uniform case) and those where the field changes sign at the interface (reversed case). We recover and extend known results for pure hydrodynamic and MHD cases, with a discussion of the dependence of the nonlinear saturation on the wavenumber, the sound Mach number and the Alfvénic Mach number for the MHD case. A reversed field acts to destabilize the linear phase of the Kelvin–Helmholtz instability compared with the pure hydrodynamic case, while a uniform field suppresses its growth. In resistive MHD, reconnection events almost instantly accelerate the build up of a global plasma circulation. They play an important role throughout the further nonlinear evolution as well, since the initial current sheet is amplified by the vortex flow and can become unstable to tearing instabilities, forming magnetic islands. As a result, the saturation behaviour and the overall evolution of the density and the magnetic field are markedly different for the uniform versus the reversed-field case.

The effects of a sheared poloidal flow on the m = 1 (poloidal mode number) and n = 1 (toroidal mode number) kinetic internal kink mode are simulated by the linearized version of the gyro-reduced MHD code, GRM3D-2F, based on a two-field and two-fluid gyro-reduced MHD model, including the kinetic effects of electron inertia and the perturbed electron pressure gradients along the magnetic field. A parameter study for different values of de (collisionless electron skin depth) with a fixed value of ρs = 0 (ion Larmor radius estimated by the electron temperature) shows that the smaller-de case, which has the smaller growth rate, is stabilized by the smaller sheared poloidal flow. When ρs is raised to ρs > de for a fixed value of de, the instability is stabilized by the smaller shear flow compared with the case of ρs < de, although the growth rate without the flow is larger for ρs > de. Since de is very much less than the minor radius, and ρs > de for the existing and future experiments, it is possible that even a quite small sheared poloidal flow may have a crucial influence on the kinetic internal kink mode.

The equations of resistive magnetohydrodynamics taking into account the Hall effect are solved analytically for the case of a planar plasma flow across the magnetic field. Waves of purely acoustic nature are revealed that propagate in the plasma medium on the background of a steady magnetically accelerated plasma flow of a rather arbitrary form. The magnetic field manifests itself in this process only in that it produces an effective gravity force, the ‘gravitational’ acceleration being proportional to ωeτe. Like acoustic–gravity waves in the atmosphere, such quasi- acoustic–gravity (QAG) waves in a plasma can increase greatly in amplitude as they propagate ‘upwards’, i.e., in this case, counter to the direction of the electric field. In a plasma channel (where the plasma flows between the electrodes), a system of standing QAG waves arises, which has a stationary component. These waves are responsible for a number of distinctive features in the behaviour of Hall plasma flows, in particular for very large gradients and unexpected small-scale fluctuations of physical quantities near the anode, revealed earlier by numerical simulation. In the cases where the plasma-flow parameters provide a high intensity of these fluctuations, the flow appears to be unstable. In another range of parameter values, the QAG waves are strongly coupled with the electric currents that they induce in the electrodes, their amplitudes increase with time, and, again, the flow cannot be steady. The existence of a rather general dimensionless similarity criterion for resistive Hall plasma planar flows is also shown. This criterion can be found directly from the structure of the equations without any restrictions on the plasma parameters or on the form of the flow.

The nonlinear wave structures of small-amplitude ion acoustic waves in a warm plasma with adiabatic negative-ion, positron and electron constituents traversed by a warm electron beam (with different temperatures) in the vicinity of the critical negative-ion density are investigated using reductive perturbation method. The basic set of equations is reduced to an evolution equation that includes quadratic and cubic nonlinearities. The effective potential of this equation agrees exactly, for small wave amplitudes, with the Sagdeev potential obtained from the original fluid equations using a pseudopotential method. This implies that the evolution equation holds not only in the vicinity of the critical negative-ion density but also in the whole range of negative-ion density under the condition of small wave amplitude.

Fluid modelling of an edge plasma is usually performed using a finite-difference scheme on a fixed structured grid. However, both experimental measurement and numerical simulation show the presence of front-like regions characterized by sharp variations of the main plasma parameters such as temperature and radiation power. This is caused in part (i) by strong nonlinearities in the fluid equation coefficients due to abrupt changes of various plasma reaction rates as a function of temperature and (ii) by high anisotropy of the plasma transport along and across magnetic field lines. Manual mesh adoption is usually applied to allow better resolution of the regions with sharp gradients. However, such an approach is very time-consuming and limited. To overcome this problem, we propose to use adaptive unstructured meshes constructed with a new quasi-one-dimensional adaption algorithm. This approach is fast and conservative because we use a new finite-volume scheme. The price of adaptation is high, because numerical algorithms became much more complicated. To avoid unwanted complexity, we suggest an alternative use of a grid-free method, which requires no connectivity of arbitrarily placed vertices. To benchmark the methods and codes in two dimensions, we find analytical and semi-analytical solutions of the nonlinear diffusion–radiation equation, which may have sharp fronts, unconnected boundaries and bifurcated solutions. We use these solutions to study the efficiency of the proposed numerical algorithms.

A new three-dimensional (3D) magnetohydrodynamic (MHD) algorithm is described. The 3D MHD equations are solved in conservative form using a finite-volume scheme. The hydrodynamic variables in a cell are updated by calculating fluxes across the cell interfaces. The fluxes of mass, momentum and energy across cell interfaces are calculated by integrating a Boltzmann-like distribution function over velocity space. The novel feature of the method is that the distribution function incorporates most of the electromagnetic terms. In addition, the electric field along cell edges, which is used to update the magnetic field at cell faces, is also calculated using the Boltzmann-like distribution function. An important aspect of the method is that it provides a theoretical framework to incorporate additional terms in the 3D MHD equations (e.g. an anisotropic ion stress tensor and anisotropic temperature distributions).

The existence and time evolution of charge separation at a plasma edge is studied using a code in which both ions and electrons are described by gyrokinetic equations that include the finite-Larmor-radius correction and the polarization drift. The ion finite-Larmor-radius effect allows the existence of charge separation between ions and electrons, and the polarization drift, which has opposite signs for ions and electrons, has a tendency to accentuate the charge separation in a time-varying electric field. We compare our results with those previously obtained using a code in which the ions were described by using a fluid guiding-centre model, and only the electrons were treated kinetically. In particular, we present results showing excellent agreement between the two codes on the transition of the spectrum of the nonlinear solution from a turbulent spectrum to one dominated by the fundamental mode, where the energy is condensing in the lowest-k modes (inverse cascade).

Wave mixing equations describing the interaction of short-wavelength sound waves and entropy waves in two-fluid cosmic ray hydrodynamics in a non-uniform, large-scale, background flow in one Cartesian space dimension are investigated. The wave interaction coefficients depend on large-scale gradients in the background flow, and consist of two physically distinct components. The first component consists of wave-damping terms due to the diffusing cosmic rays, plus squeezing instability terms associated with the large-scale cosmic ray pressure gradient. These effects were first investigated by Drury and Dorfi in a study of the propagation of short-wavelength WKB sound waves in cosmic-ray-modified flows and shocks. The second component describes gas dynamical wave mixing effects due to gradients of the gas entropy S and the gas dynamical Riemann invariants (R±) of the background flow. A Green function solution is used to illustrate the coupling of the backward and forward sound waves for the case of a uniform background flow, in which the coupling coefficients depend on the parameter α = a2c/2κ, where ac is the cosmic-ray ‘sound speed’ and κ is the hydrodynamical cosmic-ray diffusion coefficient. Analytical WKB approximation methods and numerical simulations are used to investigate the modifications of the cosmic ray squeezing instability by wave mixing in cosmic-ray-modified shocks and pressure balance structures. Astrophysical applications to instabilities in supernova remnant shocks are discussed.

The generation of axial and lateral magnetic fields due to the interaction of intense laser fields with a plasma is investigated analytically. For a CO2 laser of 10.6 μm wavelength and 5×1014 W cm−2 power flux with a plasma of temperature 3 keV, the numerical results show that the magnitude of the lateral magnetic field dominates over the axial field, and the peak value of the lateral field is at less than the critical density, whereas the axial magnetic field peaks at the critical density level. This axial field combined with the lateral field may allow the construction of a new type of tokamak, and may also be important for studying energy transport in laser-fusion schemes.

Both compressive and rarefactive solitons are found to exist in a warm adiabatic dusty plasma with two-temperature isothermal ions. The Korteweg–de Vries (KdV) equation for isothermal ions and KdV-type equations at a critical density of low-temperature ions are derived in order to discuss the properties of dust acoustic solitons. Using a quasipotential analysis, critical Mach numbers M1c and M2c are obtained such that rarefactive dust acoustic solitons exist when 1<M<M1c and compressive dust acoustic solitons exist when 1<M<M2c.

We have developed a 2½-dimensional open boundary particle simulation model and have studied the current-driven electrostatic ion-cyclotron instability and related d.c. potential difference. Fresh streaming electrons are injected smoothly from the boundaries at each time step, avoiding unphysical accumulation of charged particles in front of the boundaries. As a current-driven electrostatic ion cyclotron instability grows, a d.c. potential difference along the magnetic field lines is created.

Electron-beam propagation from a gas-filled diode is investigated. The beginning portion of the electron beam pulse creates an ion channel not only inside the diode but also in the region beyond the anode. A theoretical model is developed for the space-charge-limited current of a relativistic electron beam propagating through an ion channel. A simple analytical expression for the space-charge-limited current is obtained within the context of a thin-beam approximation, where the conducting-tube radius is much larger than the beam radius. The beam current propagating through an ion channel is measured experimentally for a mildly relativistic electron beam. Whenever the ion density inside the diode is the same as the beam electron density, the diode is short-circuited. The ion-channel density at the short-circuiting time is calculated numerically and is used to estimate the space-charge-limited current. It is shown that the experimental data agree well with the analytical results predicted by the theoretical model.

The three-dimensional currentless equilibrium code, HINT is revised so that it can handle equilibria with a net toroidal current, for example the bootstrap current. The revised HINT code is applied to Large Helical Device-like equilibria with good nested flux surfaces.

The effect of linear waves on the Charney–Hasegawa–Mima model of drift and geostrophic turbulence is studied numerically for a slowly decaying field. It is shown that wave effects can reduce the efficiency of nonlinear mode coupling, effectively ‘freezing’ the spectrum to a narrow band in wavenumber space. Selective nonlinear interactions tend to favour velocities parallel to the direction of propagation of the waves. Accordingly, anisotropic spectra are observed, steeper in the direction of wave propagation, and shallower in the perpendicular direction.

The hydrodynamic start-up problem is one of the most crucial issues in laser-driven symmetrical implosion. The target-surface roughness and initial imprint by nonuniform laser irradiation result in Rayleigh–Taylor instability in the acceleration and deceleration phase. To estimate the tolerance of the target-surface roughness, the temporal behaviour of corrugated ablation surface and rippled shock-wave propagation are investigated using a perturbation analysis of the fluid equation, which is solved under the boundary model of a fire-polished ablation surface. The results show good agreement with two- dimensional hydrodynamic simulation and experimental results [T. Endo et al., Phys. Rev. Lett.74, 3608 (1995)].

Analytical expressions for the lowest-order distribution functions of a plasma that are valid throughout the plasma are generally not easily obtainable when conditions shift from collision dominance in some regions of the plasma to absence of collisions in other regions. Indeed, the reason for the breakdown of classical approximation methods for distribution functions and the corresponding macroscopic equations in plasma kinetic theory is often the lack of such global lowest-order distribution functions. The main purpose of the present paper is to derive an approximate global distribution function for an outflowing dilute light ion component in a polar-region model of the ionosphere where conditions for the light ions shift from collision dominance in low regions to collisionless conditions high up. For this, a simplified collision integral of a form given by Chandrasekhar will be used. The proposed global solution is given after simpler solutions, as a collisionless solution, an exact collision-dominated solution and a solution corresponding to classical transport theory are derived, for reason of comparison, in the first parts of the paper.

The configuration created in the plane by the separation of a magnetic hyperbolic null point into two critical points connected by a current sheet is considered. The main parameters are the orders of the zeros of these new null points, which determine the local topology of the magnetic field. It is shown that when the magnetic field is static, the fluid tends to flow orthogonally to the field in the vicinity of the sheet endpoints. Moreover, the Lorentz force pushes one of them towards the other, so the configuration tends to collapse again into a single null point except when the order of both is precisely ½.

The dynamical development of collisionless reconnection and the consequent energy-conversion process in the presence of an external driving flow are investigated by means of a full particle simulation. Magnetic reconnection develops in two steps in accordance with the formation of ion and electron current layers. In the early phase magnetic reconnection is controlled by an ion kinetic effect, while an electron kinetic effect becomes dominant in the late phase. There exist two mechanisms associated with the particle kinetic effects, that break the frozen-in condition of magnetic field and lead to magnetic reconnection in a collisionless plasma, namely a particle inertia effect and a particle thermal orbit effect. It is found that the dominant triggering mechanism in the late phase changes from an electron thermal orbit effect to an electron inertia effect as the longitudinal magnetic field increases. Electron acceleration and heating take place in the reconnection area under the influence of the reconnection electric field, while the energy conversion takes place from electrons to ions through the action of an electrostatic field excited downstream. As a result, the average ion temperature becomes about 1.5 times the average electron temperature.

The ideal magnetohydrodynamic spectrum of gravitating plane plasmas with equilibrium flow is investigated. Flow makes the spectral problem non-self-adjoint, so that the spectrum can become overstable. The criteria for cluster spectra to appear are derived analytically and both stable and unstable sides of the spectrum are examined numerically. Above certain critical values of the shear flow at the resonant surface, the gravitating interchange modes disappear. However, the local extrema of the continua can then take over the cluster spectrum.