Two-field fluid models for low-frequency density and electrostatic potential fluctuations in a purely toroidal magnetized low-β plasma are discussed. In particular, we present some simple models suitable for investigating plasma transport close to marginal stability. For gradient-driven fluctuations, linear normal mode analysis of the interchange and resistive drift wave instabilities are reviewed, with attention to the relative phase and amplitude of density and electrostatic potential fluctuations. This reveals many characteristic features of drift-wave fluctuations that are also observed in laboratory experiments and during ionospheric irregularities. Finally, these results are used to investigate the nonlinearly conserved energy functionals, discussing the effect of magnetic field curvature and particle collisions on energy, enstrophy, and cross-correlation between density and vorticity fluctuations. Implications for turbulent fluctuations and nonlinear transport in laboratory and ionospheric plasmas are discussed.

A rigorous theoretical investigation is made of obliquely propagating low-frequency electrostatic waves in a cylindrically bounded magnetized dusty plasma. A number of different modes, such as modified convective cells, coupled ion-cyclotron and dust-ion-acoustic waves, modified lower-hybrid waves, coupled dust-cyclotron and dust-acoustic waves, etc., are investigated. It is shown that the effects of the cylindrical boundary of the dusty plasma system, the external magnetic field, and the obliqueness (of the propagating modes) significantly modify the dispersion properties of these different low-frequency electrostatic waves. The implications of our results for laboratory dusty magnetoplasmas are briefly pointed out.

The formation and propagation of ion phase-space vortices are observed in a numerical particle-in-cell simulation in two spatial dimensions and with three velocity components. The code allows for an externally applied magnetic field. The electrons are assumed to be isothermally Boltzmann-distributed at all times, implying that Poisson's equation becomes nonlinear for the present problem. Ion phase-space vortices are formed by the nonlinear saturation of the ion-ion two-stream instability, excited by injecting an ion beam at the plasma boundary. We consider the effect of a finite beam diameter and a magnetic field, in particular. A vortex instability is observed, appearing as a transverse modulation, which slowly increases with time and ultimately breaks up the vortex. When many vortices are present at the same time, we find that it is their interaction that eventually leads to a gradual filling-up of the phase-space structures. The ion phase-space vortices have a finite lifetime, which is noticeably shorter than that found in one-dimensional simulations. An externally imposed magnetic field can increase this lifetime considerably. For high injected beam velocities in magnetized plasmas, we observe the excitation of electrostatic ion-cyclotron instabilities, but see no associated formation of ion phase-space vortices. The results are relevant, for instance, for the interpretation of observations by instrumented spacecraft in the Earth's ionosphere and magnetosphere.

The Korteweg–de Vries–Zakharov–Kuznetsov (KdV–ZK) equation, governing the behaviour of long-wavelength weakly nonlinear ion-acoustic waves propagating obliquely to an external uniform magnetic field in a non-thermal plasma, admits soliton solutions having a sech2 profile. The higher-order growth rates of instability are obtained using the method developed by Allen and Rowlands [J. Plasma Phys.50, 413 (1993); 53, 63 (1995)]. The growth rate of instability is obtained correct to order k2, where k is the wavenumber of a long-wavelength plane-wave perturbation. The case where the coefficient of the nonlinear term in the KdV–ZK equation vanishes is also considered.

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.