It is shown how to construct shock-like time independent solutions of the electrostatic Vlasov and Poisson Equations in one dimension. The positive ions are assumed to be at zero temperature. The electrostatic potential is assumed to increase monotonically through the shock from zero to a constant value. The most important feature of the solution is a population of trapped electrons in the shocked plasma. In contrast to time-independent solutions based upon fluid equations, there is no upper limit on the amplitude of the shock.

Ion acoustic waves propagating in a collision-free gravity-supported one-dimeiisional plasma are studied, including conditions where the wavelength is of the order of the scale height of the equilibrium plasma. It turns out that the fluid dynamic steepening tendency of waves propagating in the direction of decreasing density is overcome by Landau damping up to wavelengths of the order of the scale height or even larger, depending on the ratio of the electron and the ion temperatures.

Variational methods are used to determine the structure of dynamically stable plasmoids. The total energy of the plasmoid is varied subject to a set of constraint integrals on the flow. It is demonstrated that the resulting flow structure results in a plasmoid of the type observed experimentally when the angular momentum of the plasmoid is not conserved. This is the collinear vortex structure. New experimental results are presented which demonstrate that the structures observed in mirror trapping experiments may be of the type predicted by the variational calculation.

It is demonstrated that the collinear plasmoid structures can propagate in a surrounding conducting gas as members of a class of non-linear transverse waves that trap and transport fluid mass. They may also exist as standing waves in a surrounding medium which supports currents and acts as a force-bearing shell. The interaction of the non-linear transverse waves (plasmoids) with each other and with the magnetic mirror field produces a reversed-field closed configuration. Experimental results are presented which illustrate these effects and show details of the structures.

It is also demonstrated that a modification of these solutions that assumes conservation of angular momentum of the plasmoid describes another type of plasma structure which is centred on the magnetic field lines and moves at right angles to the field. This is the field-aligned plasma structure.

In this paper, the electrostatic oscillations of a plasma having a Fermi distribution of energies are discussed. The electrons, assumed to be tightly bound to the magnetic lines of force, are acted upon by a linear restoring force which causes the electrons to oscillate with a fixed angular frequency ω0. The dependence of the frequencies of oscillation of the plasma on electron density is calculated in the two limiting cases ωp0/ω0 ≪ and ωp0/ω0 ≫ 1.

We present a brief survey of the phase velocities and polarizations of linear waves in an infinite, uniform, high β plasma using the two-fluid approximation. Questions of wave-particle damping are deferred. Several features of high β plasma waves differ from the familiar low β case.

Using a 337 μm gas maser (Gebbie, Stone & Findlay 1965; Gebbie, Stone, Slough, Chamberlain & Sheraton 1966) it is possible to obtain precise measurements of the submillimetre absorption and phase shift occurring in specimens of each of the phases of matter and results have already been reported for the soild, liquid and gaseous states (Chamberlain & Gebbie 1965; Gebbie, Stone, Findlay & Pyatt 1965; Chamberlain, Werner, Gebbie & Slough 1967;, Chamberlain, Findlay & Gebbie 1965).

The steady shock dicontinuity in the flow of a perfectly conducting gas with anarbitrarily oriented magnetic field is considered by taking as the parameters the Mach number, the Alfvén Mach number, the magentic field direction, and the shock angle. The shock solutions satisfying the conservation laws as well as the entrophy and evolutionary conditions are given by the roots of a simple cubic equation and the associated formulas. Several special cases are discussed analytically and numerically. The possible types of magnetohydrodynamic shock waves are shown on the speed-deflexion phase plane, and the possible shock configurations in the physical space are discussed on the basis of them.

The kinetic equation for resonant three-wave coupling is solved exactly in the one-dimensional case assuming that only a single triplet of modes in interacting. No assumptions are made as to the froms of the interaction kernel or of the oscillation frequencies as functions of wave-number. Both positive- and negative- energy waves are allowed to be present simultaenously. In explosively unstable situations the time, t∞, for divergent behaviour to occur is calculated in terms of the interaction keral and intial conditions. In situations where the system is non-linearly stable, the density of quasi-particles is found to tend time-asymptotically to a steady state which depends in detail on the initial preparation of the system.

For the case of two or three dimensions, the asymptotic state is obtained when the system is stable, the k-space is finite, and only one triplet of modes interact. If these modes all have the same sign of energy, the Rayleigh—Jeans distribution is valid; but if one of the modes has the oppsoite sign of energy, an additional conservation law leads to a modification of the Rayleigh-Jeans distribution.

The approximations usually made to truncate the BBGKY hierarchy for a plasma are discussed; their failure at small inter-particle separations leads to divergence of the Balescu—Lenard collision integral. A number of authors have obtained convergent kinetic equations, often by rather complicated methods.

It is shown here that, if the standard truncation procedure is modified in a way which makes it less obviously inconsistent for close approaches, the standard methods maybe closely followed in deriving a convergent collision integral which agrees to dominant order with the ‘cutoff’ Balescu—Lenard integral and with the other work on the problem. In fact, the kinetic equation obtained is identical with the Balescu—Lenard equation except that the Coulomb potential is replaced by another that is non-singular at the origin. A physical interpretation of this result is suggested.

In plasma, where collective motions are made possible by the long range of the Coulomb interaction, there is properly no general kinetic equation for the one-particle distribution function alone. In part 1, we gave the foundations of an enlarged kinetic theory of plasma where the time evolution of the electric field fluctuations Ik is considered simultaneously with the time evolution of the one-particle distribution F. Here we improve these equations in a systematic fashion to include all processes which are relevant in stable and weakly unstable plasma. More precisely, the equation for the waves now includes, besides Landau damping and Cerenkov emission, the effect of collisional damping and nonlinear Landau damping, as well as emission via particle-particle scattering (bremsstrahlung), wave-particle and wave-wave scattering. The particle kinetic equation is also improved accordingly so that we obtain a kinetic description which is uniformly valid for all plasma réegimes, if one excludes strong turbulence (for which there is at present no completely satisfactory statistical theory).