A study is made of the inelastic collision integral of the Boltzmann equation using scattering probability formalism. The collision operators are expanded in a power series in the square root of the ratio of masses.

Furthermore, a spherical harmonic expansion is made of all the operators so obtained. These developments are valid whatever the shape of the distribution function of the particles.

The stability of two of the short time scale solutions obtained in the filament model for a stationary field electron ring accelerator is studied by means of a linearized perturbation on the electron and ion distribution functions. The Vlasov equations for the electrons and ions are coupled. The coupling of these equations results in a Fredholm integral equation which can be converted into an infinite system of linear equations. A stability criterion is then obtained from the zeros of the truncated determinants of the coefficients of the infinite system. One of the equilibrium solutions, for which the ion density in phase space is a monotonic non-increasing function of the unperturbed ion Hamiltonian, is entirely stable. The other solution, for which this monotonicity does not hold, may be unstable, but turns out to be stable provided that both the non-monotonicity parameter ∈ and the ratio of the ion period to the electron period are not too large. In the nonmonotonic case, the ion density in physical space also does not drop off to zero monotonically from the centre of the ring. For the unstable cases, the instability is driven by a ‘spike’ in the phase-space ion density located at the maximum value of the unperturbed ion Hamiltonian.

We calculate the electric field fluctuation spectrum in a magnetized plasma considering the influence of a finite amplitude pump wave.

In this paper we propose an exact solution of Vlasov and Maxwell's equations for a bounded hot plasma in order to derive the dispersion relation of the axially-symmetric surface waves propagating along a plasma column. Assuming specular reflexion of plasma particles from the boundary, expressions for the components of the electric displacement vector are obtained on the basis of the Vlasov equation. Their substitution in Maxwell's equations, neglecting the spatial dispersion in the transverse plasma dielectric function, allows us to determine the plasma impedance. The equating of plasma and dielectric impedances gives the wave dispersion relation which, in different limiting cases, coincides with the well-known results.

Cornwall et al. (1970) suggested that if the ring current protons penetrated the plasmapause, intense resonant electromagnetic ion cyclotron turbulence would lead to their rapid precipitation loss. IN this paper we present a computer simulation study of the electromagnetic ion-cyclotron instability in a homogeneous plasma consisting of protons and electrons embedded in a static magnetic field, B0x. The plasma parameters used are and Effects such as sources and losses or space non-uniformities are not considered here. The predictions of the linear theory for the fast build-up of unstable left-hand (proton-like) electromagnetic ion-cyclotron waves are fully confirmed.

The stability of electromagnetic drift waves in high-β anti-loss-cone plasmas is investigated. These waves with propagation transverse to the external magnetic field are found to be unstable provided ρ > ρc, where ρ is the parameter which characterizes the strength of the anti-loss-cone. The growth rates associated with this instability (which may be called the anti-loss-cone drift instability) are ˜ 0·1Ωe and they increase with the strength of the anti-loss-cone.

Because of the technical difficulties associated with the production of ultrashort beam pulses, the efforts to release energy from thermonuclear microexplosions are mainly directed at present towards confinement in a high-Z material solid wall, as in the original proposal by the author for relativistic electron beam induced fusion. The most common approach today is by the implosion of a solid high-Z material shell, for example, with an intense relativistic electron beam. We will show that better utilization of the beam energy may be possible with beam bombardment of a curved concave wall, setting off a shock wave which can be focused precisely onto the thermonuclear target. In addition, by a proper variation of the atomic weight and density in the layer of the wall material to be ablated by the energy deposition of the beam, the pulse length of the shock wave can be made substantially shorter than the pulse length of the beam.

Resonant nonlinear interaction among three longitudinal waves propagating along any arbitrary angle to a uniform magnetic field in a plasma is investigated by a quantum-mechanical method. The coupled mode equations and coupling coefficients are derived.