An equilibrium state of a magnetized non-neutral plasma confined in a smooth cylindrically symmetric container is obtained. The particle number of each species is fixed, and total energy and total canonical angular momentum are conserved in the system. Moreover, the most probable state satisfies the stationary Vlasov equation exactly. The key finding from this result is that the E × B drift velocity can be significantly different from the true fluid velocity, which always corresponds here to a rigid rotation. It is suggested that this difference may also be experimentally important in situations that are not in thermal equilibrium.

Electromagnetic surface waves dissipate energy as they propagate in plasma columns. The transfer of energy to the discharge generally occurs through collisional processes — hence the name ‘collisional’ surface waves. It affects the direction of propagation of the wave, and is responsible in particular for the turning back of the axial wavenumber on the phase diagram. The rate of collisions also influences the respective contribution of surface waves and radiation (unguided) waves to the total electromagnetic field. These considerations are of interest in improving the reliability and accuracy of the electron density diagnostic based on surface waves. This paper takes advantage of the many articles published in the domain of guided waves for antennas.

A systematic analysis of low-frequency waves such as hydromagnetic and acoustic waves in a magnetized dusty plasma containing electrons, ions and dust particles is presented. Starting with the three-fluid equations and the Maxwell equations, we derive, retaining finite ion mass, an effective two-fluid model incorporating deviations from the frozen-in-fluid approximation for the ion and electron fluid motions. We show that normal modes exist in two widely separated frequency regimes. In addition to obtaining hydromagnetic waves that are generalizations of the usual Alfven and magneto-acoustic modes in a two-component electron–ion plasma, we demonstrate the existence of a new class of magneto-acoustic waves (both fast and slow type) called ‘dustmagneto-acoustic waves’. These modes have qualitatively different dependences on the equilibrium parameters such as density, magnetic field and temperature when compared with the usual magneto-acoustic waves. The new modes arise owing to finite ion mass (compared with the dust-particle mass), leading to an effective inertial resistivity that inhibits the ion (as well as the electron) fluid from being frozen to the magnetic field lines. The fast branch of the dust-magneto-acoustic waves is shown to be the electromagnetic generalization of the electrostatic dust-acoustic wave recently obtained in unmagnetized dusty plasmas. In the two-component limit the new modes degenerate into the usual type of magneto-acoustic waves. Dispersion relations for various other modes are also presented.

The influence of electron inertia, ion streaming and weak relativistic effects on the modulational instability of ion-acoustic waves in a collisionless unmagnetized plasma is investigated. The derivative expansion method is used to derive a nonlinear Schrödinger equation, from which an instability criterion is deduced. When electron inertia is ignored, ion streaming and weak relativistic effects have little effect on the instability criterion. It is shown that when electron inertia is taken into account, the instability criterion is sensitive to weakly relativistic ion streaming, but not to the ratio of electron mass to ion mass.

Nonlinear interactions of tearing modes result in chaotic magnetic fluctuations. A system of ordinary differential equations is derived to model the nonlinear interactions of magnetic islands with different helicities. For a reasonable set of parameters, the solution shows chaotic behaviour.

Approximate analytical solutions of the waves and fields inside and outside the coupling region for an arbitrary number of propagating modes of all kinds and an arbitrary number of couplings and mode conversions are presented. The method is applied to the propagation of electromagnetic fields in a plane- stratified cold plasma as an illustrative example.

In this work we analyse the stochastic dynamics of initially low-energy weakly relativistic particles moving under the action of electrostatic waves. The relevant phase space is not well described by standard nonlinear pendulum approximations, but appropriate resonance studies based on the overlap of primary and secondary islands show that three regions may be identified as the wave vector k of the electrostatic mode is varied: one for small values of k, where the dynamics is always relativistic and regular; one for moderately large values of k, where the dynamics is always relativistic, being regular for small field amplitudes and stochastic for large field amplitudes; and finally one for fairly large values of k, where the dynamics is relativistic and regular for small amplitudes of the wave field and non-relativistic and stochastic for larger values of the amplitude. We perform an extensive numerical analysis in order to check our analytical estimates, and finally we present a brief numerical study of particle diffusion in the relativistic stochastic regime.

Following renewed interest in the guiding-centre problem, we propose an alternative to previous approaches. It consists essentially in demonstrating the existence of a representative simple model for which the problem is rigorously solved in the Hamilton–Jacobi framework. It is shown that a perturbation method allows the extension of the model to more realistic cases. A further extension to cover both magnetic-mirror configurations and tokamaks can be achieved.

Fourier analysis is used to consider the characteristics of linear magnetosonic N waves propagating through a uniform background medium at rest, with constant uniform magnetic field В0. The disturbance is driven by an initial compressed and localized gas pressure perturbation, represented by a Dirac delta distribution. The solutions for the perturbed gas and magnetic field variables are expressed as second derivatives of appropriate wave potentials. The wave potentials split naturally into fast and slow magnetosonic components. The fast- and slow-mode wave potentials reduce to onedimensional integrals over the wave normal angle θ between the wave vector k and B0. Alternatively, the fast-mode wave potentials can be written as Abelian integrals over the slow-mode phase speed cs, whereas the slow-mode potentials reduce to Abelian integrals over the fast-mode phase speed cf. The structure of the integrals depends on the location of the observation point relative to the fast and slow magnetosonic eikonal or group velocity surfaces. Calculations of the time evolution of the magnetic field of the N wave show a family of magnetic field lines connecting the cusps of the slow magnetosonic group velocity surface, plus a further family of field lines not connected with the cusps. The wave disturbance is confined on and within the fast magnetosonic group velocity surface. The gas pressure perturbation shows singular N wave type disturbances on the fast- and slow-mode eikonal surfaces. The Green's function for the magneto-acoustic wave operator for a uniform background medium initially at rest is also obtained. Generalization of the N wave solutions for non-singular distributions of the initial gas pressure perturbation are also obtained.

A thermal instability is studied as an explanation of the anomalous electron density depletion observed during the electron-cyclotron resonance (ECR) heating of plasma in a tokamak device for an impurity study experiment (ISXB). Considering the fact that the background plasma has an elevated electron temperature and a localized heat source located near the ECR layer, we show that density striations having scale length 10 cm and larger can be excited via the thermal instability. The amplitude of the striations can grow by more than one e-folding during the ECR pulse period of 10 ms, which causes about 50% electron temperature elevation. A 0·1% temperature fluctuation excited by the thermal instability leads to about 50 V m-1 field fluctuation. Such a large electrostatic field can effectively cause anomalous plasma diffusion via the E ′ B drift and account for the observed 15% electron density depletion.