The paper is concerned with the influence of magnetic field shear on the structure of Alfvén waves standing along field lines in the one-dimensionally inhomogeneous box model of the magnetosphere, enclosed between two parallel, infinitely conducting planes (ionospheres). We consider the transverse small-scale Alfvén waves whose azimuthal component of the wave vector $k_y$ satisfies the condition $k_y l\,{\gg}\,1$, where $l$ is the distance between the ionospheres. For this model, the Alfvén resonance condition has been established. It is shown that resonance can also occur at a constant Alfvén velocity if the field-line inclination to the ionosphere is changed. On resonant magnetic shells there occurs a singularity of the wave field of the same kind as in the absence of shear. Moreover, there are found many resemblances between Alfvén-wave behavior in our one-dimensionally inhomogeneous model and in two-dimensional inhomogeneous models with plasma and magnetic field parallel inhomogeneity taken into account. Thus, the presence of shear leads to a difference of the frequencies of poloidal and toroidal oscillations of field lines, and to the dependence of the wave's frequency on the transversal components of wave vector. Then, in the sheared magnetic field with highly conductive boundaries the source excites multiple standing Alfvén harmonics at different locations. In general, the localization regions of different longitudinal harmonics overlap. However, in the small but finite shear limit, a total wave field represents a set of mutually isolated transparent regions corresponding to different harmonic numbers. In each of these regions the waves are found to be travelling across the magnetic shells, and the transparent region is limited in the coordinate $x$ by two turning points, at one of which the mode is poloidally polarized, and the other point it is toroidally polarized (it is at this latter point where Alfvén resonance occurs). Furthermore, the phase velocity of the wave is directed toward the poloidal point, and the group velocity is directed at the toroidal point.

In recent years, ablative plasma generated by capillary discharge attracted considerable attention because of its possible applications in electrothermal launchers, laser-driven particle accelerators, thin-film deposition and soft X-ray lasers, etc. An electrical discharge through a capillary insulator heats the capillary plasma that provides further evaporation of the capillary wall and electrode. The created plasma is confined by the capillary wall, electrode material and flow in a specified chamber through a hollow electrode. The mass flux leaving the capillary in axial motion is replenished by a radial inward flow of matter. Thus the radial component of the mass flux plays a principal role in the mass and energy balance. In this paper, we present a theoretical model for a time-dependent magneto-hydrodynamical simulation to calculate the dynamic evolution of plasma flow and transportation in two-dimensional configurations combined with turbulent effect. The thermodynamic and transport properties are characterized by a model that describes the plasma composition, equation of state, internal energy, viscosity and thermal and electrical conductivity for a partially ionized multi-component plasma in the weakly non-ideal region, similar to that which exists in the ablation-controlled arcs. Our model results show that some of the well-known experimental features of this kind of discharge are confirmed, particularly the radial mass and energy transportation.

This paper presents the possible periodic solutions and the solitons of the cubic–quintic nonlinear Schrödinger equation. Corresponding to five types of different structures of the pseudo-potentials, five types of periodic solutions are given explicitly. Five types of solitons are also obtained explicitly from the limiting procedures of the periodic solutions. This will benefit the study of the generation of fast ions or electrons, which are produced from the soliton breaking when the plasma is irradiated a high-intensity laser pulse.

Perturbation reductive procedures, as used to analyse various weakly nonlinear plasma waves (solitons and periodic waves), normally lead to the dynamical system being described by KdV, Burgers' or a nonlinear Schrödinger-type equation, with properties that can be deduced from an array of mathematical techniques. Here we develop a fully nonlinear theory of one-dimensional stationary plasma waves, which elucidates the common nature of various diverse wave phenomena. This is accomplished by adopting an essentially fluid dynamic viewpoint. In this unified treatment the constants of the motion (for mass, momentum and energy) lead naturally to the construction of the wave structure equations. It is shown, for example, that electrostatic, Hall–magnetohydrodynamic and ion–cyclotron–acoustic nonlinear waves all obey first-order differential equations of the same generic type for the longitudinal flow field of the wave. The equilibrium points, which define the soliton amplitude, are given by the compressive and/or rarefactive roots of a total plasma ‘energy’ or ‘momentum’ function characterizing the wave type. This energy function, which is an algebraic combination of the Bernoulli momentum and energy functions for the longitudinal flow field, is the fluid dynamic counterpart of the pseudo-potentials, which are characteristic of system structure equations formulated in other than fluid variables. Another general feature of the structure equation is the phenomenon of choked flow, which occurs when the flow speed becomes sonic. It is this trans-sonic property that limits the soliton amplitudes and defines the critical collective Mach numbers of the waves. These features are also obtained in multi-component plasmas where, for example, in a bi-ion plasma, momentum exchanges between protons and heavier ions are mediated by the Maxwell magnetic stresses. With a suitable generalization of the concept of a sonic point in a bi-ion system and the corresponding choked flow feature, the wave structures, although now more complicated, can also be understood within this overall fluid framework. Particularly useful tools in this context are the momentum hodograph (an algebraic relation between the bi-ion speeds and the electron speed, or magnetic field, which follows from the conservation of mass, momentum and charge-neutrality) and a generalized Bernoulli energy density for each species. Analysis shows that the bi-ion solitons are essentially compressive, but contain the remarkable feature of the presence of a proton rarefactive core. A new type of soliton, called an ‘oscilliton’ because embedded spatial oscillations are superimposed on the classical soliton, is also described and discussed. A necessary condition for the existence of this type of wave is that the linear phase velocity must exhibit an extremum where the phase speed matches the group speed. The remarkable properties of this wave are illustrated for the case of both whistler waves and bi-ion waves where, for the latter, the requisite condition is met near the cross-over frequencies. In the case of the whistler oscilliton, which propagates at speeds in excess of one half of the Alfvén speed (based on the electrons), an analytic solution has been constructed through a phase-portrait integral of the system in which the proton and electron dynamics must be placed on the same footing. The relevance of the different wave structures to diverse space environments is briefly discussed in relation to recently available high-time and spatial resolution data from satellite observations.

The fluid quintic dispersion equation and the full kinetic Boltzmann–Vlasov equation have been programmed for a one-species magnetoplasma in a form permitting direct comparison between them. The quintic equation yields five wave-modes, two electromagnetic, a Langmuir or Bernstein mode and two transversely polarized acoustic modes driven by the trace-free part of the anisotropic pressure tensor. The slower acoustic mode is found in the kinetic analysis to be evanescent, the other suffers appreciable Landau damping except in the first gyroharmonic band when its phase velocity approaches and even exceeds that of the Langmuir mode, with a resultant mixing of modal properties. The Langmuir or Bernstein mode refractive index surfaces found in the fluid and kinetic analyses are generally in good agreement, but gyroharmonic wave–particle interactions seen in the Bernstein modes are missed in the fluid analysis, such as resonant effects very close to the gyroharmonic frequencies and strong damping at all propagation angles when the wave frequency lies in a forbidden Bernstein region. In all cases the fluid analysis provides additional information on wave polarization and generalized energy fluxes–electromagnetic and acoustic–permitting easy identification of modes.

In this paper, the characteristics of dust-acoustic solitary waves in dusty plasma are studied. Dust charge and temperature are treated as variables. The authors have used the pseudopotential method to investigate the possibility of compressive as well as rarefactive solitons. An expression for the pseudopotential has been derived. The pseudopotential is a function of the Mach number, the relative temperature of low and high ion components, the relative ion concentration of dust charge and the temperature. Numerical computation shows that for the chosen set of parameters, only compressive solitons exist and their amplitudes increase with increasing Mach number. An increase in the dust temperature results in the disappearance of the compressive soliton. It is the only small parameter regime where compressive as well rarefactive solitons coexist. The effect of the relative ion temperature on solitons is also investigated. In the small amplitude limit, an increase in the dust temperature leads to a transition from compressive to rarefactive solitons.