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.

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 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.

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 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.

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.

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.

A Gaussian laser beam propagating through a plasma heats the electrons and creates a low-density duct via ambipolar diffusion. Thermal conduction plays an important role in temperature equilibrium when the electron mean free path λm is greater than the beam radius (λm ≥ ro). For λm ≫ ro thermal conduction suppresses any non-uniformities in electron temperature, and nonlinearity is dominated by the ponderomotive force. The plasma duct traps and focuses the laser radiation above a threshold power. As the beam size shrinks, thermal conduction becomes stronger, leading to periodic self-focusing of the beam. The laser beam is also susceptible to filamentation instability. The spatial growth rate is a monotonically increasing and saturating function of the incident intensity of the beam.

An action principle for the Vlasov–Maxwell system in Eulerian field variables is presented. Thus the (extended) particle distribution function appears as one of the fields to be freely varied in the action. The Hamiltonian structures of the Vlasov–Maxwell equations and of the reduced systems associated with small-ampliltude perturbation calculations are easily obtained. Previous results for the linearized Vlasov–Maxwell system are generalized. We find the Hermitian structure also when the background is time-dependent, and furthermore we may now also include the case of non-Hamiltonian perturbations within the Hamiltonian-Hermitian context. The action principle for the Vlasov–Maxwell system appears to be suitable for the derivation of reduced dynamical equations by expanding the action in various small parameters.

Long nonlinear sausage-wave propagation in a magnetic slab in an incompressible plasma is considered. The governing equation is derived with the aid of the reductive perturbation method. The solutions of this equation in the form of periodic waves of permanent shape are found numerically.

The recent interest in the electron-acoustic wave as a source of broad-band electrostatic noise in the terrestrial magnetosphere makes it interesting to ask whether it can support stationary electrostatic double layers. We investigate this problem in a fluid plasma composed of cool ions, cool electrons and a hot Boltzmann electron component – which is known to support electron-acoustic waves. Although a formal application of the reductive perturbation technique to our dynamical equations leads to an mKdV equation for electron-acoustic waves, it is found that within the present physical model the consistency conditions and required ordering of the coefficients cannot be satisfied simultaneously for reasonable parameter values. As a consequence, it is shown that the neglect of the φ(2) term in deriving the mKdV equation is unjustified under general circumstances, and furthermore that the cubic nonlinearity introduced by the mKdV equation is negligible when compared with this term. Finally, we are led to conclude that stationary, weak electron-acoustic double layers cannot exist in such a plasma.

The clarification of models of laser ablation by plasma heating is examined using a general dimensional argument and introducing a set of universal parameters. The regime of laser-plasma interaction in which collisional absorption and thermal conduction dominate is examined for spherical systems. Detailed scaling relations are derived for uninhibited and flux-limited thermal conduction. The complete set of regimes for steady spherical flow are examined, and it is found that the most important flows are thin collisional and thick local absorption.

Nonlinear wave propagation on the surface between two superposed magnetic fluids stressed by a tangential periodic magnetic field is investigated using the method of multiple scales. A stability analysis reveals the existence of both nonresonant and resonant cases. From the solvability conditions, three types of nonlinear Schrodinger equation are obtained. The necessary and sufficient conditions for stability are obtained in each case. Formulae for the surface elevation are also obtained in both the non-resonant and the resonant cases. It is found from the numerical calculation that the tangential periodic magnetic field plays a dual role in the stability criterion, while the field frequency has a destabilizing influence.

Reflection coefficients and excitation efficiency of a gridded plate (a bipolar potential structure where the grid is separate but parallel to the juxtaposed plate) and a metallic disk for ion-acoustic waves have been measured experimentally. When the grid is biased negatively with respect to the plasma potential, reflection in phase with the incident wave and excitation of an outgoing wave are observed only when the bias of the plate is positive. When the bias of the gridded plate is positive, reflection occurs when the grid bias is either negative or positive. For the metal disk, reflection and excitation are observed when the bias is positive. The small reflection detected when the bias is negative is found to be due to scattering of the incident wave at the edge of the disk.