An analysis of the induction equation shows that the level surfaces of the magnetic field in a resistive plasma satisfy a certain bound upon the time means of their areas. When this bound is applied to some configurations typical of chaotic plasmas, it is shown that the number of bidimensional sheets where the field reaches a extremum is bounded, whereas the number of extremal ropes or points need not be. This also applies to current sheets.

The orbital-motion-limited (OML) theory has been widely used to calculate the ion response to a charged grain immersed in plasma. The theory assumes there are no potential barriers preventing plasma ions from reaching positive-energy points in phase space. However, Allen et al. [J. Plasma Phys.63, 299 (2000)] have recently shown that for any finite-size negatively charged dust grain in a Maxwellian plasma, there are always potential barriers sufficient to exclude some ions. We calculate the magnitude of the potential barriers, and determine which ions are subject to barriers. The OML theory is shown to become exact in the limit of small grain size, and to be very accurate in calculating ion current to the grain for typical conditions pertinent to dusty plasma. Thus OML theory is well justified in calculating the floating potential. However, we find that potential barriers can influence the shielding of the potential at r ∼ λD under some conditions, especially large grams, high plasma density, and small Ti/Te.

The nature of stationary-wave structures in multi-ion plasmas with differential streaming between the ions is elucidated by making use of the concept of a generalized sonic point for such plasmas and the Bernoulli equation for each flowing ion species. It is shown that the Bohm criterion for the existence of solitons and double layers is an expression of either the supersonic nature of the collective ion flow or the subsonic nature of individual ion flows. From the perspective of the dispersion equation for stationary waves, both of these requirements, and hence the Bohm criterion, merely ensure that the wave is evanescent, rather than sinusoidal, which, in turn, ensures that the system can evolve nonlinearly. The structure of the ion flows in these transitions is determined by the Bernoulli equation, a fundamental property of which is that the ion plasma energy exhibits a minimum where the ion flow speed equals the local ion sound speed. This implies that for positive flowing ions, a positive change in electric potential induces a deceleration (pile-up) if the flow is supersonic or an acceleration (spread-out) if the flow is subsonic. This feature limits the maximum strength of the potential in a soliton, and sheds light on the underlying reason why double layers can only exist in very special circumstances without the introduction of additional trapped or reflected particle populations.

We investigate the nature of stationary structures streaming at subfast magnetosonic speeds perpendicular to the magnetic field in a bi-ion plasma consisting of protons and a heavy ion species in which the magnetic field is frozen into the electrons, whose inertia may be neglected. The study is based on the properties of the structure equation for the system, which is derived from the equations of motion and the Maxwell equations, and therefore reflects the coupling between the two ion fluids and the electrons through the Lorentz forces and charge neutrality. The basic features of the structure equation are elucidated by making use of conservation of total momentum and charge neutrality, which provide relations between the ion speeds in the unperturbed flow direction and the electron speed. This combination of relations, which we call the momentum hodograph of the system, reveals the structure of the flow and the magnetic field in a solitary-type pulse. In particular, we find that in the initial portion of a compressive soliton, heavy ions run ahead of the electrons and the protons lag between them until a point is reached where they all once more attain the same speed, after which the protons run ahead and are accelerated whereas the heavies now lag behind the continuously decelerating electrons. The second half of the wave is a mirror image of the first portion. The strength of the compression (the amplitude of the wave) is determined from the momentum hodograph, and depends upon the initial Mach number, abundance ratio of heavies to protons and the mass ratio. The analysis is relevant to subfast flows of mass-loaded plasmas and pile-up boundaries, which appear near comets and non-magnetic planets.

We generalize the classical work of Adlam and Allen [Phil. Mag.3, 448 (1958)] on solitons in a cold plasma propagating perpendicular to the magnetic field to include the effects of plasma pressure. This is done by making extensive use of the properties of total momentum conservation (denoted by the term ‘momentum hodograph’, since it yields a locus in the plane of the electron and proton speeds in the direction of the wave) and the energy integral of the system as a whole. These relations elucidate the phase and integral curves of stationary flows, from which soliton solutions may be constructed. In general, only compressive solitons are permitted, and we have found an analytical expression for the critical fast Mach number as a function of the proton acoustic Mach number, which shows that it varies from its classical value of 2 (at large proton acoustic Mach numbers) to unity, where the incoming flow is proton-sonic. At the critical fast Mach number, two possible soliton-like solutions can be constructed. One is the classical compression, in which the magnetic field develops a cusp in the centre of the wave. The other is a compression in the magnetic field followed by a deep depression in the centre of the wave, which is completed by the mirror image of this signature of compression–rarefaction. This structure involves a smooth supersonic–subsonic transition in the proton flow. For Mach numbers in excess of the critical one, this kind of structure can also be constructed, but now the magnetic field is cusp-like at the points of maximum compression.

Turbulent transport of heat and particles is the principle obstacle confronting controlled fusion today. We investigate quantitatively the suppression of turbulence and formation of transport barriers in spherical tokamaks by sheared electric fields generated by externally driven radiofrequency (RF) waves, in the frequency range ωA ∼ ω < ωci (where ωA and ωci are the Alfvén and ion cyclotron frequencies).

This investigation consists of the solution of the full-wave equation for a spherical tokamak in the presence of externally driven fast waves and the evaluation of the power dissipation by the mode-converted Alfvén waves. This in turn provides a radial flow shear responsible for the suppression of plasma turbulence. Thus a strongly nonlinear equation for the radial sheared electric field is solved, and the turbulent transport suppression rate is evaluated and compared with the ion temperature gradient (ITG) instability increment.