The formation of ion-acoustic solitary waves in a magnetized plasma with stationary ions and beam ions together with inertia-less electrons is investigated. The generation of waves in a plane is assumed to be one-dimensional, in a direction inclined at an angle θ to the direction of the magnetic field, with constant drift velocity of the ion beam. Remarkably, the amplitudes of the solitons are found to attain a maximum value at a particular beam-ion velocity γ, and then decrease slightly and remain almost constant for higher γ. The width of the waves is large at small y for small beam-ion density Nb, but it attains a constant minimum value at a particular value of γ. The amplitude decreases sharply to zero with decreasing y, whereas it remains almost constantly high for larger y. It is observed that as a wave approaches the direction of the magnetic field, its amplitude increases to a constant maximum value, which is larger for higher beam-ion velocities.

An analytical method for the investigation of special types of dispersion relations is presented. In particular, analysis of the propagation of small- amplitude hydromagnetic waves in a collisionless plasma in a strong magnetic field leads to such dispersion relations. The fifth-degree dispersion relation corresponding to a particular case is considered. The necessary stability condition for a steady state and conditions for the degeneration of small- amplitude waves are derived. A comparison with other methods for the analysis of similar dispersion relations is also presented.

The role of filamentary current distributions in the evolution of plasma-focus discharges is discussed. The force-free structures affect the energy balance during the acceleration of the plasma sheath. As a consequence, saturation of the neutron yield for high values of the energy stored in the capacitor bank occurs.

A generalized hydrodynamic model is used to evaluate the frequency spectra of longitudinal and transverse modes in dense strongly coupled two-component plasmas. The results are compared with available computer simulation data.

Magnetization due to a magnetic moment contributes to the non-oscillating magnetic field in a plasma. The dynamics ofclassically bound electrons in the presence of an applied circularly polarized strong electromagnetic field in the reflection region generates this field. The special case of its resonant generation when the frequency of a right circularlypolarized wave is equal to the ion gyration frequency is studied here. Another source of non-oscillating magnetization isthe interaction of electromagnetic fields, including fields in the Alfvén-wave frequency range, with a cold collisionless fully ionized magnetized plasma also in the reflection region. The induced field from a left circularly polarized field at Alfvén-wave frequencies is paramagnetic, inversely proportional to the square of the ambient field and independent of the mass per particle of both electrons and ions. The induced field from a right circularly polarized field at Alfvén-wave frequencies is diamagnetic, inversely proportional to the cube of the ambient field and depends directly on the plasma mass density.

The effect of pressure anisotropy on DRAKON equilibrium is investigated. The angle of neutral beam injection effects flux surface distortions. This can explain the increase or decrease in the equilibrium beta limit.

Nonlinear propagation of ion-acoustic waves and low-frequency electrostatic modes in a dusty plasma is investigated. The evolution equations of these modes are developed and solved analytically. It is found that for small grain charge usual ion-acoustic solitons may exist in a dusty plasma, but increasing grain charge destroys them and finally they may disappear. The low-frequency electrostatic mode may be localized, forming solitons, which may act as centres of wave scattering in a dusty plasma.

A thermodynamic analysis of tokamak plasmas is developed, starting from a single-fluid model. Some general propertiesof entropy production in the plasma are discussed. An approach is employed that is more general than the one based on Onsager symmetry relationships. This choice appears to be justified by experiments. The concept of ‘thermodynamic stability’ is introduced, and a general criterion for the stability of stationary states far from thermodynamic equilibrium is assessed. An upper limit on the particle density is found to exist as a necessary condition in order to prevent disruptions. Analysis of the entropy balance shows that this limit is modified when neutral-beam heating is applied. Radial temperature profiles are shown to be stable against external heating under specific experimental conditions, inparticular when ion and electron temperatures are comparable. An offset scaling law for the energy confinement time TE = TE(Pinp) (with Pinp total input power) is obtained for stationary states when stability against additional heating is imposed.

The dispersion properties and electromagnetic field topography of surface waves propagating along and in the azimuthal direction with respect to a cylindrical metal antenna immersed in a magneto-active plasma are investigated. The external magnetic field is directed along the antenna axis. The presence of a vacuum-gap sheath region separating the antenna from the plasma is assumed. The sheathless case is also considered. The dependence of the surface-wave dispersion properties on magnetic field intensity, plasma density, antenna radius and sheath thickness is presented for structure parameters close to experimental data. The results show qualitative agreement between our theory and experiment. The antenna surface impedance is calculated as well.

The nonlinear evolution of ion-acoustic waves in a multi-component plasma with negative ions has been studied experimentally using a double-plasma device. At a critical concentration of negative ions the phase velocity of the ion- acoustic waves increases with the wave amplitude, and the wave has negative dispersion, which show that the wave satisfies Lighthill's condition. The initial small modulation in amplitude is found to grow spatially. The observed phenomena are compared with the relevant theory using the nonlinear Schrödinger equation. The fluid equations are integrated to confirm the validity of the nonlinear Schrödinger equation.

Relaxation of a plasma in the presence of zeroth-order flows is studied in a realistic toroidal geometry. The field-aligned flow allows equilibria with finite pressure gradient but homogeneous temperature distribution. Numerical calculations have been performed for the first and second ellipticity regimes of the extended Grad–Shafranov–Schlüter equation. Two distinct classes of solutions exist, depending on the value of the safety factor: one with horizontally stratified density and pressure and one with concentric surfaces of constant density. A comparison of these results is made with those of Finn and Antonsen.

Short-wave (wavelengths smaller than the ion gyroradius) low-frequency (frequencies not exceeding the ion gyrofrequency) electromagnetic equilibrium spectra are found in a current-carrying plasma. Owing to cross-field correlations, the mean values of the integrals of motion increase, whereas their cascade rates are inhibited.

A radio wave transmitted into the ionosphere in the presence of a lower-hybrid drift wave excites a Langmuir wave, which is then damped by electrons, thereby heating them. This constitutes an important absorption mechanism. We evaluate the potential of the Langmuir wave and obtain an expression for the ratio Pr of the power of the Langmuir wave to that of the incident radio wave in the inhomogeneous ionosphere. It is found that the radio wave suffers an absorption of about 8% for a density fluctuation n1/n0 = 5%, but the electric field of the Langmuir wave becomes about 11.7 times that of the radio wave, which can lead to the excitation of parametric instabilities in the ionosphere.

In d.c. discharges the Bohm condition is the condition for sheath formation, the ion velocity at the plasma boundary having to satisfy the condition ½Mv2 = ½kB Te, if the spread of velocities is ignored. The model is a good one if the Debye distance is small compared with the relevant scale length. As there is much current interest in radio-frequency (RF) discharges, the question arises as to whether the criterion remains valid in the presence of RF fields. The question has been studied recently by Riemann, following earlier work by Allen who compared the plasma boundary to a sonic surface. Riemann considered a wider range of frequencies and obtained a dispersion relation that was a quartic equation. The present paper examines the complex roots of this equation, using a method developed by Briggs. The results substantiate Riemann's statement that the Bohm criterion is still valid in the presence of RF fields.

A time-dependent quasi-one-dimensional model is developed for studying high- pressure discharges in ablative capillaries used, for example, as plasma sources in electrothermal launchers. The main features of the model are (i) consideration of ablation effects in each of the continuity, momentum and energy equations; (ii) use of a non-ideal equation of state; and (iii) consideration of space- and time-dependent ionization.

Studies of the Zakharov—Kuznetsov equation governing solitons in a strongly magnetized ion-acoustic plasma indicate that a perturbed flat soliton is unstable and evolves into higher-dimensional solitons. The growth rate γ = γ(k) of a small sinusoidal perturbation of wavenumber k to a flat soliton has already been found numerically, and lengthy analytical work has given the value of We introduce a more direct analytical method in the form of an extension to the usual multiple-scale perturbation approach and use it to determine a consistent expansion of γ about k = 0 and the other zero at k2 = 5.By combining these results in the form of a two-point Padé approximant, we obtain an analytical expression for γ valid over the entire range of k for which the solution is unstable. We also present a very efficient numerical method for determining the growth rate curve to great accuracy. The Padé approximant gives excellent agreement with the numerical results.

This paper outlines a theory of absorption of lower-hybrid (LH) waves in an electron plasma that is based on the nonlinear relation between grad │E3│2, where E3 is the electric field component parallel to the external homogeneous magnetic field, and the space dependent quasi-linear diffusion coefficient, and consequently between grad │E3│2 and the absorption. A local absorption induces an increase of the value of the gradient in the neighbouring region and thereby extends the absorption domain. In this way virtually total ‘single-path’ absorption of the injected LH power is obtained. The theory also allows an explanation of the density limit in current drive.

Ion-acoustic surface waves in a highly collisional plasma are considered. It is shown that the dispersion and damping of these waves differ considerably from those for a weakly collisional plasma.

In view of some difficulties that appeared in previous work, the drift-wave dispersion equation has been studied in great detail by stressing some features that are not discussed in the usual textbook presentations. It is shown that any analytical approximation of a plasma dispersion equation leads to a singular perturbation problem for the roots of an algebraic equation. This property is associated with a number of parasitic roots, which can be identified and eliminated from the start. The behaviour of the remaining physical roots is discussed in detail by defining characteristic regions in the parameter space spanned by the gradients of density, electron and ion temperatures. Whereas in a large domain the usual behaviour predicted by elementary drift-wave theory is recovered, it is shown that there exists a region (whose existence is not predicted by elementary theory), where the conditions of existence of a drift wave are violated, thus causing the appearance of the (spurious) singularity previously found by Balescu. The explanation of this paradoxical situation is discussed in detail. The smooth connection of these results with the limit of a spatially homogeneous plasma is considered in an appendix.

We have studied the possibility of exciting a wake field in an electron–positron plasma by the injection of relativistic electron bunches. We have investigated the change in frequency of electronmagnetic radiation propagating through the resulting inhomogeneity. Our main conclusion is that it is not necessary to invoke a magnetic field in order to excite a wake field in an electron–positron plasma. As shown here, the necessary charge separation could come from the injection of energetic particle bunches. This mechanism of wake-field creation and subsequent particle/photon acceleration could operate in a pulsar magnetosphere, where particle bunches are extracted energetically from the pulsar surface. For example, pulsar radio emissions exhibit ultra-short intensity variations within individual pulses with time scales ranging from 1 μs to 1 ms (Cordes 1979). Several authors have proposed (Chian & Kennel 1983; Mofiz, De Angelis & Forlani 1985; Mikhailovskii, Onishchenko & Tatarinov 1985) that these pulsations can be explained as being due to soliton formation in the pulsar magnetosphere.

We believe that these micropulsations can also be explained by modulation of the radiation caused by the wake field. In order to have a quantitative estimation, we need to take into account the effects of thermal motion of particles as well as plasma inhomogeneity, etc. The present results should also be useful for understanding nonolinear photon motion in cosmic plasmas, such as those found in the early universe and in active galactic nuclei (Tajima & Taniuti 1990).