In a cold plasma, the 0 and X modes are determined by the orientation of the first-order electromagnetic fields with respect to the equilibrium magnetic field B0. In the particular case where the direction of B0 is a function of position the distinction between these types of waves is lost. In this paper, two semi-infinite regions of homogeneous cold plasma are connected by a finite zone in which the equilibrium magnetic field has a spatially periodic shear. This system is studied self-consistently to reveal the mode-con version and transmission characteristics of plasmas containing field structures of this kind, and preliminary calculations of the full coefficients are presented. The results thus obtained are directly relevant to situations where magnetic shear is important.

This paper presents an investigation of the growth of a radially symmetrical ripple, superimposed on a Gaussian electromagnetic beam in a collisionless magnetized plasma. On account of the non-uniform intensity distribution of the main beam, the d.c. component of the ponderomotive force becomes finite and leads to modification of the background density. There is feedback from the main beam to the ripple, which subsequently grows at the cost of the pump wave. The effect of the plasma and pump parameters is studied in detail. An interesting feature is that the ripple always grows, irrespective of the phase relationship of the main beam and the ripple. This is due to strong self-focusing of the main beam for the chosen set of parameters.

The general Hamiltonian-averaging transformation developed to study the motion of a charged particle in a strong magnetic field and various electromagnetic perturbations permits a clear definition of the dynamics of the guiding centre. In the case of a high-frequency electromagnetic perturbation, the equations of evolution of the phase-space co-ordinates are sums of guiding-centre terms, resonant terms at any of the cyclotron resonance frequencies n(r‖k‖–ω)+lΩ≈0(l and n are integers) and ponderomotive terms. In this paper we consider the n = 1 resonances giving a contribution one order stronger than the ponderomotive terms to the equations of motion. The guiding-centre transformation therefore suffices to derive the leading terms of the averaged dynamics. A simple case of isolated resonance is then considered for which, depending on the value of the external parameters (initial particle energy, amplitude of the perturbation), the phase space may possess one or two trapping regions. Even in the latter situation, the particle trajectories can be described analytically by the set of 12 Jacobian elliptic functions.

An alternative representation of the dielectric tensor εij(k, ω) for a relativistic magnetized plasma in thermal equilibrium is presented. This representation involves an infinite series expansion in powers of , as well as an asymptotic expansion for large Here ωc = eB0/mc is the nonrelativistic cyclotron frequency, k⊥ is the wavenumber perpendicular to the magnetic field B0êz, and α is the dimensionless parameter defined by α = mc2/KBT. The present work generalizes Shkarofsky's (1966) representation. Moreover, unlike Trubnikov's (1958) formal result, in which the k⊥ and kz dependences of εij(k, ω) are inexorably coupled, the present representation naturally separates the k⊥ and kz dependences of εij(k, ω). As an application, the general expression is simplified for the case of a weakly relativistic plasma, and the dispersion relation is obtained for electromagnetic waves, including first-order relativistic effects. The method developed in this paper can be used for other non-thermal distributions.

The energy transfer between a homogeneous heat-conducting collisionless plasma in a strong magnetic field and a harmonic external current immersed in it is studied in connection with the generation of stable magnetohydrodynamic waves in slow streams in the solar-wind plasma. The net balance of energy, given by the sum of the individual contributions that result from the interchange between each mode of oscillation and the stream, is established as function of the amplitude, frequency and growing rate of the external current and the plasma parameters.

Tokamak equilibria are considered as extremum magnetic-energy states. Two quadratic invariants ∫Ψd3x, and ∫A.Bd3x are found to yield finite-beta equilibria in toroidal geometry. The theory predicts ‘bell’-shaped current profiles for relaxed discharges at finite beta. A ‘main-sequence’ curve of ql/q0 versus βp is presented for circular discharges with low ql and is found to form a limiting curve for experimental data.

An understanding of the energy transfer that takes place during magnetic reconnection is crucial to the study of this fundamental process. It depends on two factors: the type of reconnection regime (which is determined by the boundary conditions) and the degree of compressibility. Here we examine the role of compressibility in the energetics of a family of reconnection models. When the inflow Mach number (or reconnection rate) Me is small the effects of compressibility may be more important than the differences between regimes. We find that for a slow-compression regime with Me = 0·005 compressibility decreases by 39% the efficiency of the shocks in converting magnetic energy and increases by 14% the ratio of thermal to kinetic energy in the outflow jet. This compares with a 13% decrease in the shock efficiency and a 7% decrease in the jet ratio obtained by choosing instead a flux-pile-up regime. As Me is increased, however, the differences between regimes become larger and may be comparable to or greater than the effects of compressibility. Thus when the above Mach number is doubled we find that a change of regime now has 1–6 times the effect on the jet energy ratio as the introduction of compressibility. For those regimes, therefore, which only exist at low inflow Mach numbers, compressibility will always be important. At higher values of Me the type of regime may be the dominant factor governing the energetics.

The Bineau reduction to scalar form of the equation governing ideal zero-frequency linearized displacements from a hydromagnetic equilibrium possessing a continuous symmetry is performed in ‘universal co-ordinates’, applicable to both the toroidal and helical cases. The resulting generalized Newcomb equation (GNE) has in general a more complicated form than the corresponding one-dimensional equation obtained by Newcomb in the case of circular cylindrical symmetry, but in this cylindrical case we show that the equation can be transformed to that of Newcomb. In the two-dimensional case there is a transformation that leaves the form of the GNE invariant and simplifies the Frobenius expansion about a rational surface, especially in the limit of zero pressure gradient. The Frobenius expansion about a mode rational surface is developed and the connection with Hamiltonian transformation theory is shown. The derivations of the ideal interchange and ballooning criteria from the formalism are discussed.

The wave differential operator is obtained directly from the perturbed Vlasov equation for an inhomogeneous equilibrium magnetic field including consistently the effects of strong wave damping and linear mode conversion. In the process, conditions on the parallel wavenumber and the magnetic-field gradient for which such a method is valid are obtained. From these equations it is shown that the inclusion of parameter-gradient terms arising from the spatial dependence of the equilibrium magnetic field is important for accurate calculation of mode conversion from fast to ion-Bernstein wave, although the dispersion-relation-based operator can be sufficient to describe transmission and reflection of the fast wave. Finally, the coupled second-order equations used by Fuchs & Bers (1988) are obtained, allowing direct identification of the ‘modes’ referred to in that paper in terms of components of the electric field. By reconciling these two different approaches, some insight is gained into the mode-conversion process.

We derive a Fokker–Planck equation for relativistic and degenerate electrons interacting with ions. The ions may be degenerate and relativistic. Applications to a supernova plasma and laser–plasma interaction motivate this work.