It is shown how existence domains for arbitrary-amplitude ion-acoustic solitons and double layers are determined numerically by cut-off conditions on the corresponding Sagdeev potential. A two-electron-temperature model is considered, and in positive-ion plasmas the cut-off conditions are given in terms of the electron parameters, while for negative-ion plasmas such conditions are described in terms of parameters characterizing the role of the negative ion species.

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.

Dispersion relations of plasma waves in a beam–plasma System are computed in the general case where the plasma and beam temperatures, and the; velocity of the beam, may be relativistic. The two asymptotic temperature cases, and different contributions of plasma or beam particles to wave dispersion are considered.

Exact wave solutions of the nonlinear jnagnetohydrodynamic equations for a highly conducting incompressible fluid are obtained for the cases where the physical quantities are independent of one Cartesian co-ordina.te and for where they vary three-dimensionally but both the streamlines and magnetic field lines lie in parallel planes. It is shown that there is a class of exact wave solutions with large amplitude propagating in a straight but non-uniform magnetic field with constant or non-uniform velocity.

Temporal and spatial hydrodynamical instabilities and kinetic instabilities of plasma waves are considered for a relativistic beam–plasma System. The beam and plasma temperatures, and the beam velocity, may be relativistic. Instability conditions and growth rates are evaluated. An unusual case of kinetic stability inversion, for relativistic or dense beams, is discussed.

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.

The filamentation of electromagnetic waves in a free-electron laser with deeply trapped electrons is analysed. This instability is the result of particle bunching along transverse directions (with respect to the fast wave vector), as opposed to the untrapped-electron case, where it is a result of longitudinal bunching. Two cases are considered: (i) the non-resonant or reactive one, with purely imaginary growth rates; and (ii) the resonant one, with large (small) values of the real (imaginary) part of the perturbing frequency. In particular, we find that the reactive instability occurs only when the wiggler amplitude is unusually large. On the other hand, we show that the resonant process (with frequencies close to the synchrotron frequency) may be relevant for conventional free-electron lasers and that the growth rate for quasi-trans verse perturbations may be larger than that corresponding to longitudinal perturbations. Owing to the inhomogeneity and anisotropy of our system, low-frequency magnetic fields are generated. These fields, as well as the transverse electric fields, are analysed, and their role in the low-frequency dynamics is clarified.

A relativistic study of the beat wave of two laser beams in a hot plasma is presented in the case where the modifications of the distribution function due to this beat wave are much smaller than the equilibrium distribution function. This situation corresponds to small laser energies or high plasma temperatures. The power-conversion efficiency of the laser beams is evaluated for different values of temperatures, laser energies and frequencies.

The magnetohydrodynamic stability of a streaming annular jet containing a very dense fluid cylinder and acted upon by inertial and electromagnetic forces, in the presence of a varying transverse magnetic field pervading a tenuous surrounding medium, is considered. A general dispersion relation is established and studied analytically, and the results are confirmed numerically. The magnetic fields are stabilizing or destabilizing for each of the symmetric (m = 0) and non-axisymmetric (m ≠ 0) modes under some restrictions. The streaming has a strong destabilizing character, and its influence is to enlarge the magnetohydrodynamic instability domains and shrink the stability domains. The thicker the dense fluid core, the greater the number of magneto-hydrodynamically stable states. Increasing the magnetic field intensity shrinks the unstable domains. The (in)stability situation is much worse for m ≠ 0. However, if the axial field intensity is sufficiently high and greater than the transverse field intensity, the destabilizing character of the model, in a few cases, may be suppressed. This occurs if the Alfvén-wave velocities interior and exterior to the annular jet are greater than the unperturbed fluid velocity.

Previous work on non-relativistic electrons isotropically scattered by neutral atoms is extended to the relativistic case, and an equation is derived for the electron drift velocity. In the non-relativistic case the drift-velocity equation contains a corrected momentum-transfer term arising from the fact that the collision phenomenon is characterized by the mean free path rather than by the mean collision time. In the present work it is found that the time variation of the electron mass has a very complicated effect on the relativistic equation for the drift velocity. In addition, an unexpected theoretical result is obtained: a negative magneto-resistance effect in which the magneto-resistance decreases as the magnitude of a magnetic field imposed on the plasma increases. However, this effect is not a relativistic one but is rather due to the correction in the momentum-transfer term.

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.

Using kinetic theory, low-frequency electrostatic instabilities driven by an anisotropic ion beam are investigated: In our model both the ions and electrons are magnetized, while the beam drift is across the external magnetic field. Both the ion-acoustic and ion–ion two-stream instabilities are excited. Regions of parameter space for the existence of either instability are distinguished. Detailed comparisons are made with the isotropie case.

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.

A critical analysis of nonlinear waves in a non-isothermal relativistic plasma is performed using reductive perturbation theory. The plasma is assumed to contain two-temperature electrons. Higher-order corrections to the solitary wave are also computed, and the variations of the profile with respect to v/c, the two temperatures of the electrons, and the parameters bl, and bn characterising the non-isothermal nature are depicted graphically and com-pared with previous results.

In a plasma in which both the ions and electrons are magnetized we investigate low-frequency electrostatic instabilities driven by an anisotropic ion beam drifting parallel to the external magnetic field. The instability spectrum is found to be dominated by the ion-acoustic and ion-ion two-stream instabilities. Detailed comparisons are made with the isotropie case.

The nonlinear evolution of lower-hybrid-drift waves in an inhomogeneous magnetized plasma with warm electrons and cold ions is considered. The effect of finite electron temperature on a soliton solution of the set of nonlinear equations is examined.

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 solution of the linearized Vlasov–Poisson equations describing a projectile ion moving through a classical isotropic electron plasma is investigated analytically and numerically for a wide range of projectile velocities vp Extending the range of earlier computations considerably, our calculations were performed for velocities up to vp = 15vth, showing the wake field behind the ion for distances 0 ≤ d ≤ 200λD, where vth is the thermal electron velocity and λD the Debye length of the plasma. As a new feature, we demonstrate that the amplitude of the wake field in the region vp/vth ≤ d/λD ≤/23(vp/vth)3 is almost undamped, and only for larger distances from the ion does it take the 1/d behaviour shown in other work. Thus the wake field of a single ion persists for much longer than previously thought. The question of whether this effect could have practical consequences, for example, for ion-beam cooling, is briefly addressed.