A previous analysis of anomalous width variation for a single-ion rarefactive solitary wave [S. S. Ghosh and A. N. Sekar Iyengar, Phys. Plasmas, 4, 3204 (1997)] has been extended to a multi-ion species, and shows that the corresponding width–amplitude characteristics depend crucially on the respective ion concentrations; for example, with increasing light-ion concentration, an ‘increasing- width’ rarefactive solitary wave transforms to a ‘decreasing-width’ one for a constant Mach number exhibiting an overall U-shaped variation profile. The influence of the second ion species generally decreases with increasing amplitude, being maximum for the single to multi-ion transition. However, in the neighbourhood of double-layer-like solutions, the influence again becomes prominent, which may be associated with the corresponding energy–amplitude relations for both the ions.

Absorption by trapped particles is supposed to seriously hinder current drive by Alfvén waves. However, it is shown in this paper that the same effect is rather beneficial for the emergence of the radial electric field induced by these waves, which is important for creating and maintaining transport barriers in tokamaks.

The nonlinear dynamics of resonant slow MHD waves in weakly dissipative plasmas is investigated in cylindrical geometry with a twisted equilibrium magnetic field. Linear theory has shown that the wave motion is governed by conservation laws and jump conditions across the resonant surface considered as a singularity – first derived in linear ideal MHD theory by Sakurai, Goossens and Hollweg [Solar Phys.133, 227 (1991)]. By means of the simplified method of matched asymptotic expansions, we obtain the generalized connection formulae for the variables across the dissipative layer, and we derive a non-homogeneous nonlinear partial differential equation for the wave dynamics in the dissipative layer.

The solitonic, periodic and quasiperiodic solutions that obey the full system of transport equations describing one-dimensional motion of a isotropic collisionless quasineutral plasma in a magnetic field are treated. The domains of physical parameters of such a plasma are determined for fast and slow magnetoacoustic branches, where solitary waves and generalized solitary waves exist. In the parameter domain where solitary waves are replaced by non-local generalized solitary waves, the localized disturbances are subject to decay, which has qualitatively different mechanisms for fast and slow magnetoacoustic waves. The specific feature of the decay process for fast waves is found to be characterized by a decrease of energy of the disturbance due to quasistationary radiation of a resonant periodic wave of the same nature. Analogous disturbances, having the form of a slow magnetoacoustic solitary wave core, practically do not radiate resonant Alfvénic modes, but rapidly lose energy as a result of continuous shedding of a slow-wave component. Various types of shock waves are also considered. Their structure is formed by existing solitonic configurations – solitary and generalized solitary waves. Possibilities of observations of solitary waves and their decay in a real plasma are discussed.

The regularization of magnetic islands is studied for the case when the electron temperature is larger than the ion temperature. The slab approximation is used. Drift effects are neglected, i.e., the case of superdrift magnetic islands, SDMIs, is analyzed. Then the regularization problem reduces to, first, a spreading of the step-functional velocity profile and the conventional delta-functional polarization current profile in the region near the island separatrix; second, finding the dispersion terms of the polarization current in this region; and, third, calculating the total polarization current contribution to the generalized Rutherford equation for the island width. It is shown that this problem can be solved if one allows for the effects of the electron pressure gradient in the parallel Ohm's law. The polarization current contribution in the case of islands regularized due to these effects proves to be the same as that in the case of nonregularized islands.

The scattering of transverse electromagnetic waves by turbulent density fluctuations in a magnetized plasma in the presence of external pump fields is investigated. The case where a lower-hybrid pump wave decays into daughter and ion-cyclotron waves in a plasma with ion-temperature anisotropy is considered. The situation where an upper-hybrid pump wave parametrically excites modified convective cells and electron drift waves is also analyzed. The differential scattering cross-sections in the region above the parametric instability thresholds for these three cases are calculated.

This note investigates an ion-dust streaming instability with frequency ω less than the dust collision frequency νd, in an unmagnetized collisional dusty plasma. Under certain conditions, a resistive instability can be excited by an ion drift on the order of the ion thermal speed, even when the dust acoustic wave is heavily damped. The effect of weak collisions on the usual dust acoustic instability in the regime ω > νd is also considered. Applications to experimental observations of low-frequency fluctuations in laboratory d.c. glow discharge dusty plasmas are discussed.

The transient Hartmann flow of an electrically conducting viscous incompressible non-Newtonian power-law fluid between two parallel horizontal non-conducting porous plates is studied with heat transfer, without neglecting the Hall effect. A sudden uniform and constant pressure gradient, an external uniform magnetic field that is perpendicular to the plates, and uniform suction and injection through the surface of the plates are applied. The two plates are kept at different but constant temperatures, while the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing nonlinear momentum and energy equations are obtained using finite difference approximations. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions as well as the dissipation terms are examined.

Stationary nonlinear one-dimensional electrostatic oscillations in a plasma containing dust grains with variable charge are considered through a cold-beam model. The new constraints brought by the presence of dusts on the BGK modes are clarified and the appearance of a soliton mode that was not present in the fixed-charge problem is investigated.

A theoretical analysis of spherical probes in plasmas is presented. It is assumed that the probe is at floating potential, that ion motion with respect to the probe is radial and that the electrons are Maxwellian. The analysis shows that as probe radius divided by Debye length tends to zero, the ratio of floating potential to electron temperature also goes to zero.

The results of a previous work, which describes in the magnetohydrodynamic approximation Alfvén wings in nonuniform plasmas, are extended in order to consider more general variations of the background fields. As mathematical tools we use general curvilinear coordinates and stream functions. We prove the possibility of existence of Alfvén wings when the background fields have cylindrical or helical symmetry. For the former, the wings are cylinders, and for the latter, they have helicoidal form; this last includes the case of uniform background fields. We also obtain the relations among the different physical magnitudes in the wing.

Electrical breakdown in a mixed gas is investigated. The plasma at breakdown is evaluated in terms of the mole fraction χ. The optimum condition for the highest plasma density is described in terms of the ionization energy and collisional cross-section of the mixed gas. The optimum mole fraction for the highest plasma density is found to be χ = 0.03 for the case of plasma generation in neon gas mixed with xenon for a plasma display panel. The optimum condition for the highest number of electronic excitations is also obtained.

We consider a model of viscoresistive incompressible magnetohydrodynamics in a periodic cylinder, with boundary conditions meant to idealize in a tractable way those of a laboratory plasma. The resistivity is described by a tensor presenting a field-dependent anisotropic part suggested by kinetic theory, controlled by a certain anisotropy parameter. An explicit analytical description of the corresponding axisymmetric zero-flow equilibria is given, and it is shown how tokamak-like or paramagnetic-pinch-like field profiles are obtained as the anisotropy parameter is changed. The study of the stability properties of such equilibria is deferred to a later paper.

The technique for analytical investigation of the Alfvén resonance, proposed by Dmitrienko [J. Plasma Phys.57, 311 (1997); 62, 145 (1999)] is used to obtain the matching conditions and to calculate the rate of resonant absorption and heating in a nonlinear dissipative resonance layer. It is shown that one matching condition is the invariability condition for the coefficient of the singular part of the solution describing the MHD mode outside the resonance layer, and the other condition is a jump of the coefficient of a regular solution, the value of which depends on the ratio of the dissipative to nonlinear spatial scales. It is established that the ratio of the jump of the imaginary part of the regular solution to the coefficient of the singular solution is exactly equal to the rate of resonant heating, and this heating is calculated as a function of the ratio of the linear dissipative to nonlinear scales. The resonant absorption coefficient is calculated as well. It is shown that the nonlinearity leads to a decrease of the heating rate and the absorption coefficient compared with those predicted by linear theory.

Making use of the dielectric permitivitty of a solid state plasma obtained from linearizing a quantum hydrodynamic equation, volume and surface waves in cold semibounded plasma-like media and thin layers of solid state plasmas are investigated in the presence and absence of an external magnetic field. It is shown that quantum oscillation of free charged particles and its spatial dispersion even in cold plasmas lead to new spectra of collective oscillations. Furthermore, a new volume ion-acoustic-type wave is obtained with a quadratic dependence on the wavenumber in the long-wavelength limit. Moreover, it is shown that quantum oscillation affects the surface wave spectrum and extends it to a wider frequency region.

The generation of magnetic fields due to ponderomotive forces in astrophysical plasma consisting of electrons, ions and positrons is investigated theoretically. It is seen that collisional or non-collisional interactions (between electromagnetic waves and plasma particles) via ponderomotive forces in an inhomogeneous plasma can excite a magnetic field. The growth rate of the magnetic field is illustrated graphically for different values of the temperature and concentration of positrons in the plasma.

Starting from the one-dimensional energy integral and related stability theorems given by Newcomb [Ann. Phys (NY)10, 232 (1960)] for a linear pinch system, this paper analyses the stability of one-dimensional force-free magnetic fields in cylindrical coordinates (r, θ, z). It is found that the stability of the force-free field is closely related to the radial distribution of the pitch of the field lines: h(r) = 2πrBz/Bθ. The following three types of force-free fields are proved to be unstable: (i) force-free fields with a uniform pitch; (ii) force-free fields with a pitch that increases in magnitude with r in the neighbourhood of r = 0(d[mid ]h[mid ]/dr > 0); and (iii) force-free fields for which (dh/dr)r=0 = 0, Bθ α rm in the neighbourhood of r = 0, and (h d2h/dr2)r=0 > −128π2/(2m+4)2. On the other hand, the stability does not have a definite relation to the maximum of the force-free factor α defined by [dtri ]×B = αB. Examples will be given to illustrate that force-free fields with an infinite force-free factor at the boundary are stable, whereas those with a force-free factor that is finite and smaller than the lowest eigenvalue of linear force-free field solutions in the domain of interest are unstable. The latter disproves the sufficient criterion for stability of nonlinear force-free magnetic fields given by Krüger [J. Plasma Phys.15, 15 (1976)] that a nonlinear force-free field is stable if the maximum absolute value of the force-free factor is smaller than the lowest eigenvalue of linear force-free field solutions in the domain of interest.

Generation of wake fields by a short electromagnetic pulse in a plasma with an inhomogeneous background magnetic field and density profile is considered, and a wave equation is derived. Transmission and reflection coefficients are calculated in a medium with sharp discontinuities. Particular attention is focused on examples where the longitudinal part of the electromagnetic field is amplified for the transmitted wave. Furthermore, it is noted that the wake field can propagate out of the plasma and thereby provide information about the electron density profile. A method for reconstructing the background density profile from a measured wake field spectrum is proposed and a numerical example is given.

The one-dimensional oblique propagation of magnetohydrodynamic waves with arbitrary amplitudes in a Hall plasma with isotropic pressure is studied under assumption that the plasma β is large. It is shown that the wave evolution is described by the derivative nonlinear Schrödinger equation (DNLS).

The effect of an external magnetic field Bext on the propagation of an electromagnetic wave pulse incident on a nonlinear medium is studied. It is shown that all the incident energy can be reflected in a large domain of Bext (self-screening), if the incident wave is in pulsed form. Having a complicated behavior, the reflection coefficient shows total transmission or self-screening in the intermediate range of the external magnetic field.