Stimulated Brillouin scattering of an electromagnetic wave is investigated analytically in a dissipative magnetized plasma in the presence of negative ions. With an increase in the number of negative ions (maintaining quasi-neutrality), it is found that the growth rate of ion-acoustic waves decreases very slowly up to 50% concentration (i.e. half of the total ionic contribution) of negative ions. Further increase in the number density of negative ions beyond 50% results in a sharp fall in growth rate.

The imploding plasma column of a gas-puff Ζ-pinch has been used to compress the target-gas-embedded axial magnetic field in the presence of plasma pressure. The dynamics of a two-gas gas-puff Ζ-θ pinch is studied with different forms of applied current profiles. We find that the inclusion of a kinetic pressure term introduces the usual β–term, which delays and reduces the maximum compression. On the other hand, for fixed β, compression at an earlier time can be achieved for a large density ratio of the test to the driver gas at the interface position. For the pressure-free case, our earlier results are completely recovered.

The propagation of wave packets on the surface of an electrically conducting fluid of uniform depth in the presence of a tangential magnetic field is investigated in (2 + 1) dimensions. The evolution of wave envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability analysis reveals the existence of different regions of instability. The effect of the applied magnetic field is not only significant but also different for different regions of stability. ‘Envelope soliton’ and ‘waveguide’ solutions of the amplitude equation are also discussed. The self-focusing phenomenon that arises when the amplitude of the wave becomes infinite in finite time is also examined. It is found that in a certain region of the stability diagram it may be easier to observe this phenomenon in the presence of a magnetic field. The Rayleigh-Taylor problem is also studied and various criteria for the existence of instability are obtained.

A specific type of longitudinal wave instability in a plasma due entirely to an external quasi-static electric field E0 is considered for the cases of ion-acoustic and Langmuir waves. The quasi-static time variation of the field leads to a relatively simple mechanism for the development of instability. For frequency ranges typical of ion-acoustic and Langmuir waves dispersion relations are obtained, with Landau damping and pair Coulomb collisions taken into account in addition to E0. The model integral of Bhatnagar, Gross & Krook is used to describe collisions. Two methods for taking account of the influence of the electric field on development of the instability are compared: that of Pines & Schrieffer and that of Brinca and Dysthe. Expressions are obtained for the growth rates in the framework of linear theory. Numerical simulations of both types of instabilities are performed for specific values of the plasma parameters.

Modulated electromagnetic plane waves in relativistic collisionless, unmagnetized plasmas are investigated through expansion in a small parameter, corresponding to weak dispersion and weak nonlinearity. The oscillation-centre transformation is applied to construct a Hamiltonian action principle for the slow oscillation-centre variables. A description in terms of the relativistic Vlasov equation for oscillation-centre distribution functions is introduced. A system of coupled field and kinetic eequations is obtained order by order.The final result is a generalized vector nonlineat schrödinger equation, with resonant particle effects included through the coupling to the perturbed Vlasov equations.

By means of the standard fluid equations, we consider the nonlinear coupling between a large-amplitude pump wave and the low-frequency modes in a collisional plasma. We derive the general dispersion relation in order to discuss the case where the pump-wave frequency is not much larger than the electron gyrofrequency.

A second-order approximation is formulated and studied within the context of the quasi-particle description of magnetized plasmas. The general case of relativistic particles in non-uniform but stationary magnetic fields, and in additional force fields that are strongly non-uniform but slowly evolving in time compared with particle gyrations with the cyclotron frequency, is considered. In order to reveal the physical significance of the second-order approximation, the mean (reduced) particle velocity is calculated up to second order, when polarization particle drift as well as the renormalization of the lower-order result become equally significant. A general expression for the velocity of particle polarization drift is obtained in terms of quasi-particle properties, and with account taken of finite-Larmor-radius effects and non-uniformity of magnetic fields. A guiding-centre transformation is found that makes it possible to achieve equal mean velocities of particle, guiding centre and quasi-particle up to second order. Then polarization drifts enter the particle, guiding-centre and quasi-particle equations of motion.

Solitary waves in an ion-beam-plasma system are investigated theoretically using the pseudo-potential method, including finite temperatures of plasma ions and beam ions. The beam velocity is high enough to avoid ion-ion instability. Three kinds of solitary waves are possible, corresponding to ion- acoustic waves and to fast and slow space-charge waves in the beam. To observe the formation of solitary waves from an initial positive pulse, numerical simulations are performed. For the slow beam mode, a smaller solitary wave appears at the leading part of the pulse, which is a result of negative nonlinearity and anomalous dispersion of the slow mode, and is the opposite behaviour to the cases of the ion-acoustic wave and to the fast beam mode. Overtaking collisions of a solitary wave with a fast-mode solitary wave or with a slow-mode solitary wave are simulated.

The contribution of higher-order nonlinearity to nonlinear ion-acoustic waves in a weakly relativistic plasma consisting of a warm ion fluid and hot non- isothermal electrons is studied using reductive perturbation theory. At the lowest order of the perturbation theory a modified Korteweg–de Vries equation is obtained. At the next order a linear inhomogeneous equation is obtained. The stationary solution of the coupled equations is obtained using the renormalization method introduced by Kodama and Taniuti for reductive perturbation theory.