We demonstrate that a self-consistent circularly polarized wave in an otherwise field-free homogeneous cold plasma is unstable to small amplitude perturbations. For either an electron-positron plasma or an electorn-proton plasma the instability rate is at least about the order of the effective plasma frequency when the bulk flow speed is zero. For finite bulk flow speeds of the plasma, we show that the electron-positron plasma is unstable – again with a growth rate of the order of the effective plasma frequency; we also show that the electron-proton plasma is unstable (at least at small wave number, k) with a growth rate proportional to k. The instability rates we calculate are conservative, for other modes not investigated here may be more unstable. The results of these calculations bear directly on our understanding of plasma systems thought to be driven by large amplitude waves.

The introduction of Clebsch representations allows one to formulate the problem of finding minimum energy solutions for a magneto-fluid as a well-posed problem in the calculus of variations of multiple integrals. When the latter is subjected to integral constraints, the Euler–Lagrange equations of the resulting isoperimetric problem imply that the fluid velocities are collinear with the magnetic field. If, in particular, one constraint is abolished, Alfvén velocities are obtained. In view of the idealized nature of the model treated here, further investigations of more sophisticated structures by means of Clebsch representations are anticipated. Preliminary results of a similar calculation utilizing a modified two fluid model are discussed.

The existence of periodic ion-acoustic waves propagating through an inhomogeneous moving plasma is studied. For supersonic flow speeds it is shown that periodic excitations result in periodic responses independent of the nature of the media properties and the initial conditions. For subsonic flow speeds, periodic responses exist only under certain restrictions on the media and the initial conditions. However, most cases of physical interest are in the class of problems for which periodic or asymptotically periodic responses exist.

We inject a fast ion beam across a magnetic field, through a cylindrical 5 cm diameter plasma. Shear Kelvin–Helmholtz waves, already present in the plasma, are considerably amplified. The ion beam is rapidly slowed and scattered. The observed stopping power exceeds the classical power by over two orders of magnitude. A simple theoretical estimate, ascribing beam energy loss to driving of the waves, agrees qualitatively with observations.

A novel approach to the theory of nonlinear mode coupling in hot magnetized plasma is presented. The formulation retains the conceptual simplicity of the familiar ponderomotive-scalar-potential method, but removes the approximations. The essence of the approach is a canonical transformation of the single-particle Hamiltonian, designed to eliminate those interaction terms which are linear in the fields. The new entity (the ‘oscillation centre’) then has no first-order uttering motion, and generalized ponderomotive forces appear as nonlinear terms in the transformed Hamiltonian. This viewpoint is applied to derive a compact symmetric formula for the general three-wave coupling coefficient in hot uniform magnetized plasma, and to extend the conventional ponderomotive-scalar-potential method to the domain of strongly magnetized plasma.

The results of a numerical simulation of a plasma double layer are presented. The model is of a finite, one-dimensional plasma with a specified potential difference across the system. Initially a single pulse is formed which traverses the system with constant velocity. This stage is followed by the formation of a potential drop across a limited region of the plasma. The relation between the spatial extent of the double layer and the potential drop is given approximately by L = 6(edgr;φ/kTe)½. The double layer causes electron and ion beams which tend to lead to instabilities in the upstream and downstream regions.

From a dispersion relation, linear growth rates of electromagnetic instabilities are obtained in an electron plasma whose velocity distribution function has a high-energy tail. Theory is developed to derive the reduction in the thermal flux caused by these electromagnetic instabilities. Nonlinear theory leads to the saturation level of instabilities. Numerical simulations are carried out using a particle-in-cell method. The reduction in thermal conduction predicted by the theory is found to be in good agreement with computer simulations.

A unified picture of the structure of steady, one-dimensional shock waves in partially ionized argon, in the absence of external electric or magnetic field, is presented. The investigation is based on a two-temperature, three-fluid continuum approach, using the Navier–Stokes equations as a model and including non-equilibrium ionization. Quasi charge neutrality and zero velocity slip are assumed. The analysis of the governing equations is based on the method of matched asymptotic expansions and results in the following three layers: (1) a broad thermal layer dominated by electron thermal conduction, (2) an atom-ion (A-I) shock structured by the heavy particle (atoms and ions) collisional dissipative mechanisms and (3) an ionization relaxation layer (IRL) wherein electron- atom inelastic collisions dominate. Solutions have been obtained for the first two orders with respect to a small parameter, which is the ratio of energy fluxes due to heavy particle viscous dissipation and electron thermal conduction. Whereas only electron temperature and electric potential show any marked variation in the thermal layer, the changes in all the variables in both the A-I shock and the IRL are significant.

Inclusion of electron thermal conduction terms in the governing equations has been observed to introduce numerical instabilities in the analysis of the IRL. They are circumvented by adopting a regular perturbation scheme with respect to a local small parameter, which has been identified to be the ratio of the freestream degree of ionization to the nondimensional characteristic temperature for first ionization. Numerical results show that the effect of electron thermal conduction on the IRL profiles is significant. Results in the form of tables and figures are presented for five sets of equilibrium free-stream conditions.

The energy of hydrodynamically unstable plasma waves is re-examined. The modified Landau–Lifshitz factor Re (∂/∂ω) (ω∈) recently proposed is shown to involve several difficulties when energy and momentum conservation are considered.

We consider the effect of trapped electron instability turbulence on the dynamics of a typical mode. We find its effects are turbulence induced additional collision frequencies for the trapped electrons which are stabilizing. The resulting saturation level is found to be considerably smaller than previous estimates.

The complete second-order theory of the multiple water-bag model is developed for one-dimensional collisionless electrostatic waves, in terms of the initial value problem. Nonlinear frequency spectra are obtained in Van Kampen's formulation, and a new pole, already predicted by R. W. B. Best, appears for hot plasmas. This theory is successfully checked by a full numerical experiment of the Vlasov–Poisson system.

This paper is concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized electron–ion plasma. These nonlinear waves are of fixed profile, superluminous, period.ic and transverse. The small perturbations are assumed to propagate in the same direction as the nonlinear wave. A Lagrangian method is used to derive the perturbation equations. The analysis is carried out in the frame where the nonlinear waves are space independent and then the results Lorentz transformed to the laboratory frame. Part 1 refers to circularly polarized waves. In this case it is possible to integrate the equations and obtain an algebraic dispersion relation in the form of an eighth order polynomial equation in the frequency. The analytical and numerical solution of this equation, for a wide range of variation of the parameters involved, reveals the existence of a very unstable mode. Particular attention is given to very large wave amplitudes for which the plasma behaves like an electron–positron plasma; in this case the growth rate of the unstable mode can be as high as the frequency of the nonlinear wave.

The potential energy of an ideal static MHD plasma is minimized using the invariants of motion as variational constraints and assuming a general symmetry (dependence on two space variables only). For simplicity only the plasma-on- the-wall case is considered. The first variation yields a generalized Shafranov equation, the second the desired stability criterion. It is found that equilibria with a longitudinal current increasing monotonicaily towards the boundary are always stable with respect to symmetric modes. For equilibria with an outwardly decreasing current a sufficient criterion (for symmetric modes) is derived, which only requires the solution of a linear eigenvalue problem. The theory is applied to the straight circular cylinder and to the axisymmetric torus.