This paper considers Alfvén waves in a radially stratified medium where all background quantities, namely mass density, magnetic field strength and mean flow velocity, depend only on the distance from the centre, the latter two being assumed to lie in the radial direction. It is shown that the radial dependence of Alfvén waves is the same for two cases: (i) when the velocity and magnetic field perturbations are along parallels, in the one-dimensional case of only radial and time dependence; (ii) in the three-dimensional case with dependence on all three spherical coordinates and time, for velocity and magnetic field perturbations with components along parallels and meridians, represented by the radial components of the vorticity and electric current respectively. Elimination between these equations leads to the convected Alfvén-wave equation in the case of uniform flow, and an equation with an additional term in the case of non-uniform flow with mean flow velocity a linear function of distance. The latter case, namely that of non-uniform flow with flow velocity increasing linearly with distance, is analysed in detail; conservation of mass flux requires the mass density to decay as the inverse cube of the distance. The Alfvén-wave equation has a critical layer where the flow velocity equals the Alfvén speed, leading to three sets of two solutions, namely below, above and across the critical layer. The latter is used to specify the wave behaviour in the vicinity of the critical layer, where local partial transmission occurs. The problem has two dimensionless parameters: the frequency and the initial Alfvén number. It is shown, by plotting the wave fields relative to the critical layer, that these two dimensionless parameters appear in a single combination. This simplifies the plotting of the wave fields for several combinations of physical conditions. It is shown in the Appendix that the formulation of the equations of MHD in the original Elsässer (1956) form, often used in the recent literature, does not apply if the background mass density is non-uniform on the scale of a wavelength. The present theory, based on exact solutions of the Alfvén-wave equation for a inhomogeneous moving medium, is unrestricted as to the relative magnitude of the local wavelength and scale of change of properties of the background medium. The present theory shows that the rate-of-decay of wave amplitude is strongly dependent on wave frequency beyond the critical layer, i.e. the process of change with distance of the spectrum of Alfvén waves in the solar wind starts at the critical layer.

The modified Fokker–Planck collision operator for partially degenerate electrons was derived in an earlier paper [J. Plasma Phys.58, 577 (1997)]. This is now employed to study linear electron transport for a partially degenerate, magnetized plasma. Because polynomial expansions can yield incorrect transport coefficients owing to lack of resolution of the small fraction of low-energy unmagnetized electrons, a numerical discrete-ordinate scheme is employed. The inclusion of electron–electron collisions advances the model beyond that of Lee and More, and in the classical limit agrees with the results of Epperlein and Haines.

A preformed plasma channel of light ion species, with a small percentage of high-Z atoms, can be produced by a laser prepulse. When an intense short laser pulse propagates through the channel, high-Z atoms are stripped of most of their electrons. After the passage of the pulse, recombination of electrons with high-Z ions produces population inversion for the generation of coherent X rays. However, the gain is strongly dependent on the radial coordinate r. A paraxial-ray theory of X-ray amplification in such a situation reveals that gain focusing and refraction guiding play an important role in determining the gain and the spot size of the X-ray laser.

A semi-Lagrangian two-dimensional fully relativistic Vlasov code for multicomputer environments is developed to study trapped-particle dynamics in phase space induced by relativistic modulational and Raman instabilities. Attention is focused on the efficiency properties of the numerical scheme, which allows a very fine description of particle dynamics in phase space. Vlasov simulations show the appearance of coherent vortex structures as a result of the nonlinear saturation mechanism of the relativistic modulational instability. Growth rates are computed and found to be in good agreement with theoretical values obtained from the dispersion relation by Quesnel et al, [Phys. Plasmas4, 3358–3368 (1997)] and Guérin et al. [Phys. Plasmas2, 2807–2814 (1995)]. In the case of coupling between the relativistic modulational instability and two-plasmon decay, stochastic behaviour can be observed due to the competition between different plasmas waves.

A study is made of the stability of ion-acoustic solitons in a magnetized non-thermal plasma with warm ions. A Zakharov–Kuznetsov equation (KdV–ZK, or Korteweg–de Vries equation in three dimensions) is derived. This equation admits solutions representing compressive and rarefactive solitons propagating in any direction oblique to the external magnetic field. When the coefficient of the nonlinear term of this equation vanishes, the nonlinear behaviour of ion acoustic waves is described by a modified KdV–ZK (MKdV–ZK) equation, which is also derived. This equation also has solitary-wave solutions. Finally, the three-dimensional stability of these solitons is investigated by the small-k perturbation expansion method of Rowlands and Infeld.

Transport equations are investigated for a cylindrical plasma in the presence of electrostatic fluctuations. In a weakly turbulent regime, the transport matrices that relate the anomalous particle and heat fluxes and the parallel current to the thermodynamical forces are determined by employing drift-kinetic and gyrokinetic orderings for the electrons and ions. The calculation is based on the kinetic equations for the ensemble-averaged and fluctuating distribution functions. The crucial difference with previous works is the inclusion of an extra term in the drift-kinetic equation for the fluctuating electron distribution function. This extra term, which arises from the ensemble-averaged first-order (in a Larmor radius expansion) electron distribution function, leads to the Ware pinch components of the particle and heat fluxes and a correction to the Ohmic current. Furthermore, Shaing's ansatz, which was introduced in the synthetic theory of anomalous and neoclassical transport, is shown to be connected with this extra term in the context of a turbulent plasma, and the physical meaning and the validity of this ansatz are revealed. In drift-wave turbulence, the transport matrices, expressed in an implicit form by considering the frequency of fluctuations as a parameter, are rewritten in an explicit form by determining its frequency through the dispersion relation. The Onsager symmetry is shown to be broken for this explicit form of anomalous transport matrix.

For a cold plasma that is inhomogeneous (in the direction across an external homogeneous magnetic field), the nonlinear equation describing the spatial structure and temporal behaviour of a non-stationary disturbance in a resonance layer is obtained. The matching conditions for a disturbance through the resonance layer are obtained, and in the linear limit give a well-known linear matching. It is shown that the spatial and temporal behaviour of the resonance disturbance and the evolution of the resonant absorption in terms of nonlinear theory are determined by the ratio of the nonlinear to linear non-stationary spatial scales. The spatial–temporal profile of the disturbance in the resonance layer and the resonant absorption for different values of this ratio are calculated. A nonlinear decrease in the resonant absorption and a stratification of the resonance disturbance are revealed.

We investigate a three-wave decay interaction involving a surface wave in which a bulk electromagnetic plasma wave decays into another bulk electromagnetic plasma wave and a surface polariton. It is shown that a p-polarized light wave transmitted from vacuum into a plasma at a particular angle of incidence can propagate as a bulk electromagnetic plasma wave without attenuation. The nonlinear boundary conditions for the surface wave are formulated in terms of the surface charge and the volume current, taking full account of the rippling of the free boundary. The coupled-mode equations are derived and solved in the parametric approximation to obtain the threshold and the growth rate. We assess the relative strength of the kinematic and the dynamic nonlinearities in the parametric interaction.

A high-power millimetre wave (ω1, k1) propagating through a magnetized plasma at an angle to a density ripple (0, k0) produces density perturbations (ω1, k1, k0). The density perturbations couple with the oscillatory velocity at (ω1, k1) to produce a nonlinear current at (2ω1, 2k1+k0) driving second-harmonic electromagnetic radiation. The efficiency of the process is sensitive to the angle between the density ripple and the millimetre wave.

This paper presents an analysis of the relativistic self-focusing of a rippled Gaussian laser beam in a plasma. Considering the nonlinearity as arising owing to relativistic variation of mass, and following the WKB and paraxial-ray approximations, the phenomenon of self-focusing of rippled laser beams is studied for arbitrary magnitude of nonlinearity. Pandey et al. [Phys. Fluids82, 1221 (1990)] have shown that a small ripple on the axis of the main beam grows very rapidly with distance of propagation as compared with the self-focusing of the main beam. Based on this analogy, we have analysed relativistic self-focusing of rippled beams in plasmas. The relativistic intensities with saturation effects of nonlinearity allow the nonlinear refractive index in the paraxial regime to have a slower radial dependence, and thus the ripple extracts relatively less energy from its neighbourhood.

A synthetic theory of neoclassical and anomalous transport in a weakly turbulent tokamak plasma is presented. The neoclassical effect on the anomalous particle and heat fluxes and the parallel current in the presence of electrostatic fluctuations is investigated using the kinetic equations for the ensemble-averaged and fluctuating distribution functions. It is found in the drift-kinetic and gyro-kinetic orderings for electrons and ions that the Ware pinch components of the anomalous particle and heat fluxes and the parallel current are sensitive to the toroidal effect, although the other components of particle and heat fluxes are little influenced. In the banana regime, these Ware pinch components and the anomalous parallel current are shown to be significantly reduced when the condition [mid ](ω − ωE)/ k∥ve[mid ] < (2ε)1/2 is satisfied, where ω and k∥ are the frequency and the parallel wavenumber of fluctuations, ωE is the drift frequency due to the radial electric field, ve is the thermal velocity for electrons and ε is the inverse aspect ratio. Interpolated formulae that can be used throughout all collisonality regimes are also obtained for the Ware pinch components and the anomalous parallel current.

The evolution equation for a wavepacket travelling on the surface of a conducting fluid of finite depth in 2+1 dimensions in the long-wave approximation is studied in the context of magnetohydrodynamics. The amplitude equation thus obtained is the well-known Kadomtsev–Petviashvili equation with modified coefficients in the presence of a tangential magnetic field. By taking the double limit of this equation, Schrödinger–Poisson type equations are obtained. A nonlinear evolution equation is sought, in order to study Rayleigh–Taylor instability. It is shown that the magnetic field and surface tension have a stabilizing influence on the formation of bubbles arising owing to this instability. By incorporating forcing and damping terms in the Kadomtsev–Petviashvili equation, a condition for the existence of transverse homoclinic orbits giving rise to chaotic motions is obtained by using the Melnikov function method. It is shown that the chaotic motions can be suppressed by applying a suitably strong magnetic field. A study of subharmonic bifurcation leading to surface waves is also undertaken. The tangential magnetic field has a stabilizing influence on such motions.

We demonstrate fast mixing of vortex–current filaments by means of numerical simulations of collision (strong interaction) between two straight filaments. The two filaments mutually approach, collide, and are rapidly tangled with each other. In fact, the instantaneous Lyapunov exponent shows that the dynamics becomes chaotic. Then there appear many small regions where the two filaments overlap. We consider each overlapping region to be equivalent to the traditional resistive diffusion region. We assume that the overall ‘reconnection rate’ of the two filaments is proportional to the product of the traditional (non-chaotic) resistive reconnection rate and the normalized overlapping volume. The overlapping volume rapidly increases on the time scale of ideal MHD. When many overlapping regions are produced, the overall reconnection probability, i.e. the sum of the probabilities of reconnection in every overlapping region, should be increased compared with that of the single overlapping region. Thus the overall reconnection rate becomes sufficiently large, although the basic reconnection process in each overlapping region is resistive and slow. We conclude that the fast mixing due to chaos may enhance the conventional resistive reconnection. We call this process ‘chaotic reconnection’.

The equations for the ideal, internal m = n = 1 kink mode in a toroidal plasma are derived from a direct, large-aspect-ratio perturbation expansion of the compressible magnetohydrodynamic (MHD) equations. The derivation complements earlier investigations of the internal kink mode based either on the energy principle or on direct expansions of the incompressible MHD equations. It is shown that five poloidal harmonics (m = −1, 0, 1, 2 and 3) have to be retained in a direct expansion of the compressible MHD equations, as compared with the three poloidal harmonics m = 0, 1 and 2 needed in the case of an incompressible plasma, or when working from the energy principle. Furthermore, the sound velocity is found to replace the Alfvén velocity in the generalized Pfirsch–Schlüter factor (the kinetic energy enhancement factor in a toroidal plasma) previously derived for an incompressible plasma. Taking this factor fully into account in the calculation of the growth rate of the m = n = 1 mode, it is shown that, while the Bussac result γB is recovered near marginal stability, growth rates of the order of 30% larger than γB are obtained when γB becomes of the order of the sound frequency.

The parametric interaction of an upper-hybrid pump wave with kinetic Alfvén and electromagnetic waves that propagate in parallel and perpendicular directions to the ambient magnetic field is investigated on the basis of two-fluid magnetohydrodynamics. A nonlinear dispersion relation describing three-wave interaction and instability growth rates are found. The theoretical results are used for the interpretation of satellite observations in the magnetospheric plasma. It is shown that as a result of the decay of an upper-hybrid wave, electromagnetic waves propagating in both parallel and perpendicular directions to the ambient magnetic field are generated. The instability growth rate is much higher in the case of left-polarized electromagnetic wave generation than in the case of ordinary electromagnetic wave generation. The nonlinear parametric processes studied here could also take place during powerful bursts on the Sun, and in the magnetosphere of Jupiter.

Emission of energetic ions from solid targets irradiated by intense ultrashort laser pulses is studied in the framework of a one-dimensional self-consistent hydrodynamical model. The computed ion spectra reproduce well the basic parameters of published experimental results. Optimum conditions are found for the generation of MeV ions by picosecond laser pulses.

In this work, we analyse the sequence of bifurcated equilibria in two-dimensional reduced magnetohydrodynamics. Diamagnetic effects are studied under the assumption of a constant equilibrium pressure gradient, not altered by the formation of a magnetic island. The formation of an island when the symmetric equilibrium becomes unstable is studied as a function of the tearing-mode stability parameter Δ′ and of the diamagnetic frequency, by employing fixed-point numerical technique and an initial-value code. At larger values of Δ′, a tangent bifurcation takes place, above which no small-island solutions exist. This bifurcation persists up to fairly large values of the diamagnetic frequency (of the order of one-tenth of the Alfvén frequency). The implications of this phenomenology for the intermittent MHD dynamics observed in tokamaks is discussed.

The Zakharov-Kuznetsov equation governs the behaviour of weakly non-linear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. We consider the more realistic situation in which the electrons are non-isothermal. With an appropriate modified form of the electron number density proposed by Schamel, we show that the reductive perturbation procedure leads to a modified Zakharov–Kuznetsov (mZK) equation. The stability of plane-periodic and solitary travelling-wave solutions of the mZK equation to two-dimensional long-wavelength perturbations is investigated using the method of Rowlands and Infeld.

We present a detailed ab initio calculation of wave modes in a strongly magnetized pair-plasma slab (which we shall refer to as a beam) embedded in a pair plasma of different number density. We consider a planar geometry and treat the case of small beam thickness, for which approximate analytical results can be obtained and compared with numerical calculations. We briefly compare our results with those found by others in the case of cylindrical geometry as applied in the context of radio pulsars.

Beam instabilities in the strongly magnetized electron–positron plasma of a pulsar magnetosphere are considered. We analyse the resonance conditions and estimate the growth rates of the Cherenkov and cyclotron instabilities of the ordinary (O), extraordinary (X) and Alfvén modes in two limiting regimes: kinetic and hydrodynamic. The importance of the different instabilities as a source of coherent pulsar radiation generation is then estimated, taking into account the angular dependence of the growth rates and the limitations on the length of the coherent wave–particle interaction imposed by the curvature of the magnetic field lines. We conclude that in the pulsar magnetosphere, Cherenkov-type instabilities occur in the hydrodynamic regime, while cyclotron-type instabilities occur in the kinetic regime. We argue that electromagnetic cyclotron-type instabilities on the X, O and probably Alfvén waves are more likely to develop in the pulsar magnetosphere.