Several Rossby-type vortex solutions constructed for electromagnetic perturbations in magnetized plasma encounter the difficulty that the perturbed magnetic field and the parallel current are not continuous on the boundary between two regions. We find that fourth-order differential equations must be solved to remove this discontinuity. Special solutions for two types of boundary value problem for the fourth-order partial differential equations are presented. By applying these solutions to different nonlinear equations in magnetized plasma, the intrinsic electromagnetic solitary drift-Alfvén vortex (along with solitary Alfvén vortex) and the intrinsic electromagnetic solitary electron vortex (along with short-wavelength drift vortex) are constructed. While still keeping a localized dipole structure, these new vortices have more complicated radial structures in the inner and outer regions than the usual Rossby-wave vortex. The new type of vortex guarantees the continuity of the perturbed magnetic field δB⊥ and the parallel current j‖ on the boundary between inner and outer regions of the vortex. The allowed regions of propagation speeds for these vortices are analysed, and we find that the complementary relation between the vortex propagating speeds and the corresponding phase velocities of the linear modes no longer exists.

The nonlinear interaction of whistler waves with the background plasma via the ponderomotive force gives rise to the formation of both periodic and solitary whistler envelopes. This is described in terms of the Lagrange formalism which allows us to define conserved quantities which determine, together with the parameters of the background plasma and the whistler frequency, the particular form of the envelope.

Stimulated Raman scattering from a fully focused relativistically drifting electron plasma in a parallel-plate waveguide is studied. A set of internally consistent transport relations governing the three-wave interactions is developed. These transport relations lead to the proper conservation of energy and momentum. Including small wall and bulk plasma losses, parametric and nonlinear characteristics are investigated theoretically and numerically. It is found that in an unbounded medium the saturation period of the signal wave is considerably smaller than in a bounded medium. The signal energy comes from the plasma stream through the idler wave with small depletion of the pump wave amplitude.

The ranges of temperature T, harmonic number s and wave propagation angle θ in which the loss-cone-driven electron cyclotron instability can exist are found to be limited by opposing contributions to the growth rate from adjacent harmonics. For waves with refractive index n ⋍ 1 it is found that instability is possible only if T and s satisfy saT ≲ C with a = 2 − 2·5 and where the constant C is determined by θ and the form of the distribution function. It is argued that the corresponding restrictions for waves with very large or very small n are less severe. Instability is found to be forbidden for waves propagating outside a range |θ − 90°| < φ(s), except if θ ⋍ 0, where π(s) is independent of temperature and sin2φ(s) ⋍ s−1; this restriction limits the range of potentially unstable frequencies at a given harmonic.

It has previously been observed that ion-acoustic waves exhibit two types of behaviour as the proportion of light ions in a mixed plasma is varied. Either the principal mode of the heavy ion plasma changes continuously into that of the light ion plasma, or it becomes too heavily damped to be observable while a second wave appears and develops into the principal light ion mode. A similar phenomenon is observed as the wavenumber or the ratio of electron temperature to ion temperature is changed. Criteria determining which behaviour occurs are derived by considering the form of the dielectric response function. The results may also be used to predict which of the higher-order modes of the plasma is involved in the process, and whether degeneracies exist in the dispersion relation.

A general electrostatic coupling coefficient which satisfies the Manley-Rowe relations is used to derive an explicit expression for the resonant three-wave coupling coefficient between electrostatic normal modes of a uniformly magnetized, infinite, homogeneous plasma with species described by drifting bi-Maxwellian distribution functions. The limit of this expression is taken when the phase velocities of the three waves are much larger than a species thermal speed, and also when the phase velocities are much smaller than the thermal speed. These are fluid limits and are applicable to the three-wave interaction between some low-frequency electrostatic waves, such as ion acoustic and ion cyclotron modes, in a plasma where Te ≫ Ti.

The linear dispersion relation for Bernstein modes, obtained by the integration of Vlasov's equation along the unperturbed cyclotron orbits, predicts that the modes propagating perpendicularly to the magnetic field are undamped. However, when the frequency is close to a multiple of the cyclotron frequency, most of the particles become trapped for small wave amplitude and the unperturbed orbit approximation breaks down. The trapped particle trajectories are calculated analytically here using a resonant Hamiltonian approximation. Integration, consistent with the wave, along the orbits yields the nonlinear damping rate in a manner similar to that used by O'Neil for the damping of unmagnetized electrostatic modes. The results can be extended for the general case of almost perpendicular, short-wavelength electrostatic modes near cyclotron harmonics.

A macroscopic interpretation for the problem of Landau damping of longitudinal oscillations in a collisionless plasma is investigated by including macroscopic fluid conservation of mass, momentum, and energy. It is shown that Landau damping may be derived macroscopically by appropriate consideration of the heat flux term for a collisionless plasma. This heat flux is expressed in terms of the perturbed velocity distribution function. A possible form of an equivalent complex thermal conductivity is postulated for a collisionless plasma. Both temporal and spacial damping are discussed.

Nonlinear behaviour of azimuthally symmetric compressional hydromagnetic waves propagating along a cylindrical cold magnetized plasma-filled waveguide is investigated. A nonlinear Schrödinger equation describing the nonlinear evolution of such waves is derived. Numerical evaluation of the dispersive and nonlinear terms reveals that such waves are modulationally stable in the fundamental radial mode of propagation. Calculations are presented for the amplitude dependent frequency and wavenumber shifts.

The propagation of nonlinear high-frequency TM antisymmetric surface waves on a thin un magnetized plasma slab bounded by vacuum has been studied. It is found that smooth surface wave solitons due to the modulation of finite-amplitude electron surface waves by slow ion-acoustic motion exist. When the high-frequency wave propagation is modified by a purely electronic slow motion, the governing equation is a derivative nonlinear Schröd inger equation with a cusped-soliton solution.