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.

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).

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.

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 three-dimensional particle-in-cell (PIC) code VLPL (Virtual Laser Plasma Lab) allows, for the first time, direct fully electromagnetic simulations of relativistic laser–plasma interactions. Physical results on relativistic self-focusing in under-dense plasma are presented. It is shown that background plasma electrons are accelerated to multi-MeV energies and 104 T magnetic fields are generated in the process of self-focusing at high laser intensities. This physics is crucial for the fast ignitor concept in inertial confinement fusion. Advances in the numerical PIC algorithm used in the code VLPL are reviewed here.

We describe the parallel implementation of semi-Lagrangian Vlasov solvers, which are an alternative to particle-in-cell (PIC) simulations for the numerical investigation of the behaviour of charged particles in their self-consistent electromagnetic fields. The semi-Lagrangian method, which couples the Lagrangian and Eulerian points of view, is particularly interesting on parallel computers, since the solution is computed on grid points, the number of which remains constant in time on each processor, unlike the number of particles in PIC simulations, and thus greatly simplifies the parallelization process.

Laser-beam or soliton propagation is best modelled for fast computation using a split-step Fourier method based on an orthogonal transform technique known as the beam-propagation method. The beam-propagation split-step Fourier-transform technique in one and two dimensions for the propagation of a soliton or laser beam respectively in a nonlinear plasma and a split-step Hankel-transform-based algorithm for cylindrical-beam propagation close to circular cross-sectional symmetry and its computational implementation are discussed. Attention is particularly focused on the verification of the paraxial approximations of the soliton or the laser beam using these techniques, after a brief review of the beam-propagation method.

Calculations are presented on the phenomenon of plasma–sheath resonance in an inhomogeneous plasma. In certain cases, this resonance coincides with a local resonance occurring in the plasma, the local plasma frequency being equal to the resonant frequency of the entire system. The theory does not describe the mechanism of absorption, but does predict the magnitude of the power involved. Some limitations of the theory are discussed.

Externally amplitude-modulated ion acoustic waves with high frequencies of 200–320 kHz are experimentally shown to form plasma cavities and to be trapped in them at an early stage. Thereafter, the trapped waves are observed to suffer nonlinear modulation and create new lower-frequency waves with average frequencies as low as 20–40 kHz within the cavities. As a result, the externally excited high-frequency ion acoustic waves are found to be nonlinearly converted into lower-frequency ion waves in the cavities. Finally, the pressure gradients of the waves effective in cavity formation and nonlinear modulation of the trapped waves are discussed.

An investigation of the decay laws of energy and of higher moments of the Elsässer fields z±=v±b in the self-similar regime of magnetohydrodynamic (MHD) turbulence is presented, using phenomenological models as well as two-dimensional numerical simulations with periodic boundary conditions and up to 20482 grid points. The results are compared with the generalization of the parameter-free model derived by Galtier et al. [Phys. Rev. Lett.79, 2807 (1997)], which takes into account the slowing down of the dynamics due to the propagation of Alfvén waves. The new model developed here allows for a study in terms of one parameter governing the wavenumber dependence of the energy spectrum at scales of the order of (and larger than) the integral scale of the flow. The one-dimensional compressible case is also dealt with in two of its simplest configurations. Computations are performed for a standard Laplacian diffusion as well as with a hyperdiffusive algorithm. The results are sensitive to the amount of correlation between the velocity and the magnetic field, but rather insensitive to all other parameters such as the initial ratio of kinetic to magnetic energy or the presence or absence of a uniform component of the magnetic field. In all cases, the decay is significantly slower than for neutral fluids in a way that favours for MHD flows the phenomenology of Iroshnikov [Soviet Astron.7, 566 (1963)] and Kraichnan [Phys. Fluids8, 1385 (1965)] as opposed to that of Kolmogorov [Dokl. Akad. Nauk. SSSR31, 538 (1941)]. The temporal evolution of q-moments of the generalized vorticities 〈[mid ]ω±[mid ]q〉 =〈[mid ]ω±j[mid ]q〉 up to order q=10 is also given, and is compared with the prediction of the model. Less agreement obtains as q grows – a fact probably due to intermittency and the development of coherent structures in the form of eddies, and of vorticity and current sheets.