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This report is an account of research undertaken to describe the steady, axisymmetric flow of plasmas through rocket nozzles, with attention directed to the use of magnetic fields for guiding or propelling the plasmas. The primary emphasis is on simply connected nozzles containing strictly longitudinal (B sub r, O, B sub z) magnetic fields to guide the plasma, with secondary consideration given to annular nozzles containing strictly azimuthal (O, B sub theta, O) magnetic fields to propel the plasma. The possibility and desirability of using hot plasmas in a repetitive mode is discussed, and motivates our consideration of an extensive range of parameters. Although slightly ionized gases having low temperatures (a fracture of an eV) and low magnetic Reynolds numbers often are the objects of valid and useful research (for example, in connection with MHD generators, with MPD thrusters, and with arc heaters to provide sources of hot gas for expanding gas-dynamic flow fields) , the focus is upon the effective and efficient interaction of substantial plasmas with guiding or driving magnetic fields. Thus, focus is primarily on highly ionized plasmas that are not dominated by resistive dissipation. Some of the principal physics issues associated with these concepts are addressed, including the assumptions and limitations of the ideal MHD model, the magnitude and scaling of classical and anomalous transport losses and of radiation losses in hydrogen plasma during transit of plasma through the nozzle, and the transport-related detachment problem of how the plasma leaves the exit region of the nozzle.

Some extensions of elementary plasma theory which are either not to be found or are unemphasized in other elementry presentations are discussed. It is felt that such a document will be useful and instructive to those beginning a study of classical plasma theory. (Author)

A gas of charged particles making both elastic and inelastic collisions is assumed to be in a uniform steady state in a uniform steady electric field. Supposing that the gas obeys a one-dimensional Boltzmann equation, this equation is solved exactly for the case of energy-independent elastic and inelastic mean free paths, together with the assumption of isotropic scattering. The gas drift velocity and gas temperature are then obtained from the velocity distribution, their dependences on electric field strength are displayed. The results are in good qualitative agreement with other theories and with experiments on N-type Germanium at liquid Nitrogen temperature. (Author)

The stability of a plane blast wave to surface perturbations is examined. It is found possible by making a 'thin' sheet approximation to the geometry, to obtain a set of ordinary differential equations which describe the sheet motion. These equations are effectively solved for all possible initial conditions. It is found that surface perturbations grow rapidly at first but are eventually limited in amplitude. All perturbations grow in amplitude like powers of time. (Author)

The stability of the interface between a highly conducting liquid and a flowing, non-conducting gas is studied, supposing a magnetic field to be parallel to the interface. Arbitrary angles are allowed between magnetic field, flow direction and wave-vector. (Author)

A study was made of those surface waves that can propagate along a plane interface separating a conducting (incompressible) liquid from a non-conducting, compressible gas, when there is a static magnetic field parallel to the interface. For any given direction of propagation (except exactly perpendicular to the magnetic lines), a critical field strength was found above which surface Alfven waves cannot exist. Instead, at these strong magnetic fields, there are surface sound waves in the gas. The critical magnetic field at which the transition from Alfven-type to sound-type surface waves takes place is practically independent of the gas density, depending essentially only on its temperature. (Author)

Two contra-streaming electron beams of equal densities and speeds interacting between two parallel planes are studied. The streams are cold and their average charge is compensated by a uniform positive background. For infinitely broad streams, an eigenfrequency equation is derived from the conditions that the entering beams be free of perturbations. The eigenfrequency equation is solved numerically and the results show there is no instability for omega sub b tau < pi/2(3/2), where omega sub b is the plasma frequency of either beam, and tau is half the transit time between the plates. For large values of omega sub b tau, the fastest-growing modes have a growth rate of omega sub b/2. The growth rate is also calculated from the dispersion relation assuming appropriate real values of wavenumber and is in good agreement with the exact results of the eigenfrequency equation. (Author), Also available from the authors.

The stability of strong spherical blast waves to infinitesimal perturbations is examined in the limit (gamma-1) << 1, where gamma is the ratio of specific heats. By making a 'thin sheet' approximation to the geometry it is found possible to describe all perturbations as a sum of spherical harmonics. By transforming to a new time-like variable, one can obtain a set of ordinary constant-coefficient differential equations for the perturbation corresponding to each spherical harmonic, and one then obtains a dispersion relation giving the growth rate of each harmonic. (Author)

A cylindrical plasma is given to be in an in finitely strong axial magnetic field. Taking only longitudinal temperature into account, a dispersion relation (including Landau damping) is calculated for electron charge oscillations whose wavelengths are much larger than the plasma radius. The Landau damping is found to be far larger than that of waves in an infinite plasma of the same density and temperature, and for the same wavelength. The radiation damping of these oscillations is also calculated. It is found that these oscillations do not radiate at all from an infinitely long cylin43. For a plasma cylinder of finite length it is found that the radiation damping of these oscillations can be made negligible compared to Landau damping for reasonable laboratory parameters. It is assumed throughout that the unperturbed state is a Maxwellian velocity distribution. (Author), Also available from the author.