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.

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 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.

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.

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 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 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.

It is argued that familiar nonlinear instabilities, such as three-wave decay instabilities and scattering off quasi-modes, have reactive and resistive versions. In appropriate limits these versions correspond to fixed-phase parametric instabilities and to random phase growth in weak turbulence theory, respectively. Using a simplified model it is shown that the reactive version passes over into the resistive version when the band-width of the pump is comparable with the growth rate.

The cross-field plasma diffusion coefficient is expressed in terms of the perturbed potential energy W by making use of the nonlinearity of orbit diffusion. The thermodynamic bound of the energy W for a current-carrying collisionless plasma has been determined consistently with four constraints: the invariance of averaged Hamiltonian, angular momentum, entropy and density. It is found that with momentum invariance the major contribution from the plasma current cancels, and the lowest upper bound of W is determined by the high-order toroidal effect coupled with the plasma current, which yields the neo-Alcator (TFTR) scaling for the energy confinement time. When neoclassical deformation is allowed in the plasma distribution, the thermodynamic bound has additional terms which come from the neoclassical source of free energy due to the bootstrap current. When the poloidal beta is larger than a certain critical value, the energy confinement time shows the effect of density saturation, and becomes proportional to the plasma current.

It is shown that for a plasma with ion temperature greater than electron temperature, an extraordinary electro-magnetic pump wave can parametrically decay into upper-hybrid and electron-acoustic oscillations. The threshold power flux and the growth rate of the instability are obtained. Comparison of our investigation with an earlier work and its possible application to a mirror machine is pointed out.

Ion-acoustic solitons in a collisionless plasma with adiabatic positive and negative ions with equal ion temperature and isothermal electrons are studied by using the reductive perturbation method. The basic set of fluid equations is reduced for the fast ion-acoustic wave to the Korteweg–de Vries and modified Korteweg–de Vries equation and for the slow ion-acoustic wave to the Korteweg–de Vries equation. Stationary solutions of these equations are obtained and the effect of ion temperature on fast and slow ion-acoustic solitons is investigated.