The dependences of the propagation characteristics of an intense microwave pulse on the intensity, frequency, width and shape of the pulse in an air- breakdown environment are examined. Numerical simulations lead to a useful empirical relation P3W = α = const, where P and W are the incident power and width of the pulse and α depends on the percentage of the pulse energy transferred from the source point to a given position. The results also show that, using a single unfocused microwave pulse transmitted upwards from the ground, the maximum electron density produced at, for example, 50 km altitude is limited by the tail erosion effect to below 106 cm-3. Repetitive-pulse and focused-beam approaches are then examined. Both approaches can increase the maximum electron density by no more than an order of magnitude. Hence a scheme using two obliquely propagating pulses intersecting at the desired height (e.g. 50 km) is considered. It is shown that the generated electron density at the lowest intersecting position can be enhanced by more than two orders of magnitude.

Stimulated Brillouin scattering of an electromagnetic wave is investigated analytically in a dissipative magnetized plasma in the presence of negative ions. With an increase in the number of negative ions (maintaining quasi-neutrality), it is found that the growth rate of ion-acoustic waves decreases very slowly up to 50% concentration (i.e. half of the total ionic contribution) of negative ions. Further increase in the number density of negative ions beyond 50% results in a sharp fall in growth rate.

A quasi-one-dimensional model for the steady-state flow of a plasma in an ablative discharge capillary is presented for capillaries with non-constant cross- section. It is demonstrated that small modifications of the capillary geometry can lead to significant changes in the plasma exit parameters. In this respect, the possibility of obtaining an extended range of plasma parameters makes this type of ablative capillary a useful source of plasma for a variety of applications. Numerical solution of the equations of the model for the critical-flow case allows evaluation of the main fluid-dynamic and thermodynamic parameters of the plasma inside the capillary and at its exit.

The imploding plasma column of a gas-puff Ζ-pinch has been used to compress the target-gas-embedded axial magnetic field in the presence of plasma pressure. The dynamics of a two-gas gas-puff Ζ-θ pinch is studied with different forms of applied current profiles. We find that the inclusion of a kinetic pressure term introduces the usual β–term, which delays and reduces the maximum compression. On the other hand, for fixed β, compression at an earlier time can be achieved for a large density ratio of the test to the driver gas at the interface position. For the pressure-free case, our earlier results are completely recovered.

The distribution function of the minority ions during ion-cyclotron heating is calculated from a kinetic equation composed of a Landau collision term and a surface-averaged quasi-linear heating term. The kinetic equation is solved by a moment method in which the minority-ion distribution function is expanded in irreducible tensorial Hermite polynomials. The coefficients of the expansion are shown to be solutions of a system of coupled algebraic equations, and the effective minority-ion temperature is deduced from a compatibility constraint. The latter equation is in general too complicated to be solved analytically. The distribution function obtained here is therefore a semi-analytical result.

Recently Mace et at. studied electron-acoustic solitary waves in a plasma using a pseudopotential approach. To find the finite ion-temperature Sagdeev potential, they used a numerical technique developed by Baboolal, Bharuthram & Hellberg. In this paper we show that the exact pseudopotential can be obtained in this case in an analytical form. The numerical results obtained by Mace et at. are compared with our result, and complete agreement is found. We also discuss the conditions for the existence of solitary-wave solutions, and obtain the soliton solutions in some cases when these conditions are satisfied.

Non-resonant ponderomotive force theory is applied to fluctuating electromagnetic fields in a plasma. Bootstrap-type relations between the radial transport velocity and the toroidal current driven by fluctuations are also discussed in the case of non-zero ponderomotive forces proportional to d/dr. A special case of fluctuating fields as measured in the SHEILA heliac is discussed.

The propagation of wave packets on the surface of an electrically conducting fluid of uniform depth in the presence of a tangential magnetic field is investigated in (2 + 1) dimensions. The evolution of wave envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability analysis reveals the existence of different regions of instability. The effect of the applied magnetic field is not only significant but also different for different regions of stability. ‘Envelope soliton’ and ‘waveguide’ solutions of the amplitude equation are also discussed. The self-focusing phenomenon that arises when the amplitude of the wave becomes infinite in finite time is also examined. It is found that in a certain region of the stability diagram it may be easier to observe this phenomenon in the presence of a magnetic field. The Rayleigh-Taylor problem is also studied and various criteria for the existence of instability are obtained.

Laser radiation propagating through a non-uniform plasma along the direction of the density gradient suffers total reflection at the critical layer. However, when a wiggler magnetic field exists near the critical layer, the laser drives a Langmuir wave. For suitable values of Bw and kw, the power transfer from the laser to the Langmuir wave could be as high as 60%. The Langmuir wave deposits its energy on the electrons via Landau damping. This may be an efficient mechanism of laser absorption when large self-generated magnetic fields exist in the plasma.

A specific type of longitudinal wave instability in a plasma due entirely to an external quasi-static electric field E0 is considered for the cases of ion-acoustic and Langmuir waves. The quasi-static time variation of the field leads to a relatively simple mechanism for the development of instability. For frequency ranges typical of ion-acoustic and Langmuir waves dispersion relations are obtained, with Landau damping and pair Coulomb collisions taken into account in addition to E0. The model integral of Bhatnagar, Gross & Krook is used to describe collisions. Two methods for taking account of the influence of the electric field on development of the instability are compared: that of Pines & Schrieffer and that of Brinca and Dysthe. Expressions are obtained for the growth rates in the framework of linear theory. Numerical simulations of both types of instabilities are performed for specific values of the plasma parameters.

In classical kinetic and transport theory for a fully ionized plasma in a magnetic field, collision integrals from a uniform theory without fields are used. When the magnetic field is so strong that electrons may gyrate during electron—electron and electron—ion interactions, the form of the collision integrals will be modified. Another modification will stem from strong non-uniformities transverse to the magnetic field B. Using collision terms that explicitly incorporate these effects, we derive in particular the temperature relaxation between electrons and ions and the particle transport transverse to the magnetic field. In both cases collisions between gyrating electrons, which move along the magnetic field, and non-gyrating ions, which move in arbitrary directions at a distance transverse to B from the electrons larger than the electron Larmor radius but smaller than the Debye length, give rise to enhancement factors in the corresponding classical expressions of order In (mion/mel).

Modulated electromagnetic plane waves in relativistic collisionless, unmagnetized plasmas are investigated through expansion in a small parameter, corresponding to weak dispersion and weak nonlinearity. The oscillation-centre transformation is applied to construct a Hamiltonian action principle for the slow oscillation-centre variables. A description in terms of the relativistic Vlasov equation for oscillation-centre distribution functions is introduced. A system of coupled field and kinetic eequations is obtained order by order.The final result is a generalized vector nonlineat schrödinger equation, with resonant particle effects included through the coupling to the perturbed Vlasov equations.

Electromagnetic and electrostatic instabilities driven by loss-cone particle distributions have been invoked to explain a variety of plasma phenomena observed in space and in the laboratory. In this paper we analyse how the loss- cone feature (as determined by the loss-cone index or indices) influences the growth of such instabilities in a fully ionized, homogeneous, hot plasma in a uniform magnetic field. Specifically, we consider three loss-cone distributions: a generalized Lorentzian (kappa) loss-cone distribution, the Dory—Guest—Harris distribution and the Ashour-Abdalla-Kennel distribution (involving a subtracted Maxwellian). Our findings are common to all three distributions. We find that, for parallel propagation, electromagnetic instabilities are only affected by the loss-cone indices in terms of their occurrence in the temperature anisotropy. However, for oblique propagation, even including propagation at small angles to the ambient magnetic field, the loss-cone indices do independently affect the growth of instabilities for electromagnetic waves, in contrast to certain claims in the literature. For electrostatic waves such that 1, where kx is the component of the wave vector perpendicular to the ambient magnetic field and pLa is the Larmor radius for particle species <r, we find that the loss-cone indices only enter the dispersion equation via the temperature anisotropy, and so in this case the loss-cone feature and perpendicular effective thermal speed do not independently affect wave growth.

A solution of dissipative nonlinear MHD taking account of the balance between viscous drag, the Lorentz force, resistive diffusion and inertia in a boundary- layer approximation is presented. It is a steady solution corresponding to a jet in a conducting fluid with viscosity. The problem is solved using a self-similar variable. An exact analytical solution is possible. The integrals of motion are obtained and their physical meaning is explained. The behaviour of the solutions is described. The entrainment of the jet is observed in some examples after an initial stage dominated by magnetic fields. These solutions are an extension of Bickley's jet for a case with magnetic field and resistivity.

By determining to first order the growth rate of a small, long-wavelength, perturbation to a Zakharov–Kuznetsov plane soliton moving at an angle α to the magnetic field, it has been found that such solitons are unstable for α α0( ∼ 38 °). To determine the stability for angles greater than α0, one needs the growth rate to higher order. The conventional approach generates a second-order growth rate that is singular at α = α0. We rigorously obtain an expression that is bounded at this point, by developing a method in which exponentially secular terms that arise are regrouped before their subsequent elimination. We then show that these solitons are unstable for all α, although the growth rate is small for α>α and goes to zero as α→½π. The relevant linearized equation is solved numerically, and excellent agreement between analytical and numerical results is obtained.

By means of the standard fluid equations, we consider the nonlinear coupling between a large-amplitude pump wave and the low-frequency modes in a collisional plasma. We derive the general dispersion relation in order to discuss the case where the pump-wave frequency is not much larger than the electron gyrofrequency.

The existence of various types of (fast) magnetoacoustic modes in different frequency regimes in a magnetized dusty plasma consisting of electrons, ions and dust particles is investigated. The analysis is carried out using an effective two-fluid MHD-like model which allows for the non-frozen motion of the component fluids. For frequencies much smaller than the dust particle gyro- frequency, we obtain a magnetoacoustic mode that is a generalization of the usual compressional fast hydromagnetic wave in an electron—ion plasma. In the higher-frequency regimes, we show the existence of two new types of modes called ‘Dust-magnetoacoustic waves’. Both modes are accompanied by compressional magnetic field and plasma number density perturbations, and are the electromagnetic generalizations of the dust-acoustic waves in an unmagnetized dusty plasma with thermal electrons and ions. For a two- component plasma, all three modes degenerate into the same fast magneto- acoustic wave found in the usual electron—ion plasmas. We also obtain another novel type of magneto-acoustic mode called a ‘dust—ion-magneto- acoustic wave’, which is an electromagnetic generalization of the dust—ion- acoustic wave. The dispersion relations as well as the frequency regimes for the existence of the various modes are explicitly obtained. An alternative derivation of the relevant governing equations using an approach similar to that employed in so-called ‘electron magnetohydrodynamics’ (EMHD) is also presented.

A systematic procedure is given for generating analytic approximations to the wave–particle energy transfer in magnetized transit-time interactions. The procedure can be applied to any wave-packet field structure, and yields especially simple results in the physically important limits of (i) small and large Larmor radius and (ii) small and large values of the ratio of the wave frequency to the cyclotron frequency. In many applications, the approximations developed here are the only viable means of calculating the wave—particle energy transfer, because the exact analytic theory and numerical test-particle calculations are too demanding computationally.

We reconsider the transport equation in the solar interior and calculate the effects on the opacity of photon scattering near the Raman resonance. Both spontaneous and stimulated scattering on thermal photons and thermal plasmons are taken into account, and changes in opacity (with respect to previous calculations) are calculated numerically and found to be negligible with respect to relativistic corrections to photon scattering.