The transport theory of a high-energy ion species injected isotropically in a magnetized plasma is considered for arbitrary ratios of the high-energy ion cyclotron frequency to the collisional slowing down time. The assumptions of (i) low fractional density of the high-energy species and (ii) average ion speed faster than the thermal ions and slower than the electrons are used to decouple the kinetic equation for the high-energy species from the kinetic equations for background ions and electrons. The kinetic equation is solved by a Chapman–Enskog expansion in the strength of the gradients; an equation for the first correction to the lowest-order distribution function is obtained without scaling a priori the collision frequency with respect to the gyrofrequency. Various transport coefficients are explicitly calculated for the two cases of a weakly and a strongly magnetized plasma.

The relaxation of a very dilute test particle species undergoing elastic collisions with a distinct, thermally distributed second particle species is considered. The Boltzmann equation is set up for the component of the test particle distribution function isotropic in velocity space; external forces and spatial dependence are ignored. For small test particle: heat-bath particle mass ratio, collisions are adequately described by a differential operator that is second-or der with respect to collision speed, which depends on the functional form of the collision frequency in terms of speed. The evolution equation is transformed to the form of the time-dependent Schrödinger equation, and the equivalent Schrödinger potential evaluated in terms of the collision frequency-speed relation. The relaxation problem may be solved by specifying the Green's propagator, describing the relaxation of an initial monoenergetic distribution. The case of constant Schrödinger potential is studied: the corresponding form of the collision frequency is found by an inversion process, and the evolution equation studied in Schrödinger form. The transformed speed variable has a finite range as particle speeds vary from 0 to ∞, and it is necessary to specify that particles are not lost at the finite values corresponding to small and large speeds. The Green's propagator is continued beyond this physical range, rather as in the ‘method of images’ of electrostatics. The particle conservation requirements induce a Laplace transform problem for the initial value of the Green's propagator, which is reduced to a polynomial recurrence relation and solved by finding the generating function. The Green's propagator is itself propagated forward from its initial value by a ‘primitive’ propagator which is the solution of the problem for initial delta function not only in the physical range, but anywhere in the space of the transformed variable. This primitive propagator is readily found, and the propagation quadrature performed to yield the true propagator in terms of parabolic cylinder functions. A check is made with a special case, for which relaxation to thermal form is explicitly demonstrated. Differences and similarities between this analysis and those corresponding to more general collision frequencies and potentials are considered.

Several Rossby-type vortex solutions constructed for electromagnetic perturbations in magnetized plasma encounter the difficulty that the perturbed magnetic field and the parallel current are not continuous on the boundary between two regions. We find that fourth-order differential equations must be solved to remove this discontinuity. Special solutions for two types of boundary value problem for the fourth-order partial differential equations are presented. By applying these solutions to different nonlinear equations in magnetized plasma, the intrinsic electromagnetic solitary drift-Alfvén vortex (along with solitary Alfvén vortex) and the intrinsic electromagnetic solitary electron vortex (along with short-wavelength drift vortex) are constructed. While still keeping a localized dipole structure, these new vortices have more complicated radial structures in the inner and outer regions than the usual Rossby-wave vortex. The new type of vortex guarantees the continuity of the perturbed magnetic field δB⊥ and the parallel current j‖ on the boundary between inner and outer regions of the vortex. The allowed regions of propagation speeds for these vortices are analysed, and we find that the complementary relation between the vortex propagating speeds and the corresponding phase velocities of the linear modes no longer exists.

The stimulated Brillouin scattering of Alfvén waves is studied in low-density plasmas. It is shown that ion-sound oscillations may be excited by this mechanism under suitable ionospheric conditions and that the presence of negative ions reduces the probability of such excitations.

The nonlinear interaction of whistler waves with the background plasma via the ponderomotive force gives rise to the formation of both periodic and solitary whistler envelopes. This is described in terms of the Lagrange formalism which allows us to define conserved quantities which determine, together with the parameters of the background plasma and the whistler frequency, the particular form of the envelope.

A cold-fluid model is used to describe the nonlinear evolutions of low-density non-neutral plasma immersed in a strong axial magnetic field. It is assumed that there is no axial dependence, and that the electron fluid moves with the usual E × B drift velocity. Use is made of global (spatially averaged) conservation constraints satisfied by the continuity and Poisson equations to obtain a nonlinear bound on the unstable fluctuation level for a general initial density profile.

The lasing by stimulated bremsstrahlung of a relativistic dilute electron beam passing through a spatially periodic longitudinal electrostatic field is investigated by means of the quantum-kinetic method. It is shown that the energy transfer from the electrons to the radiation field by the Lorentz force of the radiation field can be neglected compared with that by the force due to net stimulated bremsstrahlung (the emission by stimulated bremsstrahlung minus the absorption by inverse bremsstrahlung). The gain per unit length in the intensity of the laser light and the force acting on the electron due to free electron lasing are explicitly expressed as a function of the relevant parameters of the laser light and the electron beam.

Stimulated Raman scattering from a fully focused relativistically drifting electron plasma in a parallel-plate waveguide is studied. A set of internally consistent transport relations governing the three-wave interactions is developed. These transport relations lead to the proper conservation of energy and momentum. Including small wall and bulk plasma losses, parametric and nonlinear characteristics are investigated theoretically and numerically. It is found that in an unbounded medium the saturation period of the signal wave is considerably smaller than in a bounded medium. The signal energy comes from the plasma stream through the idler wave with small depletion of the pump wave amplitude.

The dispersion relation for plasma waves is considered in the ‘cold’ plasma approximation. General formulae for the dependence of the phase and group velocities on the direction of wave propagation with respect to the local magnetic field are obtained for a cold magnetized plasma. The principal cold plasma resonances and cut-off frequencies are defined for an arbitrary angle and are used to establish basic regimes of frequency where the cold plasma waves can propagate or can be evanescent. The relationship between direction of wave and energy propagation, for cold plasma waves in hydrogen atmosphere, is presented in the form of angle diagrams (angle between group velocity and magnetic field versus angle between phase velocity and magnetic field) and polar diagrams (also referred to as ‘Friedrich's diagrams’ ) for different directions of wave propagation. Morphological features of the diagrams as well as some critical angles of propagation are discussed.

The ranges of temperature T, harmonic number s and wave propagation angle θ in which the loss-cone-driven electron cyclotron instability can exist are found to be limited by opposing contributions to the growth rate from adjacent harmonics. For waves with refractive index n ⋍ 1 it is found that instability is possible only if T and s satisfy saT ≲ C with a = 2 − 2·5 and where the constant C is determined by θ and the form of the distribution function. It is argued that the corresponding restrictions for waves with very large or very small n are less severe. Instability is found to be forbidden for waves propagating outside a range |θ − 90°| < φ(s), except if θ ⋍ 0, where π(s) is independent of temperature and sin2φ(s) ⋍ s−1; this restriction limits the range of potentially unstable frequencies at a given harmonic.

Explicit analytical solutions are given for the collisionless time evolution of the distribution function for ions absorbing RF wave power through ion cyclotron resonance heating in a tokamak. Two different scenarios are considered: (i) conventional ICRH and (ii) combined neutral beam heating and ICRH with the RF wave frequency tuned to the ion cyclotron resonance frequency of the injected ions. Finally, the effect of particle trapping on the time development of the distribution function is also analysed.

The MHD equations are rederived without neglecting the electron inertia and new terms are obtained. The revised equations predict that strong magnetic fields are spontaneously generated even in an ideally symmetric ICF implosion in contrast to the conventional theory where an ideal ICF implosion is considered to be free of magnetic fields. The dynamics of the implosion is found to be governed by the space-time structure of the magnetic field. Departures from neutrality are taken into account and an explicit equation is obtained for the evolution of the charge density. The complexity of the implosion problem is illustrated with reference to cylindrical and spherical geometries. The existence of this effect has been verified in the case of a Z-pinch. Experiments can be devised to detect it in existing ICF installations. It is suggested that scientific breakeven may be achieved using existing installations if the targets are optimized in accordance with the present theory.

We present a theoretical investigation of stimulated Brillouin scattering (SBS) of whistler waves in low-density collisionless plasmas in the presence of negative ions and incorporating the effect of the ponderomotive force on electrons. It is found that the growth rate of the excited ion quasi-mode decreases with increasing concentration of negative ions. The effect of negative ions on the SBS of the whistler waves during the ionospheric modification is discussed.

It has previously been observed that ion-acoustic waves exhibit two types of behaviour as the proportion of light ions in a mixed plasma is varied. Either the principal mode of the heavy ion plasma changes continuously into that of the light ion plasma, or it becomes too heavily damped to be observable while a second wave appears and develops into the principal light ion mode. A similar phenomenon is observed as the wavenumber or the ratio of electron temperature to ion temperature is changed. Criteria determining which behaviour occurs are derived by considering the form of the dielectric response function. The results may also be used to predict which of the higher-order modes of the plasma is involved in the process, and whether degeneracies exist in the dispersion relation.

It is shown that the nonlinear dynamics of current-convective excitations in current-carrying edge plasmas allows for the existence of solitary vortices despite the effects of magnetic shear and dissipation in the form of parallel electron thermal conductivity. The potential importance of this finding with regard to heat balance is pointed out.

The propagation of whistler-mode waves at frequencies above one half the electron gyrofrequency has been investigated for a magnetospheric two-component plasma (cold and lower energy hot electrons) by use of the properties of refractive index surfaces. The presence of hot plasma is found to enhance the tendency towards field-aligned focusing of half-gyrofrequency whistler-mode propagation at large wave normal angles close to the oblique resonance angle of the whistler-mode propagation in the corresponding cold plasma.

A general electrostatic coupling coefficient which satisfies the Manley-Rowe relations is used to derive an explicit expression for the resonant three-wave coupling coefficient between electrostatic normal modes of a uniformly magnetized, infinite, homogeneous plasma with species described by drifting bi-Maxwellian distribution functions. The limit of this expression is taken when the phase velocities of the three waves are much larger than a species thermal speed, and also when the phase velocities are much smaller than the thermal speed. These are fluid limits and are applicable to the three-wave interaction between some low-frequency electrostatic waves, such as ion acoustic and ion cyclotron modes, in a plasma where Te ≫ Ti.

The coupled toroidal and poloidal modes forming a standing oscillation along the line of force and propagating azimuthally in a spherical dipole magnetic field are investigated under the magnetohydrodynamic (MHD) approximation with infinite conductivity, including the pressure effect but neglecting compressibility. We obtain a linearized coupled differential equation. When the azimuthal wavenumber becomes zero in the coupled equation, the axisymmetric toroidal wave equation is obtained with no pressure effect. For a large azimuthal wavenumber, on the other hand, a differential equation of the poloidal wave associated with a compressional magnetic component, which is different from the equation hitherto obtained under the zero pressure term, is derived from the coupled equation. It is found that the fluid pressure perturbation acts on the poloidal wave like the spring for the stretched string model and then contributes to the enhancement of the eigenvalues of the standing oscillations, especially for the first few. In this case, the magnetic pressure perturbation is in antiphase to that of the fluid pressure.

The linear dispersion relation for Bernstein modes, obtained by the integration of Vlasov's equation along the unperturbed cyclotron orbits, predicts that the modes propagating perpendicularly to the magnetic field are undamped. However, when the frequency is close to a multiple of the cyclotron frequency, most of the particles become trapped for small wave amplitude and the unperturbed orbit approximation breaks down. The trapped particle trajectories are calculated analytically here using a resonant Hamiltonian approximation. Integration, consistent with the wave, along the orbits yields the nonlinear damping rate in a manner similar to that used by O'Neil for the damping of unmagnetized electrostatic modes. The results can be extended for the general case of almost perpendicular, short-wavelength electrostatic modes near cyclotron harmonics.

The resistive instability of a simple one-dimensional current sheet model has been investigated both in the long and in the short wavelength approximation. For the linear phase of the instability it is possible to derive, by means of an expansion technique, an analytical expression for the growth rate and for the perturbation itself. The variations of each kind of energy (magnetic, kinetic and dissipated energies, Poynting vector, work against pressure gradients and magnetic forces) are then exactly computed. Different behaviour of the System is obtained for different wavelengths. In particular, the driving energy for the instability is found to come from different regions: for high wavenumber α there is a decrease of the magnetic energy in the inner resistive region where the reconnection occurs, whereas for low-α modes the magnetic energy decreases in the outer ideal region. Moreover, the amount of Joule dissipation is found to increase with decreasing α so that the low-α regime is the most efficient.