A new formulation of the Hamiltonian structure underlying the perfect fluid equations is presented. Besides time, a parameter c is also used. Correspondingly, there are two interdependent systems of equations expressing time evolution and e evolution respectively. The accessibility equations define the e dynamics and give the variation in the usual Eulerian fluid variables as determined by the generating functions. The time evolutions of both the Eulerian fluid variables and the generating functions are obtained from an action principle. The consistency of the e and the time dynamics is crucial for this formulation, i.e. the accessibility equations must be propagated in time by the Euler–Lagrange equations. The reason for introducing this new formulation is its power in certain applications where the existing Hamiltonian alternatives seem less convenient to use. In particular, it is a promising tool for Hamiltonian perturbation theory. We consider the small-amplitude expansion, and find, very simply and naturally, the Hermitian structure of the linearized ideal fluid equations as well as coupling coefficients for resonant three-wave interaction exhibiting the Manley–Rowe relations.

Linear stability of a magnetized dusty plasma is studied for the regime with ≈ 1 (where G is the universal gravitational constant, md is the grain mass and qd is the grain charge). We demonstrate that the magnetic force plays a stabilizing role and, together with electrostatic repulsion, counter gravitational condensation. The implications of this result for astrophysical situations are briefly discussed.

The new Hamiltonian formulation of the perfect fluid equations presented in part 1 of this series of papers is generalized to a class of IVIHD models, including for example ideal MHD and the Chew–Goldberger–Low equations. The mathematical structure is to a great extent unchanged by this generalization, and most results about the small-amplitude expansion of the perfect fluid equations remain obviously valid. For example, we now have a rigorous proof of the Manley-Rowe relations in resonant three-wave interaction, valid for this class of MHD models and for quite general inhomogeneous but stationary background states, including equilibrium flows.

The expansion of a bounded plasma with dust particles is investigated by means of computer modelling, taking into account the dynamics of the dust particle charge as well as the Coulomb collisions of electrons and ions with dust particles. The PIC method is used for the computer modelling. The collection of electrons and ions by dust particles is described in a way similar to orbit-limited probe theory. Coulomb interactions are described in the framework of stochastic differential equations. It is shown that the mean distribution functions of electrons and ions are influenced by the dust particles during plasma expansion. The evolution of the ion distribution function leads to a strong deviation from equilibrium. Dust particles also influence the temporal behaviour of the plasma parameters.

The theory of black-body radiation in thermal equilibrium with a homogeneous and isotropic plasma is presented. The relevant thermodynamic quantities of the radiation are obtained. The presence of the plasma changes qualitatively and often quantitatively the concept of black-body radiation, essentially through the effect of plasma density.

The general transfer integrals describing the collisional exchange of momentum and energy between the constituents of multicoimponent gases are evaluated for different plasma scenarios characterized by Maxwellian as well as non-Maxwellian distribution functions of the plasma species. Following a brief presentation of the standard approximation frequently employed in the literature, a comparison of numerical evaluations of the transfer integrals for various distribution functions reveals significant differences in the corresponding collisional momentum and energy exchange rates, which are shown to depend mainly on the core structure of the distributions. We demonstrate the inadequacy of the standard approximation and hence the importance of an accurate evaluation of the transfer integrals with an application to the electron proton as well as the helium proton interaction in the solar wind plasma.

The Hamiltonian structure underlying ideal multifluid electrodynamics is formulated in a way that simplifies Hamiltonian perturbation calculations. We consider linear and lowest-order nonlinear theory, and the results in Part 1 of this series of papers are generalized in a satisfactory way. Thus the Hermitian structure of linearized dynamics is derived, and we obtain the coupling coefficients for resonant three-wave interaction in symmetric form, giving the Manley–Rowe relations.

Two-dimensional shear Alfvén-wave turbulence is investigated for a plasma with arbitrary β value. A set of three equations, which reduces to the derivative nonlinear Schrödinger equation in the limit of parallel propagation, is derived. The genuinely two-dimensional case is governed by two coupled equations. For a non-parallel one-dimensional space dependence, the nonlinearity is shown to vanish to all orders.

It is demonstrated that the dielectric tensor for a non-relativistic magnetized plasma whose particle velocity distributions can be modelled by isotropic kappa, or generalized Lorentzian, distributions admits an expression similar to that obtained by Trubnikov for a relativistic plasma. The kappa distribution is a useful distribution for modelling space plasmas containing significant numbers of superthermal particles, i.e. those that have energies in excess of the thermal energy. The dielectric tensor is valid for arbitrary wavevectors, and is shown to reproduce the known limiting case of wave propagation parallel to the magnetic field. Even in this limiting case, the results obtained represent a generalization of previous results to arbitrary real values of the index K, the parameter that shapes the superthermal tail on the distribution. The expression for the dielectric tensor might be useful as a starting point for numerical studies of waves and instabilities in plasmas containing superthermal particles.

A time-dependent two-dimensional MHD simulation program is used to investigate the magnetic reconnection process with a spatially uniform diffusivity. Various initial conditions are considered and are allowed to evolve until a final steady state is produced. The boundary conditions are carefully handled in order that they be as strict as possible. In the first series of simulations the initial condition is taken to be an analytical solution of the ideal MHD equations given by Biskamp. Dirichlet (fixed) boundary conditions are used, with a small amount of flexibility allowed on the boundary for the stream function in order to prevent any unphysical currents forming. The final steady- state contains a current sheet whose width and length are found to vary as and respectively, and the reconnection rate is found to be independent of the value of Rm, indicative of fast reconnection. Additionally, as Rm, is increased, a region of reversed current and a high-speed jet of plasma are observed to develop along the MHD shock separating the inflow and outflow regions. The second series of simulations uses a slightly different initial condition that allows a faster outflow of plasma from the simulation region. The current sheet width of the final steady state is again found to vary as , and the reconnection rate is again independent of Rm. However, no reversed currents or plasma jetting along the shock are observed, indicating that the plasma jets of previous simulations are due to restrictive outflow conditions, which force the high-speed plasma emerging from the end of the current sheet to divert along the MHD shock. Lastly, the analytical model of Petschek is utilized to provide an initial condition. For this case, however, it is not possible to keep the boundary conditions as strict as before, since both the stream and flux functions have to be allowed to vary slightly in order to deal with the discontinuities of the Petschek model. Although steady-state solutions can be obtained, they are found, owing to the laxness of the boundary conditions, not to exhibit the well-defined structure or small current sheets of the previous results.

The warm-fluid equation derived from the drift kinetic equation is solved numerically to investigate the electrostatic low-frequency stability of an electron ribbon beam drifting in the crossed-fields of a planar magnetron. The temperature effect is manifested only for oblique propagation with respect to the drifting beam direction. The dispersion relation takes the form ω = ω(k⊥/ks∥) = ω(ks∥/k⊥), where k⊥ and k⊥ are respectively the components of the surface wave vector k parallel and perpendicular to the magnetic field. The obliqueness of the propagation direction and the non-zero temperature give rise to a resonant instability, in addition to the diocotron instability, and the wavenumber corresponding to the maximum diocotron growth rate shifts as the temperature changes.

In a recent paper, Desai et al. (1994) have reported the observed characteristics of the specularly reflected laser light from a copper plasma created by laser irradiation of a planar copper target. They have measured specular reflection, and attributed the observed diffusivity of specularly reflected radiation to the curved and rippled surface at the radiation turning point in the plasma. The aim of this comment is to reanalyse the possible causes for the diffusion of specular reflection relevant to their experimental conditions.

The generalization of the Case—van Kampen analysis to a multidimensional non-uniform plasma is presented. Application of this analysis is made to minority-ion gyrolesonant heating in an axisymmetric tokamak. In previous work the Case—van Kampen analysis, in conjunction with the Bateman—Kruskal algorithm, was used in a one-dimensional slab model to compute the collective wave spin-off (to the minority-ion Bernstein wave) and the gyroballistic continuum for minority gyroresonant absorption. The generalization to many gyroresonant dimensions and non-trivial geometries requires several important new developments: In tokamak geometry particles can be trapped, an effect that is absent in the slab model. Also, the ray propagation dynamics for both the flee gyroballistic waves and the collective minority-ion Bernstein wave is far more complicated than in the slab model. In particular, a resonance zone is identified wherein the gyroballistic waves interact strongly and cannot be treated as free. We use the Weyl calculus to construct a local form of the self-consistent gyroballistic equation within the resonance zone. This reduced equation is simplified via a metaplectic transformation (a generalization of the Fourier tiansformation). After this simplification, the equation is shown to be of Case—van Kampen type with weak non-uniformities; hence there are no true Case—van Kampen eigenfunctions. Using the Bateman—Kruskal approach, a local Case—van Kampen basis can be constructed and the initial-value problem solved. The self-consistent interactions of the gyroballistic continuum lead to a collective wave, the minority-ion Bernstein wave. The Bernstein wave is extracted by the spectral deformation approach of Crawford and Hislop. The relevance of this work to the theory of collective phenomena in nonlinear oscillator ensembles is briefly discussed.