The multi-dimensional structure of weak, energetic-particle-modified shocks is investigated by means of appropriate perturbation techniques. The time-dependent shock-structure equation is found to be a generalized form of the well-known one-dimensional Burgers equation, whose steady state, in the absence of cosmic rays, is shown to be related to an equation modelling steady transonic flow in several dimensions. The time-dependent (1 + 2)- and (1 + 3)-dimensional Burgers equations are integrated exactly by means of Hirota's technique for one-shock solutions. On the basis of the exact solutions, a discussion relating the various length scales associated with the shock is presented.

On the basis of the dynamic equations governing the evolution of magneto-hydrodynamic fluctuations expressed in terms of Elsässer variables and of their correlation functions derived by Marsch and Tu, a new set of equations is presented here describing the evolutions of the energy spectrum e± and of the residual energy spectra eR and es of MHD turbulence in an inhomogeneous magnetofluid. The nonlinearities associated with triple correlations in these equations are analysed in detail and evaluated approximately. The resulting energy-transfer functions across wavenumber space are discussed. For e± they are shown to be approximately energy-conserving if the gradients of the flow speed and density are weak. New cascading functions are heuristically determined by an appropriate dimensional analysis and plausible physical arguments, following the standard phenomenology of fluid turbulence. However, for eR the triple correlations do not correspond to an ‘energy’ conserving process, but also represent a nonlinear source term for eR. If this source term can be neglected, the spectrum equations are found to be closed. The problem of dealing with the nonlinear source terms remains to be solved in future investigations.

The existence as well as the structure of magnetosonic wave-plateau shocks driven by upper-hybrid waves in a two-component electron-ion magnetized plasma is analysed. In the incident region the field quantities have a standing-wave structure, whereas in the evanescent region they monotonically reach constant values. The plasma flow velocity undergoes a transition from submagnetosonic (in the evanescent region) to supermagnetosonic (in the incident region) values via the magnetosonic point. The number density (or the magnetic field) across the shock-front region has a steep gradient and connects a rarefaction (under-dense) wave in the incident region to a shelf-like (over-dense) structure in the evanescent region, where the upper-hybrid electric field drops to zero monotonically. For the case of small- but finite-amplitude shocks the detailed structures of the profiles are obtained analytically. For large-amplitude shocks the profiles are computed using numerical methods. An extension of the present theory as well as some possible applications are pointed out.

A symmetric factorization of the velocity-dependent charge-exchange kernel (the so-called separable-kernel model) is used in the Boltzmann equation for neutral atoms to obtain an exact solution for a half-space plasma by the Wiener-Hopf method. This work generalizes earlier work employing constant, velocity-independent charge-exchange interactions to the case of an arbitrary velocity dependence of the Maxwellian averaged charge-exchange reaction rate. The effects of velocity dependence on the speed-angle distribution of escaping neutrals and the total charge-exchange rate in the half-space are shown to be significant. It is also shown how the Wiener-Hopf method can be applied to such problems with a realistic Maxwellian plasma background, without first approximating the ion distribution.

A new System of co-ordinates is found and a method developed to determine the toroidal equilibrium of plasmas with arbitrary current distribution and plasma cross-section. The method depends on knowledge of the equilibrium of a straight plasma column of similar cross-section and similar current distribution. A large aspect ratio is assumed. By successive approximations, better solutions can be obtained. An explicit formula is presented for the poloidal flux of a nearly circular plasma. This can be written in terms of a function related to the asymmetry of the poloidal field due to toroidality. The method works provided that there is only one magnetic axis.

Kinetic effects such as those of finite Larmor radius (FLR) and. wave–particle resonances on the ideal Alfvén-wave continuum in a z-pinch geometry are investigated. The effect of FLR increases the order of the equations and is therefore treated as a singular perturbation. Similar eigenvalue curves are found as for the case when the non-ideal effect is resistivity, with a bifurcation of a global-mode branch into a boundary-mode branch and an internal-mode branch.

The energy gain of a non-relativistic charged particle in a quasi-perpendicular shock is studied. This is done by the usual procedure of transforming the shock structure to a perpendicular one. The difference with earlie'r studies is that we are able to derive a new, exact expression for this energy gain in closed form. Two successive approximations of this expression are presented and discussed. Finally, the average energy gain of an isotropie particle distribution in the original shock system is derived.

From the Vlasov-fluid model a set of approximate stability equations describing the stability of the pure z–pinch is derived. The equations are valid for equilibria with small gyroradius compared with the pinch radius, but the perturbation wavenumber k may be of the order of the gyroradius ρi, δ = kρi = 0(1) - so-called gyrokinetic ordering. The equations are used to study the stability of the m = 0 and m = 1 internal modes of the z–pinch. In the limit of zero gyroradius δ → 0 we recover previously obtained results. For δ ≠ 0 we find that increasing δ at first gives a rapidly decreasing growth rate, and for δ ≈ l the growth rate compared with perpendicular MHD is γ/γMHD ≈ 0·09. For larger δ however, the growth rate increases to a quite large value. For the m = O mode we find, provided that drift resonances can be neglected, a stability criterion for δ ≥ 1, which is fulfilled both for the Bennett equilibrium and the constant-current-density equilibrium.

A new analytical method is introduced to consider electrostatic surface waves propagating on a cold plasma. A very simple dispersion relation is derived for a plasma bounded by two dielectrics. Previous theory for solitary surface waves is also generalized.

It is well known that an anisotropic temperature distribution gives rise to thermal instability in many Systems. In their numerical simulations of a two-vane, non-relativistic planar magnetron, Thomas et al. reported a temperature anisotropy and a concomitant formation and growth of a swirling electron cloud bunch (convective cell). In this paper we present an analytic calculation of the shift in the eigenfrequencies by treating the thermal effects as a perturbation, while taking due account of the temperature anisotropy. We find the magnitude of the resulting rate to be of the order of that seen in the simulations.

Exact solutions are presented of two-dimensional steady-state incompressible stagnation point flows at a current sheet separating two colliding plasmas. They describe the process of resistive field annihilation (zero reconnection) where the magnetic field in each plasma is strictly parallel to the current sheet, but may have different magnitudes and direction on its two sides. The flow in the (x, y) plane toward the current sheet, located at x = 0, may have an arbitrary angle of incidence and an arbitrary amount of divergence from or convergence towards the stagnation point. We find the most general form of the solution for the plasma velocity and for the magnetic field. For the z compenents of the flow and field, solutions in the form of truncating power series in y are found. The cases obtained in this study contain the solutions obtained by Parker, Sonnerup & Priest, Gratton et al. and Besser, Biernat & Rijnbeek as special cases. The role of viscosity in determining the flow and field configurations is examined. When the two colliding plasmas have the same viscosity and density, it is shown that viscous effects usually are important only in strongly divergent or convergent viscous flows with viscous Reynolds number of the order of unity or smaller. For astrophysical applications the viscous Reynolds number is usually high and the effects of viscosity on the interaction of plasmas of similar properties are small. The formulation of the stagnation-point flow problem involving plasmas of different properties is also presented. Sample cases of such flows are shown. Finally, a possible application of the results from this study to the earth's magnetopause is discussed briefly.

In this paper the exact solution in a function-series form is given of the multi-fluid ion-beam plasma model proposed by Zank & McKenzie. The general condition necessary for the existence of finite-amplitude solitons propagating in the system is obtained and the upper bound on the velocity of solitary wave is found.

Analytical expressions for the weakly relativistic dielectric tensor near the electron-cyclotron frequency and harmonies are obtained to any order in finite-Larmor-radius effects for a bi-Maxwellian distribution function. The dielectric tensor is written in ternis of generalized Shkarofsky dispersion functions, whose properties are well known. Relevant limiting cases are considered and, in particular, the anti-Hermitian part of the (fully relativistic) dielectric tensor is evaluated for two cases of strong temperature anisotropy.

A new theory for fast steady-state magnetic reconnection is proposed that includes many features of recent numerical experiments. The inflow region differs from that in the classical model of Petschek (1964) and the unified linear solutions of Priest & Forbes (1986) in possessing highly curved magnetic field lines rather than ones that are almost straight. A separatrix jet of plasma is ejected from the central diffusion region along the magnetic separatrix. Two types of outflow are studied, the simplest possessing an outflow magnetic field that is potential. The other contains weak standing shock waves attached to the ends of the diffusion region and either slowing down the flow (fast-mode shock) after it crosses the separatrix jet or speeding it up (slow-mode), depending on the downstream boundary conditions. A spike of reversed current slows down the plasma that emerges rapidly from the diffusion region into the more slowly moving downstream region, and diverts most of it along the separatrix jets. In the simplest case the outflow possesses no vorticity over most of the downstream region. The models demonstrate that both upstream and downstream boundary conditions are important in determining which regime of reconnection is produced from a wide variety of possibilities.

Collisions in a cylindrically symmetric non-neutral (electron) plasma, where the Larmor radius is much smaller than the Debye length, and the consequent particle transport, are studied. The plasma is confined radially by a strong axial magnetic field and axially by electric potentials. Hence two particles may interact repeatedly. Eventually they drift too far away from each other poloidally to interact any more, owing to shear in the E × B drift. The consequent build-up of correlation is limited by correlational disintegration due to collisions with ‘third particles’ between the repeated interactions. A kinetic equation including these effects is derived, and the cross-field particle transport along the density gradient is found. An associated equilibration time is shown to scale as B and to be in good agreement with the experimentally obtained values of Briscoli, Malmberg and Fine.

In a cold plasma the wave equation for solely compressional magnetic field perturbations appears to decouple in any surface orthogonal to the background magnetic field. However, the compressional fields in any two of these surfaces are related to each other by the condition that the perturbation field b be divergence-free. Hence the wave equations in these surfaces are not truly decoupled from one another. If the two solutions happen to be ‘matched’ (i.e. V.b = 0) then the medium may execute a solely compressional oscillation. If the two solutions are unmatched then transverse fields must evolve. We consider two classes of compressional solutions and derive a set of criteria for when the medium will be able to support pure compressional field oscillations. These criteria relate to the geometry of the magnetic field and the plasma density distribution. We present the conditions in such a manner that it is easy to see if a given magnetoplasma is able to executive either of the compressional solutions we investigate.