Equations describing the resistive evolution of a cylindrically symmetric magnetic field through force-free states enable us to study its response to externally applied electric fields. The process is relaxational, and, under certain conditions, the final state is a reversed field configuration. We show, moreover, that the non-standard nature of the equations leads to a non-trivial (adiabatic) evolution in the case of vanishing resistivity.

This is part 2 of a paper concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized plasma. It refers to transverse linearly polarized waves in an electron-positron plasma. A numerical method, based on Floquet's theory of linear differential equations with periodic coefficients, is used to solve the perturbation equations and obtain the instability growth rates. All the three possible types of perturbations are discussed for a typical value of the (large) amplitude of the nonlinear wave: electrically longitudinal slightly unstable modes (with maximum growth rate γ approximately equal to 0·07ω0, where ω0 is the frequency of the nonlinear wave); purely transverse moderately unstable modes (with γ ≃ 0·26ω0); and highly unstable electrically transverse modes (with γ ≃ l·5ω0).

Forced magnetoacoustic oscillations in a fully ionized, non-uniform, current carrying plasma column of finite beta are treated theoretically. The results of numerical calculations are given for the specific case of diffuse pinch equilibrium configurations. It is found that, for these configurations, the amplitude of the axial component of the oscillating magnetic field is enhanced and the frequency at which magnetoacoustic resonance occurs is raised. It is also found that the presence of an equilibrium axial current produces a substantial azimuthal component, in addition to the axial component, of the oscillating magnetic field.

A theoretical method is proposed for predicting the properties of the backward propagating cyclotron harmonic waves from the simple dispersion curve for perpendicular propagation. This method is illustrated for the frequency range 1 ω÷ωc ω 2, where ω and ωc, are, respectively, the wave and electron cyclotron frequencies, and is applicable from very low to infinite plasma densities. The behaviour of the backward propagating cyclotron harmonic wave in the whole propagation space and then in the real space can be easily deduced. The method can be extended to any dispersion branch of backward cyclotron harmonic waves.

The Sonnerup solution for reconnexion about an X-type magnetic null point is modified to involve only stable shocks. However, the reconnexion process described does not originate at the line breaking point but is engineered by precise boundary conditions in the inflow region. Our solution is also valid in the compressible case. The limit on the reconnexion rate (in Mach number units) is about 1·5. A non-uniqueness of the solution raises the possibility of viewing flare phenomena as abrupt jumps to different branches of the solution.

From hybrid-kinetic theory an eigenvalue equation for electromagnetic perturbations with ω ≈ ωci in collisionless theta-pinches with anisotropic ion energy was recently derived. This equation is presently reduced to two ordinary second-order linear differential equations by an expansion in the thermal ion Larmor radius. The leading-order correction terms contain Cherenkov resonances absent in the homogeneous case, which are reached for speeds ≈ υ| β|-½ and wave-numbers typical for unstable modes in the homogeneous case, indicating the importance of Cherenkov resonance on the stability of modes driven by ion energy anisotropy. These equations are supplemented by appropriate boundary conditions for the case when the plasma is surrounded by a cylindrical, perfectly conducting wall. For weak inhomogeneities a local dispersion equation is obtained. The physical mechanism underlying the influence of Cherenkov resonance parallel to the confining magnetic field as a FLR effect on stability behaviour is illustrated.

The excitation of the slow extraordinary and electron whistler modes with frequencies in the vicinity of the electron plasma frequency is investigated for a plasma which is composed of thermal and suprathermal electrons. Ion dynamics are ignored. The suprathermal electrons are assumed to comprise a long, anisotropic tail parallel to the ambient magnetic field. Instability is found to occur via a relativistic, anomalous gyroresonance with the suprathermal electrons, and to excite waves with frequencies above and below the electron plasma frequency. Landau and cyclotron damping due to the thermal background is included in the treatment.

Self-similar solutions of the magnetogasynamic equations are derived which describe the resistive decay of a plane current sheet in a compressible plasma. Such current sheets are thought to provide the magnetic energy storage in solar flares. They also occur at the boundaries between regions containing different magnetic-field directions in interplanetary space, and at the interface between the solar wing and the earth' magnetic field. It is shown that the resistive decay of a current sheet in a compressible plasma must involve plasma motion. The convective effects associated with this motion are incorporated in the analysis; the inertia effects are not. The electrical and thermal conductivities are taken to be constant, but the analysis may easily be generalized to include realistic temperature and magnetic field dependences of these quantities. Radiative and viscous terms are not included. The ordinary differential equations resulting from the similarity hypothesis are solved numerically, yielding curves of the plasma density, temperature, and velocity, as well as of the magnetic and induced electric fields, as functions of the similarity variable. The non-dimensional groups of importance are: y, the ratio of specific heats at constant pressure and constant volume; Kx, the ratio of thermal to resistive diffusivity; β∞, the ratio of plasma pressure to magnetic pressure at large distances from the current sheet. The first of these ratios is kept constant and equal to 5/3, corresponding to a monoatomic gas. The behaviour of the solution when the other two ratios are varied is investigated. The plasma velocity at large distances from the current sheet does not vanish in these solutions. It is always directed toward the sheet. However, when the diffusivity ratio K∞ is small, plasma flow away from the centre of the sheet also occurs in two narrow regions, one on each side of the centre. As a result of the reversals in the flow direction, the density then displays a relative minimum at the centre of the sheet with two outward travelling maxima adjacent to it. The plasma temperature at the centre of the sheet becomes very large for small K∞ and β∞ The expansion of the sheet becomes explosive and inertia effects can no longer be neglected. The physical meaning of these results is discussed and directions for further research are outlined.

The stability problem of the double layer (electrostatic shock) is investigated using a simple model of the plasma. It is shown that local Penrose-stability in general is insufficient for global stability, owing to the existence of linerly unstable trapped Langmuir modes in the density cavity. An additional requirement for stability is that the thickness of the layer must be smaller than a critical value, which in the case of a strong layer (eΔπ/κTe ≫ 1). and for the particular model being used, is of the order (eΔπ/κTe)½ λD. Various qualitative features of the instability mechanism are discussed in terms of normal mode coupling, and quantitative results, such as mode frequencies, growth rates etc., are obtained by means of a conventional perturbation approach, which, in addition to the results expected from coupled mode theory, also shows the existence of two purely decaying modes, appearing for a sufficiently thin, stable layer. The double layer formation process is briefly commented on, and some distinguishing features of the instability in this regard are pointed out.

The stability of cylindrical flux surfaces in the presence of finite resistivity and parallel ion viscosity is reconsidered, and in particular the increment in the logarithmic derivative Δ(Q) over the inner dissipative region. Correction of the viscosity coefficient removes the branch-point behaviour at large growth rates reported earlier. Numerical results for real Q in the high-beta hard-core pinch are supported by mathematical analysis to show that parallel ion viscosity renders Δ(Q) positive definite provided D < 0, with a positive minimum increasing with temperature. This stabilization is associated with coupling of the parallel plasma motion in the presence of magnetic field curvature. The viscous compressible value of Δ(Q) is somewhat less than its inviscid compressible counterpart at small real Q, so that relative to purely compressible theory parallel ion viscosity can be slightly destabilizing.

The generation of Langmuir solitons at the resonance layer in a plasma irradiated by a strong high-frequency pump is investigated. The process is modelled by the nonlinear Schrödinger equation including an external pump, a density gradient and linear damping. The evolution equation is reformulated as an exact variational principle and the one-soliton generation process is studied by substituting various trial solutions. The applicability conditions for the nonlinear Schrödinger equation are re-examined and found to be more restrictive than previously stated.

This paper considers nonlinear interaction between three monochromatic waves in a hot non-uniform electron plasma. With the aid of coupled mode theory the interaction of three longitudinal waves is studied and a specific case of the interaction of two longitudinal waves and one perpendicular wave is derived for the limiting case of long wavelength. Furthermore, the non-uniformity involves generalization of the theory of the interaction of two transverse waves and one longitudinal wave of a previous contribution.

This paper provides an analysis of the propagation characteristics of ion cyclotron waves in a magnetized plasma whose density varies in a direction perpendicular to the ambient magnetic field. It is shown that the component of the wave energy flux across the density stratification is conserved except at a critical level (which is associated with a resonance singularity in the wave equation) at which the jump in the wave energy flux is balanced by wave absorption by the plasma. The relationship of this behaviour with field line resonance is briefly discussed, as is its possible relevance to ULF waves propagating in the vicinity of the earth's plasmapause.

It is shown that a whistler-mode signal propagating obliquely to the external magnetic field can parametrically decay into a daughter wave and an ion cyclotron wave. A dispersion relation involving a three-wave decay process is derived. Application of our results in space plasma is pointed out.