An axial emission process by a relativistic electron beam travelling in a laser beam and an electrostatic wave propagating in the direction antiparallel to the electron-beam direction (‘electric wiggler’), which is different from free-electron two-quantum Stark (FETQS) emission, is identified, and the laser gain through this process is investigated using relativistic quantum kinetics. The transverse a.c. source current for this axial emission is produced by the laser field acting as a classical electromagnetic wave to wiggle the electron in the transverse direction. From the viewpoint of quantum kinematics, this radiation-wiggled one-quantum induced Stark (RWOQIS) emission is exactly the same as FETQS emission in which the equivalent transverse source current needed for the axial emission is due to the intrinsic electron spin angular momentum. However, these two emissions differ in dynamics, since the former is an one-quantum process while the latter is a two-quantum process. It is found that the laser gain by RWOQIS emission increases with the laser intensity when ¦eA0/mc2¦ ≪ 1 and decreases with the inverse of the square of the laser intensity when ¦eA0/mc2¦ ≫ 1, where A0 is the potential amplitude of the laser wave and mc2 is the electron rest energy. This newly found emission is an inherently stimulated one, and does not have a corresponding spontaneous emission.

This paper contains a systematic exposition of a statistical method leading to a characterization of relevant equilibrium and stability properties of col-lisionless Vlasov (collective) plasma configurations according to a formalism similar to that of the classical thermodynamics of Maxwellian systems. We reconsider a statistical model, proposed in earlier works, in which the basic objects of the statistics are volume elements in a configuration space of the charge or current density. The probability distribution in this space is calculated subject to a constraint expressing the existence of static equilibria involving only the smeared-out or collective part of the above densities, while the collective energy is uncorrelated with the fluctuations arising from the single-particle structure. It is one of the aims of this paper to show that the thermodynamic quantities arising automatically in the formalism, for instance the entropy, can be consistently inserted in the physical and conceptual context of classical thermodynamics. This is achieved by studying in detail a reversible energy interaction between the collective system and the external world, in order to identify the entropy variations calculated with the model with those of the entropy as conventionally defined. Our thermodynamic concepts are illustrated by applications to electrostatic Vlasov equilibria (in unstable situations and in the Maxwellian limit) and to magnetic systems, both in a case open to energy interaction with the external world (the tokamak) and in the case of an isolated system (a plasma enclosed in a perfectly conducting shell).

The method of multiple scales is used to derive a nonlinear Schrödinger equation describing the nonlinear evolution of an ion wave packet propagating along a cylindrical plasma-filled waveguide. Numerical evaluation of nonlinear and dispersive terms shows that the wave is modulationally unstable if the wavenumber exceeds a certain critical value. On comparing with the case of an unbounded plasma, it is shown that finite geometry causes a significant shift of this critical value towards smaller wavenumbers, where Landau damping is relatively small.

Using the exact solution methods developed and illustrated previously, we systematically explore (ω, k) space in order to determine all the unstable modes of velocity-shear-produced electromagnetic waves in magnetized, relativistic electron beams (here ω and k are the complex frequency and real wavenumber). This is done for various physical parameters of the problem, namely shear factor and ratio of pipe to beam radii. The solution of the dispersion relation is supplemented by a marginal stability analysis based on the behaviour of the turning points of the purely real-frequency solution ωr, (k): these are bifurcation points where complex solutions originate or terminate.

This paper presents an analysis of the self-focusing of a rippled Gaussian laser beam in a plasma when the nonlinear part of the effective dielectric constant is arbitrarily large. Considering the nonlinearity to arise from ponderomotive, collisional or thermal-conduction phenomena and following the approach of Akhmanov, Sukhorukov and Khokhlov (which is based on the WKB and paraxial-ray approximation) the phenomenon of self-focusing of rippled laser beams is studied for arbitrary magnitude of nonlinearity. For ponderomotive and collisional nonlinearities, the present theory leads to two values of the critical power for self-focusing of the beam, Pcrl and Pcr2, which depend on the amplitudes and phase difference of the main beam and the ripple. When the beam power P lies between the two critical values (i.e. Pcr1 < P < Pcr2), the medium behaves as an oscillatory waveguide; the beam first converges and then diverges, again converges, and so on. For P < Pcr2, the beam first diverges, then converges, then diverges, and so on. When thermal conduction is the dominant mechanism of nonlinearity of the dielectric constant, only one value of the threshold critical power Pcr for self-focusing of the beam exists. When the beam power P < Pcr, the medium behaves as an oscillatory waveguide.

When Bernstein waves (B waves) are excited in a magnetized plasma, their self-interaction by nonlinear Landau damping (NLD) becomes the dominant mechanism for the electron heating of the bulk plasma. We examine this behaviour numerically. This occurs only for B waves with relatively small k∥ because the damping of the B waves becomes very small. This occurs in the relatively broad B-wave frequency range betweenω/ωc = 1.45 and 1.78. For B waves with large k∥ (k∥R > 0.15), virtual waves are not generated via self-interaction due to NLD because the quasi-linear cyclotron damping of the B waves becomes the dominant mechanism. The numerical results agree well with experimental ones.

In this paper we study the relation between the collective magnetic entropy of the Vlasov systems, introduced previously on a phenomenological basis, and the Lagrangian description of the motion of a system of independent particles in a magnetic field, subject to a constraint that introduces collective behaviour. The main result is the equivalence of the first variations of the action integral and of the collective entropy with respect to a certain family of variations of the Lagrangian co-ordinates corresponding to reversible variations of the collective system considered as isolated. In the case of irreversible transformations the collective entropy is not determined dynamically, but acquires its meaning through the procedure of maximum probability assignment according to the standard formalism of information theory, under the requirement of macroscopic reproducibility.

The influence of ion streaming and weak relativistic effects on the modulational instability of ion-acoustic waves in a collisionless unmagnetized plasma is investigated. An averaging method is used to derive a weakly nonlinear dispersion relation, from which the instability criterion is deduced. Conflicting results in the literature are resolved.

This paper studies modulational instabilities of intensely propagating, circularly polarized, plane electromagnetic plasma waves in the presence of an external magnetic field pointing exactly in the direction of propagation. By ‘intense propagation’, we mean that eEo/mw (where Eo is the amplitude of the wave's transverse electric field) is comparable to unity, so that the problem is fully nonlinear and cannot be solved by regular perturbation methods. The positive component may consists of either positrons or singly charged ions. The plasma is assumed to be fully ionized and cold. Modulated intensely propagating electromagnetic waves couple (in general) to longitudinal motions via the ponderomotive force. For given wavenumber, the frequency of the wave depends on the amplitude not only via the obvious mechanism of relativistic mass increase but also via the density inhomogeneities induced by the ponderomotive force. This coupling effectively involves derivatives of the envelope, and the effect of longitudinal motions is comparable to that of relativistic nonlinearities. For this reason, a proper expansion procedure requires verification that one has obtained a self-consistent solution of all the field equations up to the appropriate order, including the longitudinal equations. This is best accomplished using the well-known two-timing approach. Modulational instability arises in the case of an ion-electron plasma with relativistic electrons but non-relativistic ions. However, for parameter values appropriate to pulsar magnetospheres, where the electron-cyclotron frequency is much larger than the frequency of the wave, there is no instability on the time scale of a micropulse.

We investigate a new mechanism of nonlinear wave interaction in a plasma with an electromagnetic wave, a Langmuir plasma wave and a self-generated quasi-stationary magnetic field involved in the three-wave process. It is demonstrated that magnetic field generation supports a new wave of hybrid polarization, which can be changed during the nonlinear evolution. Periodic regimes, as well as regimes of soliton (instanton) formation and kink-shaped transitions, can be realized.

The characteristics of Alfvén surface waves along a cylindrical annular streaming column with a solid core and surrounded by a tenuous medium, and pervaded by a longitudinal magnetic field are studied analytically and numerically. Both axisymmetric (m = 0) and non-axisymmetric (m ≠ 0) modes are found to be dispersive. The Alfvén-wave velocity decreases with increasing magnetic field. Under an infinitesimal perturbation, the motion of the system is laminar and stable for all values of m for all short and long wavelengths if the unperturbed state is non-streaming. If the system is streaming, there will be unstable domains not only for m = 0 but also for m ≠ = 0 owing to the strong destabilizing influence of the streaming. However, this instability can be suppressed completely if the magnetic field is sufficiently high that the Alfvén-wave velocity is greater than the streaming velocity. The thicker the solid core the greater is its stabilizing influence for m = ±1, and vice versa for m = 0. A longitudinal field imparts a degree of rigidity to the conducting fluid, so it always has a strong stabilizing influence.

The nonlinear interaction of an arbitrarily large-amplitude circularly polarized electromagnetic wave with an unmagnetized electron-positron plasma is considered, taking into account relativistic particle-mass variation as well as large-scale density perturbations created by radiation pressure. It is found that the interaction is governed by an equation for the electromagnetic wave envelope, which is coupled with a pair of equations describing fully nonlinear longitudinal plasma motions. The dynamics of the nonlinear electromagnetic wave packet is studied.

Das, Kamp and Sluijter have proposed equations describing three-dimensional electron inertia Alfvén waves for which the characteristic length scales in directions parallel and perpendicular to the ambient magnetic field are of the same order. Planar, obliquely propagating soliton solutions of these equations are known to be linearly unstable. Numerical simulations reveal the nonlinear phase of the evolution of these solitons: a transition from flat to cylindrical solitons is observed, followed by breaking-up into three-dimensional localized cavities. The final stage corresponds to wave breaking; no final stable structure is achieved within the model.

The decay rate of an Alfvén or plasma surface wave propagating along an inhomogeneous layer of plasma is calculated. The inhomogeneous profile is thin and odd, but otherwise arbitrary. The wave's decay rate is determined using two fundamentally different methods, the integro-differential equation approach of Sedl´ček and the Sturm-Liouville expansion technique of Cally, and found by both to depend only on the slope of the Alfvén or plasma frequency profile at the ‘resonant point’, and not on other details of its shape. The result is verified numerically. This problem represents a good example with which to compare and contrast the two methods.

We use a one-dimensional quasi-neutral fluid model to study the formation of an electrostatic shock associated with the lower-hybrid mode propagating almost perpendicularly to the magnetic field that exists in the auroral zone of the magnetosphere containing cold downward-streaming electrons, cold upward-streaming ions and beam electrons. We examine the effects of finite electron-beam temperature by describing the beam electrons with fluid equations. We then show how exact time-stationary shock solutions may be found when quasi-neutrality is considered.