It is shown that stimulated emission is an intrinsically incoherent-phase phenomenon arising from the uncertainty principle, and that therefore the laser gain cannot be described by any classical model, which must be coherent in all aspects. The force due to the net inverse-bremsstrahlung (‘NIB force’) acting on a high-energy electron beam travelling in an undulating field whose wave vector is collinear with the electron beam (‘collinear wiggler’) is found by extending the quantum kinetic theory of the free-electron laser. In the case that an axial electrostatic wave is used as the catalysing field for the net multi- photon inverse bremsstrahlung, it is shown that NIB acceleration is practical only when the potential amplitude (in terms of the electron energy) of the laser wave, [eA0], is comparable to or larger than the electron rest energy mc2.

An equilibrium state of a magnetized non-neutral plasma confined in a smooth cylindrically symmetric container is obtained. The particle number of each species is fixed, and total energy and total canonical angular momentum are conserved in the system. Moreover, the most probable state satisfies the stationary Vlasov equation exactly. The key finding from this result is that the E × B drift velocity can be significantly different from the true fluid velocity, which always corresponds here to a rigid rotation. It is suggested that this difference may also be experimentally important in situations that are not in thermal equilibrium.

Emissions from relativistic electrons travelling in periodic electrostatic fields were observed by Smith and Purcell (1953) and Doucas et at. (1992) as extraordinarily (e.g. 1018 times) stronger than any emission that can be conceived with classical electrodynamics under any equivalent condition. The mechanism is identified as the free-electron two-quantum Stark (FETQS) emission generated by the axial uniform motion, which cannot be radiated in the axial direction. From the excellent agreement between the theoretical result for FETQS emission driven by the axial uniform motion, and the experimental observations and many emission phenomena in plasmas, it is concluded that a high-energy electron follows a quantum-mechanically derived formula (without taking the classical limit ←0), although this diverges in the classical limit. From the extraordinarily large FETQS emission due to macroscopic motion, we speculate that even the FETQS emission generated by electron spin can be macroscopically observable. The spin-generated FETQS emission in an arbitrary direction is calculated using relativistic quantum mechanics. It is found that the total power of this emission scales as γ2 times the emission power in the equivalent magnetic wiggler, where γ is the Lorentz factor of the electron, and the emission is practically confined in a cone of angle 1/γ about the axial direction.

The MHD stability of a gas jet surrounded by a streaming radially finite liquid cylinder (with solid cylindrical edge) is studied. The system is acted upon by capillary, electromagnetic and inertial liquid forces. The eigenvalue relation is established to all kinds of perturbations. The streaming has a strong destabilizing influence that is independent of all problem parameters. The capillary force is destabilizing only for small axisymmetric modes and stable for the rest. The electromagnetic force is strongly stabilizing whatever the intensities of the magnetic field. If the influence of the latter is sufficiently strong, the influence of the streaming can be completely suppressed. It is found that for an axisymmetric perturbation the domain of instability is the same whatever the value of the liquid radial distance.

Electromagnetic surface waves dissipate energy as they propagate in plasma columns. The transfer of energy to the discharge generally occurs through collisional processes — hence the name ‘collisional’ surface waves. It affects the direction of propagation of the wave, and is responsible in particular for the turning back of the axial wavenumber on the phase diagram. The rate of collisions also influences the respective contribution of surface waves and radiation (unguided) waves to the total electromagnetic field. These considerations are of interest in improving the reliability and accuracy of the electron density diagnostic based on surface waves. This paper takes advantage of the many articles published in the domain of guided waves for antennas.

The modulational interaction of two waves propagating in a cubically nonlinear medium is considered. It is shown that the correct theory operates with ‘renormalized’ equations for the linear dielectric function and for an effective third-order medium response. This renormalization is due to so-called interference terms. The appearance of interference terms is a specific feature of the two-mode modulational instability in comparison with the well-known instability of a single mode.

A systematic analysis of low-frequency waves such as hydromagnetic and acoustic waves in a magnetized dusty plasma containing electrons, ions and dust particles is presented. Starting with the three-fluid equations and the Maxwell equations, we derive, retaining finite ion mass, an effective two-fluid model incorporating deviations from the frozen-in-fluid approximation for the ion and electron fluid motions. We show that normal modes exist in two widely separated frequency regimes. In addition to obtaining hydromagnetic waves that are generalizations of the usual Alfven and magneto-acoustic modes in a two-component electron–ion plasma, we demonstrate the existence of a new class of magneto-acoustic waves (both fast and slow type) called ‘dustmagneto-acoustic waves’. These modes have qualitatively different dependences on the equilibrium parameters such as density, magnetic field and temperature when compared with the usual magneto-acoustic waves. The new modes arise owing to finite ion mass (compared with the dust-particle mass), leading to an effective inertial resistivity that inhibits the ion (as well as the electron) fluid from being frozen to the magnetic field lines. The fast branch of the dust-magneto-acoustic waves is shown to be the electromagnetic generalization of the electrostatic dust-acoustic wave recently obtained in unmagnetized dusty plasmas. In the two-component limit the new modes degenerate into the usual type of magneto-acoustic waves. Dispersion relations for various other modes are also presented.

Quasi-periodic variations in the electric field intensity near the dayside magnetopause are studied within a planar, dissipative MHD model of a stagnation-line flow embedded in a rectilinear magnetic field. The model is based on an exact time-dependent solution of the resistive MHD equations applied to a Parker-type diffusion region of field-line merging. The results lead to the prediction of certain relations between physical parameters of the solar- wind plasma, and these are compared with actual measurements.

The modulational instability of two pump Langmuir waves is investigated for the case of comparatively small instability rates, when ‘renormalized’ expressions for linear and nonlinear plasma polarization responses should be used. The rates found are compared with the modulational instability rates for a single monochromatic Langinuir mode.

The influence of electron inertia, ion streaming and weak relativistic effects on the modulational instability of ion-acoustic waves in a collisionless unmagnetized plasma is investigated. The derivative expansion method is used to derive a nonlinear Schrödinger equation, from which an instability criterion is deduced. When electron inertia is ignored, ion streaming and weak relativistic effects have little effect on the instability criterion. It is shown that when electron inertia is taken into account, the instability criterion is sensitive to weakly relativistic ion streaming, but not to the ratio of electron mass to ion mass.

A class of parametric instabilities of finite-amplitude, circularly polarized Alfvén waves in a plasma with pressure anisotropy is studied by application of the CGL equations. A linear perturbation analysis is used to find the dispersion relation governing the instabilities, which is a fifth-order polynomial and is solved numerically. A large-amplitude, circularly polarized wave is unstable with respect to decay into three waves: one sound-like wave and two side-band Alfvén-like waves. It is found that, in addition to the decay instability, two new instabilities that are absent in the framework of the MHD equations can occur, depending on the plasma parameters.

The stability of an inhomogeneous finite-β plasma confined by a sheared magnetic field is analysed in the two-fluid slab approximation. The stationary plasma involves an electron plasma current that is self-consistently generated by magnetic shear through Ampère's law. Magnetic shear is found to be stabilizing (destabilizing) if the electron drift consistent with it is antiparallel (parallel) to the propagation direction of drift waves. Mode stability arises from competition between the Doppler shifts resulting from both the electron diamagnetic drift and the electron drift related to magnetic shear, and the wave frequency. The finite-β effects reduce the growth rate but do not stabilize the mode. In contrast with the hydromagnetic tearing instabilities, the growth rate is proportional to the electron-ion collision frequency, which is regarded as the lowest-order term in powers of the electron-ion collision frequency by Taylor's theorem.

Nonlinear interactions of tearing modes result in chaotic magnetic fluctuations. A system of ordinary differential equations is derived to model the nonlinear interactions of magnetic islands with different helicities. For a reasonable set of parameters, the solution shows chaotic behaviour.

We use a Hamiltonian formalism to analyse the self-consistent wave–particle dynamical interaction involving magnetized electrons and ordinarily polarized electromagnetic waves. Considering first-harmonic cyclotron resonances, we show that there is a critical value of the electronic average density. For systems with lower than critical densities the saturation process is dictated by relativistic detuning effects, and wave dynamics may be disregarded. However, for systems with larger densities, saturation is governed by the available electromagnetic free energy, and the wave dynamics turns out to be essential.

Starting from the hydrodynamic equations for a cold electron fluid, we develop a theory of the ponderomotive effect of the interaction of high-frequency electromagnetic radiation with a magneto-active plasma. Using the method of averaging on high-frequency oscillations, we obtain expressions for the low- frequency nonlinear currents. We also obtain an equation describing the space–time evolution of a quasi-stationary magnetic field in the plasma.

Electromagnetic wave propagation along the interface between a magnetoactive plasma and a metallic screen is investigated analytically and numerically. It is shown that the waves have a Rayleigh character: they are superpositions of two partial waves. It is concluded that electromagnetic waves propagate only at frequencies lower than min (ωp, ωc), where ωp is the plasma frequency and ωc is the cyclotron frequency. The field topology is found, and the physical character of the waves is discussed.

Approximate analytical solutions of the waves and fields inside and outside the coupling region for an arbitrary number of propagating modes of all kinds and an arbitrary number of couplings and mode conversions are presented. The method is applied to the propagation of electromagnetic fields in a plane- stratified cold plasma as an illustrative example.

We consider the plasma heating nonlinearities that are important in many wave-interaction processes. By means of some simple examples, we analyse the nonlinear terms originating from the collision integral for a weakly collisional plasma. As a result, it turns out to be necessary to generalize the collisional Zakharov equations by including the contribution from the non-diagonal part of the pressure tensor. A new system of equations is thus presented.

In this work we analyse the stochastic dynamics of initially low-energy weakly relativistic particles moving under the action of electrostatic waves. The relevant phase space is not well described by standard nonlinear pendulum approximations, but appropriate resonance studies based on the overlap of primary and secondary islands show that three regions may be identified as the wave vector k of the electrostatic mode is varied: one for small values of k, where the dynamics is always relativistic and regular; one for moderately large values of k, where the dynamics is always relativistic, being regular for small field amplitudes and stochastic for large field amplitudes; and finally one for fairly large values of k, where the dynamics is relativistic and regular for small amplitudes of the wave field and non-relativistic and stochastic for larger values of the amplitude. We perform an extensive numerical analysis in order to check our analytical estimates, and finally we present a brief numerical study of particle diffusion in the relativistic stochastic regime.