The spatial structure of the magnetohydrodynamic shear Alfvén and cusp continuum modes in axisymmetric toroidal geometry is analyzed for an incompressible plasma. The normal component $\xi_{\psi}$ of the plasma displacement is found to have an oscillatory type of singularity, $\xi_{\psi} \sim (\psi - \psi_0)^{\delta} \sim \sin(|\delta| \ln|\psi-\psi_0| + \mbox{const})$, or, for example, in the case of up/down symmetry, a purely logarithmic behavior. This result was also obtained in the more general case of a compressible plasma (Salat, A. and Tataronis, J. A. 1999 Phys. Plasmas6, 3207). However, in that work the incompressible limit could not be taken because the continuum equations were written in terms of a variable that becomes ill-defined in the limit. The present ab initio derivation shows that, in general, the incompressible limit in the previous work, $\gamma \rightarrow\infty$, where $\gamma$ is the ratio of the specific heats, does give the correct spatial dependence. Furthermore, we prove that it is possible to recover the oscillatory type of singularity for the cylindrical screw pinch from the logarithmic singularity of an up/down symmetric torus.

Two plasma channels, corresponding to a slow capillary discharge and a fast capillary discharge plasma, are investigated numerically. A long-lifetime parabolic plasma channel is formed in the slow capillary discharge channel. Its radial density profile is determined by the energy balance between Ohmic heating and thermal conduction, together with force balance. The profile and the on-axis density value vary only weakly with the peak value of the slow discharge current (300–600 A). A rather dynamic plasma channel is formed under the compression by a magnetic piston in the fast capillary discharge channel. In a narrow time window of the order of nanoseconds a suitable hollow relatively low density channel is reached, followed by a shock-dominated rebound phase. The on-axis density minimum features of these two channels make both of them suitable guiding channels for the laser wakefield accelerators. In particular, a low-density channel ($n_{\rm e}\sim 5\times 10^{16}~{\rm cm}^{-3}$) formed in the fast capillary discharge is in favor of controlled beam injection, but requires precise timing, while the slow capillary discharge is in essence steady. We discuss possible strategies for using them in a segmented approach.

In the present paper the long-term behavior of the nonlinear dynamical evolution of modulational instability is investigated by using a simplified model for one-dimensional Zakharov equations, which couples the electrostatic electron plasma wave and ion-acoustic wave propagation. The manuscript details on the occurrence of fixed points and fixed-point attractors for a suitable value of the wavenumber of perturbation through associated bifurcations, both for the adiabatic (nonlinear Schrödinger equation) and non-adiabatic cases for Zakharov equations. It is shown that these evolutions are quite sensitive to initial conditions, Fermi–Pasta–Ulam recurrence is broken up and a chaotic state develops for the non-adiabatic case. Regular patterns with a periodic sequence in space and time and spatiotemporal chaos with irregular localized patterns are formed in different regions of unstable wavenumbers, hence producing a self-organizing dynamical system. The results are consistent with those obtained by numerically solving Zakharov equations as previously reported and summarized in the present manuscript.

This paper presents an analysis of relativistic self-focusing of intense laser radiation in an axially inhomogeneous plasma. The nonlinearity in the dielectric constant arises on account of the relativistic variation of mass for an arbitrary magnitude of intensity. An appropriate expression for the nonlinear dielectric constant has been used in the analysis of laser-beam propagation in the paraxial approximation for a circularly polarized wave. The variations of the beam width parameter with the propagation distance, the self-trapping condition and the critical power have been evaluated. The saturating nature of the nonlinearity yields two values of the critical power for beam self-focusing, $P_{\rm cr1}$ and $P_{\rm cr2}$. It is seen that the laser beam width tends to attain a constant value depending upon the plasma inhomogenity and the initial laser intensity. Numerical estimates are made for typical values of the laser–plasma interaction applicable for underdense and overdense plasmas. The most important experiments described by this model are related to the fast ignitor concept.

This paper is devoted to first-principles calculations of hydrogen and helium thermodynamics. We use the direct path integral Monte Carlo method to compute isochors and isotherms in a wide range of parameters in comparison with available theoretical and experimental results. New results for hydrogen and hydrogen–helium plasmas with the mass concentration of helium $Y\,{=}\,0.988$ are analysed with the help of a model based on the chemical picture.

The statistical theory of absolute equilibrium ensembles is extended to describe ideal, three-dimensional, magnetohydrodynamic (MHD) turbulence with and without rotation, and with and without a mean magnetic field. Results from seven long-time numerical simulations of five general cases on a $32^{3}$ grid are presented. One notable result is the discovery of a new ideal invariant, the ‘parallel helicity,’ which arises when rotation and mean magnetic field vectors are aligned. Although the basic equations and statistical theory are symmetric under parity or charge reversal, the presence of invariant cross, magnetic or parallel helicity dynamically breaks this symmetry. Ideal MHD turbulence is, in general, non-ergodic due to the decomposability of the constant energy surface in phase space. Non-ergodicity can be manifested in the appearance of coherent structure as long as magnetic or parallel helicity is invariant. The fact that MHD turbulence inherently contains coherent structure in certain general cases may have important implications for dynamo theory.

The momentum balance equations and the balance equations for the pressure tensors of a collision-free multi-species magnetoplasma are linearized and Fourier-transformed, together with Maxwell's curl equations. They are combined in an algebraic dispersion system for the electric wave vector. The vanishing determinant of this system is the dispersion equation. It is of degree $2+3s$ in the square of the refractive index if $s$ is the number of different particle species.

The nonlinear coupling between the Alfvén–Rao (AR) and dust–Alfvén (DA) modes in a uniform magnetized dusty plasma is considered. For this purpose, multi-fluid equations (composed of the continuity and momentum equations), the laws of Faraday and Ampère and the quasi-neutrality condition are adopted to derive a set of equations, which show how the fields of the modes are nonlinearly coupled. The equations are then used to investigate decay and modulational instabilities in magnetized dusty plasmas. Stationary nonlinear solutions of the coupled AR and DA equations are presented. The relevance of the investigation to nonlinear phenomena (instabilities and localized structures) in interstellar molecular clouds is also discussed.

The non-ideal collective and plasma screening effects on elastic electron–atom collisions are investigated in partially ionized hydrogen plasmas using the first-order eikonal method. The effective pseudopotential model, taking into account the screening and collective effects, is applied to describe the interaction potential in non-ideal plasmas. Semiclassical trajectory analysis is applied to the path of the projectile electron in order to investigate the variation of the eikonal phase and cross section as functions of the impact parameter, the non-ideality plasma parameter, the Debye length, and the collision energy. The results show that the collective and screening effects enhance the differential eikonal cross section for small impact parameters, but suppress the cross section for large impact parameters. It is also found that the non-ideal collective effects enhance the total eikonal cross section.

This paper presents an investigation of the filamentation process of a uniform plane Alfvén wave for a compressible magnetohydrodynamics case, when a transverse perturbation (perturbation having non-uniform intensity distribution in a plane perpendicular to the direction of wave propagation) is present on it. The physical mechanism of the filament formation is discussed in detail with the applications to the Solar wind turbulence and the coronal heating. The dependence of the critical field of the perturbation, its critical transverse size and the formation of filaments, on the plasma $\beta $, main Alfvén field and other parameters has been studied in detail.

The drift model is an extention of magnetohydrodynamics (MHD) with the ion finite Larmor radius effects. It is demostrated with a one-dimensional simulation code that the dispersion relation of the kinetic Alfvén wave is reproduced with the drift model. The simulation code for MHD and energetic alpha particles (MEGA) has been extended with the drift model and an extended Ohm's law where the electron Landau damping is taken into account with the Landau fluid model. The linear stability of the alpha-particle driven Alfvén eigenmode in the Tokamak Fusion Test Reactor (TFTR) deuterium-tritium (D-T) plasma was investigated with the extended MEGA code. The nonlinear simulation results of an ITER-like plasma with a weak negative shear are presented.

Stimulated Brillouin backscattering (SBBS) of an extraordinary electro- magnetic wave from a magnetized homogeneous plasma is investigated. A system of equations that describes the problem is derived and solved for a weak-field limit. A modified expression for the maximum growth rate in magnetized plasmas is derived, which recovers the growth rate expression for non-magnetized plasma known in literature. Small values of static magnetic field are found to increase the instability growth rate, while high magnetic fields reduce the instability bringing it to zero at a cut-off field, beyond which the plasma becomes stable, a result that is consistent with numerical results known in the literature (Bawa'aneh, M. S. 2003 Contrib. Plasma Phys. 43, 447). Also, a threshold for incident laser intensity is found, below which the SBBS maximum growth rate is suppressed. The value of this threshold is found to increase as the static magnetic field increases.

The electron distribution function in xenon in the low-energy region comprising the Ramsauer–Townsend minimum was obtained by solving the Boltzmann equation in the hydrodynamic approximation, for electric field to gas density ratios $E/N$ in the range (0.01, 3) Td. The distortion of the electron distribution function due to the minimum is analysed and correlated to the behaviour of the electron transport coefficients: the drift velocity $W_{\rm d}$ and the ratio of the transverse and longitudinal diffusion coefficient to mobility, $D_{\rm T}/\mu$ and $D_{\rm L}/\mu$. The results are discussed in view of the different theoretical and experimental cross-section data used.

A rectangular periodically corrugated waveguide is considered in the exponential gain regime. In general, gain obeys a nonlinear cubic equation. In this paper it is solved numerically. Also the behavior of gain diagrams versus beam velocities for various parameters of the problem is surveyed. Furthermore, in the context of a slow-wave periodic structure oscillator, the threshold current which cause the system to be self-sustained, is obtained from a nonlinear cubic equation similar to the one obtained for gain, and the variation of its diagrams with other parameters is also considered.

The equilibrium of an axisymmetric magnetically confined plasma with anisotropic resistivity and toroidal flow is investigated within the framework of magnetohydrodynamics (MHD). The stationary states are determined by an elliptic differential equation for the poloidal magnetic flux function $\psi$, a Bernoulli equation for the pressure and two relations for the resistivity components $\eta_\parallel$ and $\eta_\perp$ parallel and perpendicular to the magnetic field, respectively. The flow can affect the equilibrium properties solely in the presence of toroidicity because in the limit of infinite aspect ratio, the axial velocity does not appear in the equilibrium equations. The equilibrium characteristics of a tokamak with rectangular cross-section are studied by means of eigenfunctions in connection with exact solutions for the cases of ‘compressible’ flows with constant temperature, $T(\psi)$, but varying density on magnetic surfaces and incompressible ones with constant density, $\varrho(\psi)$, but varying temperature thereon. Those eigenfunctions can describe either single or multiple toroidal configurations. In the former case the equilibrium has the following characteristics: (i) the $\eta_\parallel$- and $\eta_\perp$-profiles on the poloidal cross-section having a minimum close to the magnetic axis, taking large values on the boundary and satisfying the relation $\eta_\perp > \eta_\parallel$ are roughly collisional; (ii) the electric field perpendicular to the magnetic surfaces possesses two local extrema within the plasma and vanishes on the boundary; and (iii) the toroidal current density is peaked close to the magnetic axis and vanishes on the boundary. The impact of the flow and the aspect ratio on the aforementioned quantities is evaluated for both ‘compressible’ and incompressible flows.

In the interstellar medium (ISM), a broad range of turbulent plasmas can be observed by using radio waves. However, only density fluctuations are directly measurable with these radio astronomic tools. If one wants to deduce the underlying features of the turbulence, it is necessary to calculate the relation between density and magnetic fluctuations. Here a magnetohydrodynamic (MHD)-ansatz is taken into account for the ISM turbulence to calculate the fluctuations for the three low-frequency MHD waves.

Kadomtsev proposed a self-generation mechanism of microislands (whose half-width is smaller than the Larmor radius of the ions) based on momentum and energy exchange between the electrostatic field of the islands and the ions of the background tokamak plasma. In this paper we study the motion of the ions intersecting, within a Larmor rotation, the electric field in the interspace between adjacent microisland chains. After appropriate average over the ensemble of ions and island chains, the interaction with the electric field gives rise to a net slow cumulative drift of the assembly of ions in the outward direction of the major radius. This effect is the consequence of nonlinearity and toroidal geometry in the equation of motion. The outward motion is associated with a decrease of the perpendicular plasma kinetic energy and a concomitant increase of the island's electrostatic energy, which can be described consistently by a ‘pumping term’ in the energy integral of the magnetohydrodynamic reduced equations for the islands. The pumping term can be contrasted by anomalous dissipation due to resonant interaction between the background electrons and the island waves. A stationary system of self-sustained microisland chains can then be formed in the tokamak plasma preferentially in the region $q > 2$ of the safety factor. Thus, the plasma acquires a spongy structure, where the sponginess (that is to say, the density of packing of the island structures) is measured by the ratio, lower than one, between the island width and the distance between adjacent rational surfaces. This structure determines an electron heat conductivity, which is strictly related to the sponginess and to the macroscopic equilibrium. Examples of scalings of the electron confinement time, predicted in zero-dimensional approximation, are given for typical tokamak conditions.

Zonal flow behaviour and its effect on turbulent transport in reversed magnetic shear tokamaks are investigated by global simulations of electrostatic ion temperature gradient driven turbulence. When the safety factor $q$ is reduced, zonal flows in a minimum $q$ region change from oscillatory to stationary and suppress the turbulent transport effectively. This result indicates that the change of zonal flow behaviour in the minimum $q$ region may trigger the formation of ion transport barriers.

The weakly nonlinear evolution of linearly stable perturbations in Hall magnetohydrodynamic plasmas is investigated by the method of strained coordinates. Unperturbed self-similar equilibrium solutions for Z-pinches with time- dependent total current $I\,{\sim}\, t^S$, are subjected to sausage perturbations in the lossless short scale approximation in which the temporal and spatial variation of basic state is treated as slow. The experimentally observed enhanced stability of the Z-pinches previously explained by the linear stability of the core in the interior of the unperturbed pinch is supported by the present nonlinear analysis. The nonlinear evolution results in an axially periodic series of wave breakings, which are confined to a thin shell around the stable pinch core. The wave breaking time may reach the levels of the pinch lifetime in the vicinity of the near-axis branch of the boundary neutral curve, where the inverse Hall parameter is less than unity and the Hall effects are most significant.

A general nonlinear theory for low-frequency electromagnetic field generation due to the action of non-uniform and non-stationary high-frequency electromagnetic radiation (ponderomotive force) in uniform multicomponent dusty magnetoplasmas is developed. The anisotropic thermal pressure of all species in slow and fast oscillations is taken into account. This theory permits us to consider the nonlinear action of all waves that can exist in such plasmas. As an example, the equations for dust particle velocities arising due to nonlinear electric fields induced by electromagnetic cyclotron waves travelling along an external magnetic field are obtained. The dust grains are considered to be magnetized as well as unmagnetized. Various regimes of dust grain dynamics depending on the spatio-temporal variation of a fast wave amplitude are discussed. It is shown that induced nonlinear electric fields can have both an electrostatic and an electromagnetic nature. In some cases these fields across the background magnetic field in warm plasmas are considerably larger than those in cold plasmas. The longitudinal nonlinear electric field remains the same in warm and cold plasmas in its order of magnitude. Regimes are found for which the transverse acceleration of dust grains is much larger than the longitudinal one.