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Results for “dispersive equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

The theory of magnetohydrodynamic wave generation by localized sources. II - Collisionless dissipation of wave packets

The dispersion equation of Barnes (1966) is used to study the dissipation of asymptotic wave packets generated by localized periodic sources. The solutions of the equation are linear waves, damped by Landau and transit-time processes, in a collisionless warm plasma. For the case of an ideal MHD system, most of the waves emitted from a source are shown to cancel asympotically through destructive interference. The modes transporting significant flux to asymptotic distances are found to be Alfven waves and fast waves with theta (the angle between the magnetic field and the characteristics of the far-field waves) of about 0 and about pi/2.

Collins, William↗
NASA NTRS1990

A current disruption mechanism in the neutral sheet - A possible trigger for substorm expansions

A linear analysis is performed to investigate the kinetic cross-field streaming instability in the earth's magnetotail neutral sheet region. Numerical solution of the dispersion equation shows that the instability can occur under conditions expected for the neutral sheet just prior to the onset of substorm expansion. The excited waves are obliquely propagating whistlers with a mixed polarization in the lower hybrid frequency range. The ensuing turbulence of this instability can lead to a local reduction of the cross-tail current causing it to continue through the ionosphere to form a substorm current wedge. A substorm expansion onset scenario is proposed based on this instability in which the relative drift between ions and electrons is primarily due to unmagnetized ions undergoing current sheet acceleration in the presence of a cross-tail electric field. The required electric field strength is within the range of electric field values detected in the neutral sheet region during substorm intervals. The skew in local time of substorm onset location and the three conditions under which substorm onset is observed can be understood on the basis of the proposed scenario.

Lui, A. T. Y.↗
NASA NTRS1990

Plasma instabilities of a finite-radius electron beam in a uniform plasma

To study electromagnetic radiation induced by electronn beam injection from the Space Shuttle, the electromagnetic dispersion equation or a finite-radius cold electron beam in a neutralizing background was solved numerically. The numerical solutions indicate that a keV electron beam can drive the beam and whistler modes unstable, regardless of whether the beam is homogeneous or has a finite radius. The results obtained were applied to explain the whistler waves radiated from the keV electron beam injected from Spacelab 2.

Wong, H. K.↗
NASA NTRS1990

Collisionless tearing instability in magnetotail plasmas

The problem of the linear stability of collisionless tearing modes in the earth's magnetotail is revisited. It is found that the collisionless tearing mode is linearly unstable with wavelengths of the order of 10 R(E). It is shown that an important feature neglected in earlier theories is a nonzero equilibrium B(y)-field. The physics of the instability is elucidated in the context of a simple slab model and a sheared parabolic model which is representative of the magnetotail in which all three components of the magnetic field are nonzero. The dispersion equation for the instability is obtained by a boundary-layer analysis. The implications of the theory for recent observations on current disruption and diversion during substorms is discussed.

Wang, Xiaogang↗
NASA NTRS1990

Layering, interface and edge effects in multi-layered composite medium

Guided waves in a cross-ply laminated plate are studied. Because of the complexity of the exact dispersion equation that governs the wave propagation in a multi-layered fiber-reinforced plate, a stiffness method that can be applied to any number of layers is presented. It is shown that, for a sufficiently large number of layers, the plate can be modeled as a homogeneous anisotropic plate. Also studied is the reflection of guided waves from the edge of a multilayered plate. These results are quite different than in the case of a single homogeneous plate.

Datta, S. K.↗
NASA NTRS1992

Nongyrotropy as a source of instability and mode coupling

Nongyrotropic particle populations can bring about linear mode coupling in homogeneous media among the three eigen-modes of parallel propagation in gyrotropic magnetoplasmas. These interactions stimulate, in general, wave activity that does not occur in corresponding (random gyrophase) gyrotropic ambients. Solutions of the dispersion equation illustrate that simple introduction of gyrophase organization can (1) excite electrostatic (and electromagnetic) perturbations in media whose free energy sources are solely electromagnetic, and (3) drive hybrid (both electrostatic and electromagnetic) wave growth in thoroughly stable Maxwellian plasmas.

Brinca, A. L.↗
NASA NTRS1993

Ion anisotropy instabilities in the magnetosheath

Recent observations in Earth's magnetosheath have delineated several different kinds of magnetic fluctuation spectra below the proton cyclotron frequency. This paper provides a theoretical interpretation for some of these observations describing solutions of the linear Vlasov dispersion equation for fully electromagnetic instabilities for particle distributions which model those observed in the magnetosheath. This model yields three growing modes: the proton cyclotron anisotropy the helium cyclotron anisotropy, and the mirror instabilities. The results show very good agreement with the observations of mirror-like and proton-cyclotron-like events. This agreement with observations implies that the transition between cyclotron and mirror fluctuation dominance is consistent with linear theory.

Gary, S. P.↗
NASA NTRS1993

Investigation of plasma instabilities in the Polar cusp

During the last six months, our efforts concentrated on studying the excitation of electromagnetic waves in the whistler frequency range by an anisotropic electron beam. A paper entitled 'Electron Cyclotron Wave Generation by Relativistic Electrons' was submitted to Journal of Geophysical Research and was accepted for publication. This paper is in collaboration with Dr. M. L. Goldstein at Goddard Space Flight Center. It was shown that an anisotropic electron beam (or gyrating electron beam) is capable of generating electron cyclotron waves with frequency from above to below the electron plasma frequency in a low density plasma. This instability may account for the observed Z mode and the electromagnetic component of auroral hiss in the Earth's polar region. The abstract of this paper is enclosed. For a high density plasma in which the electron plasma frequency is considerably higher than the electron cyclotron frequency, a new left-hand electromagnetic wave at whistler frequencies, which is also driven unstable by an anisotropic electron beam, was found. The basic notion of this new instability is the significant change of the dispersion equation due to the contribution of the beam component, which can shift the usual right hand whistler waves into left hand waves.

Wong, H. K.↗
NASA NTRS1994

Electron cyclotron wave generation by relativistic electrons

We show that an energetic electron distribution which has a temperature anisotropy (T perpendicular to b is greater than T parallel to b), or which is gyrating about a DC magnetic field, can generate electron cyclotron waves with frequencies below the electron cyclotron frequency. Relativistic effects are included in solving the dispersion equation and are shown to be quantitatively important. The basic idea of the mechanism is the coupling of the beam mode to slow waves. The unstable electron cyclotron waves are predominantly electromagnetic and right-hand polarized. For a low-density plasma in which the electron plasma frequency is less than the electron cyclotron frequency, the excited waves can have frequencies above or below the electron plasma frequency, depending upon the parameters of the energetic electron distribution. This instability may account for observed Z mode waves in the polar magnetosphere of the Earth and other planets.

Wong, H. K.↗
NASA NTRS1994

The whistler heat flux instability: Threshold conditions in the solar wind

Solar wind electrons are observed often to consist of two components: a core and a halo. The anisotropics and relative average speeds of these components correspond to a heat flux that has the potential to excite several different electromagetic instabilities; wave-particle scattering by the resulting enhanced fluctuations can limit this heat flux. This manuscript describes theoretical studies using the linear Vlasco dispersion equation for drifting bi-Maxwellian component distributions in a homogeneous plasma to examine the threshold of the whistler heat flux instability. Expressions for this threshold are obtained from two different parametric baselines: a local model that yields scalings as functions of local dimensionless plasma paramaters, and a global model based on average electron properties observed during the in-eliptic phase of the Ulysses mission. The latter model yields an expression for the heat flux at threshold of the whistler instability as a function of helisopheric radius that scales in the same way as the average heat flux observed form Ulysses and that provides an approximate upper bound for that same quantity. This theoretical scaling is combined with the observational results to yield a semi-empirical closure relation for the average electron heat flux in the solar wind between 1 and 5 AU.

Gary, S. Peter↗
DOE OSTI2020

Fundamental Study of Migration Behavior of Cesium under the Unsaturated Condition through One-dimensional Column Simulating Soil around the Disposal Site - 20262

Using a packed column simulating unsaturated soil around the disposal site, flow experiments of cesium ions were conducted in order to examine the difference of retardation effect between saturated and unsaturated conditions. The column was packed with silica sand particles of 350 μm in diameter. In this study, it was confirmed that the X-ray CT images of the column showed that the water saturation was mostly uniform within the column under unsaturated conditions. The values of water saturation in the flow experiments of Cs ions were in a range from 0.85 to 0.93. The retardation coefficients(Rd) were estimated by applying the one-dimensional advection-dispersion equation to the experimental results. The comparison of the Rd-values estimated experimentally and theoretically showed that the experimental value was estimated to be larger than the theoretical value. This means that the theoretical value evaluated through a conventional method would bring the conservative value as an apparent retardation coefficient, at least when the flow direction is from top to bottom as shown in this study. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1992

Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons

The initial results for femtosecond electromagnetic soliton propagation and collision obtained from first principles, i.e., by a direct time integration of Maxwell's equations are reported. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit the modeling of 2D and 3D optical soliton propagation, scattering, and switching from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1991

Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses

The initial results for femtosecond pulse propagation and scattering interactions for a Lorentz medium obtained by a direct time integration of Maxwell's equations are reported. The computational approach provides reflection coefficients accurate to better than 6 parts in 10,000 over the frequency range of dc to 3 x 10 to the 16th Hz for a single 0.2-fs Gaussian pulse incident upon a Lorentz-medium half-space. New results for Sommerfeld and Brillouin precursors are shown and compared with previous analyses. The present approach is robust and permits 2D and 3D electromagnetic pulse propagation directly from the full-vector Maxwell's equations.

Joseph, Rose M.↗
NASA NTRS1983

Stochastic differential equations and turbulent dispersion

Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.

Durbin, P. A.↗
NASA NTRS1995

Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves

In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.

Webb, G. M.↗
NASA NTRS1995

The modulational instability for the TDNLS equations for weakly nonlinear dispersive MHD waves

In this paper we study the modulational instability for the TDNLS equations derived by Hada (1993) and Brio, Hunter, and Johnson to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. We employ Whitham's averaged Lagrangian method to study the modulational instability. This complements studies of the modulational instability by Hada (1993) and Hollweg (1994), who did not use the averaged Lagrangian approach.

Webb, G. M.↗
NASA NTRS2016

Hyperbolic Method for Dispersive PDEs: Same High-Order of Accuracy for Solution, Gradient, and Hessian

In this paper, we introduce a new hyperbolic first-order system for general dispersive partial differential equations (PDEs). We then extend the proposed system to general advection-diffusion-dispersion PDEs. We apply the fourth-order RD scheme of Ref. 1 to the proposed hyperbolic system, and solve time-dependent dispersive equations, including the classical two-soliton KdV and a dispersive shock case. We demonstrate that the predicted results, including the gradient and Hessian (second derivative), are in a very good agreement with the exact solutions. We then show that the RD scheme applied to the proposed system accurately captures dispersive shocks without numerical oscillations. We also verify that the solution, gradient and Hessian are predicted with equal order of accuracy.

Mazaheri, Alireza↗