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All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

The ion cyclotron dispersion relation in a proton-alpha solar wind

Solutions to the WKB warm plasma dispersion relation are investigated for the case of a proton-alpha plasma, to determine when parallel ion cyclotron waves can propagate at the alpha particle gyrofrequency. Examples are given of the behavior of the dispersion curves in this resonant regime, for several types of plasma states that are appropriate to the fast solar wind. It is found that while ion cyclotron waves can propagate at the alpha particle gyrofrequency for a bounded set of plasma parameters, use of the correct dispersion relation will probably make resonant cyclotron acceleration of solar wind plasma particles less feasible as a mechanism for the generation of the observed preferential effects.

Isenberg, P. A.↗
NASA NTRS1985

Quantitative study on dispersion relations of TIDs observed by an HF Doppler array

A quantitative study on the dispersion relation of traveling ionospheric disturbances (TIDs) was performed by using data obtained by an HF Doppler array. Observed data at three stations are digitized continuously with a sampling period of 10 sec. A schematic illustration of a running analysis method is given. Fourier components omega's and their wave vectors k's of the TIDs are calculated from these subset data from three stations by means of the cross-spectrum analysis. Diagrams of horizontal trace velocity V sub ph versus wave period T were also obtained. From these diagrams one can see clear cutoff periods of the internal mode of the atmospheric gravity waves. A morphological classification of the mode of the omega - k and V sub ph - T obtained through one year was performed. The estimation of the horizontal velocity vectors of the thermospheric wind form their dispersion relations was performed also. A key point of the method of obtaining the vectors is to estimate the tilt, in azimuthally different omega - k diagrams, of a resonant branch ascribed to the Brunt oscillations.

Tsutsui, M.↗
NASA NTRS1977

The influence of the directional energy distribution on the nonlinear dispersion relation in a random gravity wave field

The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.

Huang, N. E.↗
DOE OSTI2024

Dispersion Relations Alone Cannot Guarantee Causality

We show that linear superpositions of plane waves involving a single-valued, covariantly stable dispersion relation ω ( k ) always propagate outside the light cone unless ω ( k ) = a + b k . This implies that there is no notion of causality for individual dispersion relations since no mathematical condition on the function ω ( k ) (such as the front velocity or the asymptotic group velocity conditions) can serve as a sufficient condition for subluminal propagation in dispersive media. Instead, causality can only emerge from a careful cancellation that occurs when one superimposes all the excitation branches of a physical model. This happens automatically in local theories of matter that are covariantly stable. Hence, we find that the need for nonhydrodynamic modes in relativistic fluid mechanics is analogous to the need for antiparticles in relativistic quantum mechanics. Published by the American Physical Society 2024

Physics↗
NASA NTRS1995

Solutions of the benchmark problems by the dispersion-relation-preserving scheme

The 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.

Tam, Christopher K. W.↗
DOE OSTI2022

Monte-Carlo modeling of phonon thermal transport using DFT-based anisotropic dispersion relations over the full Brillouin zone

In this work, we present a Monte Carlo (MC) approach to solve the phonon Boltzmann transport equation (BTE) in which the anisotropic phonon dispersion relations over the full Brillouin zone (BZ) are used. In this approach, the discretization of the BZ used to compute the phonon relaxation time places constraints on the direction of scattered phonons in the real-space simulation domain. The phonon dispersion and phonon relaxation times are calculated using the density functional theory (DFT) approach. The modified MC approach is validated by a close examination of its ability to simulate phonon transport in both the ballistic and diffusive regimes for multiple materials including GaAs, InAs, ThO 2 , and α-U. In doing so, the phonon thermal conductivities from 100 K to 1000 K are calculated and compared with traditional non-transport solution of the phonon BTE. It is found that the phonon thermal conductivities of α-U and ThO 2 obtained from MC simulations using isotropic dispersion are larger than the values obtained using anisotropic phonon dispersion relations over the full BZ. The effect of phonon-defect scattering on the thermal conductivity of ThO 2 is also studied as an application of the current MC approach and found to agree with previously computed values in the literature. The MC solver developed here has been parallelized as a step to demonstrate its potential to solving computationally intensive phonon thermal transport problems at the mesoscale.

36 MATERIALS SCIENCE↗
NASA NTRS1974

Predictions of three-body-decays of mesons from pole-dominated dispersion relations

The investigation shows that the method of finite dispersion relations (FDR) as developed by Aviv and Nussinov (1970) is consistent with a wide range of three-body meson decays. The specific results vary with each reaction. For each possibility a definite form for the t-channel Regge-pole terms is selected. The results of the investigation indicate the basic reliability of an approach based on the FDR method and the finite-energy sum rules.

Thews, R. L.↗
NASA NTRS1988

Further study of a new dispersion relation for electron-atom scattering

A recently proposed dispersion relation (DR) is tested for e-He scattering; the results show that the new DR is not satisfied. Therefore, the analytic structure of the difference amplitude, previously assumed to be nonsingular, is investigated on the negative scattering energy axis. Even under severe approximations, the difference amplitude contains both poles and branch points. This suggests, however, a useful approximation of these contributions to the DR which gives very satisfactory agreement in both e-H and e-He scattering.

Bhatia, A. K.↗
NASA NTRS1986

A new dispersion relation for electron-atom scattering

A new forward-angle dispersion relation (DR) for electron-atom scattering is proposed. It is based on a subtraction of the static-exchange amplitude from the exact elastic scattering amplitude. Arguments are advanced to explain why this should obviate the difficulties associated with the Gerjuoy-Krall DR, specifically with the exchange Born amplitude. The new DR is tested in the elastic energy range for e-H scattering and compared with the GKDR.

Temkin, A.↗
DOE OSTI2022

Locality and analyticity of the crossing symmetric dispersion relation

This paper discusses the locality and analyticity of the crossing symmetric dispersion relation (CSDR). Imposing locality constraints on the CSDR gives rise to a local and fully crossing symmetric expansion of scattering amplitudes, dubbed as Feynman block expansion. A general formula is provided for the contact terms that emerge from the expansion. The analyticity domain of the expansion is also derived analogously to the Lehmann-Martin ellipse. Our observation of type-II super-string tree amplitude suggests that the Feynman block expansion has a bigger analyticity domain and better convergence.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1993

Dispersion-relation-preserving finite difference schemes for computational acoustics

Time-marching dispersion-relation-preserving (DRP) schemes can be constructed by optimizing the finite difference approximations of the space and time derivatives in wave number and frequency space. A set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed, and a sequence of numerical simulations is conducted to test the effectiveness of the DRP schemes and the radiation and outflow boundary conditions. Close agreement with the exact solutions is obtained.

Tam, Christopher K. W.↗
NASA NTRS2009

The Dispersion Relation for the 1/sinh(exp 2) Potential in the Classical Limit

The dispersion relation for the inverse hyperbolic potential is calculated in the classical limit. This is shown for both the low amplitude phonon branch and the high amplitude soliton branch. It is shown these results qualitatively follow that previously found for the inverse squared potential where explicit analytic solutions are known.

Campbell, Joel↗
DOE OSTI2024

A new approach to the evaluation and solution of the relativistic kinetic dispersion relation and verification with continuum kinetic simulation

Here, the present work describes a new approach to evaluation and root finding for the kinetic dispersion relation of Langmuir waves, which is central to the analytical understanding of collisionless damping in plasmas. The plasma dispersion function is solved to machine precision using direct integration in the complex plane in combination with an analytic evaluation of the residue to account for the deformation along the Landau contour. To efficiently attain machine precision, the contour is displaced in the complex plane prior to integration, and numerical subtleties related to the placement of the contour are discussed. The approach is generic in that it applies to arbitrary distribution functions, with the present manuscript focused on relativistic cases. Detailed verification of results via direct kinetic simulation in a variety of configuration space dimensions is also presented. Finally, the technique is applied to the challenging case of highly relativistic (i.e. extremely hot) plasmas. Here we show both qualitative agreement with prior work, as well as the disappearance of the Landau root which would have significant implication for real-life observation or experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗