A study is made of ion-acoustic solitons in a low-β magnetized plasma consisting of any number of adiabatic positive and negative ion species in addition to the presence of isothermal electrons. A KdV equation in three dimensions or KdV-ZK equation is derived. This equation admits comprehensive or rarefactive solitons propagating in any oblique direction with respect to the direction of the external magnetic field, depending on the density of the negative ion species. When the nonlinear coefficient of this equation vanishes, the nonlinear ion-acoustic wave is described by a modified KdV equation in three dimensions. This equation is also derived and its solitary-wave solutions are discussed. Both compressive and rarefactive solitons are possible. Finally, the three-dimensional stability of these solitons is investigated by the small-k perturbation expansion method of Rowlands and Infeld. Stability criteria and growth rates of instabilities are derived.

The stochastic non-resonant energization of ions in non-sinusoidal coherent plane-polarized magnetosonic waves is investigated. It is found that, as in the case of sinusoidal magnetosonic waves, the process does not follow quasi-linear theory, i.e. it is a diffusion in velocity space, but with a diffusion coefficient D ∝ ν–α, α ≈ 1, instead of D ∝ ν–3. Moreover, it is found that the presence of strong harmonics lowers the stochasticity threshold of the wave amplitude by as much as one order of magnitude (depending on the form of the power spectrum), but at the same time it suppresses the diffusion rate of the ions in velocity space. Our results indicate that waves with a saw-tooth wave form are the most efficient for ion energization.

A longitudinal undulating electric field in the lasing electron beam direction (or the longitudinal direction) and an electromagnetic wave propagating in the longitudinal direction (laser wave) drive a current that cannot be in the longitudinal direction. Thus this current can emit an electromagnetic wave having the same wave vector and polarization vector as those of the incident electromagnetic wave. This process is called stimulated bremsstrahlung in the longitudinal electric wiggler. Because of recent strong interest in this free electron lasing mechanism, it is appropriate to correct errors in numerical factors in the gain formula and equations in our paper.

The equilibrium properties of a two-dimensional plasma are examined theoretically, using a model where the finite-Larmor-radius corrections to the simple guiding-centre description are included. The analysis is carried out in a truncated Fourier representation of the resulting equations. This system has three ‘rugged’ quadratic invariants. A canonical-ensemble probability distribution characterized by three temperatures is derived. The resulting partition function is obtained and the equilibrium spectral energy density is calculated. The possibility of negative-temperature states leading to an inverse energy cascade is pointed out.

This paper explores the properties of Rossby-type electrostatic electron plasma waves at frequencies very much less than the electron gyrofrequency but very much greater than the ion gyrofrequency. Such waves represent the electron counterpart of ion Rossby waves, which propagate at frequencies very much less than the ion gyrofrequency in a plasma in which the ambient magnetic field possesses a spatial gradient perpendicular to its line of action. This feature simulates the ‘β-effect’ that operates in the classical atmospheric Rossby wave: the wave dynamics associated with both ion and electron Rossby waves are structurally similar to those associated with wave perturbations in a rotating fluid, where the β-effect arises from a spatial gradient in the Coriolis acceleration. It is shown that this plasma β-effect gives rise to a ‘new’ mode of the Rossby type, and in addition considerably modifies the conical wave propagation properties characteristic of the electron cyclotron mode. The highly dispersive and anisotropic nature of these waves is described in terms of the topology of the wavenumber surfaces concomitant with plane-wave solutions of the wave equation for the system as a whole.

The three-dimensional stability of solitary shear kinetic Alfvén waves in a low-β plasma is investigated by the method of Zakharov & Rubenchik (1974). It is found that there is no instability if the direction of perturbation falls within a certain region of space. The growth rate of the instability for the unstable region is determined. This growth rate is found to decrease with increasing angle between the direction of propagation of the solitary wave and the direction of the external uniform magnetic field. A particular case of the present analysis gives results on the stability of ion-acoustic solitons in a magnetized plasma.

The problem of propagation of an ion-acoustic soliton and its reflection in a weakly inhomogeneous plasma is considered, taking into account the effect of finite ion temperature. A reductive perturbation analysis is carried out to obtain expressions for the local speed, amplitude and width of the soliton. The peak value of the soliton amplitude increases and the soliton width decreases with increasing ion temperature. An equation describing the dependence of the reflected-wave amplitude on ion temperature is obtained. The amplitude of the reflected wave is observed to decrease with increasing ion temperature on account of Landau damping.

In order to find the equations for the nonlinear energy exchange between low-frequency waves in magnetized plasmas in the presence of pressure anisotropy, we start from the Chew–Goldberger–Low equations, the isothermal MHD equations, as well as a new hybrid system of equations. The coupling coefficients describing the interaction between two Alfvén waves and one magnetosonic wave as well as the interaction between two magnetosonic waves and one Alfvén wave are deduced.