The resonant interaction between three waves in a uniform magnetized plasma is considered. Using the somewhat inaccessible result of the general theory, we deduce the explicit expressions for the coupling coefficients of a cold magnetized two-component plasma.

The nonlinear interaction between a large-amplitude whistler pump and the modified ion-cyclotron perturbations is studied. A nonlinear dispersion relation for the modulation/filamentation interaction is derived and solved numerically to investigate the instability properties. We discuss the relevance of the present study with regard to recent laboratory experiments where the modulation/filamentation of a whistler pump by the modified ion-cyclotron waves has been observed.

The relativistic modified formula for the energy loss of the relativistic electron beam due to binary electron–electron collisions is obtained. Another important energy loss mechanism, the excitation of Langmuir collective plasma oscillation, is also treated within the relativistic framework. Then the relevant physics parameters in the fast-ignitor scenario, including the continuous winded range, the maximum penetration depth and the stopping time, have been calculated. The results obtained are much better than those from non-relativistic cases and even partially relativistic modified theories. Thus, we re-examine theoretically the possibility of igniting hot spots in a super-compressed deuterium–tritium plasma.

It is shown that the ponderomotive force of magnetic-field aligned circularly polarized electromagnetic waves can create space charge electric fields in a magnetized electron–positron–ion plasma. The space charge electric fields can, in turn, accelerate ions. Possible applications to the origin of energetic ions in laboratory plasmas and astrophysical settings are discussed.

The unstable plasma sheath resonance in a pulsed low-pressure hollow-cathode discharge was found to occur when the Bohm criterion fails. This happens during the transition of the discharge to a steady state. The duration of this transition is determined by the time required for the ion sound to cross the plasma volume. During this time a strong radio-frequency (RF) component may appear in the discharge current due to the instability of the plasma sheath near the cathode. The frequency of the RF oscillations is associated with the ion plasma frequency. The conditions required for the instability of the plasma sheath were investigated. We suggest a theoretical model which extends our earlier theory and explains the existing experimental results. The model also predicts a certain shift in the resonance frequency during the pulse, which was indeed discovered experimentally.

In the present analysis we study the self-consistent propagation of nonlinear electromagnetic pulses in a one-dimensional relativistic electron–ion plasma, from the perspective of nonlinear dynamics. We show how a series of Hamiltonian bifurcations give rise to the electric fields which are of relevance in the subject of particle acceleration. Connections between these bifurcated solutions and the results of earlier analysis are made.

The free energy associated with the relative streaming of plasma and dust particles can feed streaming instabilities. Here we consider the case of an unmagnetized plasma and use the results of kinetic theory which consistently take into account the plasma particles–dust collisions and dust charge fluctuations. These are valid in the parameter regime where the plasma particles–dust collisions dominate with respect to the binary plasma collisions.

This paper presents an analysis of relativistic self-focusing of intense laser radiation in an axially inhomogeneous plasma. The nonlinearity in the dielectric constant arises on account of the relativistic variation of mass for an arbitrary magnitude of intensity. An appropriate expression for the nonlinear dielectric constant has been used in the analysis of laser-beam propagation in the paraxial approximation for a circularly polarized wave. The variations of the beam width parameter with the propagation distance, the self-trapping condition and the critical power have been evaluated. The saturating nature of the nonlinearity yields two values of the critical power for beam self-focusing, $P_{\rm cr1}$ and $P_{\rm cr2}$. It is seen that the laser beam width tends to attain a constant value depending upon the plasma inhomogenity and the initial laser intensity. Numerical estimates are made for typical values of the laser–plasma interaction applicable for underdense and overdense plasmas. The most important experiments described by this model are related to the fast ignitor concept.

The non-ideal collective and plasma screening effects on elastic electron–atom collisions are investigated in partially ionized hydrogen plasmas using the first-order eikonal method. The effective pseudopotential model, taking into account the screening and collective effects, is applied to describe the interaction potential in non-ideal plasmas. Semiclassical trajectory analysis is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase and cross section as functions of the impact parameter, the non-ideality plasma parameter, the Debye length, and the collision energy. The results show that the collective and screening effects enhance the differential eikonal cross section for small impact parameters, but suppress the cross section for large impact parameters. It is also found that the non-ideal collective effects enhance the total eikonal cross section.

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and toroidal flow is investigated within the framework of magnetohydrodynamics (MHD). The stationary states are determined by an elliptic differential equation for the poloidal magnetic flux function $\psi$, a Bernoulli equation for the pressure and two relations for the resistivity components $\eta_\parallel$ and $\eta_\perp$ parallel and perpendicular to the magnetic field, respectively. The flow can affect the equilibrium properties solely in the presence of toroidicity because in the limit of infinite aspect ratio, the axial velocity does not appear in the equilibrium equations. The equilibrium characteristics of a tokamak with rectangular cross-section are studied by means of eigenfunctions in connection with exact solutions for the cases of ‘compressible’ flows with constant temperature, $T(\psi)$, but varying density on magnetic surfaces and incompressible ones with constant density, $\varrho(\psi)$, but varying temperature thereon. Those eigenfunctions can describe either single or multiple toroidal configurations. In the former case the equilibrium has the following characteristics: (i) the $\eta_\parallel$- and $\eta_\perp$-profiles on the poloidal cross-section having a minimum close to the magnetic axis, taking large values on the boundary and satisfying the relation $\eta_\perp > \eta_\parallel$ are roughly collisional; (ii) the electric field perpendicular to the magnetic surfaces possesses two local extrema within the plasma and vanishes on the boundary; and (iii) the toroidal current density is peaked close to the magnetic axis and vanishes on the boundary. The impact of the flow and the aspect ratio on the aforementioned quantities is evaluated for both ‘compressible’ and incompressible flows.

We report here on the expansion dynamics of a non-equilibrium plasma produced by an excimer laser interaction with a Cu solid target. Its characteristics were investigated in the fast and slow time regime by two Faraday cups of different diameter. The larger cup had an 8 cm diameter collector and was fixed along a drift tube at a distance of 20 cm from the plasma source; the smaller cup had a 3.3 cm diameter collector and was fixed transversally to the target at a distance of about 6 cm. During the experiments the target support signal was also recorded. The laser beam was focused onto the target and the spot dimensions were analysed by scanning it on the lens focal plane. An average power density on the target of 0.3 GW cm$^{-2}$ was achieved with a 15 cm focal length lens. Using signals from the Faraday cups we obtained information on the overall plasma evolution in the slow and fast time regimes. Fitting the plasma current waveform by a ‘shifted’ Maxwell–Boltzmann distribution, a Knudsen-layer temperature of $5.3 \times 10^{5}$ K ($\sim$50 eV) and a drift velocity of 5300 m s$^{-1}$ resulted. The system efficiency in ablation yield and ion production was 0.235 $\mu$g pulse$^{-1}$ and $5 \times 10^{13}$ ion pulse$^{-1}$, respectively.

The surface dust-acoustic wave is investigated in a semi-bounded dusty plasma containing elongated and rotating dust grains. The dispersion relation of the low-frequency surface ion plasma wave is obtained by the plasma dielectric function with the specular reflection boundary condition. The results show that the phase and group velocities of the surface dust-acoustic wave propagating along the plasma–vacuum interface decrease with an increase of the rotation frequency. However, for long wavelengths it is found that the phase and group velocities of the surface wave are independent of the magnitude of the rotation frequency.

The influence of self-generated magnetic and electric fields on the transport of relativistic electrons in dense plasmas was studied using a particle-in-cell simulation. For conditions relevant to the fast ignitor, the laser-driven relativistic electrons may have significant energy spread along or perpendicular to the propagation direction of the beams. The effect of electron energy spread on the growth rate, the occurrence threshold of both the Weibel-like filamentation instability and the electrostatic two-stream instability and the competition between them were investigated. The Weibel instability results in the formation of a magnetic channel, which may collimate inward fast electrons without significant deviation, and the excitation of a longitudinal electric field due to two-stream instability is destructive to the stability of the magnetic channel. The generation of relativistic electrons by the interaction of a high-intensity laser beam at the vacuum–dense plasma boundary and propagation of the electrons in the dense plasma were studied using a three-dimensional particle-in-cell code. It is shown that the electron velocity spread owing to transverse collective heating saturates the magnetic field and the longitudinal electrostatic field may play a dominant role in limiting the stable propagation of fast electrons into over-dense plasmas.

In most practical situations, for multi-component non-ideal complex plasma mixtures in pressure–temperature ($P$–$T$) phase space, the problem of solving the system of coupled nonlinear Saha equations subjected to the constraints of electro-neutrality and conservation of nuclei is found to be effectively a one-dimensional nonlinear problem, i.e. solving a single transcendental equation. Computation of ionization stages and partition functions in the $P$–$T$ phase space is particularly important for non-ideal plasmas generated in devices in which pressure is a reliably measurable parameter while it is difficult to measure the number density of heavy particles. The methodology and algorithm presented herein are based on deriving an equivalent single transcendental equation, for which the solution is eminently trivial. The algorithm takes into account different practical models for non-ideality corrections (lowering of ionization potentials, truncation of partition functions and a corrected equation of state). The ease and efficiency of the introduced algorithm allows, with significant simplicity, the computations of population densities of all plasma species (ionized and excited) up to maximum ionization states equal to the atomic numbers of the involved elements with minimal computational work. It also considers an extensive database of energy levels of the excited states. The algorithm presented herein is analytically known to be safe, fast and efficient. It shows no numerical instabilities, no convergence problems and no accuracy limitations or lack of change problems, which have been reported in the literature. A couple of non-trivial problems are worked out and presented herein showing the effectiveness of the present methodology. For completeness, a criterion for the validity of the assumption of local thermodynamic equilibrium (LTE) is applied to the results from the sample problems, showing the regions of the pressure–temperature phase space over which the assumption is valid.

Two methods for identifying the flux of high-energy photons as emitted by ball lightning are proposed. It is assumed that ball lightning has a core consisting of oscillating clouds of electrons and totally ionized ions. A search for tooth enamel changes due to the influence of high-energy photons from ball lightning to reveal the influence of such photons on human beings is also proposed. This diagnostic measure should be taken if after observation of ball lightning symptoms similar to those of radiation sickness arise or ball lightning causes heavy burns.