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.

A finite-element code is used to study the excitation of a perturbation with a range of azimuthal mode numbers in hollow magnetized plasma columns, and the subsequent nonlinear development and evolution of coherent vortices interacting to coalesce, while cascading to a lower azimuthal mode number. It is shown that, even for initially higher azimuthal mode numbers, the angular momentum remains a slowly varying ideal invariant, while the system cascades to lower azimuthal mode numbers. A detailed study of the evolution is presented for initially excited m = 3, m = 4, and m = 5 azimuthal modes, which underlines the physics of the inverse cascade of angular momentum.

Conditions for exciting higher-harmonic electrostatic dust cyclotron waves in a collisional dusty plasma are investigated. Linear kinetic theory is used, and the effects of neutral–charged particle collisions are taken into account. In a plasma with negatively charged dust, electrostatic dust cyclotron waves can be driven unstable by ions drifting along the magnetic field. It is found that, under certain conditions, the critical ion drift for the excitation of higher-harmonic electrostatic dust cyclotron waves (i.e., ω ∼ mΩd, where m [ges ] 2 and Ωd is the dust cyclotron frequency) can be comparable to the critical drift for the excitation of the fundamental cyclotron harmonic (i.e., ω ∼ Ωd). Stability conditions are investigated for ranges of parameters that may be relevant to laboratory dusty plasmas.

We consider the motion of charged particles in a static magnetic reversal with a shear component, which has application for the stability of current sheets, such as in the Earth's geotail and in solar flares. We examine how the topology of the phase space changes as a function of the shear component by. At zero by, the phase space may be characterized by regions of stochastic and regular orbits (KAM surfaces). Numerically, we find that as we vary by, the position of the periodic orbit at the centre of the KAM surfaces changes. We use multiple-timescale perturbation theory to predict this variation analytically. We also find that for some values of by, all the KAM surfaces are destroyed owing to a resonance effect between two timescales, making the phase space globally chaotic. By investigating the stability of the solutions in the vicinity of the fixed point, we are able to predict for what values of by this happens and when the KAM surfaces reappear.

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.