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NASA NTRS1977

Microscopic Lagrangian description of warm plasmas. I - Linear wave propagation. II - Nonlinear wave interactions

It is pointed out that the conventional iterative analysis of nonlinear plasma wave phenomena, which involves a direct use of Maxwell's equations and the equations describing the particle dynamics, leads to formidable theoretical and algebraic complexities, especially for warm plasmas. As an effective alternative, the Lagrangian method may be applied. It is shown how this method may be used in the microscopic description of small-signal wave propagation and in the study of nonlinear wave interactions. The linear theory is developed for an infinite, homogeneous, collisionless, warm magnetoplasma. A summary is presented of a perturbation expansion scheme described by Galloway and Kim (1971), and Lagrangians to third order in perturbation are considered. Attention is given to the averaged-Lagrangian density, the action-transfer and coupled-mode equations, and the general solution of the coupled-mode equations.

Kim, H.↗

NASA NTRS1978

Computer simulation of the velocity diffusion of cosmic rays

Monte Carlo simulation experiments have been performed in order to study the velocity diffusion of charged particles in a static turbulent magnetic field. By following orbits of particles moving in a large ensemble of random magnetic field realizations with suitably chosen statistical properties, a pitch-angle diffusion coefficient is derived. Results are presented for a variety of particle rigidities and rms random field strengths and compared with the predictions of standard quasi-linear theory and the nonlinear partially averaged field theory.

Kaiser, T. B.↗

NASA NTRS1978

Nonlinear pitch angle scattering of energetic electrons by coherent VLF waves in the magnetosphere

A study is made of nonlinear cyclotron resonance wave-particle interaction in the magnetosphere with attention to the pitch angle scattering of energetic electrons by coherent VLF whistler mode signals. A computer simulation of the full nonlinear equations of motions for energetic particles interacting with a longitudinal whistler mode wave in an inhomogeneous magnetosphere are used. The results are compared to those of a linear theory. Test electrons distributed in energy and pitch angle are used to simulate the full distribution of particles. The scattering of the test particles and their integration over energy and pitch angle yield the precipitated flux. The results suggest that coherent VLF waves significantly influence the dynamics and lifetimes of energetic electrons trapped in the magnetosphere and magnetic shells illuminated by the waves.

Inan, U. S.↗

NASA NTRS1979

Aerodynamic design and analysis of the AST-200 supersonic transport configuration concept

The design and analysis of a supersonic transport configuration was conducted using linear theory methods in conjunction with appropriate constraints. Wing optimization centered on the determination of the required twist and camber and proper integration of the wing and fuselage. Also included in the design are aerodynamic refinements to the baseline wing thickness distribution and nacelle shape. Analysis to the baseline and revised configurations indicated an improvement in lift-to-drag ratio of 0.36 at the Mach 2.7 cruise condition. Validation of the design is planned through supersonic wing tunnel tests.

Walkley, K. B.↗

NASA NTRS1978

Lower-hybrid-drift wave turbulence in the distant magnetotail

Recent satellite observations of electrostatic and magnetic noise in the distant magnetotail (Gurnett et al., 1976) can be explained by the excitation of the lower-hybrid-drift instability. In particular, it is shown that (1) existence conditions for the lower-hybrid-drift instability can be met, (2) the observed frequency spectra and polarization are in good agreement with the predictions of linear theory, and (3) the observed amplitudes of fluctuations are consistent with the nonlinear theory of this mode. Moreover, the observation of this instability suggests that the anomalous transport properties associated with these waves, which are important in many laboratory devices, may play a crucial role in the macroscopic evolution of magnetotail processes such as field line merging, tearing instabilities, or 'fireballs'.

Huba, J. D.↗

NASA NTRS1979

Vortex development on slender missiles at supersonic speeds

A theoretical and experimental effort has been made to develop a vortex-prediction capability on circular and noncircular missiles at supersonic speeds. Predicted vortex patterns are computed by two linear-theory computer codes. One calculates the strengths and initial locations of the vortices, and the other calculates their trajectories. A short color motion picture has been produced from the calculations to illustrate the predicted vortex patterns on a typical missile. Experimental vapor-screen photographs are presented to show the longitudinal development of the vortices on a fin-control missile. Comparisons are made between these data and the predicted vortices to assess the accuracy of the theory. The theory appears to be fairly accurate in predicting the number, locations, and relative strengths of individual vortices which develop over the missile, but cannot predict vortex sheets or diffuse vorticity whenever they occur.

Allen, J. M.↗

NASA NTRS1979

On the role of shocks in the 'sub-transonic' flutter phenomenon

A semi-quantitative investigation is reported on the influence of partial-chord transonic shocks on flutter of 'typical-section' wing models. Unsteady airloads are assumed as the sum of linearized theory and a 'shock-force doublet' centered at the measured steady shock location. The shock is shown usually to destabilize single-degree pitching motion; it may affect flexure-torsion flutter either way - often profoundly. Various typical-section parameters are studied, along with the important phase lag known to be present in the shock oscillation. Energy transfer during flutter is examined. Simplified calculations are presented that are believed relevant to the transonic tests by Farmer and Hanson.

Ashley, H.↗

NASA NTRS1978

Phase-locked loops and their application

A collection of papers is presented on the characteristics and capabilities of phase-locked loops (PLLs), along with some applications of interest. The discussion covers basic theory (linear and nonlinear); acquisition; threshold; stability; frequency demodulation and detection; tracking; cycle slipping and loss of lock; phase-locked oscillators; operation and performance in the presence of noise; AGC, AFC, and APC circuits and systems; digital PLL; and applications and miscellaneous. With the rapid development of IC technology, PLLs are expected to be used widely in consumer electronics.

Lindsey, W. C.↗

NASA NTRS1978

Some observations on four current subjects related to aeroelastic stability

After introductory comments on the literature and the purposes of this paper, a table is presented summarizing the author's views on some currently solved vs partially unsolved problems related to aeroelastic stability. The term 'solved' is used in the practical sense that engineers are able to cope confidently with that problem during the process of structural design. Selected entries in the table are reviewed, partially to motivate the topics in the rest of the paper. The 'four current subjects' are chosen both for timeliness and because they are among the ongoing interests of the Stanford group. The first involves the prediction of linearized unsteady aerodynamic loads due to arbitrary motions of streamlined shapes. Some contributions by Edwards are refined, which were motivated by the requirements of active control system design. The second subject is nonlinear unsteady aerodynamics for the transonic regime. After describing a few useful developments from locally-linear theory and computational fluid dynamics, there is suggested an empirical procedure for interim-analysis purposes. The third and fourth subjects concern recent discoveries regarding the aeroelastic stability of large-aspect-ratio wings and wind turbines. The former work is mainly that of Petre and Boyd. The latter includes some of the author's own preliminary discoveries about the performance and dynamics of vertical-axis machines.

Ashley, H.↗

NASA NTRS1977

Evolution of weak disturbances in inert binary mixtures

The evolution of weak disturbances in inert binary mixtures is determined for the one-dimensional piston problem. The interaction of the dissipative and nonlinear mechanisms is described by Burgers' equation. The binary mixture diffusion mechanisms enter as an additive term in an effective diffusivity. Results for the impulsive motion of a piston moving into an ambient medium and the sinusoidally oscillating piston are used to illustrate the results and elucidate the incorrect behavior pertaining to the associated linear theory.

Rasmussen, M. L.↗

NASA NTRS1979

Thermal cycling graphite-polyimide

The effects of repetitive thermal cycling on the temperature-thermal deformation relation of graphite-polyimide were determined. The bending and axial strains, measured with strain gages, of unsymmetric 0 deg sub 2/90 deg sub 2 and 0 deg sub 4/90 deg sub 4 laminates were used as an indication of thermal deformation. The strains were measured as a function of temperature and two temperature ranges were used, room temperature to 180 C and room temperature to 315 C. Five cycles were run in each temperature range and the cycling was done in quasistatic fashion. The response of a flat 0 deg sub 8 laminate was measured as were the effects of repetitive cycling on the strain gages themselves. A piece-wise linear theory, based on classical lamination theory and using the variation of mechanical and thermal expansion properties with temperature, was compared with the experimental results. The correlation between theoretical predictions and experimental results for the thinner laminate was poor.

Hyer, M. W.↗

NASA NTRS1980

Estimation of wing nonlinear aerodynamic characteristics at supersonic speeds

A computational system for estimation of nonlinear aerodynamic characteristics of wings at supersonic speeds was developed and was incorporated in a computer program. This corrected linearized theory method accounts for nonlinearities in the variation of basic pressure loadings with local surface slopes, predicts the degree of attainment of theoretical leading edge thrust, and provides an estimate of detached leading edge vortex loadings that result when the theoretical thrust forces are not fully realized.

Carlson, H. W.↗

NASA NTRS1981

Charts for determining potential minimum sonic-boom overpressures for supersonic cruise aircraft

Charts which give an estimation of minimum achievable sonic-boom levels for supersonic cruise aircraft are presented. A minimization method based on modified linear theory was analyzed. Results show several combinations of Mach number, altitude, and aircraft length and weight. Overpressure and impulse values are given for two types of sonic boom signatures for each of these conditions: (1) a flat top or minimum overpressure signature which has a pressure plateau behind the initial shock, and (2) a minimum shock signature which allows a pressure rise after the initial shock. Results are given for the effects of nose shape.

Darden, C. M.↗

NASA NTRS1980

Transmitted sound field due to an impulsive line acoustic source bounded by a plate followed by a vortex sheet

The propagation of sound due to a line acoustic source in the moving stream across a semiinfinite vortex sheet which trails from a rigid plate is examined in a linear theory for the subsonic case. A solution for the transmitted sound field is obtained with the aid of multiple integral transforms and the Wiener-Hopf technique for both the steady state (time harmonic) and initial value (impulsive source) situations. The contour of inverse transform and hence the decomposition of the functions are determined through causality and radiation conditions. The solution obtained satisfies causality and the full Kutta conditions. The transmitted sound field is composed of two waves in both the stady state and initial value problems. One is the wave scattered from the edge of the plate which is associated with the bow wave and the instability wave. These waves exist in the downstream sectors. The other is the wave transmitted through the vortex sheet which is also associated with the instability wave. Regional divisions of the transmitted sound field are identified.

Miura, T.↗

NASA NTRS1980

The observation and production of ion acoustic waves during the Trigger experiment

The third flight of the Trigger experiment is described here. Band-limited electric field and density waves were observed shortly after the ion cloud was detected. Since the electric field and density components had similar spectral shape and the wave electric field was oriented parallel to the ambient magnetic field, the waves were identified as collisionless ion acoustic waves. The linear theory of ion-ion streaming is considered a likely generation mechanism for the waves.

Kintner, P. M.↗

NASA NTRS1981

Vibration and local instability of thermally stressed plates

The vibration and buckling of a double wedge square cantilever plate has been investigated. It is shown that the free vibration modes, which occur at Delta T ref = 0, transition into the buckled modes which occur at Delta T ref = Delta T ref-cr for the respective mode. Delta T ref-cr for a particular mode is defined as the magnitude of thermal load at which the frequency of the particular mode vanishes. The analysis yields the same number of buckling eigenvalues and buckling modes as there are vibration eigenvalues and vibration modes. Gradual application of the load in the analysis permits the change in each vibration frequency of interest and its associated mode to be followed up to the load at which the frequency of the mode becomes zero. This constitutes the limit of linear theory. As the load is increased, the thin edges of the plate begin to deform during vibration. This local deformation, which begins in the vibration mode, is shown to transition into the phenomena of local edge buckling at Delta T ref-cr for the mode.

Bailey, C. D.↗

NASA NTRS1981

Formation of a conical distribution and intense ion heating in the presence of hydrogen cyclotron waves

In the considered investigation, it is assumed that the field aligned currents are responsible for producing electrostatic harmonic cyclotron waves (EHC). Using a one-dimensional simulation model in which the electron velocity distribution is maintained by a constant injection of the initial distribution, it is shown that, in contrast to earlier initial value simulations, EHC waves grow to a large amplitude, resulting in the formation of an anisotropic ion velocity distribution. Both the heating rate and the anisotropy are in reasonable agreement with the quasi-linear theory, taking into account the cyclotron resonance. The results show that the saturation is due to the combined effects of wave induced diffusion in an electron velocity space and the heating of ions perpendicularly. Both these effects reduce the growth rate.

Okuda, H.↗

NASA NTRS1981

Saturation and energy-conversion efficiency of auroral kilometric radiation

A quasi-linear theory is used to study the saturation level of the auroral kilometric radiation. The investigation is based on the assumption that the emission is due to a cyclotron maser instability as suggested by Wu and Lee and Lee et al. The thermodynamic bound on the radiation energy is also estimated separately. The energy-conversion efficiency of the radiation process is discussed. The results are consistent with observations.

Wu, C. S.↗