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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Electron acceleration by an obliquely propagating electromagnetic wave in the regime of validity of the Fokker-Planck-Kolmogorov approach

The relativistic motion of an ensemble of electrons in an intense monochromatic electromagnetic wave propagating obliquely in a uniform external magnetic field is studied. The problem is formulated from the viewpoint of Hamiltonian theory and the Fokker-Planck-Kolmogorov approach analyzed by Hizanidis (1989), leading to a one-dimensional diffusive acceleration along paths of constant zeroth-order generalized Hamiltonian. For values of the wave amplitude and the propagating angle inside the analytically predicted stochastic region, the numerical results suggest that the diffusion probes proceeds in stages. In the first stage, the electrons are accelerated to relatively high energies by sampling the first few overlapping resonances one by one. During that stage, the ensemble-average square deviation of the variable involved scales quadratically with time. During the second stage, they scale linearly with time. For much longer times, deviation from linear scaling slowly sets in.

Hizanidis, Kyriakos↗
NASA NTRS1988

Wave/current interaction model

The wave-current interaction for the application to remote sensing data via numerical simulations and data comparison is modelled. Using the field data of surface current shear, wind condition and ambient wave spectrum, the numerical simulations of directional wave spectrum evolution were used to interpret and to compare with the aircraft data from Radar Ocean Wave Spectrometer (ROWS) and Surface Contour Radar (SCR) across the front during Frontal Air Sea Interaction Experiment (FASINEX). The wave-ice interaction was inspired by the observation of large amplitude waves hundreds of kms inside the ice pack in the Weddell Sea, resulting in breakup of the ice pack. The developed analysis of processes includes the refraction of waves at the pack edge, the effects of pack compression on wave propagation, wave train stability and buckling stability in the ice pack. Sources of pack compression and interaction between wave momentum and pack compression are investigated. Viscous camping of propagating waves in the marginal ice zone are also studied. The analysis suggests an explanation for the change in wave dispersion observed from the ship and the sequence of processes that cause ice pack breakup, pressure ridge formation and the formation of open bands of water.

Liu, A. K.↗
NASA NTRS1993

On the dispersion relations for parametric instabilities of parallel-propagating Alfven waves

We consider the dispersion relation for the parametric instabilities of large-amplitude circularly polarized Alfven waves propagating parallel to the ambient magnetic field. A linear perturbation analysis is employed, and the perturbations are taken to propagate along the ambient field. We present an analysis based on Floquet's theorem. The result is a hierarchy of dispersion relations. However, all the dispersion relations are found to be equivalent to the one obtained via the standard analysis; the differences between them are due only to how ca and k are defined. Thus we conclude that physically there is really only one dispersion relation, namely the 'electrostatic dispersion relation', which is in agreement with earlier works. However, we disagree with Vinas and Goldstein (1991), who obtained additional dispersion relations which they have called the 'electromagnetic dispersion relations'. Their additional dispersion relations are a consequence of first truncating the dispersion relation for obliquely propagating perturbations and then taking the limit of parallel-propagating perturbations.

Yajanti, Venku↗
NASA NTRS1986

Propagation of sound waves in tubes of noncircular cross section

Plane-acoustic-wave propagation in small tubes with a cross section in the shape of a flattened oval is described. Theoretical descriptions of a plane wave propagating in a tube with circular cross section and between a pair of infinite parallel plates, including viscous and thermal damping, are expressed in similar form. For a wide range of useful duct sizes, the propagation constant (whose real and imaginary parts are the amplitude attenuation rate and the wave number, respectively) is very nearly the same function of frequency for both cases if the radius of the circular tube is the same as the distance between the parallel plates. This suggests that either a circular-cross-section model or a flat-plate model can be used to calculate wave propagation in flat-oval tubing, or any other shape tubing, if its size is expressed in terms of an equivalent radius, given by g = 2 x (cross-sectional area)/(length of perimeter). Measurements of the frequency response of two sections of flat-oval tubing agree with calculations based on this idea. Flat-plate formulas are derived, the use of transmission-line matrices for calculations of plane waves in compound systems of ducts is described, and examples of computer programs written to carry out the calculations are shown.

Richards, W. B.↗
NASA NTRS1993

Whistlers and plasmaspheric hiss - Wave directions and three-dimensional propagation

Wave propagation directions are determined on the basis of wave data from the DE 1 satellite showing simultaneously nonducted whistlers and hiss. Hiss wave normal angles are determined as about 70 and 77 deg for f = 3.5 and 2.5 kHz, respectively, with the wave vector being almost perpendicular to the meridional plane. A novel approximate analytical formulation of 3D propagation of whistler waves is developed and used to model the drift of magnetospherically reflected whistlers in azimuth. It is shown that depending on initial parameters, the time of arrival of whistler rays at a fixed observation point can differ by 10-20 s, with signals from different magnetospherically reflected whistlers overlapping to evolve into a hisslike signal. The total azimuthal drift of whistler rays is found to not exceed about 30 deg, so that plasmaspheric hiss may be produced by nonducted whistlers at longitudes correlated with the location of thunderstorm activity.

Draganov, A. B.↗
NASA NTRS1993

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

Saatchi, Sasan S.↗
NASA NTRS1993

Acceleration of cometary H2O group pickup ions by obliquely propagating nonlinear magnetosonic waves

The observations made during the encounter with comet Giacobini Zinner show that the character of MHD turbulence is governed by the magnetosonic (MS) waves generated by the pickup ions via a resonant cyclotron instability. The interaction of cometary ions in the mass loaded solar wind with MS waves propagating away from the comet and oblique to the interplanetary magnetic field (IMF) is investigated using the test particle approach. Ion trajectories, distribution functions, widths of pitch angle scattering and energy diffusion are obtained. We have also investigated the relationship between pitch angle scattering and the three parameters, namely, alpha, the angle between the solar wind flow direction and the ambient magnetic field, theta(sub BK), the angle between the ambient magnetic field and the wave propagation vector, and the ion injection velocity.

Srivastava, Krishna M.↗
NASA NTRS1993

Parametric instabilities of parallel-propagating Alfven waves: Some analytical results

We consider the stability of a circularly polarized Alfven wave (the pump wave) which propagates parallel to the ambient magnetic field. Only parallel-propagating perturbations are considered, and we ignore dispersive effects due to the ion cyclotron frequency. The dissipationless MHD equations are used throughout; thus possibibly important effects arising from Landau and transit time damping are omitted. We derive a series of analytical approximations to the dispersion relation using A = (Delta B/B(sub O))(exp 2) as a small expansion parameter; Delta B is the pump amplitude, and B(sub O) is the ambient magnetic field strength. We find that the plasma beta (the square of the ratio of the sound speed to the Alfven speed) plays a crucial role in determining the behavior of the parametric instabilities of the pump. If 0 less than beta less than 1 we find the familiar result that the pump decays into a forward propagating sound wave and a backward propagating Alfven wave with maximum growth rate gamma(sub max) varies A(sup 1/2), but beta cannot be too close to 0 or to 1. If beta approx. 1, we find gamma(sub max) varies A(sup 3/4), if beta greater than 1, we find gamma(sub max) varies A(sup 3/2), while if beta approx. 0, we obtain gamma(sub max) varies A(sup 1/3); moreover, if beta approx. 0 there is a nearly purely growing instability. In constrast to the familiar decay instability, for which the backward propagating Alfven wave has lower frequency and wavenumber than the pump, we find that if beta greater than or approx. equal to 1 the instability is really a beat instability which is dominated by a transverse wave which is forward propagating and has frequency and wavenumber which are nearly twice the pump values. Only the decay instability for 0 less than beta less than 1 can be regarded as producing two recognizable normal modes, namely, a sound wave and an Alfven wave. We discuss how the different characteristics of the instabilities may affect the evolution of Alfven waves in the solar wind. However, for a solar wind in which beta approx. 1 the growth times of the instabilities are probably too long for these instabilities to have an appreciable effect inside 1 AU.

Jayanti, V.↗
NASA NTRS1995

Particle interactions with obliquely propagating magnetosonic waves

Four cases of nonlinear obliquely propagating magnetosonic (MS) waves are considered using a test particle approach for particles interaction with (1) monochromatic waves propagating both sunward and antisunward, (2) monochromatic waves propagating unidirectionally toward the Sun, (3) a broad band spectrum, propagating both sunward and antisunward, and (4) a broadband spectrum, propagating sunward only. As the solar wind decelerates rapidly inside the bow shock, the interplanetary magnetic field (IMF) increases. Calculations have been performed taking into account such a spatially dependent IMF (based on observations). We find that significant particle acceleration is achieved for both the monochromatic wave and the 'turbulent' MS waves, for oblique propagation (angles between the interplanetary magnetic field and the propagation vector larger than 30 deg). This is due to the fact that at oblique angles resonance width increases. We have compared the relative acceleration of particles for the four cases. Pitch angle scattering and acceleration of particles are found to be much larger in the case of sunward and antisunward propagating waves than those for the sunward waves only. This is due to larger relative phase velocities in the two cases. Also, acceleration of particles is less in the case of a uniform magnetic field than that in the case of spatially increasing magnetic field. The particles get more pitch angle scattered and accelerated in the latter case.

Srivastava, Krishna M.↗
NASA NTRS1976

Magnetostrictive ultrasonic probes

The principles underlying the design and use of magnetostrictive ultrasonic probes is illustrated by oscillograms and sketches. Attention is given to such concepts as magnetostrictive transduction, broadband pulse shaping, guided wave propagation, wave impedance, reflection, transmission, and attenuation coefficients, coupling methods, and impulse-induced resonance. A number of applications of such probes are discussed including the measurement of elastic moduli, temperature, and acoustic emission and resonance studies.

Lynnworth, L. C.↗
NASA NTRS1984

Acoustic-radiation stress in solids. I - Theory

The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.

Cantrell, J. H., Jr.↗
NASA NTRS1990

Consistency and convergence for numerical radiation conditions

The problem of imposing radiation conditions at artificial boundaries for the numerical simulation of wave propagation is considered. Emphasis is on the behavior and analysis of the error which results from the restriction of the domain. The theory of error estimation is briefly outlined for boundary conditions. Use is made of the asymptotic analysis of propagating wave groups to derive and analyze boundary operators. For dissipative problems this leads to local, accurate conditions, but falls short in the hyperbolic case. A numerical experiment on the solution of the wave equation with cylindrical symmetry is described. A unified presentation of a number of conditions which have been proposed in the literature is given and the time dependence of the error which results from their use is displayed. The results are in qualitative agreement with theoretical considerations. It was found, however, that for this model problem it is particularly difficult to force the error to decay rapidly in time.

Hagstrom, Thomas↗