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NASA NTRS1988

Filamentation instability of large-amplitude Alfven waves

An instability that leads to the filamentation of large-amplitude Alfven waves and gives rise to purely growing density and magnetic field fluctuations is studied. The dispersion relation of the instability is derived, from which the threshold conditions and the growth rates of the instability are analyzed quantitatively for applications to the solar wind plasma. Their dependence on the filamentation spectrum, the plasma beta, and the pump frequency and intensity was examined for both right-hand and left-hand circularly polarized Alfven waves. The excitation of filamentation instability for certain cases of interest is discussed and compared with that of the parametric decay and modulation instability. The relevance of the proposed instability to some observations is discussed.

Kuo, S. P.↗

NASA NTRS1989

Absorbing boundary conditions for second-order hyperbolic equations

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Jiang, Hong↗

NASA NTRS1989

The electron beam instability revisited: Growth above and below f sub p

The growth of electrostatic waves near the plasma frequency (fp) due to an unstable electron beam is investigated by solving the unmagnetized electrostatic dispersion equation numerically. The numerical solutions are compared with analytic theories for reactive (or fluid-type) and kinetic versions of the beam instability, and for the O'Neil/Malmberg connection of the beam and Langmuir modes. Conditions for growth significantly above or below fp are given. Three general results are found: (1) The unstable waves do not grow on a mode with Langmuir dispersion except in the limit of a very dilute beam with growth on O'Neil/Malmberg's connected mode; (2) The properties of the unstable mode depend strongly on beam parameters such as beam density, speed and temperature; and (3) The frequency of maximum growth frequently lies significantly above or below fp, and differs significantly from that predicted by the Langmuir dispersion relation. Results imply important consequences for theories of strong turbulence and nonlinear wave-wave processes, and observational identification of fp from observed wave frequencies.

Cairns, I. H.↗

NASA NTRS1989

Observations of gravity waves in the mesosphere with the MU radar

Wind motions were observed at 60 to 90 km altitudes with the MU radar during daylight hours (0800 to 1600 LT) from 13 to 31 October 1986. Quasi-monochromatic gravity waves were evident on 16 of the 19 days of observations. They were characterized by typical vertical wavelength of 5 to 15 km and intrinsic periods centered at about 9 hours. The propagation direction of the gravity waves, determined by the gravity wave dispersion relation, was mostly equatorward. The vertical wave number spectra of the horizontal components of the mesoscale wind fluctuations are explained well by saturated gravity wave theory. The frequency spectrum of vertical wind component has a slope of + 1/3, while the oblique spectra have a slope of -5/3 up to 4 x 10(-3) (c/s); these agree fairly well with model gravity wave spectra. Doppler shift effects on the frequency spectra are recognized at higher frequencies. Upward flux was determined of horizontal momentum flux induced by waves with periods from 10 min to 8 hours, and westward and northward body forces of 5.1 and 4.0 m/s/day, were estimated respectively.

Tsuda, T.↗

NASA NTRS1988

Surface and body waves in magnetic flux tubes

The dispersion relation of surface and body waves in a magnetic flux tube is studied in detail. The properties of the fast and slow bodywaves are described in terms of the filtering characteristics of the flux tube. In addition to the axisymmetric and nonaxisymmetric distinction between the modes, an additional distinction is made between the fundamental mode and the rest of the modes. New results concerning the thin and large flux tube approximation are derived. The behavior of surface and body waves in the solar convection zone, photosphere, and corona is discussed.

Abdelatif, T. E.↗

NASA NTRS1989

Magnetohydrodynamic waves and particle acceleration in a coronal loop

A model is presented for the acceleration of electrons in a flaring solar coronal loop. It is suggested that the primary energy release event in the flare establishes a spectrum of MHD waves within the loop which accelerate electrons by wave-particle resonant interactions. The nature of the MHD oscillations are described and numerical and analytic solution of the dispersion relation are examined. It is found that the behavior of a particle depends on whether or not it is in resonance with the wave spectrum. Resonant particles follow chaotic trajectories and can diffuse in velocity space between wave effective potentials, thereby gaining energy.

De La Beaujardiere, Jean-Francois↗

NASA NTRS1988

Current driven instabilities of an electromagnetically accelerated plasma

Quantitative measurements of the plasma instability that strongly affects the efficiency and lifetime of electromagnetic plasma accelerators were obtained. Experimental results are presented for the dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries of accelerators. The measured critical wave parameters are found to agree well with theoretical predictions. A kinetic theoretical model was used to study current driven instabilities which are intrinsic to the high-current-carrying magnetized plasma of a magnetoplasmadynamic accelerator. Under certain conditions, marginally stable waves travelling almost perpendicular to the magnetic field are found which travel at a velocity equal to that of the electron current.

Kelly, A. J.↗

NASA NTRS1989

Interfacial wave theory for dendritic structure of a growing needle crystal. I - Local instability mechanism. II - Wave-emission mechanism at the turning point

The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.

Xu, Jian-Jun↗

NASA NTRS1989

A current disruption mechanism in the neutral sheet for triggering substorm expansions

Two main areas were addressed in support of an effort to understand mechanism responsible for the broadband electrostatic noise (BEN) observed in the magnetotail. The first area concerns the generation of BEN in the boundary layer region of the magnetotail whereas the second area concerns the occassional presence of BEN in the neutral sheet region. For the generation of BEN in the boundary layer region, a hybrid simulation code was developed to perform reliable longtime, quiet, highly resolved simulations of field aligned electron and ion beam flow. The result of the simulation shows that broadband emissions cannot be generated by beam-plasma instability if realistic values of the ion beam parameters are used. The waves generated from beam-plasma instability are highly discrete and are of high frequencies. For the plasma sheet boundary layer condition, the wave frequencies are in the kHz range, which is incompatible with the observation that the peak power in BEN occur in the 10's of Hz range. It was found that the BEN characteristics are more consistent with lower hybrid drift instability. For the occasional presence of BEN in the neutral sheet region, a linear analysis of the kinetic cross-field streaming instability appropriate to the neutral sheet condition just prior to onset of substorm expansion was performed. By solving numerically the dispersion relation, it was found that the instability has a growth time comparable to the onset time scale of substorm onset. The excited waves have a mixed polarization in the lower hybrid frequency range. The imposed drift driving the instability corresponds to unmagnetized ions undergoing current sheet acceleration in the presence of a cross-tail electric field. The required electric field strength is in the 10 mV/m range which is well within the observed electric field values detected in the neutral sheet during substorms. This finding can potentially account for the disruption of cross-tail current and its diversion to the ionosphere to form the substorm current wedge. Furthermore, a number of features associated with substorm expansion onset can be understood based on this substorm onset scenario.

Lui, A. T. Y.↗

NASA NTRS1990

Asymptotic boundary conditions for dissipative waves: General theory

An outstanding issue in the computational analysis of time dependent problems is the imposition of appropriate radiation boundary conditions at artificial boundaries. Accurate conditions are developed which are based on the asymptotic analysis of wave propagation over long ranges. Employing the method of steepest descents, dominant wave groups are identified and simple approximations to the dispersion relation are considered in order to derive local boundary operators. The existence of a small number of dominant wave groups may be expected for systems with dissipation. Estimates of the error as a function of domain size are derived under general hypotheses, leading to convergence results. Some practical aspects of the numerical construction of the asymptotic boundary operators are also discussed.

Hagstrom, Thomas↗

NASA NTRS1990

Theory of circular dielectric waveguide with anisotropic sheet cover

A circular dielectric waveguide consisting of an isotropic core covered with a thin anisotropic sheet is considered. The sheet is represented as a jump immittance and Maxwell's equations are applied. Solution of the boundary value problem yields the characteristic equation, or dispersion relation, which is then solved numerically. The results are verified for the step-index fiber and circular, metallic waveguides. Finally, examples are included to investigate the effects of the anisotropic sheet.

Kish, Jerome Thomas↗

NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗

NASA NTRS1990

A wave dynamical interpretation of Saturn's polar hexagon

The hexagonal, pole-centered cloud feature in Saturn's northern atmosphere, as revealed in Voyager close-encounter imaging mosaics, may be interpreted as a stationary Rossby wave. The wave is embedded within a sharply peaked eastward jet (of 100 meters per second) and appears to be perturbed by at least one anticyclonic oval vortex immediately to the south. The effectively exact observational determination of the horizontal wave number and phase speed, applied to a simple model dispersion relation, suggests that the wave is vertically trapped and provides a diagnostic template for further modeling of the deep atmospheric stratification.

Allison, M.↗

NASA NTRS1990

Collisional electrostatic ion cyclotron waves as a possible source of energetic heavy ions in the magnetosphere

A new mechanism is proposed for the source of energetic heavy ions (NO/+/, O2/+/, and O/+/) found in the magnetosphere. Simulations using a multispecies particle simulation code for resistive current-driven electrostatic ion cyclotron waves show transverse and parallel bulk heating of bottomside ionospheric heavy ion populations. The dominant mechanism for the transverse bulk heating is resonant ion heating by wave-particle ion trapping. Using a linear kinetic dispersion relation for a magnetized, collisional, homogenous, and multiion plasma, it is found that collisional electrostatic ion cyclotron waves near the NO(+), O2(+), and O(+) gyrofrequencies are unstable to field-aligned currents of 50 microA/sq m for a typical bottomside ionosphere.

Providakes, Jason↗

NASA NTRS1990

Absorbing boundary conditions for second-order hyperbolic equations

Jiang, Hong↗

NASA NTRS1990

Simulation studies of plasma waves in the electron foreshock - The transition from reactive to kinetic instability

Particle simulation experiments were used to analyze the electron beam-plasma instability. It is shown that there is a transition from the reactive state of the electron beam-plasma instability to the kinetic instability of Langmuir waves. Quantitative tests, which include an evaluation of the dispersion relation for the evolving non-Maxwellian beam distribution, show that a quasi-linear theory describes the onset of this transition and applies again fully to the kinetic stage. This stage is practically identical to the late stage seen in simulations of plasma waves in the electron foreshock described by Dum (1990).

Dum, C. T.↗

NASA NTRS1991

Nonaxisymmetric instabilities in rotating shear flows - Internal gravity modes in stratified media and analogies with plane flows

The role of the internal gravity modes in mediating the growth of nonaxisymmetric instabilities is investigated by studying the instability of stratified incompressible differentially rotating fluid cylinders to global nonaxisymmetric modes. The results indicate that, in addition to a modified version of the well-known principal branch mediated by surface modes of the system (analogous to f-modes of stars), there exist unstable branches of the dispersion relation mediated by internal gravity modes of the system (similar to the g-modes of stars). These branches arise due to the interaction between the g-modes. It is shown that the maximum growth rate on one of the new branches can sometimes equal or exceed that on the principal branch, thus modifying the principal branch.

Ghosh, P.↗

NASA NTRS1990

Effect of anisotropic thermal conductivity on the morphological stability of a binary alloy

A linear morphological stability analysis is presented for a planar interface during unidirectional solidification of a binary alloy, in the case of a crystal having an anisotropic thermal conductivity. A dispersion relation shows that the onset of instability depends on the orientation of the growth direction with respect to principal crystallographic axes and on the orientation of the wavevector of the perturbation. The onset of instability can be either oscillatory (traveling waves) or nonoscillatory in time. For growth along a principal axis of the crystal there is an exchange of stabilities, and the onset of instability is nonoscillatory.

Coriell, S. R.↗