We present a covariant theory of photon acceleration in time-varying plasmas. This is a ray-tracing model for frequency upshift of waves interacting with relativistic plasma perturbations, such as ionization fronts and plasma wakefields. This theory explores the formal analogy between a photon in a plasma and a relativistic particle with a finite rest mass. The covariant ray-tracing theory is applied to the case of photon acceleration by a modulated wakefield. Threshold criteria for transition to chaos are derived.

Stationary flows of an ideal plasma with translational symmetry along the (vertical) z axis are considered, and it is demonstrated how they can be described in the intrinsic (natural) coordinates (ξ, η, &), where ξ is a label of flux and stream surfaces, η is the total pressure and ϑ is the angle between the horizontal magnetic (and velocity) field and the x axis. Three scalar nonlinear equilibrium equations of mixed elliptic–hyperbolic type for ϑ(ξ, η), ξ(η, ϑ) and η(ϑ, ξ) respectively are derived. The equilibrium equation for ϑ(ξ, η) is especially useful, and has considerable advantages compared with the coupled system of algebraic–differential equations that are conventionally used for studying plasma flows. In particular, for this equation the location of the regions of ellipticity and hyperbolicity can be determined a priori. Relations between the equilibrium equation for ϑ(ξ, η) and the nonlinear hodograph equation for ξ(η, ϑ) are elucidated. Symmetry properties of the intrinsic equilibrium equations are discussed in detail and their self-similar solutions are described. In particular, magnetohydrodynamic counterparts of several classical flows of an ideal fluid (the Prandtl–Meyer flows around a corner, the spiral flows and the Ringleb flows around a plate, etc.) are found. Stationary flows described in this paper can be used for studying both astrophysical and thermonuclear plasmas.

A four-dimensional systematic mathematical approach for investigating propagation and coupling of wave modes in a slowly varying (in all space directions and time) anisotropic, absorbing plasma is represented. The formalism is especially useful for energy considerations of the waves. It is applicable to general cases of mode couplings in plasmas with general geometries of space–time and magnetic field configurations. A simple example of how this formalism can be applied to practical cases is given.

The nonlinear dynamics of a finite-amplitude Alfvén wave in a dispersive modulational regime is analysed. Use is made of a conservative model to show that turbulence may arise via deterministic chaos. The behaviour of the system is studied as one varies the initial amplitude of the pump Alfvén wave, the dispersion parameter and the plasma parameter β.

A large-amplitude upper-hybrid wave in a plasma cylinder is susceptible to parametric decay into a lower-hybrid wave and an upper-hybrid wave. The perpendicular and parallel motions of electrons play equally important roles in the nonlinear interaction. The coupled-mode equations are solved using a perturbation technique. The growth rate of the instability is less sensitive to the radial mode number of the sideband. However, for higher-order radial modes it falls off as the overlap of the interacting wave functions decreases.

We consider the spectrum and stability of a compressible, rigidly rotating plasma column with constant magnetic pitch. It is found that when the pressure on axis is zero, a continuous spectrum arises, which may become unstable. When the pressure on axis is finite or a conducting core is included, the spectrum is discrete, but may still be unstable. The instability is due to the poloidal magnetic field and/or the rotation of the cylinder in combination with the density profile. It is found numerically that the pressure stabilizes both types of instabilities.

A stability criterion for axisymmetric modes of ideal MHD equilibria without wall stabilization is derived for linear profiles with vanishing current density at the edge. Using perturbation theory, the critical half-axis ratio of the elliptical cross-section is computed for finite aspect ratio.

The two-dimensional spatial and temporal evolution of a plasma surrounding an electrode whose potential is suddenly decreased is experimentally investigated. The electrode contains a localized convex or a localized concave perturbation. The quasineutral plasma consists of positive ions and various proportions of negative ions and electrons. The results are compared and contrasted with those that are obtained numerically using a particle-in-cell (PIC) simulation and those that had previously been obtained using a fluid-model code.

Transverse focusing or filamentation of weakly nonlinear Alfvén waves propagating in a dispersive medium is studied using an amplitude-equation formalism. Special attention is devoted to the small-β regime, where kinetic effects are weak and Alfvén-wave trains are unstable to convective filamentation. It is shown that, according to their initial duration, focusing wave packets can collapse in a finite distance or, conversely, the focusing can be arrested by the development of magnetosonic waves, which in both cases may lead to the formation of sharp acoustic fronts. This effect, which dominates the usual longitudinal steepening, provides an efficient mechanism to heat the plasma without requiring large-amplitude waves. It can significantly contribute to the acceleration of the solar wind.

This paper gives a complete kinetic theory of atomic discharges whatever their parameters. Very high-frequency discharges and high-pressure continuous discharges were studied in an earlier paper by the same authors [J. Plasma Phys. 54, 309 (1995)]; in the present paper we study low-pressure continuous discharges or high-frequency discharges whose parameters satisfy different conditions and therefore cannot be described by the earlier model. Analytical results are applied to a high-frequency argon discharge and to a low-pressure continuous argon discharge. The results are in good agreement with the numerical results of Ferreira and co-workers.

The radially symmetric self-similar expansion of a dusty plasma is investigated in cylindrical and spherical geometries. The electrons and ions are assumed to be in Boltzmann equilibria, while the dynamics of the dust particles is governed by the fluid equations. The effects of finite dust pressure as well as dust-charge variation are included.

The velocity distribution functions of newly born (t=0) charged fusion products (protons in DD and alpha particles in DT plasmas) of tokamak discharges can be approximated by a monoenergetic ring distribution with a finite v∥ such that v⊥≈v∥≈Vj, where ½Mj V2j=Ej, the directed birth energy of the charged fusion-product species j of mass Mj. As the time t progresses, these distribution functions will evolve into a Gaussian in velocity (i.e. a drifting Maxwellian type), with thermal spreads given by the perpendicular and parallel temperatures T⊥j(t)=T∥j(t), with Tj(t) increasing as t increases and finally reaching an isotropic saturation value of

formula here

Here Td is the temperature of the background deuterium plasma ions, M is the mass of a triton or a neutron for j=protons and alpha particles respectively, and τj≈¼τsj is the thermalization time of the fusion product species j in the background deuterium plasma, with τsj the slowing-down time. For times t of the order of τj, the distributions can be approximated by a Gaussian in the total energy (i.e. a Brysk type). Then, for times t[ges ]τsj, the velocity distributions of the fusion products will relax towards their appropriate slowing-down distributions. Here we shall examine the radiative stability of all these (i.e. a monoenergetic ring, a Gaussian in velocity, a Gaussian in energy, and the slowing-down) distributions.

The weakly nonlinear dynamics of fast magnetosonic waves ducted by a region of density enhancement in a cold plasma is considered. A self-consistent 2D quasi-hyperbolic equation with quadratic and cubic nonlinearities is derived for perturbations of the transverse component of the plasma velocity. For a wave package with a narrow spectrum, the governing equation is reduced to the nonlinear Schrödinger equation, whose structure is independent of the detailed density profile provided that it has a maximum (to be a potential well for the waves). The derived equation allows us to take into account the effect of the shape and steepness of the density profile on the wave dynamics.

A spectral representation for the isotropic part of the Coulomb collisional operator is given. The particle distribution function is expanded in a series of generalized Laguerre polynomials, and the Coulomb collisional operator is expressed in terms of the spectral amplitudes. When the spectral representation is applied to the Fokker–Planck equation, a system of coupled ordinary differential equations for the spectral amplitudes is obtained. The spectral coefficients related to the Coulomb operator are defined through recurrence relations, which we reduce to simplified form. This makes possible accurate and efficient analytical and numerical evaluations of the interaction matrices. The results presented can be used in analytical investigations of the properties of the Coulomb collisional operator as well as in numerical calculations for plasmas far from thermal equilibrium. The method can also be generalized to include angular dependencies for non-isotropic particle distributions.

Using a kinetic model for low-frequency dust acoustic waves (DAW) in a dusty plasma, we have examined the effects of a dust-size distribution on their propagation and damping. Both Landau damping and damping due to dust-charge variation are included. We consider Gaussian and power-law dust-size distributions. In accordance with earlier results of Melandsø et al., we find that the dust Landau damping dominates at short wavelengths. At wavelengths longer than the Debye length λD0, the dust-charge variation is generally dominant. It is always dominant for the power-law size distributions that we have studied. We also find that if the upper and lower size limits of the dust are chosen so that the average dust size remains constant, regardless of the power-law exponent γ, the wave properties are practically identical to those of a monosize distribution of the average dust size. For a Gaussian dust-size distribution, Landau damping may be the dominant damping mechanism if the dust plasma is tenuous (P[Lt ]1) and the width of the distribution is large.

Assuming the averaged (background) electron distribution in a crossed-field device, such as a magnetron or crossed-field amplifier, to be slowly varying between the cathode and the anode, we develop a WKB approximation for the cold-fluid plasma equations of a planar magnetron. In this approximation, we can give general expressions for the solution of linearized, high-frequency oscillations in such a device in terms of two integrals. Assuming also that the high-frequency wave in the slow-wave structure drives the response in the electron plasma, we are then able to show that the current drawn by a crossed-field device will be proportional to the power propagating in the slow-wave structure. Thus the device will operate as a linear amplifier. We also show, in the same approximation, that the averaged electron sheath that forms when the device is operating is independent of the current being drawn. Thus the current will not be limited by the sheath, but only by the ability of the cathode to emit electrons. In the process, we also obtain expressions for the linear growth rate and the value of the quasilinear diffusion coefficient at the diocotron resonance, in terms of parameters of the background electron sheath.

Expressions for the linear response tensor are derived using a covariant forward-scattering method for unmagnetized relativistic thermal distributions restricted to one-dimensional (strictly parallel) and two-dimensional (strictly perpendicular) motions. The freedom to make Lorentz transformations is used to generalize the strictly perpendicular distribution to a counterpart of the nonrelativistic Dory–Guest–Harris (DGH) distribution.

It is shown that the recently published work of Pandey and Dwivedi [J. Plasma Phys. 55, 395 (1996)] dealing with dust-acoustic waves in a self-gravitating unmagnetized dusty plasma is erroneous. This is demonstrated on the basis of a dispersion relation in which gravitational and electrostatic forces are kept on an equal footing. Furthermore, a general linear dispersion relation for the dust-acoustic and dust-ion acoustic waves in self-gravitating dusty plasmas is obtained, taking into account the dust-charge perturbations. Specific results for limiting cases are discussed.

Some aspects of plasma dynamics with electron-inertia effects are considered. The behaviour of (i) one-dimensional steady current sheets, (ii) two-dimensional steady reconnection models, (iii) one-dimensional current-sheet evolution, (iv) linear tearing-mode evolution and (v) nonlinear magnetic-island evolution in this regime is investigated. Stability of the two-dimensional plasma in this regime is then discussed, and necessary conditions for linear stability in the Liapunov sense for steady states are then given.

The present study consists of two parts. Here in Part 1, a model set of conservationlaws exactly preserving the MHD hyperbolic singularities is investigated to develop the general theory of the nonlinear evolution of MHD shock waves. Great emphasis is placed on shock admissibility conditions. By developing the viscosity admissibility condition, it is shown that the intermediate shocks are necessary to ensure that the planar Riemann problem is well-posed. In contrast, it turns out that the evolutionary condition is inappropriate for determining physically relevant MHD shocks. In the general non-planar case, by studying canonical cases, we show that the solution of the Riemann problem is not necessarily unique – in particular, that it depends not only on reference states but also on the associated internal structure. Finally, the stability of intermediate shocks is discussed, and a theory of their nonlinear evolution is proposed. In Part 2, the theory of nonlinear waves developed for the model is applied to the MHD problem. It is shown that the topology of the MHD Hugoniot and wave curves is identical to that of the model problem.