Electron-cyclotron maser emission is investigated in the regime where wave growth in the electrostatic Bernstein modes dominates (ωp/Ωe>1.5). A semirelativistic growth rate is derived assuming that the wave dispersion is dominated by a cool background electron distribution and the instability is driven by a low-density hot loss-cone-like electron distribution. The properties of Bernstein wave growth are most strongly dependent on the relative temperatures of the hot and cool electron distributions. For Thot/Tcool[gsim]10, the fastest growing Bernstein waves are produced at frequencies just below each cyclotron harmonic in Bernstein modes lying below the upper-hybrid frequency. For Thot/Tcool[lsim]10, additional Bernstein modes above the upper-hybrid frequency are excited, with wave frequencies in each excited mode lying significantly above the corresponding cyclotron harmonic. The dependence of Bernstein wave growth on the relative hot and cool electron number densities and emission angle is also discussed.

The linear response tensor for a relativistic counterpart of a bi-Maxwellian distribution is calculated in closed form for a magnetized plasma. The method used involves the following steps: (1) a covariant form of the response tensor for an arbitrary distribution of particles is derived using both a forward-scattering method and a covariant version of Vlasov theory; (2) the response tensor is evaluated for a strictly perpendicular, thermal distribution using a method due to Trubnikov; (3) the parallel distribution is built up by applying a Lorentz transformation to sum over a weighted, continuous distribution of parallel speeds. A convenient starting point for a detailed investigation of waves in such a plasma is the small-gyroradius approximation to the general expression for the response tensor, and the relevant approximation is derived and discussed briefly. The expansion of the general expression for the response tensor in Bessel functions in given in an appendix.

The effect of a beam of radio waves of very high brightness passing through a cold, magnetized, electron–positron plasma is discussed. The properties of the natural wave modes in such a plasma are summarized, and approximate forms for the nonlinear response tensor are written down. Photon-beam-induced instabilities of low-frequency waves in the pair plasma are analysed in the random-phase approximation. When three-wave interactions involve two high-frequency waves in the same mode and a low-frequency wave in a different mode, wave–wave interactions are similar to wave–particle interactions in that photons act like particles that emit and absorb low-frequency waves. The absorption coefficients for various low-frequency waves due to a photon beam are evaluated. In a pure electron–positron plasma, photon-beam-induced instabilities can be effective only when either the high-frequency or the low-frequency waves are strongly modified by the magnetic field. The growth of the low-frequency waves is most effective when the high-frequency photon beam has a frequency close to the cyclotron frequency.

In Part 1 of this study, a model set exactly preserving the MHD hyperbolic singularities was considered. By developing the viscosity admissibility condition, it was shown that the intermediate shocks are necessary to ensure that the planar Riemann problem is well-posed. Here in Part 2, the MHD Rankine–Hugoniot condition and rarefaction-wave relations are presented in phase space, which allows construction of analytical solutions of the planar MHD Riemann problem. In this process, a viscosity admissibility condition is proposed to determine physically admissible shocks. A complete account of MHD Hugoniot loci is given, leading to a classification of several subproblems in which the solution patterns are qualitatively same. Finally, it is shown that the planar MHD Riemann problem is well-posed using intermediate shocks that have been considered non-evolutionary.

Staged pinch implosions provide a means to couple energy to a small-diameter fibre on an extremely fast time scale, circumventing the limitations of conventional pinches. In this scheme the generator current initially traverses an intermediate hollow plasma shell, which compresses onto the fibre placed coaxially and transfers the current to the fibre with a significantly reduced risetime. The results are impressive, since the delivered peak power is increased by several orders of magnitude, the coupling efficiency improves, and the most dangerous plasma instabilities that commonly plague high-density/high-temperature pinches are eliminated. This technique can be fielded on both fast and slow generators (i.e. tens of nanoseconds to microseconds), making it feasible to extend the concept to a wide range of presently assembled systems. Staging may therefore present a dramatically new means of pulsed-energy conversion, which could find many applications. In addressing the requirements for thermonuclear fusion in a staged Z pinch, our preliminary calculations based on zero-D models suggest the potential for a significant thermonuclear burn with generator currents of the order of a few megaamperes and one microsecond risetime. Studies are actively underway at various places around the world (England, France, Germany and Russia) as well as in the USA (UCI/UCR) to investigate different aspects of staged pinching and its applications, particularly those leading to controlled thermonuclear fusion.

A procedure has previously been developed for the iterative construction of invariants associated with magnetic field-line Hamiltonians that consist of an axisymmetric zeroth-order term plus a non-axisymmetric perturbation. Approximate field-line invariants obtained with this procedure are used to examine the topological properties of magnetic field lines in a parabolic-current MHD equilibrium that was slightly perturbed from axisymmetry in the limit of a periodic cylindrical configuration. Excellent agreement between Poincaré maps and the level curves of the first-order invariant is found for small perturbations. A means of circumventing the ‘small-divisor problem’ in some cases is identified and implemented with outstanding results. These results indicate that this perturbation method can have valuable consequences for future investigations of magnetic field-line topology.

The transverse part of the linear response tensor is evaluated for a highly relativistic thermal electron gas, starting from Trubnikov's response tensor for an arbitrary temperature. Three contributions to the response tensor are important. The diagonal components are dominated by an unmagnetized term, which gives the familiar dispersion k2=w2p0, where wp0 is the proper plasma frequency. The difference between the diagonal components is larger in magnitude than the off-diagonal components, implying that the natural modes are nearly linearly polarized. This leads to a generalized form of Faraday rotation in which linear polarization is partially converted into circular polarization at a rate per unit path length ∝λ3 (λ=wavelength).

Parametric instabilities of upper-hybrid oscillations trapped in a plasma density depletion across an ambient magnetic field are investigated. Approximate dispersion relations are derived, which lead to the identification of two parametric instabilities of the localized upper-hybrid bounded wave structure. Both are related to trapped upper-hybrid oscillation resonances. The first is a decay to a frequency of a trapped wave resonance, downshifted from the applied frequency, where the downshift must be slightly larger than the lower-hybrid frequency. The second instability can exist when the applied frequency is slightly below the arithmetic mean of the frequencies of two trapped oscillation resonances; then the antiStokes component of one is in resonance with the Stokes component of the other. Both slab and two-dimensional geometries are considered.

Analytic results for the time dependences of the kinetic and magnetic energies of an incompressible magneto fluid threaded by a strong uniform magnetic field B0 are obtained. The governing equations are the linearised magnetohydrodynamic (MHD) ones, but with the conventional Laplacian dissipation replaced by ion parallel viscous effects. The behaviour is shown to depend on the relative sizes of the Alfvén frequency and the viscous and resistive dissipation rates. For many cases equipartition of the kinetic and magnetic energy holds at the (Fourier) modal level. An important exception to this behaviour occurs for two-dimensional fluctuations, that is when the wavevectors are perpendicular to B0.

In a recent study Tsytovich et al. [J. Plasma Phys. 56, 127 (1996)] claimed to obtain new expressions for electron–ion bremsstrahlung in plasmas. It is shown, however, that they interpreted earlier work incorrectly and simply reproduced well-known results.