Bounds are established for the permanent-state radiation-conditioned response to a vibrating charge in the MWB (‘multiple water-bag’) model of a warm Maxwellian plasma. Those bounds vary with the observation position beyond the charge and, along any radial direction, serve as boundary curves of potential bands containing the exact potential curves. They can therefore be employed for potential estimation. The bounds are actually Poisson potentials and are independent of (the degree of accuracy in) the MWB modelling when the charge frequency ω exceeds the electron plasma frequency ωp. In this case each potential band narrows to improve potential estimation as ω/ωp increases, and in fact a relative error in estimation can be uniformly predetermined to as small as one desires for all MWB models, charge distributions and observation points by setting ω beyond an appropriate level above ωp. The bounds are, however, model-dependent if ωp exceeds ω in magnitude, in which case, they are partially Poissonian; moreover, potential estimation based on them improves as ω/ωp decreases, and an error analysis is again performed. In either case, a sharper estimation is obtained by averaging the bounds to get an estimate; thus, for instance, the associated relative error cannot exceed 0·01, 0·02 and 0·05 when ω/ωp = (101)½, (51)½ and (21)½ respectively. Applications are described.

By means of a kinetic description for ions and Braginskii's fluid model for electrons, we derive three coupled nonlinear equations governing the dynamics of low-frequency short-wavelength electrostatic waves in the presence of equilibrium density, temperature and magnetic-field gradients in a two-component magnetized plasma. In the linear limit we present a dispersion relation that admits new instabilities of drift waves. An estimate of the anomalous electron energy transport due to non-thermal drift waves is obtained by making use of the saturated wave potential, which is deduced from the mixing-length hypothesis. We also present stationary solutions of the nonlinear equations governing the interaction of linearly unstable drift waves. The relevance of our investigation to wave phenomena in space and laboratory plasmas is pointed out.

The three basic mechanisms that produce either classical or anomalous transport are spatial variation of magnetic field strength, spatial variation of electrostatic potential in magnetic surfaces, and loss of magnetic surfaces. A Monte Carlo code is written to study transport due to these three mechanisms interacting with collisional effects. The equations of motion are obtained from the canonical drift Hamiltonian, but non-canonical co-ordinates are used to simplify the integrations. The code is applied to the reversed-field-pinch ZT-40 and the Tokapole II. For ZT-40 the Bessel-function model is used to represent the magnetic field geometry. The effects of pitch-angle scattering, loop voltage and the break-up of magnetic surfaces resulting from resistive MHD perturbations on the drift particle trajectories are illustrated. The particle diffusion coefficients are obtained for varying amplitudes of resistive MHD perturbations. For Tokapole II the spectrum of both the ideal and resistive MHD perturbations is constructed from the experimental data. The drift trajectories for trapped and passing electrons in the presence of such perturbations are obtained. The particle diffusion coefficients for the neo-classical regime in Tokapole II are obtained for varying collision frequency. By comparing the transport coefficients for various groups of particles with the experimental data, we hope to obtain far more information on the transport mechanisms than can be obtained by the standard confinement time measurements. The various groups of particles that can be studied using the code include runaway electrons, thermal electrons, and both passing and trapped diagnostic beam ions.

Numerical results for the bootstrap current in a stellarator-reactor plasma are presented. The distribution function f is computed numerically from a kinetic equation that is averaged over the helical ripple. The parallel flows and the current are obtained as v‖ moments of f. The physics issues embedded in the code are discussed concisely, concentrating on the justification as to why the bootstrap current can be estimated from an averaged scheme. Results are presented for typical stellarator-reactor parameters. The numerical code FLOCS predicts that the momentum-restoring terms in the collision operator have no significant impact on the value of the bootstrap current (the difference being about 10%). The results obtained are related to the equilibrium flows, and a physical interpretation based on the kinetic picture is presented. Finally, an estimate for the impact of J‖ on the rotational transform is given.

The electrodynamic instability of a self-gravitating dielectric annular fluid jet possessing a very dense fluid (of negligible inertia) cylinder mantle surrounded by another dielectric self-gravitating medium pervaded by a radial varying electric field is investigated. A general eigenvalue relation valid for all possible symmetric m = 0 and asymmetric m ≠ 0 perturbation modes is derived and discussed. The electrodynamic force has a strong destabilizing influence not only to m = 0 but also to m ≠ 0 disturbance modes. The self-gravitational force is stabilizing to all pure m ≠ 0 modes, while to m = 0 it is stabilizing or destabilizing according to conditions. The destabilizing effects of the internal and exterior varying electric fields shrink the gravitationally stable states and simultaneously increase the unstable ones. The electrogravitodynamic instability character of the model can be minimized if the electrodynamic force effect is extremely small in comparison with that of the self-gravitational force, but the instability will never be suppressed.

The transformation approximation for the plasma dispersion fonction is applied to an electromagnetic ion-cyclotron instability caused by proton temperature anisotropy. The transformation method gives an improved dispersion relation and instability growth rate compared with the asymptotic expansion for the plasma dispersion fonction. It is found that the maximum growth rate is slightly suppressed when the transformation approximation for the plasma dispersion function is used. However, it is shown that the transformation approximation method yields an unreliable estimate of the growth rate for values greater than a critical thermal anisotropy. Cold-heavy-ion effects on the ion-cyclotron instability are also investigated.

In recent work by the present author the full dispersion relation for multi-dimensional perturbations propagating in saturated free-electron lasers was derived. A number of approximations were used in order to derive a simplified description of the unstable modes. Although this simplified analysis was shown to be appropriate for quasi-transverse modes, it was not possible to describe the generic case of non-transverse ones. In the present paper, via a numerical analysis of this dispersion relation, we argue that a considerable number of modes do indeed not satisfy the quasi-transversality condition. The generation of low-frequency maenetic fields is also analysed.

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.

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.

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.