The storage of magnetic energy in many natural systems is driven by localized convection. Since the initial state can often be described as a potential field, the stress arising from subsequent magnetic twisting is characterized by vanishing net-current flow. Such a layering scheme provides the lowest global energy excess for a given local field twist. In this paper we investigate the nonlinear release of this stored energy by the resistive magnetic-tearing instability. Our aim is to discover whether the evolution of this dynamic reconnection process is modified by the finite width and restoring force of the energizing field reversal. We use a force-free magnetic-field model with the sheared reversing component varying as tanh y sech Ky. We study the unstable nonlinear evolution by a 2·5-dimensional resistive magnetohydrodynamic simulation in a slab geometry. Almost all of the perpendicular (with respect to the ignorable coordinate) stored magnetic energy is released for some cases in this model. Although the magnetic reconnection is due to resistivity, the resulting closed flux surfaces evolve to a lower-energy state, i.e. to a nearly circular one, by mostly ideal MHD. Thus an elongated flux surface drives the plasma flow, and the flow speed is comparable to the Alfvén speed. The excess or stored magnetic energy is thereby released. In general, however, these processes take place only after reconnection occurs, and thus the release of energy is limited by the reconnection rate. The evolution of our new current/field system, which is more realistic as a model of a solar flare, exhibits an energy-release rate similar to that of more conventional field configurations. This rate can be increased, however, by the effects of an assumed anomalous resistivity enhancement.

The nonlinear behaviour of azimuthally symmetric Alfvén waves propagating along the axis of a cylindrical ideally conducting compressible fluid-filled waveguide is investigated. It is shown that the nonlinear evolution of such waves is governed by the nonlinear Schrödinger equation. Modulational instability for fundamental (m = 1) radial mode is discussed for α2 = 0·1,0·2, 0·3 and different values of k. The amplitude-dependent frequency and wavenumber shifts are calculated and their variations with wavenumber are shown graphically.

A solution is presented for electron plasma oscillations in a thermalized plasma, at arbitrary ratios of the Debye length AλD and the perturbation wavelength λ. The limit λD≪λ corresponds to the conventional fluid-like theory of small particle excursions, whereas λD≫λ corresponds to the free-streaming limit of strong kinetic phase mixing due to large particle excursions. A strong large-Debye-distance (LDD) effect already appears when λD ≳ λ. The initial amplitude of the fluid-like contribution to the macroscopic density perturbation then becomes small compared with the contribution from the free-streaming part. As a consequence, only a small fraction of the density perturbation remains after a limited number of kinetic damping times of the free-streaming part. The present analysis can be considered as a first exercise in an attempt to tackle the far more difficult problem of large-Larmor-radius (LLR) effects in a magnetized plasma. The analysis further shows that a representation in terms of normal modes of the form exp (— iωt) leads to amplitude factors of these modes that are related to each other and that depend on the combined free-streaming and fluid behaviour of the plasma. Consequently, these modes are coupled and cannot be treated as independent of each other.

The possibility of a new set of thermonuclear cone instabilities in tokamaks is demonstrated. These instabilities are caused by an inherent anisotropy existing in the alpha-particle velocity distribution function owing to the finite width of the particle orbits in combination with a spatially varying particle source. The conditions for the excitation of shear Alfvén waves by well-trapped alpha particles are studied.

The velocity-space diffusion equation describing distortion of the velocity distribution function due to resonant wave-wave scattering of electromagnetic and electrostatic waves in an unmagnetized plasma is derived from the Vlasov-Maxwell equations by perturbation theory. The conservation laws for total energy and momentum densities of waves and particles are verified, and the time evolutions of the energy and momentum densities of particles are given in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation.

Subgrid-scale closures for magnetohydodynamic (MHD) turbulence are examined using the filtering technique. From the similarities between incompressible MHD turbulence and its hydrodynamic counterpart, as well as ideas from dynamo theory, a subgrid model is constructed from the large-eddy simulation (LES) of MHD turbulence. This model should find applicability in treating LES of the reversed-field pinch.

Runaway processes on neutron stars leading to the sudden release of large quantities of energy (up to of order 1040 erg) on time scales as short as a fraction of a second involve plasma heating and particle acceleration in superstrong magnetic fields H (of order 1012 G). These transient events are interesting from a theoretical standpoint because they require knowledge of particle transport properties in low-density plasmas (εe ≲ 1025 cm−3) threaded by both electric (E) and magnetic fields. The evaluation of matrix elements involving solutions to the Dirac equation for such a field configuration is often difficult and sometimes impossible, since no completely normalized wave function has yet been found. Here it is shown that, in the special case of E/H ≲ 10−4, a simplification of the overlap integrals permits an analytical integration that yields explicit expressions for the relativistic charge currents needed in the computation of the anisotropic conductivity tensor when E.H ≠ 0. The application of these results to the evaluation of the conductivity is briefly discussed. Among other things, this work is relevant to a theory of resistive magnetic tearing instabilities in a quantizing field.

Computer simulations are used to investigate the basic three-dimensional structure of the fast reconnection mechanism spontaneously developing from a long current sheet. It is shown that if three-dimensional effects (∂sol;∂z ≠ 0) are not so strong, a locally enhanced resistivity results in current-sheet thinning, and a fast reconnection process, involving switch-off shocks, is eventually set up in a region limited in the z direction. The fast reconnection process near the z = 0 plane becomes quasi-steady and two-dimensional (∂/∂z = 0), so that the well-known Petschek mechanism is fully applicable. Distinct plasma rarefaction occurs inside the fast reconnection region, so that fast-mode expansion may propagate in the z direction, and the resulting inflow velocity uz takes the magnetic field into the fast reconnection region and contracts the latter. The global current system undergoes drastic changes during the fast-reconnection development. The current flow, initially directed in the z direction, first converges towards the neutral line, and is then largely deflected away from this line in the inner reconnection region.

Within the framework of studies of the stability of magneto-plasmas to non-ideal modes, such as resistive modes, the problem of determining the asymptotic matching data arising from the outer (ideal) region is considered. Modes possessing both tearing and interchange (ballooning) parity are considered in finite-pressure plasmas. The matching data, which form a matrix whose elements represent the small solution response to forcing by a big solution, are shown to derive from a variational (energy) principle. The variational principle, as presented, applies to both cylindrical and two-dimensional (toroidal) geometries. Allowing for the presence of multiple rational surfaces, a reciprocity relation between off-diagonal elements of the matching data matrix is obtained. The variational principle is suitable for numerical approximation, and, in particular, for the finite-element method, for which convergence rates are estimated. By packing nodes near the rational surface, maximum convergence, proportional to the inverse square of the number of mesh nodes for tent functions, is achieved.

A large-amplitude whistler wave excited at the difference frequency of two high-frequency electromagnetic pump waves is shown to decay parametrically into a lower-hybrid wave (LHW) and a low-frequency ion–Bernstein wave (IBW) in a collisionless magnetized multi-ion-species plasma,. A nonlinear dispersion relation describing this parametric interaction process is derived. The low-frequency ponderomotive force along the direction of the external magnetic field leads to the dominant coupling. Possible applications to ion heating in the ionosphere, in the earth's magnetosphere and in laboratory plasmas are discussed.

The effect of a sheared equilibrium mass flow on the resistive tearing mode is studied numerically by calculating Δ′. Both stabilizing and destabilizing effects are found, depending on the velocity and magnetic field profiles. Specifically, when q0 ≈ 1, the flow is strongly stabilizing for centrally peaked current profiles, whereas the flow has a strongly destabilizing effect for flatter current profiles. While the extreme effects are more pronounced for larger flows, a smaller flow may have more influence on marginal stability. The case where the flow speed becomes comparable to the Alfvén speed is also examined. It is found that this may lead to the equations being singular at points other than a rational surface, drastically changing the behaviour of the mode.

The classical incompressible MHD or cold plasma phase mixing problem, which involves Alfvén or plasma waves in inhornogeneous media, is re-examined using a spatial Fourier series rather than the usual temporal Fourier or Laplace transform approach. A number of exact and near-exact analytic and numerical results are derived which reveal an attractive picture of energy cascading to smaller length-scales in a manner reminiscent of turbulence. Furthermore, we present a simple and unambiguous description of how a surface wave arises in the limit in which the inhomogeneity becomes a discontinuity.

The permittivity tensor Є¸(K, ω) of an electron–ion plasma with paramagnetic atoms as neutral component (a paramagnetic plasma) is obtained. Based on this tensor, new types of slow electromagnetic waves in the paramagnetic plasma are predicted.

There exist plasma waves that transport helicity although they do not propagate electromagnetic energy. The dispersion relations of such helicity waves are studied. The electric field of the waves is parallel to the perturbed magnetic field, and both are perpendicular to the perturbed current. In cross-field propagation, a helicity wave is decomposed into two transverse modes with different polarizations and a longitudinal part. The helicity waves are principally Alfvénic in the low-frequency limit. At high frequencies, the Faraday effect comes into the polarization.

Nonlinear propagation of acoustic-type waves in a partially ionized three-component collisional plasma consisting of electrons, ions and neutral particles is investigated. For bidirectional propagation, we show that the small- but finite-amplitude waves are governed by the Boussinesq equation, which for unidirectional propagation near the acoustic speed reduces to the usual Korteweg de Vries equation. For large-amplitude waves, we demonstrate that the relevant fluid equations are integrable in a stationary frame, and we explicitly obtain the parameter values for the existence of finite-amplitude solutions. In both cases, we take into account the different temperatures of the individual species. The relevance of the results to the earth's ionospheric plasma in the lower altitude ranges is pointed out.