Nonlinear structures in the formof coherent tripolar vortices, associated with shear-Alfvén perturbations in the presence of both magnetic and velocity shears, are studied analytically.

A nonlinear equation for electrostatic electron surface waves at the boundary between a cold plasma and a dielectric is derived. Our analysis of this equation shows that the nonlinear disturbances at the plasma–dielectric interface may take the form of periodic travelling waves or standing waves with oscillating amplitudes. While the travelling waves are always periodic in space, the standing waves can be both periodic and localized.

The classical transport coefficients provide an accurate description of transport processes in collision-dominated plasmas. These transport coefficients are used in a cylindrically symmetric, electrically driven, steady-state magnetohydrodynamic (MHD) model with flow and an energy equation to study the effects of transport processes on MHD equilibria. The transport coefficients, which are functions of number density, temperature and magnetic field strength, are computed self-consistently as functions of radius R. The model has plasma-confining solutions characterized by the existence of an inner region of plasma with values of temperature, pressure and current density that are orders of magnitude larger than in the surrounding, outer region of plasma that extends outward to the boundary of the cylinder at R=a. The inner and outer regions are separated by a boundary layer that is an electric-dipole layer in which the relative charge separation is localized, and in which the radial electric field, temperature, pressure and axial current density vary rapidly. By analogy with laboratory fusion plasmas in confinement devices, the plasma in the inner region is confined plasma, and the plasma in the outer region is unconfined plasma. The solutions studied demonstrate that the thermoelectric current density, driven by the temperature gradient, can make the main contribution to the current density, and that the thermoelectric component of the electron heat flux, driven by an effective electric field, can make a large contribution to the total heat flux. These solutions also demonstrate that the electron pressure gradient and Hall terms in Ohm's law can make dominant contributions to the radial electric field. These results indicate that the common practice of neglecting thermoelectric effects and the Hall and electron pressure-gradient terms in Ohm's law is not always justified, and can lead to large errors. The model has three, intrinsic, universal values of β at which qualitative changes in the solutions occur. These values are universal in that they only depend on the ion charge number and the electron-to-ion mass ratio. The first such value of β (about 3.2% for a hydrogen plasma), when crossed, signals a change in sign of the radial gradient of the number density, and must be exceeded in order that a plasma-confining solution exist for a plasma with no flow. The second such value of β (about 10.4% for a hydrogen plasma), when crossed, signals a change in sign of the poloidal current density. Some of the solutions presented exhibit this current reversal. The third such value of β is about 2.67 for a hydrogen plasma. When β is greater than or equal to this value, the thermoelectric, effective electric-field-driven component of the electron heat flux cancels 50% or more of the temperature-gradient-driven ion heat flux. If appropriate boundary conditions are given on the axis R=0 of the cylinder, the equilibrium is uniquely determined. Analytical evidence is presented that, together with earlier work, strongly suggests that if appropriate boundary conditions are enforced at the outer boundary R=a then the equilibrium exhibits a bifurcation into two states, one of which exhibits plasma confinement and carries a larger axial current than the other state, which is close to global thermodynamic equilibrium, and so is not plasma-confining. Exact expressions for the two values of the axial current in the bifurcation are presented. Whether or not a bifurcation can occur is determined by the values of a critical electric field determined by the boundary conditions at R=a, and the constant driving electric field, which is specified. An exact expression for the critical electric field is presented. Although the ranges of the physical quantities computed by the model are a subset of those describing fusion plasmas in tokamaks, the model may be applied to any two-component, electron–ion, collision-dominated plasma for which the ion cyclotron frequency is much larger than the ion–ion Coulomb collision frequency, such as the plasma in magnetic flux tubes in the solar interior, photosphere, lower transition region, and possibly the upper transition region and lower corona.

It is shown that the truncation of the infinite hierarchy of fluid equations obtained as moments of the Vlasov kinetic equation leads to a system of nonlinear equations that describe finite-Larmor-radius effects with good accuracy. Inertial terms in the momentum balance, viscosity and heat-flux evolution equations are crucial for a uniform description of the plasma response with an arbitrary Larmor radius. In the low-frequency ordering, the obtained equations are simplified by an expansion in the parameter 1/B, where B is the equilibrium magnetic field. The results of the second-order [Oscr ](1/B2) and the fourth-order [Oscr ](1/B4) closures are compared. It is shown that the accuracy of the description improves for higher-order closures.

Starting from a more general formalism due to Lamalle [Plasma Phys. Contr. Fusion32, 1409 (1997)], the dielectric response of a tokamak plasma to a radiofrequency (RF) perturbation is evaluated using a simple decorrelation model, assuming the poloidal cross-section of the magnetic surfaces to be circular and retaining leading-order terms in the drift parameter. Toroidicity, poloidal magnetic field and particle trapping are included in the model. Constants of the motion are used as independent variables. A semi-analytical method is adopted to evaluate the bounce spectrum of the dielectric response (needed to solve the wave equation) and the associated RF diffusion operator (required for solving the Fokker–Planck equation). The accent is on a study of this bounce spectrum. In particular, the link between the discrete bounce spectrum and the continuous bounce integral is highlighted. The critical parameter for the global justification of the replacement of the sum on the bounce spectrum by a bounce average is the relative magnitude of the decorrelation and bounce times. That for the local justification is the second derivative of the periodic part of the relative wave–particle phase. Numerical examples are provided to give a qualitative feeling for the justification of this substitution. The relation between the results presented here and those based on Hamiltonian models or on a simplified geometry is discussed.

In the heliosphere large fluctuations of the magnetic field are sometimes observed, especially at shocks (e.g. travelling interplanetary shocks, planetary bow waves, and shocks related to corotating interaction regions). The large fluctuations very often have an amplitude that reaches easily four or five times the magnitude of the quiet magnetic field. Since the plasma mostly contains a non-negligible fraction of heavy ions (e.g. helium ions or cometary water ions), these magnetic field fluctuations are described in terms of three-fluid equations. Here electrons, protons and heavy ions are considered as separate fluids interacting with themselves by electromagnetic forces. The three-fluid equations are treated in such a way that we are searching for one-dimensional stationary waves. Thus the equations are reduced to a fully nonlinear set of ordinary differential equations, which have been evaluated numerically with respect to solitary waves. Subsequently, examples of solitary waves in a electron- proton plasma loaded with 10 % 4He2+ ions are presented. For instance, an enrichment of helium ions is observed within the solitary waves.

A modified Kadomtsev–Petviashvili equation is derived for ion-acoustic waves in a multispecies plasma consisting of non-isothermal electrons. This equation is used to investigate the stability of modified KdV solitons against long-wavelength plane-wave perturbation using the small-k perturbation expansion method of Rowlands and Infeld. It is found that modified KdV solitons are stable.

A molecular plasma generated by a particle beam generally departs strongly from a Maxwellian distribution and exhibits a pronounced depletion of electrons as soon as cold electrons cross the first vibrational barrier. We show that this situation produces screened Coulomb interactions that enlarge the Coulomb cross-section in the neighbourhood of this first vibrational threshold. Including these screened interactions through the Balescu–Lenard operator with all excitation transitions leads to a modification of the distribution at the first vibrational barrier. An application is given to the case of low-pressure nitrogen lasers.

We study the long-time behaviour of light particles, for example an electron swarm in which Coulomb interactions are unimportant, subjected to an external field and elastic collisions with an inert neutral gas. The time evolution of the velocity and position distribution function is described by a linear Boltzmann equation (LBE). The small ratio of electron to neutral masses, ε, makes the energy transfer between them very inefficient. We show that, under suitable scalings, the LBE reduces, in the limit ε→0, to a formally exact equation for the speed (energy) and position distribution of the electrons that contains mixed spatial and speed derivatives. When the system is spatially homogeneous, this equation reduces to and thus justifies, for small-enough ε, the commonly used ‘two-term’ approximation.

We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case, the coupled amplitude equations are derived up to third-order terms. The nonlinear coefficients are singular in the limit in which the linear growth rates vanish together. These singularities are analysed using techniques developed in previous studies of a single unstable wave. In addition to the singularities familiar from the single-mode problem, there are new singularities in coefficients coupling the modes. The new singularities are most severe when the two waves have the same linear phase velocity and satisfy the spatial resonance condition k2=2k1. As a result, the short-wave mode saturates at a dramatically smaller amplitude than that predicted for the weak-growth-rate regime on the basis of single-mode theory. In contrast, the long-wave mode retains the single-mode scaling. If these resonance conditions are not satisfied then both modes retain their single-mode scaling and saturate at comparable amplitudes.

A theoretical investigation of extraordinary polarized surface waves at the second harmonics of ion and electron cyclotron frequencies propagating across an external steady magnetic field is carried out in the case of weak plasma spatial dispersion when the thermal velocities of plasma particles are much less than the phase velocities of the considered waves. These waves are eigenmodes of a planar plasma–vacuum waveguide structure that is situated in a steady magnetic field oriented parallel to the plasma surface. A cold charged-particle beam is assumed to propagate over the plasma interface. Excitation of surface X modes at the second harmonics of electron and ion cyclotron frequencies due to the beam–plasma interaction is studied analytically. The dependence of surface-type X-mode (STXM) growth rates on the considered waveguide structural parameters is also studied.

A perturbation method for the Vlasov–Poisson system is presented. It is self-consistent and entirely based on Lie transformations, which are considered as active transformations, generating the dynamics of the particle distribution function in the space of distribution functions. The main result is a set of three equations that forms a good starting point for a wide variety of problems concerning nonlinear wave propagation. Besides being efficient, the new perturbation method is systematic and therefore also suited for the use of computer algebra.

A recently proposed method to calculate the spectrum of linear, incompressible, unbounded plasma flows is applied to magnetohydrodynamic flows about X points. The method transforms the two-dimensional spectral problem in physical space into a one-dimensional problem in Fourier space. The latter problem is far easier to solve. Application of this method to X-point plasma flows results in two kinds of essential spectra. One kind corresponds to stable perturbations and the other one to perturbations that become overstable whenever the square of the poloidal Alfvén Mach number becomes larger than 1. Apart from these two spectra, no other spectral values were found.

We reply here to a criticism of our paper (Tsytovich et al. 1996) by Iglesias (1997).

In our paper we present a very general formulation of collective effects in bremsstrahlung that is valid for any non-equilibrium non-Maxwellian particle distribution. This result is given in (2.20) early in the paper. The standard treatments of bremsstrahlung found in books like Bekefi (1966) are only for thermal plasmas, where the fluctuation–dissipation theorem is valid. Note that the fluctuation–dissipation theorem cannot be used for non-thermal or non-dipole fields, and in this respect the method we use is more general. Our method is the more complex of the approaches used, but, as stated, it can handle situations that cannot be treated by the standard approach. Our main result is the formula (2.20), which is valid for any non-equilibrium non-Maxwellian particle distribution, and which cannot be found anywhere else in the literature. Furthermore, we find new qualitative effects indicating that the ion–ion bremsstrahlung (which is always neglected in the literature) is not small in the case where the collective effects are taken into account, and is in fact, for certain frequencies, of the order of the electron–electron bremsstrahlung. The other qualitatively new result is that, where collective effects are important, the electron–electron bremsstrahlung is not of the order v2Te/c2, as it is for the case in the absence of collective effects, but of the order ω2pe/ω2 times less – which, for example in the solar interior, where ω2pe/ω2 is of the order of v2Te/c2, is then of the order of v4Te/c4.

The relativistically correct solution of the dispersion relation of linear plasma waves in an isotropic unmagnetized equilibrium electron plasma leads to two new effects unknown from the nonrelativistic dispersion theory. First, the number of damped subluminal modes is limited to a few (mode-limitation effect); secondly, for relativistic plasma temperatures the few individual modes complement each other in the sense that the dispersion relations ωR=ωR(k) continuously match each other (mode-completion effect). The second effect does not occur at nonrelativistic temperatures.