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Wave experiments on shuttle are needed to verify dispersion relations, to study nonlinear and exotic phenomena, to support other plasma experiments, and to test engineering designs. Techniques based on coherent detection and bistatic geometry are described. New instrumentation required to provide modules for a variety of missions and to incorporate advanced signal processing and control techniques is discussed. An experiment for Z to 0 coupling is included.
Estimates of the radial distribution of seismic velocities and density and of seismic attenuation within the earth are obtained through inversion of body wave, surface wave, and normal mode data. The effect of attenuation related dispersion on gross earth structure, and on the reliability of eigenperiod identifications is discussed. The travel time baseline discrepancies between body waves and free oscillation models are examined and largely resolved.
The IR absorption spectrum of a 75% sulphuric acid solution is obtained experimentally in the 20-50 micron wavelength region. The complex refractive index is determined from these measurements by integration of the Kramers-Kronig dispersion relation. The application of this data to radiative transfer processes in the atmosphere of Venus is briefly discussed.
The stability of waves in unbounded, longitudinally periodic media is studied for index and gain coupling. Time-independent periodic media are found to support both stable and absolutely unstable waves. The wave characteristics depend upon average gain or loss, coupling type, and Bragg order. The extended coupled waves equations provide explicit values of threshold, frequency, and temporal growth rate for instabilities at all Bragg resonances through the dispersion relation. Applications to multiharmonic periodicities and complex couplings are briefly discussed with particular note taken of possible reductions of the stability thresholds and removal of threshold degeneracies. Comparisons are made to the longitudinally bounded case of distributed feedback lasers.
The kinematics of normal and oblique interactions between a plane acoustic wave and a plane shock wave are investigated separately using an approach whereby the shock is considered as a sharp discontinuity surface separating two half-spaces, so that the dispersion relation on either side of the shock and the wavenumber jump condition across a discontinuity surface completely specify the kinematics of the problem in the whole space independently of the acoustic-field dynamics. The normal interaction is analyzed for a stationary shock, and the spectral change of the incident wave is investigated. The normal interaction is then examined for the case of a shock wave traveling into an ambient region where an acoustic disturbance is propagating in the opposite direction. Detailed attention is given to the consequences of the existence of a critical shock speed above which the frequency of the transmitted wave becomes negative. Finally, the oblique interaction with a fixed shock is considered, and the existence and nature of the transmitted wave is investigated, particularly as a function of the angle of incidence.
Stress wave propagation in a multilayer composite plate due to impact was examined by means of the anisotropic elasticity theory. The plate was modelled as a number of identical anisotropic layers and the approximate plate theory of Mindlin was then applied to each layer to obtain a set of difference-differential equations of motion. Dispersion relations for harmonic waves and correction factors were found. The governing equations were reduced to difference equations via integral transforms. With given impact boundary conditions these equations were solved for an arbitrary number of layers in the plate and the transient propagation of waves was calculated by means of a Fast Fourier Transform algorithm. The multilayered plate problem was extended to examine the effect of damping layers present between two elastic layers. A reduction of the interlaminar normal stress was significant when the thickness of damping layer was increased but the effect was mostly due to the softness of the damping layer. Finally, the problem of a composite plate with a crack on the interlaminar boundary was formulated.
The Lin-Shu dispersion relation, with corrections to match experimental conditions and in combination with a quantization rule, permits growth rates to be calculated for axisymmetric disturbances in an axisymmetric disk of stars. Growth rates calculated this way are in reasonable quantitative agreement with recently published results from a series of numerical experiments. The agreement confirms the physical basis of the theory and demonstrates that the theory remains valid even when strained somewhat in the application to galactic models.
The dispersion relation for small amplitude waves in a hot relativistic plasma embedded in a uniform magnetic field is derived. Four plasma modes exist for propagation oblique to the magnetic field, and the mode properties are summarized in a hot relativistic generalization of the cold plasma pond diagram of Stix (1962). The two-fluid approximation is considered, and two-fluid equations are applied in this procedure which summarizes properties of linear waves in an unbounded magnetized relativistic plasma by means of a parameter-space diagram of wave phase velocity.
Ershkovich's (1978) criticism of previous arguments in favor of magnetic fields of approximately 100 gammas in cometary plasma tails are shown to be unjustified. It is argued that the folding velocity of tail streamers indicates a substantial tail magnetic field and that much of Ershkovich's disagreement stems from the choice of completely different models for a comet's plasma tail. It is concluded that the use of growth rates or phase-velocity information obtained from a dispersion relation to interpret large-amplitude disturbances, such as those in comet tails, is categorically incorrect.
The paper considers the effects of a weak ambient magnetic field on the oscillating two-stream and parametric decay instabilities with emphasis on the dependence of the angular variation of the instability thresholds and growth rates on the magnetic field. A dispersion relation is derived in the limit in which the electron plasma frequency is much greater than the cyclotron frequency, and is solved for dipole and monochromatic pump spectra. The analysis shows that the presence of a magnetic field can substantially enhance thresholds and reduce growth rates for waves propagating at an oblique angle with respect to the ambient magnetic field, so that the magnetic field has a stabilizing influence on the off-parallel propagating modes.
An analysis is presented of the parallel neutral stability of three-dimensional incompressible, isothermal boundary-layer flows. A Taylor-series expansion of the dispersion relation is used to derive the general eigenvalues. These equations are functions of the complex group velocity. These relations are verified by numerical results obtained for two- and three-dimensional disturbances in two- and three-dimensional flows.
Spectral analyses of optical images of the ocean surface, obtained by a digital video system, are presented and compared with wave data measured simultaneously by the JPL Waverider-mounted laser slope meter. The image analyses, which incorporate several new ideas, provide two-dimensional wave number spectra of slope, covering wavelengths from 10 cm to 10 m. These slope spectra are converted to wave height spectra by a new technique which includes the effects of sky radiance gradients. Space-time spectra are also presented for waves whose frequencies are less than 2 Hz. The JPL slope frequency spectra are compared with image wave number spectra which have been converted to frequency spectra by use of the gravity wave dispersion relation. Results of comparisons between the frequency spectra obtained from the two different measurements show reasonable agreement for frequencies less than 3 Hz.
The damping in theoretical waveforms is described phenomenologically and a classification is proposed. A method for studying the Earth's crust was developed which includes this damping as derived from reflection seismograms. Seismic wave propagation by absorption, attenuation of seismic waves by scattering, and dispersion relations are considered. Absorption of seismic waves within the Earth as well as reflection and transmission of elastic waves seen through boundary layer absorption are also discussed.
The stability of a self-consistent, large-amplitude, circularly polarized wave in a warm plasma is investigated. For perturbations to the system propagating normal to the plane of circular polarization, a dispersion relation is derived employing an expansion in the nonlinear wave amplitude and the momentum of the plasma particles in the plane of polarization. Instability results both in the absence and presence of a large-scale magnetic field with a growth rate of the order of the nonlinear wave amplitude.
The linear Vlasov dispersion relation for the lower hybrid density drift instability is studied in a four component (hot electrons and protons, cold electrons and protons) plasma. The introduction of a cold ion population monotonically reduces the maximum growth rate of the instability. Reduction of the ratio of temperatures of the cold and hot plasmas reduces both the real frequency and the growth rate of the instability. Near a ratio of the cold and hot plasma temperatures of 0.01 a higher frequency branch of this instability emerges and for a fixed ratio of cold and hot electron density exhibits an increasing maximum growth rate as the ratio of the cold and hot plasma temperatures decreases further. The ratio of the cold and hot plasma temperatures for the ions is the crucial parameter and deserves detailed magnetospheric studies.
The effect of turbulence on the coupling of the magnetosphere and ionosphere has been investigated by including an effective collision frequency in the electron equation of motion. When this term is combined with the continuity equation, the ion equation of motion and Maxwell's equations, a dispersion relation for the kinetic Alfven wave including effective collisions is found. The wave-particle interaction leads to a strong damping of the wave. Inclusion of the effects of plasma sheet kinetics yields a scale size transverse to the magnetic field which corresponds to the size of visual auroral arcs.
The linear dispersion relation for a collisionless plasma in a sheared one-dimensional current sheet is calculated with reference to conditions in the daytime magnetopause. Calculations are extended to include plasmas with beta approximately equal to 1. It is found that the tearing mode eigenstructure and temporal growth rate are a sensitive function of the ratios l sub s/l sub G, l sub s/l sub T, and l sub s/l sub n, where l sub s is the shearing length of the magnetic field, l sub G is the gradient scale length, and l sub T is the temperature gradient scale length. In particular, if beta is approximately equal to 1, and l sub s is less than l sub G, l sub n, and l sub T, then the thickness of the layer over which particles are resonantly accelerated by the induction magnetic field is approximately rho, a thermal gyroradius. If the above conditions are not satisfied, plasma gradients may electrostatically stabilize the mode.
An instability analysis is presented for parallel and antiparallel propagating electromagnetic waves generated by reflected and diffuse suprathermal ions upstream of the earth's bow shock. Calculations are performed on the basis of upstream particle observations made by the ISEE 1 Quadrispheric Lepedea instrument and low-energy electron measurements made by the ISEE 1 electron spectrometer for a single period. The electromagnetic dispersion relation is computed and the unstable modes and growth times of the fastest growing waves are determined. It is found that the reflected ions destabilize the plasma most strongly at a wave frequency 0.1 that of the ion gyrofrequency by a resonant ion beam instability for waves propagating upstream and by a nonresonant firehose-like instability for waves propagating downstream. The diffuse ions also destabilize the plasma most strongly at the same frequency by means of resonant instabilities of both right- and left-hand polarized waves propagating away from the bow shock.