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(Previously announced in STAR as N82-12043)

Features of the interaction of flow distortions, such as gusts and wakes with blade rows of advance type fans and compressors having high tip Mach numbers are modeled. A typical disturbance was assumed to have harmonic time dependence and was described, at a far upstream location, in three orthogonal spatial coordinates by a double Fourier series. It was convected at supersonic relative to a linear cascade described as an unrolled annulus. Conditions were selected so that the component of this velocity parallel to the axis of the turbomachine was subsonic, permitting interaction between blades through the upstream as well as downstream flow media. A strong, nearly normal shock was considered in the blade passages which was allowed curvature and displacement. The flows before and after the shock were linearized relative to uniform mean velocities in their respective regions. Solution of the descriptive equations was by adaption of the Wiener-Hopf technique, enabling a determination of distortion patterns through and downstream of the cascade as well as pressure distributions on the blade and surfaces. Details of interaction of the disturbance with the in-passage shock were discussed. Infuences of amplitude, wave length, and phase of the disturbance on lifts and moments of cascade configurations are presented. Numerical results are clarified by reference to an especially orderly pattern of upstream vertical motion in relation to the cascade parameters.

This report describes the SUMMA superconducting magnetic mirror facility at the NASA Lewis Research Center and the hot-ion plasma research conducted therein. SUMMA is characterized by intense magnetic fields (designed for 8.6 T at the mirrors) and a large-diameter working bore (41 cm diameter) with room-temperature access. The goal of the plasma research program is to produce steady-state plasmas of fusion reactor densities and temperatures (but not confinement times). The program includes electrode development to produce a hot, dense, large-volume, steady-state plasma and diagnostics development to document the plasma properties. SUMMA and its hot-ion plasma are ideally suited to develop advanced plasma diagnostics methods. Two such methods whose requirements are well matched to SUMMA are: (1) heavy ion beam probing to measure plasma space potential, and (2) submillimeter wavelength laser Thomson scattering to measure local ion temperature. Two NASA University Grants were established to identify major requirements for developing these two diagnostic techniques in SUMMA.

The theoretical model accounts for drift and cyclotron components of ion motion in a partially ionized plasma. Density and velocity distributions are systematically prescribed. The flux into the neutral particle analyzer (NPA) from this plasma is determined by summing over all charge exchange neutrals in phase space which are directed into apertures. Calculation of the process is continued through the NPA using appropriate cross section data to obtain analyzer output distributions. Theoretical results were compared with NPA measurements on four plasma heating devices having radial electric, E, and axial magnetic, B, fields. Drift velocity, in the azimuthal direction is identified with E/B. Selection of randomized cyclotron velocity distributions about mean azimuthal drift yield energy distributions which compare well with experiment.

Initial empirical results are presented for the hot-ion plasma heating experiments conducted in the new SUMMA (Superconducting Magnetic Mirror Apparatus) at NASA Lewis Research Center. A discharge was formed by applying a radially inward dc electric field near the mirror throats. Data were obtained at midplane magnetic flux densities from 1.0 to 3.5 tesla. Charge-exchange neutral particle energy analyzer data were reduced to ion temperatures using a plasma model that included a Maxwellian energy distribution superimposed on an azimuthal drift, finite ion orbits, and radial variations in density and electric field. Using this plasma model, the highest ion temperatures computed were 5 keV, 1.2 keV, and 1 keV for He(+), H2(+), and H(+), respectively. These were obtained at a midplane magnetic flux density of 1.6 T.

An attempt is made to model the essential features of ion motion in a plasma. A guiding center model is hypothesized for a plasma heating device whose radial electric fields and axial magnetic fields are crossed. The guiding center model is shown to give results which agree with experimental data from four different plasma heating devices and are helpful for the interpretation of neutral particle analyzer results.

A new superconducting magnetic mirror apparatus (SUMMA) is described using photographs, diagrams, characteristics graphs, and block diagrams. The apparatus consists of a magnet facility, a plasma test section, the electrode assembly, a charge-exchange neutral particle analyzer, and apparatus for emission spectroscopy. Initial results of hot ion plasma heating experiments conducted in this facility are reported. The purpose of these experiments was twofold: (1) to make a reliable electrode assembly for steady-state operation in the new SUMMA magnetic field configuration and test-section geometry; and (2) to see how ion heating scales as the midplane magnetic field is varied up to 3.5 tesla.

The theoretical model is discussed, which accounts for drift and cyclotron components of ion motion in a partially ionized plasma. Density and velocity distributions are systematically precribed. The flux into the neutral particle analyzer (NPA) from this plasma is determined by summing over all charge exchange neutrals in phase space which are directed into apertures. Especially detailed data, obtained by sweeping the line of sight of the apertures across the plasma of the NASA Lewis HIP-1 burnout device, are presented. Selection of randomized cyclotron velocity distributions about mean azimuthal drift yield energy distributions which compared well with experiment. Use of data obtained with a bending magnet on the NPA showed that separation between energy distribution curves of various mass species correlate well with a drift divided by mean cyclotron energy parameter of the theory. Use of the guiding center model in conjunction with NPA scans across the plasma aid in estimates of ion density and E field variation with plasma radius.

Use of microscopic detail in random walk theory describing the initial formations of a large number of avalanches shows that concomitant electron transport coefficients quickly relax to equilibrium values. This enables the use of random walks having step sizes and probabilities based only on local electric field strengths and densities. A self-consistent avalanche solution which accounts for collective long range Coulomb interactions as well as short range elastic and inelastic collisions between electrons and background atoms is demonstrated for helium. Avalanche growth retardation followed by an abrupt growth augmentation as time proceeds is shown to be associated with the formation of regions of charge density extrema near the avalanche axis and within the axial distance covered by the electron swarm.

Initial results are presented for the hot-ion plasma heating experiments conducted in the new SUMMA (superconducting magnetic mirror apparatus) at NASA Lewis Research Center. A discharge is formed by applying a radially inward dc electric field between cylindrical anodes and hallow cathodes located at the peak of the mirrors. Data were obtained at midplane magnetic field strengths from 1.0 to 3.5 tesla. Charge-exchange neutral particle energy analyzer data were reduced to ion temperatures using a plasma model that included a Maxwellian energy distribution superimposed on an azimuthal drift, finite ion orbits, and radial variations in density and electric field. The best ion temperatures in a helium plasma were 5 keV and in hydrogen the H2(+) and H(+) ions were 1.2 keV and 1 keV respectively. Optical spectroscopy line broadening measurements yielded ion temperatures about 50 percent higher than the charge-exchange neutral particle analyzer results. Spectroscopically obtained electron temperature ranged from 3 to 30 eV. Ion temperature was found to scale roughly linearly with the ratio of power input-to-magnetic field strength, P/B.

Trajectories of charged particles were determined over a wide range of parameters characterizing motion in cylindrical low-pressure gas discharges and plasma heating devices which have steady radial electric fields perpendicular to uniform steady magnetic fields. Consideration was given to radial distributions characteristic of fields measured in a modified Penning discharge, in two NASA Lewis burnout-type plasma heating devices, and that estimated for the Ixion device. Numerical calculations of trajectories for such devices showed that differences between cyclotron frequency and qB/m and between azimuthal drift and a guiding center approximation are appreciable.

A plasma model, previously developed to interpret neutral-particle analyzer measurements on E x B heating devices, is adapted to analyze Doppler broadened charge-exchange-neutral lines measured by an optical monochromator. Comparison of theoretical with experimental results indicates that azimuthal drift as well as cyclotron motion are quite influential in determining line shapes and widths, and thus important in temperature determination, even when the monochromator line of sight is intersecting the plasma axis of symmetry. At this central sighting position, however, results are quite insensitive to radial ion density distribution when time lag between the charge-exchange-excitation events and emission is neglected. Line shapes and widths obtained by sighting across chords of plasma at various distances from the plasma axis of symmetry indicate a strong dependence on time lag.

Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.

A model of the random walk is formulated to allow a simple computing procedure to replace the difficult problem of solution of the Fokker-Planck equation. The step sizes and probabilities of taking steps in the various directions are expressed in terms of Fokker-Planck coefficients. Application is made to many particle systems with Coulomb interactions. The relaxation of a highly peaked velocity distribution of particles to equilibrium conditions is illustrated.

Random walk theory applied to electron motion in early stage of He breakdown in electric field, based on integral and differential cross section data

Simulation of Fokker-Planck equation by random walks of test particles in velocity space with application to magnetic mirror systems

Hydrogen propellant acceleration along magnetic tube of flux by high energy ion beam

Thermonuclear propulsion using superconducting magnet and pyrotron reactor, discussing fuel, cryoplant and shield selection

Thermonuclear propulsion using superconducting magnets

Controlled thermonuclear fusion for spacecraft propulsion - use of deuterium-helium 3 as reactor fuel contained by superconducting magnets

A self-consistent avalanche solution which accounts for collective long range Coulomb interactions as well as short range elastic and inelastic collisions between electrons and background atoms is made possible by a random walk technique. Results show that the electric field patterns in the early formation stages of avalanches in helium are close to those obtained from theory based on constant transport coefficients. Regions of maximum and minimum induced electrostatic potential phi are located on the axis of symmetry and within the volume covered by the electron swarm. As formation time continues, however, the region of minimum phi moves to slightly higher radii and the electric field between the extrema becomes somewhat erratic. In the intermediate formation periods the avalanche growth is slightly retarded by the high concentration of ions in the tail which oppose the external electric field. Eventually the formation of ions and electrons in the localized regions of high field strength more than offset this effect causing a very abrupt increase in avalanche growth.