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.

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.

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.

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 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.

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.

Linear stability of a magnetized dusty plasma is studied for the regime with ≈ 1 (where G is the universal gravitational constant, md is the grain mass and qd is the grain charge). We demonstrate that the magnetic force plays a stabilizing role and, together with electrostatic repulsion, counter gravitational condensation. The implications of this result for astrophysical situations are briefly discussed.

The theory of black-body radiation in thermal equilibrium with a homogeneous and isotropic plasma is presented. The relevant thermodynamic quantities of the radiation are obtained. The presence of the plasma changes qualitatively and often quantitatively the concept of black-body radiation, essentially through the effect of plasma density.

It is demonstrated that the dielectric tensor for a non-relativistic magnetized plasma whose particle velocity distributions can be modelled by isotropic kappa, or generalized Lorentzian, distributions admits an expression similar to that obtained by Trubnikov for a relativistic plasma. The kappa distribution is a useful distribution for modelling space plasmas containing significant numbers of superthermal particles, i.e. those that have energies in excess of the thermal energy. The dielectric tensor is valid for arbitrary wavevectors, and is shown to reproduce the known limiting case of wave propagation parallel to the magnetic field. Even in this limiting case, the results obtained represent a generalization of previous results to arbitrary real values of the index K, the parameter that shapes the superthermal tail on the distribution. The expression for the dielectric tensor might be useful as a starting point for numerical studies of waves and instabilities in plasmas containing superthermal particles.

A time-dependent two-dimensional MHD simulation program is used to investigate the magnetic reconnection process with a spatially uniform diffusivity. Various initial conditions are considered and are allowed to evolve until a final steady state is produced. The boundary conditions are carefully handled in order that they be as strict as possible. In the first series of simulations the initial condition is taken to be an analytical solution of the ideal MHD equations given by Biskamp. Dirichlet (fixed) boundary conditions are used, with a small amount of flexibility allowed on the boundary for the stream function in order to prevent any unphysical currents forming. The final steady- state contains a current sheet whose width and length are found to vary as and respectively, and the reconnection rate is found to be independent of the value of Rm, indicative of fast reconnection. Additionally, as Rm, is increased, a region of reversed current and a high-speed jet of plasma are observed to develop along the MHD shock separating the inflow and outflow regions. The second series of simulations uses a slightly different initial condition that allows a faster outflow of plasma from the simulation region. The current sheet width of the final steady state is again found to vary as , and the reconnection rate is again independent of Rm. However, no reversed currents or plasma jetting along the shock are observed, indicating that the plasma jets of previous simulations are due to restrictive outflow conditions, which force the high-speed plasma emerging from the end of the current sheet to divert along the MHD shock. Lastly, the analytical model of Petschek is utilized to provide an initial condition. For this case, however, it is not possible to keep the boundary conditions as strict as before, since both the stream and flux functions have to be allowed to vary slightly in order to deal with the discontinuities of the Petschek model. Although steady-state solutions can be obtained, they are found, owing to the laxness of the boundary conditions, not to exhibit the well-defined structure or small current sheets of the previous results.

The generalization of the Case—van Kampen analysis to a multidimensional non-uniform plasma is presented. Application of this analysis is made to minority-ion gyrolesonant heating in an axisymmetric tokamak. In previous work the Case—van Kampen analysis, in conjunction with the Bateman—Kruskal algorithm, was used in a one-dimensional slab model to compute the collective wave spin-off (to the minority-ion Bernstein wave) and the gyroballistic continuum for minority gyroresonant absorption. The generalization to many gyroresonant dimensions and non-trivial geometries requires several important new developments: In tokamak geometry particles can be trapped, an effect that is absent in the slab model. Also, the ray propagation dynamics for both the flee gyroballistic waves and the collective minority-ion Bernstein wave is far more complicated than in the slab model. In particular, a resonance zone is identified wherein the gyroballistic waves interact strongly and cannot be treated as free. We use the Weyl calculus to construct a local form of the self-consistent gyroballistic equation within the resonance zone. This reduced equation is simplified via a metaplectic transformation (a generalization of the Fourier tiansformation). After this simplification, the equation is shown to be of Case—van Kampen type with weak non-uniformities; hence there are no true Case—van Kampen eigenfunctions. Using the Bateman—Kruskal approach, a local Case—van Kampen basis can be constructed and the initial-value problem solved. The self-consistent interactions of the gyroballistic continuum lead to a collective wave, the minority-ion Bernstein wave. The Bernstein wave is extracted by the spectral deformation approach of Crawford and Hislop. The relevance of this work to the theory of collective phenomena in nonlinear oscillator ensembles is briefly discussed.