The stochastic representation of fluid equations describing a plasma transport in the peripheral region is discussed, which is based on the theorem of Yasue (1983 J. Funct. Anal.51, 133). The scheme solving the stochastic equations is given by employing a path integral method.

The stability of the neutral current sheet is analyzed in the frame of Hall dynamics. The problem is treated analytically and results are verified by numerical processing. A new version of tearing instability is found and described. It scales more favorably with the Lundquist number and has smaller wavelengths. Combined Hall magnetohydrodynamic analysis shows that Hall effects dominate the diffusion layer and growth rate of the instability in a relatively large range of sheet widths. The effect of finite beta on instability is described.

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.

The electron temperature gradient driven electromagnetic-drift waves and associated instabilities and electron thermal diffusion in a magnetized plasma have been investigated by employing kinetic ion and fluid electron responses. A new dispersion relation has been derived analytically and studied numerically. Two broad classes of unstable fluctuations, namely ‘low’ and ‘high’ frequency unstable modes, have been identified and studied in detail. The instabilities of these modes and associated electron thermal diffusion coefficients are also estimated. The results of our theoretical model can be considered as a plausible explanation for experimentally observed fluctuations in Burke et al. (2000a Phys. Plasmas7, 1397).

This paper gives a first application of the reduced-phase-space Lagrangian for kinetic theories obtained in a sister paper in this issue by means of Kruskal's averaging coordinates. The approximations made within Kruskal's formalism are of first order in the smallness parameter $\epsilon$, given by the ratio of the gyroperiod to the macroscopic time scale, which is the same as the ratio of the gyroradius to the macroscopic scale length in the drift-kinetic case, or as the ratio of the amplitudes of the fluctuations to the background fields in the gyrokinetic case. This paper presents methods and results concerning local conservation laws for the density of gyrocentres and the charge, energy, momentum and angular momentum. A very important feature of our treatment is that throughout the theory is gauge invariant. The methods consist of a modified Noether formalism with gauge-invariant shift variations which in a very straightforward way lead to, in particular, the symmetric energy–momentum tensor instead of the canonical tensor. The shift variations are defined both within the reduced phase space, which does not contain the gyroangle, and also for gyroangle-dependent quantities which subsequently have to be averaged. A clear definition of the Lagrange density needed for the derivation of the local conservation laws for energy, momentum and angular momentum is given. The discovery of combinations of terms such as the polarization and the magnetization allows the conservation laws to be cast in a very clear form affording insight into their structure.

The modified Kadomtsev–Petviashvili (KP) (1970) equation, describing the long-time evolution of weakly nonlinear and weakly dispersive ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons, admits soliton solutions having a sech4 profile. The higher-order stability analysis of this soliton is made using the method developed by Allen and Rowlands [J. Plasma Phys.50, 413 (1993); 53, 63 (1995)]. Though there is stability at the order $k$, there may arise instability at the order $k^{2}$, where $k$ is the wave number of a long-wavelength plane-wave perturbation. This instability occurs when the dimensionless width of the soliton exceeds a critical value.

We have constructed an analytical model for an axisymmetric magnetosphere with azimuthal plasma flow. A dipole-like model of the geomagnetic field was used. It is shown that within the framework of this model of the magnetosphere, plasma at each magnetic shell moves with a constant angular velocity. The possibility of formation of a twin plasmapause is demonstrated. Abrupt changes in plasma density are directed across magnetic shells separating regions with strongly differing plasma velocities, as well as on the cylindrical surface whose radius coincides with the equatorial radius of the plasmapause.

Low-frequency instabilities excited by energetic oxygen ions are investigated. The model consists of Maxwellian distributions for electrons and protons and Dory–Guest–Harris loss-cone distribution for oxygen ions. The electrons and protons are treated as magnetized and oxygen ions as unmagnetized. The response of the electrons is fully electromagnetic and that of the protons and oxygen ions is electrostatic. A possible application of the investigation to space plasmas is pointed out.

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.

Electron acceleration by the ponderomotive force of a laser pulse with duration less than the plasma wavelength in inhomogeneous underdense plasmas is studied by two-dimensional relativistic parallel particle-in-cell (PIC) code. Particular attention is paid to the mechanism of electron acceleration associated with the increasing group velocity of the laser pulse. In an underdense plasma layer with linearly descending density profile, the accelerated electrons move together with the laser pulse which propagates with increasing group velocity. In an inhomogeneous pre-plasma with linearly ramping density profile, as the incident laser propagates up the density gradient with decreasing group velocity, ponderomotive acceleration is reduced compared with the uniform pre-plasma. As the reflected laser propagates down the density gradient with increasing group velocity, the ponderomotive acceleration by the reflected laser is more effective due to increasing group velocity of the reflected light and the return currents induced by the incident laser light. Relativistic electrons with multi-tens-MeV energies are generated.

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.

Starting from the full set of governing equations including the weak relativistic effect, three coupled nonlinear equations with higher order nonlinear and dispersive terms are derived, which describe the nonlinear evolution of a three-dimensional electromagnetic wave packet propagating in a plasma. Two particular cases are considered, where the space dependence of the dependent variables is either on the space coordinate along the direction of propagation of the wave or on that along an arbitrary fixed direction. In both cases the three coupled equations reduce to a single equation. This single equation is used to study the modulational instability of a uniform electromagnetic wave train. It is found that due to the inclusion of the weak relativistic effect there is always modulational instability, and a higher order nonlinear term in the evolution equation has a stabilizing influence.