A cylindrically symmetric, electrically driven, dissipative, energy-conserving magnetohydrodynamic equilibrium model is considered. The high-magnetic-field Braginskii electron electrical resistivity η parallel to a constant axial magnetic field B and ion thermal conductivity ĸ perpendicular to B are included in an energy equation and in Ohm's law. The expressions for η and ĸ depend on number density and temperature, which are functions of radius that are obtained as part of the equilibrium solution. The model has plasma-confining solutions, by which are meant solutions characterized by the separation of the plasma into two regions separated by a relatively thin transition region that is an internal boundary layer across which temperature and current density vary rapidly. The inner region has a temperature, pressure and current density that are much larger than in the outer region. The number density and thermal conductivity attain their minimum values in the transition region. The model has an intrinsic value of β, about 6.6%, which must be exceeded in order that a plasma-confining solution exist. The model has an intrinsic length scale, which, for plasma-confining solutions, is a measure of the thickness of the transition region separating the inner and outer regions of plasma. A larger class of transport coefficients is modelled by artificially changing η and ĸ by changing the constant coefficients ηO and ĸO that occur in their expressions. Increasing ĸO transforms a state that does not exhibit confinement into one that does, improves the confinement in a state that already exhibits it, and leads to an increase in ĸ in the confined region of plasma. The improvement in confinement consists in a decrease in the thickness of the transition region. Decreasing ηO subject to certain constraints, also transforms a state that does not exhibit confinement into one that does, improves the confinement in a state that already exhibits it, and leads to a decrease in η in the confined region of plasma. Increasing ηO up to a critical point increases the current, temperature, and volume of the confined region of plasma, and causes the thickness of the transition region to increase. If ηO is increased beyond the critical point, a plasma-confining state cannot exist. In all cases it is found that an increase in ĸ and a decrease in η in the confined region of plasma are associated with an improvement in the confinement properties of the equilibrium state. If the pressure and temperature are given on the cylinder wall, the equilibrium bifurcates when the electric field decreases below a critical value. The equilibrium can bifurcate into a state that exhibits confinement and a state that does not.

The propagation of an electromagnetic wave through a transparent plasma characterized by a spatial modulation of the density in the direction of propagation is analysed by computing the reflection coefficient of a single plasma slab and then that relevant to a set of many identical or slightly different slabs. The transmission spectra relevant to different density profiles of a single slab are computed to show the effects of (a) the density gradient, (b) a slight non-uniformity among adjacent slabs and (c) plasma modulation on the linear cut-off.

Quasi-one dimensional hydrodynamic continuity, momentum and energy equations describing the plasma flow in high-pressure-discharge ablative capillaries are derived. To overcome the formidable difficulties arising in the solution of a fully two-dimensional system of equations, experimental information on the structure (geometry) of the generated plasma is used. Thus the two-dimensional hydrodynamic equations are averaged over the cross-section of the capillary to obtain a quasi-one-dimensional system of equations in which, however, the essential two-dimensional features are present. These include the radial outwards radiative transfer of energy and the radial inwards ablative mass flow. Some particular cases, including their thermodynamical aspects, are discussed. Illustrative analytical and numerical solutions of the equations are also presented.

Sheath potential distributions in electrostatic plasmas including negative ions have been studied using the Bohm equation. Since the mean velocity of the negative ions is not necessarily negligible compared with their thermal velocity, the contribution from non-thermal negative ions has been considered. The Sagdeev potential has been introduced to consider structural instabilities of the Bohm system. Wavy solutions related to ion-acoustic solitons bifurcate from the monotone asymptotic Bohm sheath solutions. The solvability conditions have also been discussed for characteristic parameter such as the concentration of negative ions and the Mach numbers of positive and negative ions.

We consider the nonlinear propagation of magnetosonic waves along an unperturbed magnetic field in a plasma of high but finite conductivity when the Hall effect is taken into account, and we give a discussion of the analytical solutions of the nonlinear evolution equation that governs the latter problem. This equation is a generalization of the well-known modified Schrödinger equation and of the modified Burgers equation (it is referred to here as the modified Burgers-Schrödinger equation). Explicit analytical expressions for both a stationary kink-type solution and circularly polarized quasi-periodic waves are obtained and investigated.

The effect of a large Larmor radius on the stability of an infinitely conducting infinitely extended inhomogeneous plasma with two-dimensional magnetic field has been studied. A dispersion relation is obtained for the homogeneous system, and it is found that it is stable and MHD waves propagate. For an inhomogeneous plasma, a dispersion relation is also obtained and discussed for disturbances propagating transverse to inhomogeneity in (a) a cold plasma and (b) an incompressible plasma. It is found that the inhomogeneous system is unstable in both the cases, in agreement with the results of Lee and Roberts. The values of ωr and ωi are computed numerically, and the variations of ωi>0 and the corresponding ωr with the large-Larmor-radius parameter are shown graphically.

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).

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.

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.

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.