Weakly nonlinear surface waves rippling an MHD tangential discontinuity (TD) of finite thickness are studied. The waves are two-dimensional and evanescent in the direction normal to the inhomogeneous layer. A novel approach is utilized to treat weakly nonlinear evanescent wave fields in physical space. The evolution equation obtained, which governs the interface displacement as a function of time and position, extends previous results of Ruderman and Goossens, valid for propagation along a unidirectional magnetic field in a stationary incompressible plasma, to a TD of general field geometry in a compressible plasma in the presence of stable velocity shear. Certain conservation properties of the evolution equation are presented, including the Hamiltonian formulation. Exploratory numerical results are reported. The model is of potential use in the analysis of observed quasi-stationary perturbations at the earth's magnetopause.

We consider the splitting of a reconnecting current sheet into MHD discontinuities, which is observed in many numerical simulations of the magnetic reconnection process. We suppose that the splitting takes place as a consequence of non-evolutionarity of the reconnecting current sheet as a onedimensional discontinuity. This means that the problem of the time evolution of its small perturbations does not have a unique solution. Since a physical problem must always have a unique solution, a non-evolutionary discontinuity cannot exist in a real plasma, and splits into evolutionary discontinuities. Solving the linear MHD equations inside and outside the sheet, we show that for large enough plasma conductivity, certain small perturbations interact with the sheet as with a discontinuity. On the basis of the non-evolutionarity criterion, with respect to these perturbations, we obtain a condition on the flow velocity at the sheet surface, under which the splitting takes place.

The transverse modulational instabilities of two finite-amplitude electron-cyclotron waves due to the ponderomotive force and relativistic mass variation of electrons are considered using the coupled nonlinear Schrödinger equation model. The waves are modulationally unstable, with maximum growth rate larger than that of a single wave. The stable waves can be unstable by the effect of coupling. The instability is caused only by the mass variation of electrons, and the contribution of the ponderomotive force is negligibly small. The instability of copropagating waves has a convective nature and that due to the counterpropagating waves has an absolute nature, no matter how large the pump intensities are. The threshold of modulational instability is also considered for finite-length plasmas.

Using the derivative nonlinear SchrÖdinger equation, resonant four-wave mixing of finite-amplitude Alfvén waves is explored in this paper. The evolution equations governing the amplitudes of the interacting waves and the conservation relations ale derived from the basic equation. These evolution equations are used to study parametric amplification and oscillation of two small-amplitude Alfvén waves due to two large-amplitude pump (Alfvén) waves. It is also shown that three pump waves can mix together to generate a low-frequency Alfven wave in a dissipative plasma.

The nonlinear behaviour of unstable drift waves in magnetized plasmas is analysed analytically. Most attention is paid to low-frequency waves created in electron density and temperature gradients of opposite sign. This situation is typically encountered in radiofrequency-produced discharges. The model developed explains nonlinear features such as mode competition, amplitude saturation and magnetic field hysteresis, which are observed experimentally.

The possible crest forms of magnetoacoustic travelling waves of small amplitude satisfying the full system of equations describe the wave propagation in a cold quasineutral collisionless plasma are determined. For a certain range of the inclination angle of the magnetic induction vector we find solitary waves. We find also families of periodic waves of two different types, as well as quasiperiodic waves aiid generalized solitary waves with non-decreasing oscillations at infinity.

Low-frequency density and temperature oscillations (ω « νj, ωcj, where νj is the collision frequency with neutrals and ωcj is the cyclotron frequency; j = i, e) observed in magnetized radiofrequency-produced plasmas with electron density and temperature gradients across the magnetic field are analysed using a local two-fluid model. This model incorporates the electron energy equation. The resulting dispersion relation permits study of the parameter dependence of the complex angular wave frequency. Instability is found in the case where the election density and temperature gradients have opposite signs. This instability is classified as a low-frequency drift wave, and the criteria for its onset are obtained.

The magnetogravitational instability of compressible streaming superposed fluids pervaded by different transverse magnetic fields is investigated. A perturbed sinusoidal wave is assumed to propagate along the direction of the streaming velocities. The stability criterion has been derived in a general form, and some limiting cases are recovered from it. The influences of different forces and factors are identified. The system under consideration is unstable not only for states with long wavelengths but also for those with short wavelengths.

An equation is derived for the growth rates of the beam-plasma instability excited by non-thermal electrons with arbitrary distribution function, and it is shown that the reactive instability does not depend on the assumption of a monoenergetic distribution. Hence the properties of electromagnetic waves are calculated for the hollow beam and loss-cone distribution. Hence the properties of electromagnetic waves are calculated for the hollow beam and loss-cone distribution functions. The general characteristics and structures of the growth rates are similar to the results for the monoenergetic distribution, but there are still some differences in the relation between the growth rates and the relevant parameters, such as the ambient parameter ωpe/Ωe, the angle of propagation θ and the pitch angle a. The main purpose of this paper is to compare the properties of the beam-plasma instability (reactive) and the electron-cyclotron maser instability (kinetic) under similar ambient conditions. The calculations show that both kinds of instabilities are easily excited at larger angles of propagation with respect to the ambient magnetic field, which means that both depend mainly on the free energy of the non-thermal electrons perpendicular to the magnetic field. The magnitudes of the growth rates of the two kinds of instabilities are comparable under the same ambient conditions. However, because the non-resonant wave—particle interaction is taken into consideration for the beam-plasma instability, which makes the resonant peaks broaden and connect with each other, the spectra of the beam-plasma instability are also more complicated than that of the maser instability, and the range of the angle of propagation of the growing waves in the non-resonant case is also larger than that in the resonant case.

The thermal instability of a compressible plasma in a porous medium is considered in the presence of a uniform vertical magnetic field to include the Hall-current and finite-Larmor-radius effects. The system is found to be stable for (cp/g) β < 1, where cp, β and g are the specific heat at constant-pressure, the uniform adverse temperature gradient and the acceleration due to gravity respectively. The uniform vertical magnetic field, Hall-current and finite. Laimor-radius effects introduce oscillatory modes in the system for (cp/g) β ≤ 1, which were non-existent in their absence. The Hall current and finite Larmor radius (FLR) individually have destabilizing and stabilizing effects respectively on the system. In their simultaneous presence there is competition between the destabilizing role of the Hall current and the stabilizing role of the FLR, and each succeeds in stabilizing a certain wavenumber range. In the absence of a magnetic field (and hence the absence of an FLR and Hall current), the destabilizing effect of medium permeability is seen, but in the presence of a magnetic field (and hence the presence of an FLR and Hall current), the medium permeability may have a stabilizing or a destabilizing effect on the thermal instability of the plasma. The effect of compressibility is found to postpone the onset of thermal instability in plasma.

Wave mixing resulting from the resonance of electromagnetic waves with ion acoustic waves modified by dust charge fluctuations is investigated. The corresponding nonlinear susceptibilities are derived and applied to the study of phase conjugation by four-wave mixing. It is shown that dust charge fluctuations can lead to a filling-up of the resonance-induced splitting of the phase-conjugate reflectivity, making the latter a useful tool for the diagnostics of dusty plasmas.

The turbulence of the toroidal ηi mode has a forward spectral cascade. This means that most of the energy initially placed in the low-wavenumber region (the linear instability region) will be spread out towards high-wavenumber modes. Therefore the linear instability may be reduced by this energy cascade. An elementary estimate of the critical amplitude for nonlinear mode coupling to balance the linear growth rate is given. As a consequence of three wave cascade process derivable from the fully toroidal fluid model equations, the formation of zonal flows ηi-mode turbulence is predicted.

The existence of novel electrostatic solitary pulses in an electron–positron plasmas with two distinct groups of positrons is demonstrated. It is found that the soliton potential can assume both the rarefactive and compressive polarities. The results might be useful in understanding the properties of localized disturbances in astrophysical plasmas.

We generalize Silin's dispersion equation for electrostatic parametric resonances in an unmagnetized plasma to include interactions hitherto overlooked. Of particular interest to ionospheric physicists in this generalization is the interaction between an ion acoustic wave (shifted up in frequency by that of the pump) and an unshifted Langmuir wave. This yields growth rates equal to that of its counterpart in the Silin version, namely the ‘classical’ interaction between a Langmuir wave (shifted down by the pump frequency) and an unshifted ion acoustic wave. The more general (truncated) dispersion equation also displays resonances between ion acoustic sidebands, but this requires pump frequencies of the order of, or less than, the ion plasma frequency and therefore may be of little practical interest in the ionosphere. The system is analysed using Fourier techniques, which lead to two dispersion equations governing the Fourier transforms of the ion and electron perturbation densities. It is shown that, as far as the structure of the coupled recursion relations for the ion and electron Fourier components is concerned, there is an equivalence between the fluid and kinetic treatments. In the case of weak pump fields we calculate the growth rates associated with the various instabilities from a truncated three-wave interaction dispersion relation. Where it is appropriate, these growth rates are compared both with those from the Sum dispersion equation and the counterparts from the Zakharov model. We also discuss the case of very strong pump fields where the ‘natural’ interacting mode frequencies are not those associated with the usual Langmuir—ion acoustic modes of the unpumped plasma, but rather the oscillator frequencies corresponding to the coupled oscillator paradigm that is applicable to the system. Here again we find instabilities of a nature analogous to those arising in the weak pump case.

An increase in the expansion rate towards vacuum of a plasma column with density of order 108 cm−3 and radius 0·5–2·0 mm produced by photoionization in the presence of a 9·4 GHz microwave field is found. The microwave field imposed by the TEM005 Gaussian mode of a spherical Fabry–Pérot resonator acts on the plasma through its ponderornotive force. First, the use of a potential barrier spectrometer allows us to measure the increase, in the number and energy of escaping electrons compared with the same plasma without microwave field. Secondly, the expansion of the modified photoplasma is checked by applying a small polarization voltage on the Fabry-Pérot mirrors to collect the ions. In the presence of the microwave field the time-resolved ion peak. Which presents a two-lobe profile faster than the single one observed without the field, indicates strong modification of the plasma dynamics. All these observations are interpreted by a simple model including the ponderomotive microwave force and the electrostatic plasma force, which act in opposite directions.

The nonlinear stability of surface waves propagating between two superposed streaming magnetic fluids is investigated. The fluids are stressed by a constant tangential magnetic field and a vertical periodic acceleration. The solution employs the method of multiple scales. Owing to the periodicity, resonant cases appear. Two parametrically nonlinear Schrödinger equations are derived for the resonant cases to describe the elevation of weakly nonlinear capillary waves. The standard nonlinear Schrödinger equation is satisfied for the non resonant cases. Necessary and sufficient conditions for stability are obtained. A formula for the surface elevation is obtained in each case. It is found that the magnetic field, the velocities and the frequency of the applied periodic force play dual roles in the resonant region. Investigation of the stability criterion by nonlinear perturbation shows that an increase in the acceleration frequency has a stabilizing effect. The stabilizing role of the frequency is due to the destabilizing effect of the amplitude of the periodic acceleration.

An intense relativistic electron beam propagating through a plasma creates a low-density plasma duct capable of guiding a free-electron laser mode. The beam dynamics plays an important role in the propagation of TM modes. For (where and are the beam and plasma densities respectively, and a and b are the x and y dimensions of the duct) and beam energy of about 2 MeV, the threshold current turns out to be about 20 kA. For marginal radiation guiding, the size of the plasma duct decreases with beam voltage. Application of a strong DC magnetic field shows that an even narrower duct can guide high-frequency radiation.

We study the stability of the cold-plasma dispersion relation for circularly polarized waves in a plasma composed of an ion background and an ion beam. The presence of the beam introduces a resonant branch into the dispersion relation for right-hand-polarized waves propagating in the direction of the external magnetic field, which, for V>Vφ, has negative energy (here V is the beam velocityVφ is the wave phase velocity). Therefore this branch may give rise to explosive instabilities when the waves experience parametric decays. It is shown graphically that resonant right-hand-polarized and non-resonant left-hand-polarized waves, propagating parallel to the external magnetic field, can be unstable. It is also shown that the instability region can extend to large frequencies and wavenumnbers, and that the instability regions have a band structure. The parametric dependence of instability thresholds and marginal modes is also studied.

The gravitational instability of a dusty plasma with ion dynamics taken into account is studied. For the range of parameters relevant to planetary rings and interstellar media, we demonstrate that the inclusion of ion dynamics cannot cause additional destabilization of a gravitating dusty plasma system. Streaming of the cold ions, on the other hand, enhances the Jeans condensation of a dusty plasma. Consistency of the results with previous work and new aspects arising owing to consideration of ion dynamics is discussed.