Nonlinear oscillations within a plasma slab are analyzed. Two types of solutions are found, depending on the initial value of the electron density. The first represents regular oscillations within the plasma slab, while the second gives rise to explosive growth at the slab centre or at the edges. The results are discussed.

The nonlinear dynamics of the ion temperature gradient (ITG) mode is investigated in a dusty plasma assuming the dust grains to be tiny and highly charged. The electrostatic drift waves cannot be ignored in the linear dispersion relation if polarization drifts of ions and dust are taken into account. The dipolar vortices are predicted to be formed in the nonlinear regime. The relevance of this study to space and astrophysical plasmas is pointed out.

Analytical solutions for the minimum Ohmic dissipation states satisfying helicity balance in a cylindrical vessel with circular electrodes on the plane surfaces are presented. The solutions show the basic features of flux core spheromaks and are given in terms of Fourier–Bessel series. The total plasma current and magnetic field profiles are determined for different values of resistivity, elongation and electrode radius.

Stationary magnetohydrodynamic (MHD) flows with a symmetry are analyzed for very-low-density plasmas in strong magnetic fields, in the infinite conductivity limit. In this particular case the simplified form of Ohm's law usually employed in the ideal MHD case is no longer valid, because Hall's and electron pressure terms in the generalized Ohm's law must be retained. Thus we include them in our equations. The assumption of symmetry makes possible the definition of an ignorable coordinate and of current functions for the divergence free magnitudes. In the case without Hall's effect and electron pressure terms in Ohm's law, there is only one independent current function; in the present case, instead, two Stokes functions are independent. We choose the current function of the magnetic induction field and that of the plasma flux, $\psi$ and $\chi$, to be independent. Then we can express the other Stokes functions of our problem as functions of $\psi$ and $\chi$. We assume helical symmetry, as it is the most general form of spatial symmetry and impose incompressibility, that is ${\bf v\cdot\nabla\rho =}\,0$. We obtain a system of two differential equations for $\psi$ and $\chi$, and solve them for the particular case of constant density. Then we calculate the limit of our solution for Hall's effect that tends to zero, in order to make a comparison with the results obtained for the case without Hall's effect. Finally, we find the necessary conditions to obtain confined plasma columns embedded in a force-free plasma or in a vacuum.

From the width of the emitted 656.3 nm Balmer $\alpha$ line, it was found that low-pressure (0.5 torr) capacitively coupled radio-frequency (RF) ${\rm He}/{\rm H}_2$ (95/5%) as well as ${\rm Ar}/{\rm H}_2$ (95/5%) plasmas showed excess broadening throughout the volume (13.5 cm ID $\times$ 38 cm length) of a General Electronics Conference (GEC)-type cell; not merely in the vicinity of the electrodes of ${\rm Ar}/{\rm H}_2$ plasmas as reported by several groups. About 50% of the hydrogen of the ${\rm He}/{\rm H}_2$ was ‘hot’ with an average hydrogen atom energy of 40–50 eV, compared to $\sim$1 eV for pure hydrogen, whereas ${\rm Ar}/{\rm H}_2$ showed a single fast or ‘hot’ 40–50 eV population. The broadening was undiminished at 15 cm from the powered electrode, independent of power over a substantial range, but dependent on the hydrogen concentration. In contrast to the atomic hydrogen lines, no broadening was observed in helium or argon lines. Also, in ‘control’ ${\rm Xe}/{\rm H}_2$ plasmas run in the same cell at similar pressures and absorbed power, no significant broadening of atomic hydrogen, ${\rm Xe}$, or any other lines was observed. Stark broadening or acceleration of charged species due to high electric fields cannot explain the results since: (i) the electron density was insufficient by orders of magnitude, (ii) the RF field was essentially confined to the cathode fall region in contrast to the broadening that was independent of position, and (iii) only the atomic hydrogen lines were broadened. Rather, the data are consistent with a model wherein ${\rm He}^+$ and ${\rm Ar}^+$ act catalytically through a resonant energy transfer mechanism to create ‘hot’ hydrogen atoms in plasmas.

The stable conditions and gravitational effects on the surface dust-acoustic wave are investigated in self-gravitating semi-bounded dusty plasmas. The dispersion relation of the surface dust-acoustic wave is obtained by the plasma dielectric function with the specular reflection boundary condition. It is shown that the surface dust-acoustic wave become unstable for any values of the wave number when $\tfrac{1}{2}\leq (\omega_{\rm J}/\omega_{\rm pd})^2\leq 1$. However, when $(\omega_{\rm J}/\omega_{\rm pd})^2 > 1$ or $(\omega_{\rm J}/\omega_{\rm pd})^2 < \tfrac{1}{2}$, the Jeans instability does not occur for the domain of the wave number $k_z \lambda_{\rm D} > (\omega_{\rm J}/\omega_{\rm pd})|[(\omega_{\rm J}/\omega_{\rm pd})^2 - 1]/[2(\omega_{\rm J}/\omega_{\rm pd})^2 - 1]|^{1/2}$. It is also found that the phase velocity of the surface wave decreases with increasing Jeans frequency.

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.

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 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.

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.

The coupling of shear and fast Alfvén waves in the vicinity of a magnetic X-point is studied for the case in which a weak longitudinal guide field $B_{z0}$ is present, with variations in the longitudinal direction and plasma pressure effects neglected. It is shown that an analytical solution for the shear wave in the limit of ideal magnetohydrodynamics (MHD) and $B_{z0}\,{=}\,0$ exhibits phase mixing and equilibration of the field and kinetic energy at a rate that increases with the spatial extent of the initial disturbance. Equations describing perturbatively the pumping of fast waves by shear waves in the presence of finite $B_{z0}$ are derived and solved numerically, taking into account resistivity and electron inertial effects. It is shown that shear wave energy is most rapidly and efficiently converted to plasma kinetic energy when the collisionless skin depth exceeds the resistive scale length. The conversion of incompressible MHD modes to compressible modes at X-points provides a possible mechanism for solar coronal heating, and mode conversion processes of this type are also likely to occur in tokamak plasmas with X-points.

The Korteweg–de Varies–Zakharov–Kuznetsov (KdV–ZK) equation describes the behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external magnetic field in a non-thermal plasma consisting of warm adiabatic ions. When the coefficient of the nonlinear term of this equation vanishes, the nonlinear behaviour of ion-acoustic wave is described by a modified KdV–ZK (MKdV–ZK) equation. A combined MKdV–KdV–ZK equation more efficiently describes the nonlinear behaviour of ion-acoustic waves at points in the neighbourhood of the curve in the parametric plane along which the coefficient of the nonlinear term of the KdV–ZK equation vanishes. This combined MKdV–KdV–ZK equation admits both double-layer and alternative solitary-wave solutions having profile different from sech$^{2}$ or sech. In this paper the three-dimensional stability of the alternative solitary-wave solution having profile different from sech$^{2}$ or sech has been investigated by the recently developed multiple-scale perturbation expansion method of Allen and Rowlands. The instability condition and the growth rate of instability have been derived at the lowest order. The correct expression of the growth rate of instability at the lowest order has been obtained for a limiting case and the stability analysis has been carried out numerically from our model as presented in this paper for arbitrary values of the parameters involved in the system.