A stationary theoretical model giving an asymptotic description of the propagation of nonlinear electromagnetic waves in an inhomogeneous plasma is presented. The plasma, considered within the hydrodynamic approximation and assumed to be cold, collisionless, unmagnetized and electroneutral, is described in terms of a nonlinear dielectric function giving the effect of the Miller ponderomotive force. In an infinitely extended slab geometry, a variable transverse density gradient, assumed to be parabolic, is considered in the case when a monochromatic electromagnetic wave is incident upon the slab at an arbitrary angle. The transverse structure of the wave electric field is determined along with the perturbed plasma density profile. The nonlinear wave equation with slowly varying coefficients derived using this model is solved in first and second approximations using an asymptotic multiple-space-scale method due to Bogolyoubov and Mitropolskii. The critical conditions for resonant electrostatic absorption and mode conversion are derived and discussed within these approximations, and some reference numerical calculations are performed.

The propagation of long, nonlinear, non-axisymmetric surface waves in a magnetic cylinder is considered. It is supposed that the electrical conductivity is infinite, the fluid is incompressible and there is no magnetic field outside the cylinder. The nonlinear integro-differential equation governing the wave propagation is derived using the reductive perturbation method. The interesting and important point is that this equation governs the evolution of all nonaxisymmetric modes simultaneously. This is because the phase velocities of all non-axisymmetric modes are equal to the kink speed in the linear, infinitely long-wavelength approximation, and as a result all non-axisymmetric modes interact strongly in the nonlinear case. Solutions of the governing equation in the form of periodic helical waves of permanent form are obtained numerically.

Equilibrium of non-neutral clouds in a toroidal vessel with toroidal magnetic field is demonstrated in the presence of a toroidal current, finite mass and finite pressure. With a toroidal current, it is shown that in a large-aspect-ratio conducting torus the equilibrium is governed by competition between forces produced by image charges and image currents. When (where Er and Bθ are the self electrostatic and self magnetic fields of the cloud), the confinement is electrostatic and plasma shifts inwards; when the confinement is magnetic and plasma shifts outwards. For there is no equilibrium. With finite mass or finite pressure, it is shown, in a large-aspectratio approximation, that the fluid drift surfaces and equipotential surfaces are displaced with respect to each other. In both cases the fluid drift surfaces are shifted inwards from the equipotential surfaces.

A self-consistent reductive perturbation analysis for parallel-propagating magnetohydrodynamic waves in warm multi-species plasmas, in which different constituents can have differing equilibrium drifts, leads to a derivative nonlinear Schrödinger equation for the wave magnetic field. Soliton solutions are discussed, including applications to plasmas with two ion species. Such solitons are larger (in amplitude) and wider than in the non-streaming and/or cold-plasma case, other parameters being equal.

We construct a continuity equation for electrons in microwave-afterglow plasmas. The self-similar solution of the equation is obtained for a plasma with plane, cylindrical or spherical geometry.

The coupling coefficients for resonant three-wave interaction of magnetosonic and Alfvén waves, derived by means of kinetic theory, are presented. The calculations allow for anisotropic background temperatures. The results are compared with previous ones from fluid theory.

The collisional relaxation of various plasma distributions that are initially far removed from thermal equilibrium is investigated numerically using a Fokker–Planck code. It is shown that self-similar and kappa distributions do not remain self-similar or kappa, and that this is due to the velocity dependence of the effective collision frequency. For the relaxation of an isotropic two temperature plasma it is shown that a constant-temperature three-component distribution function is a plausible model for analytical calculations. Investigation of the relaxation of bi-Maxwellian plasmas resolves some discrepancies that have arisen from earlier studies.

It is shown that the phase of the electromagnetic wave emitted through stimulated emission is intrinsically random. The insensitivity of the phase of the laser field to any disturbance in the laser cavity parameter derives from the fact that stimulated and spontaneous emissions take place concurrently at the same wave vector, the phases of spontaneous emission are mildly bunched, and the central limit theorem can be applied to the phase of the laser field. The two spectral lines observed in the Smith-Purcell free-electron laser experiment show that both classical and quantum-mechanical free-electron lasings, in which the wigglers behave as classical waves and wiggler quanta respectively, take place concurrently at different laser wavelengths in the case of the electric wiggler. It is shown that the coherence of the classical free-electron laser is achieved through modulation of the relativistic electron mass by the electric wiggler. The classical free-electron lasing is calculated using the quantum-augmented classical theory. In this, the probability of stimulated emission is first evaluated by interpreting the classically derived energy exchange between an electron and the laser field from a quantum-mechanical viewpoint. Then the laser gain is obtained from this probability by using a relationship between the two quantities derived by quantum kinetics. The wavelength of the fundamental line of classical free-electron lasing is twice the wavelength of the fundamental line of the free-electron two-quantum Stark emission, which is the quantum free-electron lasing in the electric wiggler. The gain of the classical free-electron lasing appears to scale as λ3w/γ3, where γ is the Lorentz factor of the electron beam and λw is the wavelength of the wiggler.

A nonlinear treatment is given for MHD waves that propagate parallel to the external magnetic field in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts. Both the wave electric and magnetic fields obey a derivative nonlinear Schrödinger equation. Soliton solutions are discussed, in particular for plasmas with two ion species.

It is shown using the photon concept that free-electron lasing (or net stimulated bremsstrahlung) is unrelated to the electron phase with respect to the laser wave, while the net acceleration (or net two-photon absorption) in an RF acceleration cavity depends on the electron phase with respect to the RF wave. The gain formula for the free-electron laser using a magnetic wiggler (MFEL) derived using the recently developed quantum-augmented classical theory in which the electron phase is ignored is in excellent agreement with that obtained quantum-mechanically. It is found by means of this theory that if an electric wiggler is added to a MFEL, the synchronization between the transverse velocity and the laser wave, which is required for coherence of the laser light, is not affected, while the laser gain is enhanced owing to the increase in the amplitude of the energy modulation by the electric wiggler. As a configuration of this turbo-MFEL, a two-beam elliptical wake-field cavity is proposed. An electron beam injected in the antiparallel direction along the lasing-beam path in this cavity lases through transverse wiggling by the transverse wake field and energy modulation by the longitudinal wake produced by relativistic drivingbeam bunches. This laser (WFEL) becomes of greater advantage compared with the MFEL as the laser wavelength is made shorter. It is also shown that the amplification of the WFEL is much greater than that of the present MFEL if we can produce a wake field whose longitudinal component has field strength greater than 1 MV m–1.

A new theoretical model to study surface wave–particle interaction in a cylindrical plasma has been developed. This model is based on linear resolution of the Vlasov equation, with the specular reflection hypothesis. Expressions for the breakdown time of the linear solution and for the rate of increase of kinetic energy per electron, as a function of the critical parameters, have been obtained.

Large-amplitude Alfvén waves, propagating along the magnetic field in an inhomogeneous plasma with non-uniform streaming, are shown to be governed by the DNLS equation modified by the inhomogeneity and the streaming. For weak but arbitrary inhomogeneity this modified DNLS leads to accelerated solitary Alfvén waves. The acceleration is modified further owing to streaming. For certain values of the plasma β, streaming can change the accelerating solitons into decelerating solitons, and vice versa.

Field variables in a slowly varying plasma are solutions of a system of differential and integral equations. To solve these equations, the fields are expanded in the eigenvectors of an algebraic plasma tensor, and the plasma equations can be transformed into a system of transport equations. The expansion becomes singular when eigenvalues coincide (for example in the case of mode conversion). It is shown how this problem can be resolved for an arbitrary system of Maxwell and/or fluid equations in arbitrary dimensions and for every kind of medium. The method is applied to horizontal stratified media as a simple example.

The collisionless Vlasov–Poisson system in the drift approximation is examined for the existence of maximum-entropy nonlinear coherent solutions in the steady state. Two major nonlinear effects are taken into account. The first is the velocity-space trapping of particles, leading to closed trajectories in phase space. The second is the physical-space trapping of particles, leading to closed trajectories in the plane perpendicular to the magnetic field. The regions of validity of these nonlinearities are discussed and their relative importance demonstrated. Numerical solutions of the equations describing the nonlinear stationary states in one and two dimensions are presented.

The propagation of a Langmuir wave with a small group of trapped particles in a weakly non-uniform plasma along a density gradient is considered. The dynamics of trapped electrons accelerated by the wave is investigated in the adiabatic approximation, including the relativistic case. The set of equations describing the self-consistent spatial evolution of the wave—trapped-particles system is obtained and analysed. It is shown that the possibility exists of wave transmission through a classically forbidden barrier as a consequence of the reversibility of the wave—particle interaction. The conditions of validity of the theory developed are also discussed.

The hydrodynamic echo on the surface helicon-type modes radiated to vacuum in a magnetized plasma with steepened density profile is investigated. It is shown that perturbations induced by an initial pulse at the plasma boundary are modulated by a later applied second pulse of different wavelength, to yield a non-vanishing echo signal, which can be radiated to vacuum. The angle of the radiation and the density of the energy flow of this signal are determined.

We have investigated a mode-coupling mechanism between kinetic Alfvén waves and a collisional drift wave in an inhomogeneous cylindrical plasma. Drift waves satisfying the condition k⊥D > 1/r0 (where r0 is the radius of the plasma cylinder) are stabilized by the low-frequency ponderomotive force generated by the kinetic Alfvén waves. For typical plasma parameters and a moderate level of Alfven-wave intensity the stabilization factor is comparable to the destabilization mechanism due to collisions.

Weakly relativistic electron-acoustic solitons are investigated in a two-electron-component plasma whose cool electrons form a relativistic beam. A general Korteweg-de Vries (KdV) equation is derived, in the small-|ø| domain, for a plasma consisting of an arbitrary number of relativistically streaming fluid components and a hot Boltzmann component. This equation is then applied to the specific case of electron-acoustic waves. In addition, the fully nonlinear system of fluid and Poisson equations is integrated to yield electron-acoustic solitons of arbitrary amplitude. It is shown that relativistic beam effects on electron-acoustic solitons significantly increase the soliton amplitude beyond its non-relativistic value. For intermediate- to large-amplitude solitons, a finite cool-electron temperature is found to destroy the balance between nonlinearity and dispersion, yielding soliton break-up. Also, only rarefactive electronacoustic soliton solutions of our equations are found, even though the relativistic beam provides a positive contribution to the nonlinear coefficient of the KdV equation, describing relativistic, nonlinear electron-acoustic waves.

The poloidal electric field generated by electron-cyclotron resonance heating is investigated for a tokamak plasma in the collisionless regime. This poloidal electric field is calculated by solving an adjoint equation to the linearized Fokker-Planck equation with a quasi-linear diffusion term. It is found from this calculation that the magnitude and the sign of the poloidal electric field depend strongly on the values of the inverse aspect ratio, the poloidal angle of the absorption point, the parallel velocity of resonant electrons normalized by the thermal velocity, and the strength of the relativistic correction to the resonance condition.

The Zakharov-Kuznetsov equation is used to describe ion-acoustic wave propagation in a magnetic environment. An initial-value problem is solved for this equation on the basis of a numerical method that uses the fast-Fourier-transform technique for calculating space derivatives and a fourth-order Runge-Kutta method for the time scheme. Numerical simulations show that the disturbed flat (planar) solitary waves can break up into more robust cylindrical ones. Interactions between these two types of wave, and recurrence phenomena, are also studied.