Obliquely propagating ion-acoustic nonlinear periodic waves in a magnetized plasma consisting of warm adiabatic ions and two Maxwellian electron species are studied. Using the reductive perturbation method, the Korteweg–de Vries (KdV) equation is derived and its cnoidal wave solution is discussed. It is found that as the amplitude of the cnoidal wave increases, so does its frequency. The effects of variations in the density and temperature ratios of the two electron species, the ion temperature, the angle of obliqueness and the magnetization on the characteristics of the cnoidal wave are discussed in detail. When the coefficient of the nonlinear term of the KdV equation, a1, vanishes, the modified Korteweg–de Vries equation is derived, and its periodic-wave solutions are discussed in detail. In the limiting case these periodic-wave solutions reduce to soliton or double-layer solutions.

We derive a dispersion relation for the perpendicular propagation of ioncyclotron waves around the ion gyrofrequency ω+ in a weaklu relaticistic anisotropic Maxwellian plasma. These waves, with wavelength greater than the ion Larmor radius rL+ (k⊥ rL+ < 1), propagate in a plasma characterized by large ion plasma frequencies (). Using an ordering parameter ε, we separated out two dispersion relations, one of which is independent of the relativistic terms, while the other depends sensitively on them. The solutions of the former dispersion relation yield two modes: a low-frequency (LF) mode with a frequency ω < ω+ and a high-frequency (HF) mode with ω > ω+. The plasma is stable to the propagation of these modes. The latter dispersion relation yields a new LF mode in addition to the modes supported by the non-relativistic dispersion relation. The two LF modes can coalesce to make the plasma unstable. These results are also verified numerically using a standard root solver.

A Riemann solver is used, and a set of numerical simulations are performed, to study the structures of reconnection layers in the approximation of the one- dimensional ideal MHD equations. Since the Riemann solver may solve general Riemarin problems, the model used in this paper is more general than those in previous investigations on this problem. Under the conditions used in the previous investigations, the structures we obtained are the same. Our numerical simulations show quantitative agreement with those obtained through the Riemann solver.

A family of three-dimensional models of reconnection is presented in which the different members of the family are characterized by the vorticity with which plasma flows towards the reconnection site. The nature of this inflow also determines the size and speed of the outflow jet that carries reconnected field lines away from the reconnection site, and the shape of the MHD shocks that bound it. Flows with positive vorticity are of a flux pile-up type, for which the outflow jet is fastest and narrowest. Among those with negative vorticity is the three-dimensional analogue of Petschek reconnection. Not all combinations of vorticity and reconnection rate are possible; for those solutions with negative vorticity, there is a maximum reconnection rate. As the magnetic Reynolds number Rme or the current density is increased, this maximum is reduced and the possible types of solution become more polarized towards the two extremes of flux pile-up and slow compression regimes. Given a distribution of vorticities and inflow speeds, these models give the corresponding distribution of possible steady-state reconnection rates. As an illustrative example, we take Gaussian distributions of both to show that the resulting distribution is dominated by the flux pile-up regime.

Dynamical equations are derived for the evolution of weakly nonlinear electron plasma waves when the electron distributions are characterized by more than one temperature component. The presence of electron-acoustic modes in multi- temperature plasmas opens a new decay channel. By considering an explicit example, it is demonstrated that these distributions imply significant modifications of the standard models for the decay spectrum of electron plasma waves. In particular, long-wavelength Langmuir waves can decay to shorter wavelengths. The results can have implications for ionospheric heating experiments.

At lower-hybrid frequencies in tokamaks, ponderomotive forces at fast-wave launching typically lead in the vicinity of the launching structure to a boundary plasma density increase. This results in a decrease in the reflection coefficient, and, in detached plasmas, to the appearance of a local electric field maximum at several centimetres from the launching grill structure; this electric field maximum is connected to the reversal of the plasma density gradient near the grill mouth because of ponderomotive force effects.

Large-amplitude relativistic nonlinear Langmuir waves are analysed using the pseudo-potential method. The existence conditions for nonlinear Langmuir waves are confirmed by considering relativistic high-speed electrons in a two- fluid plasma. The significant feature of this investigation is that the propagation of nonlinear Langmuir waves depends on the ratio of the electron streaming velocity to the velocity of light, the normalized potential and the ratio of ion mass to electron mass. The constant energy depends on the ratio of electron velocity to that of light. In the non-relativistic limit large-amplitude relativistic Langmuir waves do not exist. This investigation predicts new findings of large-amplitude nonlinear Langmuir waves in space plasma phenomena in which relativistic electrons are important.

The nonlinear stability of a horizontal interface separating two streaming magnetic fluids of finite thickenss is investigated in two dimensions. The fluids are considered to be inviscid and incompressible. The magnetic field is applied along the direction of streaming. The method of multiple scales, in both space and time, is used to examine the stability properties of the system arising from second-harmonic resonance. A pair of partial differential equations for the amplitude of the wave and its second harmonic are derived. These describe the evolution of the wave train up to cubic order, and may be regarded as the counterparts of the single nonlinear Schrödinger equation that occurs in the non-resonant case. The stability condition of this equation is discussed both analytically and numerically, and stability diagrams are obtained. Regions of stability and instability are identified. The nonlinear cut-off wavenumber separating the regions of stability from those of instability is obtained. The equation governing the evolution of the amplitude at the critical point is also obtained, which leads to a nonlinear Klein—Gordon equation.