Previous computations concerning the allowed magnetohydrodynamic steady states of a visco-resistive magnetofluid in a toroid are extended. The current is supported by an externally imposed toroidal electric field, and a scalar resistivity and viscosity are assumed. Emphasis is on the character of the necessary velocity fields (mass flows) that toroidal geometry demands. Non-ideal boundary conditions are imposed at the toroidal boundary. One of the more interesting results to emerge is the sensitive dependence of the flow pattern on the shape of the toroidal cross-section boundary: the dipolar poloidal flow that had appeared for cross sections that were symmetric about the midplane is seen to deform continuously into a monopolar pattern for a ‘D-shaped’ cross section as the viscous Lundquist number $M$ is increased. A net toroidal mass flow also develops. A boundary layer whose properties scale with fractional powers of $M$ is also studied. The interior of the magnetofluid is approximately force-free, with current densities and magnetic fields that are nearly parallel for JET-like parameters. Steep velocity derivatives and a steep pressure drop in this boundary layer become steeper with increasing $M$ (decreasing viscosity). The magnetic quantities do not reflect the rapid velocity and vorticity variations in the boundary layer. The maximum velocities, in the region where the viscosity is large enough for the numerics to work, are of the order of a few hundreds of centimetres per second. Measurements of velocity fields confined to the boundary layer would misrepresent the interior plasma conditions. Uncertainties in the magnetized plasma viscosity remain as an obstacle to unambiguous tests of the results in the case of real plasmas.

The parametric instability of parallel-propagating circularly polarized Alfvén waves (pump waves) is revisited. The stability of these waves is determined by the linearized system of magnetohydrodynamic equations with periodic coefficients. The variable substitution that reduces this system of equations to a system with constant coefficients is suggested. The system with constant coefficients is used to derive the dispersion equation that was previously derived by many authors with the use of different approaches. The dependences of general stability properties on the dimensionless amplitude of the pump wave $a$ and the ratio of the sound and Alfvén speed $b$ are studied analytically. It is shown that, for any $a$ and $b$, there are such quantities $k_1$ and $k_2$ that a perturbation with the dimensionless wavenumber $k$ is unstable if $k_1^2<k^2<k_2^2$, and stable otherwise. It is proved that, for any fixed $b$, $k_2$ is a monotonically growing function of $a$. The dependence of $k_1$ on $a$ is different for different values of $b$. When $b^2<1/3$, $k_1$ is a monotonically decreasing function of $a$. When $1/3<b^2<1$, $k_1$ monotonically decreases when $a$ varies from zero to $a_c(b)$, takes its minimum value at $a = a_c$ and then monotonically increases when $a$ increases from $a_c$ to infinity. When $b > 1$, $k_1$ is a monotonically increasing function of $a$. For any $b$, $k_1$ tends to a limiting value approximately equal to 1.18 as $a \to \infty$.

The linear stability of tearing modes in a cylindrical plasma subject to a sub-Alfvénic equilibrium shear flow along the equilibrium magnetic field is considered. The equations in the resistive boundary layer at the rational surface are solved numerically using a Fourier transform combined with a finite-element approach. The behaviour of the growth rate as a function of the flow and the various parameters (including a perpendicular fluid viscosity) is obtained. Marginal stability curves showing the dependence of the familiar matching parameter $\Delta'$ with flow and shear are also given.

The authors have identified three regimes of propagation of circularly polarized laser beams in plasmas, taking into account the relativistic laser plasma interaction. An appropriate expression for the nonlinear dielectric constant has been used in the analysis of laser-beam propagation in the paraxial approximation. Three regimes of propagation in a homogeneous plasma have been identified, viz.

I. In this regime the beam keeps on diverging.

II. In this regime the beam travels in a guided oscillatory and diverging mode, with the width lying between the original value and a maximum value.

III. In this regime the beam becomes self-focused, with the width lying between the original value and a minimum value.

For a given value of $\omega _{\rm p}/\omega $ the regimes are characterized by dimensionless power and dimensional beam width. The variation of beam width with distance of propagation has also been obtained for typical values of parameters in the three regimes.

The variation of beam-width parameter with distance of propagation has also been studied for inhomogeneous plasma and penetration in overdense plasmas is indicated.

The destabilization of fast magnetoacoustic waves (FMWs) and Alfvén waves (AWs) in plasmas with energetic ions having strongly anisotropic velocity distribution is considered. It is shown that when the ratio of the energetic ion velocity to the Alfvén velocity is large enough, the growth rate of the low-frequency FMW instability has sharp maxima at certain angles of the wave propagation. On the other hand, low-frequency FMWs are always stable, whereas the AWs and high-frequency FMWs can be unstable when the waves propagate along the magnetic field. The developed theory is applied to a plasma of the flashing loops of the Solar Corona. It is found that the presence of a very small amount of the energetic ions can lead to instabilities with the growth rate, which considerably exceeds the inverse characteristic collisional times. It is concluded that the frequency spectrum of the destabilized waves can be rather wide, which may lead to the heating of the bulk plasma ions on the sub-harmonics of the ion gyrofrequency due to the mechanism suggested by Chen et al.

The emission coefficient due to classical electron–ion bremsstrahlung is calculated for a non-ideal plasma with an effective interaction. An approach due to Gould is used to obtain the emission coefficient for bremsstrahlung. It is shown that this result can also be derived from an approximation to the force–force correlation function assuming no correlations among particles. The trajectory for electrons in the effective potential is determined by the numerical solution of Newton's equation. Comparison is made with molecular dynamics results for the dynamical collision frequency.

The energy–momentum tensor is usually obtained by symmetrizing the canonical tensor, which is sometimes difficult. The fact that the energy–momentum tensor must always be gauge invariant, and insight gained by investigating the Maxwell kinetic equations, lead one to conclude that this tensor should be readily obtainable for a certain class of Lagrange densities. The appropriate method to achieve this consists in performing gauge-invariant variations within the framework of Noether's theory. These variations are equivalent to shifts in space and time, and are considered here instead of the usual shift variations, which are not gauge invariant. These features indicate the existence of a certain underlying structure which is made evident by the proposed method. The Lagrange densities of the class in question are characterized by having a gauge-invariant contribution additional to the Maxwell part. For vanishing potentials, such Lagrange densities lead directly to a symmetric canonical tensor; this implies that there are only scalar fields. Maxwell's equations, being the basic part of such theories, are treated first. Then, the coupled system of electromagnetic fields and the usual scalar fields describing charged matter is considered. Finally, a different kind of scalar field which occurs in a structural non-standard form in collisionless phase-space theories (Vlasov or collisionless Boltzmann-like equations) is treated.

The results of magnetohydrodynamic (MHD) plane shock waves with infinite electrical conductivity are generalized for a plasma with a finite conductivity. We derive the adiabatic curves that describe the evolution of the shocked gas as well as the change in the entropy density. For a parallel shock (i.e. in which the magnetic field is parallel to the normal to the shock front) we find an expression for the shock thickness which is a function of the ambient magnetic field and of the finite electrical conductivity of the plasma. We give numerical estimates of the physical parameters for which the shock thickness is of the order of, or greater than, the mean free path of the plasma particles in a strongly magnetized plasma.

Recent experimental and theoretical research efforts have focused on the use of plasma to optimize and control solid propellant ignition and combustion processes in an energetic fluid bed. However, prediction of electrothermal plasmas in terms of temperature, velocity and density distributions have been difficult. We present here a two-phase flow model for flame-spreading and spatial variation in solid propellant ignition and combustion processes. An integral-numerical method is used to describe the plasma jet penetration for the early part of the combustion process. A mixing length model with an electrical enhancement factor of the burning rate is used for the major combustion cycle. The model plasma jet results agree with the gross features of those determined experimentally.

The nonlinear propagation of electrostatic solitary structures in unmagnetized multispecies plasmas is studied in the wave frame, where they are stationary, via the recently developed McKenzie approach as an alternative to the more usual Sagdeev pseudo-potential method. This way of looking at the problem brings out the gas-dynamic aspects, which then allow a straightforward characterization of the solitary wave possibilities in terms of the species' own sonic points and of the global charge neutral points. A qualitative discussion of ion-, dust- and electron-acoustic solitary waves is given in terms of these concepts and the results are contrasted with those obtained by other methods. Ion-acoustic solitons can be shown to always be compressive, without invoking simplifying assumptions such as cold ions or Boltzmann electrons. Beam-plasmas can also be studied, as in the electron-acoustic solitary wave model for the spiky structures of the broadband electrostatic noise observed in the auroral regions of the Earth's magnetosphere. Such solitons always show a potential dip.