Constant feedback, which has been used exclusively, fails to stabilize more than one mode of a plasma instabiliity. It is shown that a suitable dynamic or frequency-dependent feedback can stabilize all modes. Methods are developed in which such a feedback strucutre can be chosen in terms of its poles and zeros in relation to those of the plasma transfer function in the complex frequency plane. The synthesis procedure for such a feedback sturcure, in the form of an integrated electronic circuit is also discussed. As an example, a dynamic feedback for multi-mode stabilization of a collisional drift wave instability is developed in detail.

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 effect of finite ion Larmor radius on the Kelvin–Helmholtz instability is investigated in the cases of an incompressible and a compressible plasma. When a wave vector is perpendicular to a uniform magnetic field, the effect of finite Larmor radius (FLR) stabilizes perturbations with a wavenumber exceeding a critical value, while there exists another case that the FLR effect destabilizes still more than the usual MHD approximation. The difference between these cases is decided from the configuration of flow velocity and magnetic field. When a wave vector is parallel to a magnetic field, the FLR effect tends to stabilize perturbations with a larger wavenumber.

Baker proposed a method of injecting charged particles into a static magnetic field such that particles on these ‘trapping orbits’ never return to the vicinity of the injector and remain permanently trapped. Their infinite confinement time requires that their energy, Eo, be specified with infinite precision. When the energy differs from this by a small amount, E, the particle escapes after a finite confinement time, of the order of In (Eo/E) cyclotron periods.

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 ion density in the wake of extended bodies in collisionless flows of unmagnetized plasmas is qualitatively investigated. Both the deflexion of the ions in a surface potential field, and the collective response of the ambient plasma are incorporated in a model which reveals the connexion between the wakes of extended bodies and those of point charges. The differences between the wake features of small and large bodies in strongly non-isothermal plasmas (Te » Ti) are related to the excitation of different types of waves. In isothermal plasmas no sharp wake features can be expected, because the appropriate waves are heavily damped, and other features are smoothed by the thermal motion of the ions.

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.

This paper is concerned with the derivation of linear wave equations for nonuniform magnetized Vlasov plasmas. By the operator method it is shown that a close connection exists between the case of perpendicular propagation and the general one. Combining this with previous results, expressions for the perturbed density and velocity are derived for the case of propagation at any angle to the uniform static magnetic field in a two-temperature Maxwellian plasma. These results apply for arbitrary inhomogeneities of equilibrium density and temperatures in directions perpendicular to the static magnetic field.

The Sonnerup merging model for an incompressible plasma is extended to allow a flow component along the field lines in the inflow regions. Solutions are found to exist as long as the difference between the quantities B. V for the two inflow regions does not exceed a critical magnitude dependent on the inflow field magnitudes and plasma densities. All such solutions satisfy Vasyliunas' definition of merging, but some classes of solution have radically altered geometries, i.e. geometries in which the inflow regions are much smaller than the outflow regions. The necessary but not sufficient condition for these unusual geometries is that the field-aligned flow component in at least one inflow region be super Alfvénic. A solution for the case of a vacuum field in one inflow region is obtained in which any flow velocity is allowed in the non-vacuum inflow region, although super-Alfvénic flow can still result in an unusual geometry. For symmetric configurations, the usual geometry, that of Petschek and Sonnerup, is retained as long as both field-aligned flow components in the inflow regions are less than twice the inflow Alfvén speed. For the case of a vacuum field on one side and fields approximating the boundary between the solar wind and the earth's dayside magnetosphere, the usual geometry is retained for flow less than about 2·5 times the local Alfvén speed.

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.

The linear Vlasov dispersion relation for electrostatic waves in a homogeneous plasma is studied for instabilities driven by an electron heat flux. A two Maxwellian model of the electron distribution function gives rise to three unstable modes: the electron beam, ion-acoustic and ion cyclotron heat flux instabilities. At large Te/Ti the ion-acoustic instability has the lowest threshold; at small Te/Ti the electron beam instability is dominant; and at intermediate values of Te/Ti the ion cyclotron mode is the first to go unstable. The presence of a high energy tail on the electron distribution function raises the value of the dimensionless heat flux qe/(nemev3e) at the ion-acoustic threshold, but increasing atomic number of the ions decreases this value.

We consider nonlinear surface waves on a cold plasma half-space. It is found that for a certain region of the wavenumber spectrum, supersonic envelope surface wave solitons exist.

Stability and growth rates of resistive axisymmetric modes for doublets have been studied numerically. Because of the many parameters entering the problem this study has the form of a survey of features that are believed to be most important for stability. In general it is found that the most dangerous mode is one that either elongates or contracts the plasma in the vertical direction. Stability, and in the case of instability, the growth rate, depends on the proximity of a conducting wall surrounding the plasma. Numerical examples of this are given both for cases of a rectangular wall shape and an indented wall shape. Examples are also given that indicate the sensitivity to parameters characterizing the equilibrium. Finally, an example is given for the case of a wall with a finite resistivity. It is shown that such a wall does not affect the stability, but decreases the growth rate relative to a case where the wall is absent.

We investigate the problem of spatial depletion of propagating lower-hybrid waves in an inhomogeneous plasma. In particular, we consider the nonlinear evolution of a lower-hybrid pump which is coupled to a daughter lower-hybrid decay wave excited by low-frequency density perturbations. Our results show that pump depletion occurs when three-dimensional effects are included. This phenomenon competes with the filamentation of the pump caused by self- interaction. Implications to lower-hybrid heating experiments are discussed.

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 development of Buneman's kinetic-type instability in plasma with hot ions and cold electrons is investigated. Expressions for the frequencies and growth rates of oscillations when the current velocity slightly exceeds the instability threshold velocity have been derived in the linear approximation. The quasilinear theory of instabilities has been developed, and it has been shown that the quasi-linear effects lead to the amplification of the instability.

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.

A formal derivation of the quasi-linear equation of a plasma in a magnetic field is presented. The theory accounts for spatial inhomogeneity in one direction and for bounce motion of particles confined in a mirror magnetic field.

The collision operator that appears in the equation of motion for a particle distribution function that has been averaged over an ensemble of random Hamiltonians is non-Markovian. It is non-Markovian in that it involves a propagated integral over the past history of the ensemble averaged distribution function. All formal expansions of this nonlinear collision operator to date preserve this non-Markovian character term by term yielding an integro-differential equation that must be converted to a diffusion equation by an additional approximation. In this note we derive an expansion of the collision operator that is strictly Markovian to any finite order and yields a diffusion equation as the lowest nontrivial order. The validity of this expansion is seen to be the same as that of the standard quasi-linear expansion.

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.