The tearing-mode instability of a magnetic-field-reversing current sheet in the presence of coplanar incompressible stagnation-point flow is examined. The unperturbed equilibrium state is an exact solution of the steady-state, dissipative, incompressible magnetohydrodynamic equations; thus the analysis is valid even for small viscous and resistive Lundquist numbers Sν and Sη. The instability problem has no known analytical solution; for this reason, it is studied numerically by use of a finite-element method. Simulation results indicate stability for sufficiently small values of Sν or Sη and instability for large values. The boundary separating stable and unstable regions in the (Sν, Sη) plane is located. In the unstable regime, the simulation results show formation and subsequent convection of magnetic islands along the current sheet at about 80% of the unperturbed outflow flow speed, on average. Stretching and pinching of convecting magnetic islands are also observed. The results show the occurrence of multiple X-line reconnection at the centre of the current sheet (x = 0). Small-scale structures of vorticity and current density near the X-point reconnection sites are found to be qualitatively consistent with results obtained by Matthaeus. Normalized global linear growth rates are found to obey the approximate power law, within the ranges 20 ≦ Sν ≦ 70 and 200 ≦ Sη 1000. At least for Sν ≦ 1000, the number of magnetic islands is found to be nearly independent of Sν indicating the existence of a narrow band of dominant wavelengths in this range. The stretching of magnetic islands, which is present in this coplanar flow and field configuration, but not in the perpendicular flow and field configuration examined by Phan and Sonnerup, causes a substantial decrease in linear growth rate relative to that obtained by those authors. The stability curves obtained are qualitatively similar in both analyses, but the stable region is much larger for coplanar flow and field. Unlike most simulations of the tearing mode, no symmetry conditions are imposed on the perturbations; nevertheless, they develop in a symmetric manner.

The stability of the MHD tangential discontinuity is studied in compressible plasmas in the presence of anisotropic viscosity and thermal conductivity. The general dispersion equation is derived, and solutions to this dispersion equation and stability criteria are obtained for the limiting cases of incompressible and cold plasmas. In these two limiting cases the effect of thermal conductivity vanishes, and the solutions are only influenced by viscosity. The stability criteria for viscous plasmas are compared with those for ideal plasmas, where stability is determined by the Kelvin—Helmholtz velocity VKH as a threshold for the difference in the equilibrium velocities. Viscosity turns out to have a destabilizing influence when the viscosity coefficient takes different values at the two sides of the discontinuity. Viscosity lowers the threshold velocity V below the ideal Kelvin—Helmholtz velocity VKH, so that there is a range of velocities between V and VKH where the overstability is of a dissipative nature.

From recent tokamak research, there is considerable experimental evidence that superthermal ions slow down and diffuse classically in the presence of turbulent fluctuations that cause anomalous transport of thermal ions. Further more, research on field-reversed configurations at Los Alamos is consistent with the view that kinetic effects suppress instability growth when the ratio of plasma radius to ion orbital radius is small; turbulence is enhanced and confinement degrades when this ratio increases. Motivated by these experiments, we consider a plasma consisting of large-orbit non-adiabatic ions and adiabatic electrons. For such a plasma, it is possible that the anomalous transport characteristic of tokamaks can be avoided and a compact reactor design becomes viable.

Following a previous investigation in which the growth rates of tearing modes at weak instability were determined for a frequently used plasma model with convected resistivity, two further models are considered that appear to be more appropriate for realistic situations. In both of them viscosity is included. One has a self-consistently determined equilibrium resistivity that is kept constant during time evolution. In the other Spitzer resistivity is assumed, which, through its temperature dependence, evolves according to the energy law including thermal conductivity. All calculations are carried out for specific equilibria in a sheet pinch. A salient feature of the two models is the emergence of a stability threshold, which was not present in the previous model. Surprisingly, the results obtained for the two new models are almost the same, thus favouring the much simpler model with constant resistivity.

The Debye length, the characteristic shielding distance in a plasma, is, when the electrons and ions have Maxwellian velocity distributions, determined by the ratio of the temperatures of these components, to the electron (or ion) number density. Plasmas encountered in space, however, commonly exhibit non-Maxwellian velocity distributions, where the evaluation of an appropriate ‘temperature’ from an observed velocity distribution is no longer a recognized procedure. This paper evaluates the shielding distance for a plasma having a modified power-law, or kappa, family of distribuitons characteristic of some space plasmas.

Absolute equilibrium statistical theory and numerical simulations are reviewed in the context of inverse cascades in two- and three-dimensional incompressible fluid and magnetofluid turbulence. Turbulent fluctuations of physically interesting quantities undergo inverse cascade to larger spatial scales, leading to self-organization under certain circumstances. In particular, most systems with more than one quadratic ideal invariant, or, having some kind of imposed anisotropy, exhibit inverse cascades. Anisotropic fluid turbulence in the presence of a uniform rotation and magnetofluid turbulence in the presence of a uniform magnetic field are considered.

Solutions of the Vlasov-Fokker-Planck-Poisson system in a current-carrying plasma are analysed theoretically and numerically in the collisionless and weakly collisional approximations. The class of electron holes is extended, and new solitary electron hole and hump equilibria are found. Numerical solutions of the full time-dependent self-consistent problem are presented that show the non-existence of structural dissipative equilibria as long as ions are treated as an immobile background.

The linear response 4-tensor for a relativistic quantum electron gas may be calculated by reinterpreting the electron propagator in the expression for the vacuum polarization tensor as statistical averages over the electron gas. We apply a similar procedure to two other radiative corrections: the electron self-energy and the vertex correction. When the photon propagator in these expressions is interpreted as a statistical average over a distribution of waves in the medium, these radiative corrections lead to a relativistic quantum expression for the ponderomotive force and to a new class of ‘hybrid’ emission processes.

New dissipative structural equilibria of the Vlasov-Fokker-Planck-Poisson system in a current-carrying plasma with mobile ions are presented. The dynamical evolution towards these final equilibrium states is explored. First consequences for the parallel transport are derived and it is shown that the anomalous resistivity depends on non-symmetric distortions of the electron distribution function in the thermal range which are affected by collisions and ion mobility. The fundamental role of electron holes as the underlying collisionless structure is emphasized.

The Josephson map describes the nonlinear dynamics of systems characterized by the standard map with a uniform external bias superposed. The intricate structures of the phase-space portrait of the Josephson map are examined here on the basis of the associated tangent map. A numerical investigation of stochastic diffusion in the Josephson map is compared with the renormalized diffusion coefficient calculated using the characteristic function. The global stochasticity of the Josephson map occurs at far smaller values of the stochastic parameter than is the case of the standard map.

The viscous damping of surface Alfvén waves in a non-uniform plasma is studied in the context of linear and incompressible MHD. It is shown that damping due to resonant absorption and damping on a true discontinuity are two limiting cases of the continuous variation of the damping rate with respect to the dimensionless number Rg = Δλ2Re, where Δ is the relative variation of the local Alfvén velocity, λ is the ratio of the thickness of the inhomogeneous layer to the wavelength, and Re is the viscous Reynolds number. The analysis is restricted to waves with wavelengths that are long in comparison with the extent of the non-uniform layer (λ ≪ 1), and to Reynolds numbers that are sufficiently large that the waves are only slightly damped during one wave period. The dispersion relation is obtained and first investigated analytically for the limiting cases of very small (Rg ≪ 1) and very large (Rg ≫ 1) values of Rg, For very small values of Rg, the damping rate agrees with that found for a true discontinuity, while for very large values of Rg, it agrees with the damping rate due to resonant absorption. The dispersion relation is subsequently studied numerically over a wide range of values of Rg, revealing a continuous but nonmonotonic variation of the damping rate with respect to Rg.

Two approaches to defining almost-invariant surfaces for magnetic fields with imperfect magnetic surfaces are compared. Both methods are based on treating magnetic field-line flow as a 1½-dimensional Hamiltonian (or Lagrangian) dynamical system. In the quadratic-flux minimizing surface approach, the integral of the square of the action gradient over the toroidal and poloidal angles is minimized, while in the ghost surface approach a gradient flow between a minimax and an action-minimizing orbit is used. In both cases the almost-invariant surface is constructed as a family of periodic pseudo-orbits, and consequently it has a rational rotational transform. The construction of quadratic-flux minimizing surfaces is simple, and easily implemented using a new magnetic field-line tracing method. The construction of ghost surfaces requires the representation of a pseudo field line as an (in principle) infinite-dimensional vector and also is inherently slow for systems near integrability. As a test problem the magnetic field-line Hamiltonian is constructed analytically for a topologically toroidal, non-integrable ABC-flow model, and both types of almost-invariant surface are constructed numerically.

Linear null points of a magnetic field may come together and coalesce at a secondorder null, or vice versa a second-order null may form and split, giving birth to a pair of linear nulls. Such local bifurcations lead to global changes of magnetic topology and in some cases release of magnetic energy. In two dimensions the null points are of X or O type and the flux function is a Hamiltonian; the magnetic field may undergo addle-centre, pitchfork or degenerate resonant bifurcations. In three dimensions the null points and their creation or annihilation by bifurcations are considerably more complex. The nulls possess a skeleton consisting of a spine curve and a fan surface and are of radial-type (proper or improper) or spiral-type; the type of null and the inclination of spine and fan depend on the magnitudes of the current components along and normal to the spine. In cylindrically symmetric fields a comprehensive treatment is given of the various types of saddle-node, Hopf and saddle-node—Hopfbifurcations. In fully three-dimensional situations examples are given of saddle-node and degenerate bifurcations, in which generically two nulls are created or destroyed and are joined by a separator field line, which is the intersection of the two fans. Furthermore, global bifurcations can create chaotic field lines that could perhaps trigger energy release in, for example, solar flares.

The results of recent developments in the theory of fluctuations in plasmas show that the previously used theory of bremsstrahlung is incomplete and the exact expressions for bremsstrahlung should include transition bremsstrahlung. The collective effects in bremsstrahlung known previously as Debye screening are changed to a qualitatively different structure, which removes the effect of ion polarization in bremsstrahlung and introduces a new effective polarization which depends on an effective ion charge and electron velocity. The results may be relevant for applications in plasmas when the wavelength is greater than the Debye length. It is shown that for the problem of photon transport in the solar interior the correct collective corrections to the bremsstrahlung change the opacity by only about −0·35%, which is less than was calculated previously when collective effects in bremsstrahlung where estimated without taking recent results of plasma fluctuation theory into account.

The hypothesis that the steady, or statistically steady, states of a magnetofluid can be predicted by minimizing the integral of the total energy dissipation is discussed in relation to theorems in fluid dynamics. A survey is made of the recent literature wherein the hypothesis is used to predict magnetofluid behaviour and some related work. A detailed discussion of boundary conditions is provided, and we close with a brief summary of the current state of research.

A theoretical investigation of radio-frequency (RF) current drive via helicity injection in low aspect ratio tokamaks is carried out. A current-carrying cylindrical plasma surrounded by a helical sheet-current antenna and situated inside a perfectly conducting shell is considered. Toroidal features of low-aspect-ratio tokamaks are simulated by incorporating the following effects: (i) arbitrarily small aspect ratio, Ro/a ≡1/∈; (ii) strongly sheared equilibrium magnetic field; and (iii) relatively large poloidal component of the equilibrium magnetic field. This study concentrates on the Alfvén continuum, i.e. the case in which the wave frequency satisfies the condition , where is an eigenfrequency of the shear Alfven wave (SAW). Thus, using low-β magneto- hydrodynamics, the wave equation with correct boundary (matching) conditions is solved, the RF field components are found, and subsequently current drive, power deposition and efficiency are computed. The results of our investigation clearly demonstrate the possibility of generation of RF-driven currents via helicity injection by Alfvén waves in low-aspect-ratio tokamaks, in the SAW mode. A special algorithm is developed that enables one to select the antenna parameters providing optimal current drive efficiency.

The Charney-Hasegawa-Mima equation and two-dimensional magnetohydrodynamics (MHD) have ideal Lagrangian invariants that are used as the basis for most probable state analysis. An information-theoretic entropy defined in terms of the Lagrangian invariants leads to predictions for relationships between the field quantities. These relationships are tested through numerical solution of the equations through the turbulent relaxation of random initial conditions to coherent states. It is found that the predictions for the most probable state for the Charney—Hasegawa—Mima equation are essentially correct, whereas for two-dimensional MHD they are not. Questions and issues are raised pertaining to why a most probable state analysis based upon Lagrangian invariants seems to work in the case of the Charney—Hasegawa—Mima equation but not for two-dimensional MHIJ. A qualitatively correct entropy is proposed for two-dimensional MHD based upon field variables that are not local invariants.

A theoretical investigations is made of the stability of electrostatic waves in a magnetized non-thermal plasma. The Zakharov-Kuznetsov equation (or Korteweg-de Vries equation in three dimensionas) for these solitary waves in this plasma system is derived, and their three-dimensional stability is studied by the small-k (long wavelength plane-wave) perturbation expansion method. The instability criterion and its growth rate depending on the magnetic field and the propagation directions of the solitary wave and its perturbation mode are discussed.