The conservation equations for a suspension composed of an ionized gas and small solid dust particles are formulated and solved numerically. Such flows can be found downstream of strong normal shock waves propagating into dusty gases. The solution indicates that the presence of the dust has a significant effect on the post-shock flow field. Owing to the dust, the relaxation zone will be longer than in the pure plasma case; the equilibrium values for the suspension pressure and density will be higher than in the dust-free case, while the obtained values for the temperature, degree of ionization and velocity will be lower. The numerical solution was executed for shock Mach numbers ranging from 10 to 17. It was found that the thermal relaxation length for the plasma decreases rapidly with increasing shock Mach number, while the thermal relaxation length for the suspension mildly increases with increasing M. The kinematic relaxation length passes through a pronounced maximum at i M = 12·5. Throughout the investigated range of Mach numbers, the kinematic relaxation is longer than the suspension thermal relaxation length.

The conservation equations appropriate to a steady, one-dimensional flow of dusty ionized argon were solved numerically. The specific effect of each of the physical parameters of the dust upon the flow properties in the relaxation zone was studied. It was found that increasing the dust particle mass causes an increase in both the kinematic and thermal relaxation lengths. In addition to these changes, the flow field inside the relaxation zone is also affected. An increase in the dust mass (caused either by an increase in the dust density or its diameter) causes an increase in the plasma velocity, temperature and electron number density and a decrease in its density and pressure. Similar effects are encountered when the specific heat capacity of the dust is changed. An increase in the emissivity of the dust causes an increase in the plasma density and pressure and a decrease in its velocity, temperature and electron number density. Increasing the emissivity of the dust results in a decrease in the relaxation zone length.

The mean electromotive force and ponderomotive force generated by nonlinear random Alfvén waves propagating along the mean magnetic field and linear random Alfvén waves propagating in arbitrary directions in a collisionless plasma are calculated by use of Fourier analysis methods. It is shown that the a-effect can exist in the interaction between two different waves and that the magnetic turbulent diffusivity can be negative depending on the energy spectrum functions of the initial values of the magnetic and velocity perturbations. The results are applied to the substorms in the Earth's magnetosphere.

A magnetically confined two-fluid plasma is considered in which the Ohmic heating of the electrons by a current driven parallel to an applied magnetic field is balanced by bremsstrahlung and equipartition to the ions. It is found that for a steady state the applied electric field must be below a critical value which in absence of bremsstrahlung is given by where the electrical conductivity is and the total pressure is p. Under this condition it is found that there are two /Futions for Te/Ti which satisfy the steady electron energy balance equation in a homogeneous, fully ionized plasma. One of these /Futions always has values above the critical value of Te/Ti (= 132 in absence of bremsstrahlung) for the onset of the electrothermal instability in a fully ionized gas. Inclusion of electron thermal conduction transverse to the magnetic field (with Hall parameter ) yields a wavelength for maximum growth of the instability of about , where ae is the electron Larmor radius. The steady non linear profiles showing current filamentation have been calculated. Runaway electrons and ion-acoustic instabilities can occur in the spatial maximum of the current density and electron temperature. Inclusion of bremsstrahlung loss reduces the value of Te/Ti for the onset of the instability, and at Te = Ti yields a maximum ion temperature obtainable by Ohmic heating in a stable plasma.

Thirteen moments are taken of the collision term in the Boltzmann–Fokker– Planck equation for a multi-species, multi-temperature, hot plasma, following the method first developed by Grad for neutral gases. The collision integrals are evaluated for each colliding species pair. These integrals give, in particular, the rate of exchange of momentum and energy produced by collisions. The set of integrals may be combined with moments of the remaining terms in the Boltzmann equation to give thirteen moment equations for each species of particle. To complete the calculation, extensive use was made of the symbolic computer language REDUCE.

In the first part of this work a higher-order solution of the anharmonic oscillator equation describing the nonlinear rippled equilibrium state of magnetically focused, partially neutralized electron beams is given. Thus, using the method of harmonic balance, we derive a ripple-&litude solution of the form

where ø=ω1t+β0,ω1 being the nonlinear proper frequency and β0 a phase shift depending on the initial conditions. In the second part of the work we carry out a stability analysis of the nonlinear equilibrium state found in the first part with respect to long- and short-wavelength surface space-charge perturbations. In the framework of a local approximation the wave equation for the rippled beam is found to be a Hill type of equation which contains harmonic terms up to cos 3kSz (ks is the wavenumber of the ripple). This equation is solved by a resonant-mode coupling method; coupling of fast-fast, slow-slow and slow-fast waves is considered. The growth rates and band widths for different possible wave couplings are derived and compared.

A kinetic analysis is made of a reacting plasma dominated by three-body recombination and ionization, together with collisional and radiative excitation and de-excitation of atomic states. The plasma includes excited atoms, ions, electrons and photons. The kinetic theory yields rate equations for these species, together with explicit expressions for relevant rate coefficients. In the limit of spatial homogeneity and assuming atom and electron densities are close to equilibrium, an explicit form is obtained for the radiation absorption coefficient per unit length. A criterion is then constructed for population inversion. Application to a helium-like active medium (e.g. Al+11) and hydrogen-like passive medium (e.g. A1+12), at electron temperature of 300 eV, reveals that population inversion ensues at electron densities in excess of 1020 cm−3. Algebraic solution of atomic state rate equations demonstrates that the absorption coefficient grows insensitive to photon-atom interactions with increasing electron density.

Using ideal, one-dimensional MHD equations, numerical and analytic solutions are presented which describe the nonlinear behaviour of an imploding current sheet in a low-fl plasma. Initially the current density is uniformly distributed in asheet of finite thickness, and the Lorentz force tending to pinch the plasma together is unopposed by any fluid pressure force. As the implosion develops the current density in the sheet is concentrated into a thin layer at the centre of the sheet, and both the current density and the current in this layer become infinite in a finite time if β = 0. At the moment this occurs, fast-mode shocks are produced which propagate outward from the centre of the current sheet, and as the shocks move away an infinitely thin current sheet is left behind. Although the solutions are related to electric discharges, they are also closely related to a problem posed by Dungey concerning the evolution of a uniformly distributed current in the vicinity of an X-type magnetic neutral line. The implications of these solutions for Dungey's problemare discussed.

For slowly varying wave trains in a linear system, it is known that a quantity proportional to the square of the amplitude propagates with the group velocity. It is shown here, by considering a specific problem of longitudinal waves in a hot electron-plasma and using an asymptotic analysis, that this result continues to be valid even when weak nonlinearities are introduced into the system provided they produce slowly varying wave trains. The method of analysis fails, however, for weakly nonlinear ion-acoustic waves.

The relativistic dielectric tensor of a magnetized Maxwellian plasma is obtained in a general way, for electron cyclotron waves at arbitrary incident angle. A new expression is provided for the computation of the relativistic (Shkarofsky) dispersion functions.

In the interaction of high-intensity lasers with target plasmas the transport of thermal enelgy from the region in which the radiation is absorbed, to the cold dense plasma in the interior of the target, is an issue of central importance. It is also one of great complexity and as such is still largely unresolved. Ion-acoustic turbulence, self-generated magnetic fields and the inadequacy of classical transport theory have all been widely canvassed by way of explaining the observations which show thermal transport much reduced below what would be expected from conventional arguments.

In this paper the role of ion turbulence as a flux limiter is addressed with particular regard to recent experiments in which target plasmas were irradiated by 1·06 µm neodymium laser light at irradiances of 1015W cm−2 and greater. Saturation levels of the ion-acoustic turbulence driven by a combination of a suprathermal electron current and a heat flux have been calculated on the basis of perturbed orbit theory.

The levels of turbulence are found to be markedly lower than those commonly estimated from simple trapping arguments and too low to explain the thermal flux inhibition observed in the experiments used as a basis for the model.

The interaction of two weakly nonlinear sinusoidal ion-acoustic waves produces mainly a fundamental and a second harmonic diffraction pattern. The former is similar to the double slit pattern well known from physical optics, while it is found that the latter resembles a linear pattern generated by the superposition of three waves. The third wave is formed by mutual nonlinear interaction of the two fundamental waves. The intensity of the second harmonic pattern is modulated by the recurrence effect and it depends also on the angle between the local wave vectors.

It is shown that, under the influence of a monochromatic HF electric field (laser beam), both the electrons and the ions in a high-Z plasma reach a homogeneous and isotropic self-similar state (SSS) in which the distribution functions are of the factorized form: where W±(t) is a scaling velocity, the square of which is proportional to the effective temperature. Whereas the SSS for the electrons was known from previous work, with

it is shown here that the corresponding ion SSS exists and is characterized by a simple Maxwellian, øi ø exp (−v2). The discussion of the thermal velocities W±(t), which are obtained in analytical form, provides a transparent physical insight into the heating mechanism of the plasma by inverse bremsstrahlung absorption.