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.

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 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.

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.

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.

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 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.

A single particle is subjected to the combined action of a static uniform magnetic field and an electromagnetic wave. The equations of motion are solved using the perturbation method up to second order. In the results, two different types of second-order effects appear: (i) the always present non-resonant effects, resulting in a ponderomotive drift and a nonlinear cyclotron frequency shift, and (ii) the resonant effects appearing at the half-integer harmonics of the gyrofrequency and leading to perpendicular heating and diffusion.

Ionization wave frequency spectra and their spatial distribution along argon and neon plasma positive columns are detected by microwaves in the 8–18 GHz frequency band. The plasmas are created at medium pressure by d.c. discharges in narrow tubes. Detection takes place in a rectangular waveguide on the microwave fields reflected and transmitted by plasma columns which are placed transversely across the waveguide in different positions and at several values of the discharge current. The frequency of the microwaves is adjusted for a parametric resonance condition with respect to Langmuir's electron frequency. The properties and dispersion relations of these waves are derived from a linear theory developed by K. W. Gentle, in which, for discharge operation below the Pupp limit, metastables are also included in the ionization and species conservation equations. An estimate of the total collision frequency is derived from a simplified two-fluid model valid essentially near the Pupp equilibrium limit.

Nonlinear magneto-acoustic waves in a turbulent plasma are simulated by collisional MHD equations. Damping of these waves due to electrical conductivity arising from micro-instabilities and collisional viscosity are analyzed. Numerical investigation of competing effects due to non-linearity and dissipation has been carried out. It is found that finite amplitude perturbation leads to the formation of a shock in both the slow and the fast mode propagation. Collisional viscosity plays an important role in the damping of nonlinear magneto-acoustic waves in the astrophysical and space plasmas.

Resonant excitation of Alfvén waves by fast particles in a finite pressure plasma in a non-uniform magnetic field is studied. Plasma compressibility in the wave field is determined both by the curvature of the magnetic lines of force and finite Larmor radius of fast particles. A general expression for the instability growth rate is obtained and analyzed; the applicability of the results obtained in the previous paper has also been studied. The finite pressure stabilization of the trapped particles instability has been found. The bounce-resonance effects are analyzed.