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.

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.

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.

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.

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.

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.

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.

Nonlinear MHD waves propagating obliquely to the external magnetic field in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts are treated without imposing the customary quasi-neutrality between the different species or neglecting the displacement current in Ampère's law. The wave magnetic field obeys a vector nonlinear evolution equation, which in the limits of parallel propagation or of both the neglect of the displacement current and the imposition of quasi-neutrality reduces to the vector formulation of the well-known derivative nonlinear Schrödinger equation.

Oblique propagation of MHD waves in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts is described by a modified vector derivative nonlinear Schrödinger equation, if charge separation in Poisson's equation and the displacement current in Ampère's law are properly taken into account. This modified equation cannot be reduced to the standard derivative nonlinear Schrödinger equation, and hence requires a new approach to solitary-wave solutions, integrability and related problems. The new equation is shown to be integrable by the use of the prolongation method, and by finding a sufficient number of conservation laws, and possesses bright and dark soliton solutions, besides possible periodic solutions.

Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long-wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded.

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of warm ion-fluid and hot isothermal electrons is investigated using reductive perturbation theory. A Korteweg-de Vries-type equation, with temperature- and relativistic-parameter-dependent coefficients is obtained. The renormalization method is applied to the equations obtained from the different orders of perturbation theory to obtain a stationary solution. Relativistic cold and non-relativistic warm plasma limits are considered in order to make comparisons with previous results.

The following property is shown of the entropy functional constructed in previous work and associated with a Vlasov electrostatic or magnetostatic collective equilibrium (a static solution of the Vlasov equation): the vanishing of the first variation of the functional is equivalent to Hamilton's principle applied to a Lagrangian describing motion of the underlying system of particles compatible with the collective equilibrium, provided that the variations are associated with reversible processes. This property is shown in two cases: (i) a system of particles in Coulomb interaction admitting a collective (Vlasov) equilibrium in the presence of a scalar pressure; and (ii) a system of independent electrons in a background of fixed ions subject to an external electric field and to a magnetic field (created in part by electron currents) associated with a cylindrically or toroidally symmetric equilibrium in the presence of the electron–ion friction force and an anisotropic pressure.

A study is made of electrostatic waves in a cold equal-mass plasma. Numerical simulation reveals that cold equal-mass plasmas are fundamentally unstable to such oscillations, in contrast to the behaviour of these waves in electron-ion plasmas. A quasi-linear analysis of the problem is performed and an analytic solution found that duplicates the early evolution of the plasma.