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Results for “Dispersive wave relations”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Nonlinear theory of type I irregularities in the equatorial electrojet

By allowing for the effect of wave electric fields on electron orbits, a nonlinear dispersion relation for type I irregularities is obtained. This relation predicts (1) isotropy of the Doppler shift with elevation, (2) a limiting phase velocity equal to the ion acoustic speed, and (3) a saturation amplitude which is maximum for horizontally propagating waves and decreases with elevation. With the theory presented here, the in situ electric field measurements of Pfaff et al. (1980) in the electrojet environment could provide a quantitative check for the theory of orbit diffusion by stochastic electric fields.

Sudan, R. N.↗
DOE OSTI2024

Theoretical and global simulation analysis of collisional microtearing modes

Microtearing modes (MTMs) are suggested as a candidate for anomalous thermal transport in tokamak H-mode discharges. This study investigates MTMs in tokamak plasmas, employing simulations in the BOUT++ framework. It simplifies and linearizes the governing equations in detailed linear simulations. The study meticulously evaluates various conductivity models under diverse plasma conditions and collision regimes. The research thoroughly assesses different conductivity models across a range of plasma conditions and collision regimes. A unified dispersion relation that includes both MTM and Drift-Alfvén Wave (DAW) instabilities is derived, showing that DAW and MTM instabilities occur at varying distances from the rational surface. Specifically, MTMs become unstable near the rational surface but stabilize farther away, while drift-Alfvén instability appears farther from the rational surface. The study also re-derives MTM dispersion relations using Ohm's law and the vorticity equation, providing a thorough analysis of electromagnetic and electrostatic interactions in tokamaks. Global simulations demonstrate an inverse correlation between MTM growth rates and collisionality, and a direct correlation with temperature gradients. The nonalignment of the rational surface with the peak ω*e stabilizes the MTMs. Nonlinear simulations highlight electron temperature relaxation as the primary saturation mechanism for MTMs, with magnetic flutter identified as the dominant mode of electron thermal transport.

Fan, K. (ORCID:0000000227518809)↗
NASA NTRS1986

On the applicability of relativistic dispersion to auroral zone electron distributions

An examination is made to identify appropriate times to include weakly relativistic wave dispersion in calculations of auroral zone electron distributions. Two dispersion relations are examined. First, solutions are found for a ring distribution of particles around a cold ambient plasma. The solutions are found only for modes near the electron gyrofrequency. A trapped mode which is decoupled from the freely propagating R-X mode of cold plasmas is found to be the most unstable mode. Wave dispersion is examined with a spherically symmetric Dory-Guest-Harris (DGH) distribution, which describes a shell distribution that has a peak momentum larger than the thermal spread. The trapped mode is again found to be the most unstable. The analysis indicates it is beneficial to include relativistic effects whenever calculating auroral plasma distributions, and that a simple model will have sufficient accuracy.

Strangeway, R. J.↗
DOE OSTI2022

Modified gravitational wave propagation with higher modes and its degeneracies with lensing

Low-energy alternatives to General Relativity (GR) generically modify the phase of gravitational waves (GWs) during their propagation. As detector sensitivities increase, it becomes key to understand how these modifications affect the GW higher modes and to disentangle possible degeneracies with astrophysical phenomena. We apply a general formalism — the WKB approach — for solving analytically wave propagation in the spatial domain with a modified dispersion relation (MDR). We compare this WKB approach to applying a stationary phase approximation (SPA) in the temporal domain with time delays associated to the group or particle velocity. To this end, we extend the SPA to generic signals with higher modes, keeping careful track of reference phases and arrival times. We find that the WKB approach coincides with the SPA using the group velocity, in agreement with the principles of wave propagation. We then explore the degeneracies between a GW propagation with an MDR and a strongly-lensed GW in GR, since the latter can introduce a frequency-independent phase shift which is not degenerate with source parameters in the presence of higher modes. We find that for a particular MDR there is an exact degeneracy for wave propagation, unlike with the SPA for particle propagation. For the other cases, we search for the values of the MDR parameters that minimize the χ 2 and conclude that strongly-lensed GR GWs could be misinterpreted as GWs in modified gravity. As a result, future MDR constraints with higher mode GWs should include the possibility of frequency-independent phase shifts, allowing for the identification of modified gravity and strong lensing distortions at the same time.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1986

Electron-cyclotron maser instability in relativistic plasmas

The electron-cyclotron maser instability is studied for the case of an anisotropic electron velocity distribution in the regime where the relativistic corrections to the wave dispersion are significant. Solution of the linear dispersion relation reveals that when the plasma frequency-gyrofrequency ratio is less than v(te)/c, the instability is localized just below k(perpendicular)c/Omega(e) = 1. The growth rate is then strongly peaked for emission at 90 deg to the magnetic field and is considerably larger than would be the case if the cold-plasma dispersion theory were valid. These features are confirmed by EM particle simulations.

Pritchett, P. L.↗
NASA NTRS2015

Comparison of High-Order and Low-Order Methods for Large-Eddy Simulation of a Compressible Shear Layer

The objective of this work is to compare a high-order solver with a low-order solver for performing Large-Eddy Simulations (LES) of a compressible mixing layer. The high-order method is the Wave-Resolving LES (WRLES) solver employing a Dispersion Relation Preserving (DRP) scheme. The low-order solver is the Wind-US code, which employs the second-order Roe Physical scheme. Both solvers are used to perform LES of the turbulent mixing between two supersonic streams at a convective Mach number of 0.46. The high-order and low-order methods are evaluated at two different levels of grid resolution. For a fine grid resolution, the low-order method produces a very similar solution to the highorder method. At this fine resolution the effects of numerical scheme, subgrid scale modeling, and filtering were found to be negligible. Both methods predict turbulent stresses that are in reasonable agreement with experimental data. However, when the grid resolution is coarsened, the difference between the two solvers becomes apparent. The low-order method deviates from experimental results when the resolution is no longer adequate. The high-order DRP solution shows minimal grid dependence. The effects of subgrid scale modeling and spatial filtering were found to be negligible at both resolutions. For the high-order solver on the fine mesh, a parametric study of the spanwise width was conducted to determine its effect on solution accuracy. An insufficient spanwise width was found to impose an artificial spanwise mode and limit the resolved spanwise modes. We estimate that the spanwise depth needs to be 2.5 times larger than the largest coherent structures to capture the largest spanwise mode and accurately predict turbulent mixing.

large eddy simulations↗
NASA NTRS2015

Comparison of High-Order and Low-Order Methods for Large-Eddy Simulation of a Compressible Shear Layer

The objective of this work is to compare a high-order solver with a low-order solver for performing large-eddy simulations (LES) of a compressible mixing layer. The high-order method is the Wave-Resolving LES (WRLES) solver employing a Dispersion Relation Preserving (DRP) scheme. The low-order solver is the Wind-US code, which employs the second-order Roe Physical scheme. Both solvers are used to perform LES of the turbulent mixing between two supersonic streams at a convective Mach number of 0.46. The high-order and low-order methods are evaluated at two different levels of grid resolution. For a fine grid resolution, the low-order method produces a very similar solution to the high-order method. At this fine resolution the effects of numerical scheme, subgrid scale modeling, and filtering were found to be negligible. Both methods predict turbulent stresses that are in reasonable agreement with experimental data. However, when the grid resolution is coarsened, the difference between the two solvers becomes apparent. The low-order method deviates from experimental results when the resolution is no longer adequate. The high-order DRP solution shows minimal grid dependence. The effects of subgrid scale modeling and spatial filtering were found to be negligible at both resolutions. For the high-order solver on the fine mesh, a parametric study of the spanwise width was conducted to determine its effect on solution accuracy. An insufficient spanwise width was found to impose an artificial spanwise mode and limit the resolved spanwise modes. We estimate that the spanwise depth needs to be 2.5 times larger than the largest coherent structures to capture the largest spanwise mode and accurately predict turbulent mixing.

large eddy simulations↗
DOE OSTI2023

Interaction of Inner Heliosheath Ions with Electromagnetic Ion Cyclotron Waves

Abstract Inner heliosheath (IHS) ions are expected to be exposed to various waves, shocks, and turbulence, which can affect ion distributions and thus their charge-exchange rates with interstellar neutral atoms. This work addresses the potential significance of electromagnetic ion cyclotron (EMIC) waves under expected IHS conditions. From a kinetic dispersion relation, we find the possibility of frequent triggering of EMIC instability in the IHS. The threshold anisotropy of proton temperatures required for the instability is small, ( T ⊥ – T ∣∣ )/ T ∣∣ ≈ 0.1 or less, mainly due to high plasma β (ratio of the plasma to magnetic pressures). Numerical calculations on the scattering of ions (protons, He + , and He 2+ with energy of 0.01–50 keV) based on two models for EMIC waves with a moderate intensity indicate significant scattering in the pitch angle (mostly a few tens of degrees) and energy (mostly a few tens of percent) although details depend on the energy and pitch angle of each species and adopted EMIC wave models. This occurs on a short timescale (<100 times the gyro-period of each ion species). Resonant scattering in a few to a few tens of keV (corresponding to the expected pickup ion energy in the IHS) is easily expected unless the wavenumber is too large. The scattering effect is distinguished among different species such that for lower gyrofrequency ions (He + versus He 2+ and He 2+ versus protons), the main scattering effect moves toward a lower energy domain. All these results imply continuous disturbance of ion distributions by possibly prevailing EMIC waves in the IHS.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1985

Resistive wave dissipation on magnetic inhomogeneities Normal modes and phase mixing

Numerical solutions of the linearized, resistive MHD equations indicate the presence of two characteristic forms of wave decay on magnetic inhomogeneities. Solutions for relatively long-wavelength disturbances and large values of the resistivity have the behavior of decaying normal modes. In the opposite limits, phase mixing becomes important, with the eventual build-up of large spatial gradients in which the resistive terms dominate. This composite behavior is shown to be conceptually consistent with analytic results, which predict that the complete solution consists of the sum of collective and noncollective contributions. The numerical simulations go beyond analytic theory by defining where each contribution prevails and computing wave decay when phase mixing is effective. The dispersion relation in the normal-mode regime is also determined analytically, with some approximations, and is in good agreement with the numerical solution. The decay time of the normal modes varies with Lundquist number at S1/6, while the phase-mixed decay time scales as S1/3.

Steinolfson, R. S.↗
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 NTRS1997

Algorithmic Extensions of Low-Dispersion Scheme and Modeling Effects for Acoustic Wave Simulation

Accurate computation of acoustic wave propagation may be more efficiently performed when their dispersion relations are considered. Consequently, computational algorithms which attempt to preserve these relations have been gaining popularity in recent years. In the present paper, the extensions to one such scheme are discussed. By solving the linearized, 2-D Euler and Navier-Stokes equations with such a method for the acoustic wave propagation, several issues were investigated. Among them were higher-order accuracy, choice of boundary conditions and differencing stencils, effects of viscosity, low-storage time integration, generalized curvilinear coordinates, periodic series, their reflections and interference patterns from a flat wall and scattering from a circular cylinder. The results were found to be promising en route to the aeroacoustic simulations of realistic engineering problems.

Kaushik, Dinesh K.↗
DOE OSTI2023

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. So our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

42 ENGINEERING↗
DOE OSTI2023

Gauge-invariant gravitational waves in matter beyond linearized gravity

Modeling the propagation of gravitational waves (GWs) in media other than vacuum is complicated by the gauge freedom of linearized gravity in that, once nonlinearities are taken into consideration, gauge artifacts can cause spurious acceleration of the matter. To eliminate these artifacts, we propose how to keep the theory of dispersive GWs gauge-invariant beyond the linear approximation and, in particular, obtain an unambiguous gauge-invariant expression for the energy–momentum of a GW in a dispersive medium. Using analytic tools from plasma physics, we propose an exactly gauge-invariant 'quasilinear' theory, in which GWs are governed by linear equations and also affect the background metric on scales large compared to their wavelength. As a corollary, the gauge-invariant geometrical optics of linear dispersive GWs in a general background is formulated. As an example, we show how the well-known properties of vacuum GWs are naturally and concisely yielded by our theory in a manifestly gauge-invariant form. We also show how the gauge invariance can be maintained within a given accuracy to an arbitrary order in the GW amplitude. These results are intended to form a physically meaningful framework for studying dispersive GWs in matter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1976

Shuttle wave experiments

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.

Calvert, W.↗
NASA NTRS1992

Runge-Kutta methods combined with compact difference schemes for the unsteady Euler equations

Recent development using compact difference schemes to solve the Navier-Stokes equations show spectral-like accuracy. A study was made of the numerical characteristics of various combinations of the Runge-Kutta (RK) methods and compact difference schemes to calculate the unsteady Euler equations. The accuracy of finite difference schemes is assessed based on the evaluations of dissipative error. The objectives are reducing the numerical damping and, at the same time, preserving numerical stability. While this approach has tremendous success solving steady flows, numerical characteristics of unsteady calculations remain largely unclear. For unsteady flows, in addition to the dissipative errors, phase velocity and harmonic content of the numerical results are of concern. As a result of the discretization procedure, the simulated unsteady flow motions actually propagate in a dispersive numerical medium. Consequently, the dispersion characteristics of the numerical schemes which relate the phase velocity and wave number may greatly impact the numerical accuracy. The aim is to assess the numerical accuracy of the simulated results. To this end, the Fourier analysis is to provide the dispersive correlations of various numerical schemes. First, a detailed investigation of the existing RK methods is carried out. A generalized form of an N-step RK method is derived. With this generalized form, the criteria are derived for the three and four-step RK methods to be third and fourth-order time accurate for the non-linear equations, e.g., flow equations. These criteria are then applied to commonly used RK methods such as Jameson's 3-step and 4-step schemes and Wray's algorithm to identify the accuracy of the methods. For the spatial discretization, compact difference schemes are presented. The schemes are formulated in the operator-type to render themselves suitable for the Fourier analyses. The performance of the numerical methods is shown by numerical examples. These examples are detailed. described. The third case is a two-dimensional simulation of a Lamb vortex in an uniform flow. This calculation provides a realistic assessment of various finite difference schemes in terms of the conservation of the vortex strength and the harmonic content after travelling a substantial distance. The numerical implementation of Giles' non-refelctive equations coupled with the characteristic equations as the boundary condition is discussed in detail. Finally, the single vortex calculation is extended to simulate vortex pairing. For the distance between two vortices less than a threshold value, numerical results show crisp resolution of the vortex merging.

Yu, Sheng-Tao↗
DOE OSTI2021

Dispersion and the speed-limited particle-in-cell algorithm

This paper discusses temporally continuous and discrete forms of the speed-limited particle-in-cell (SLPIC) method first treated by Werner et al. [Phys. Plasmas 25, 123512 (2018)]. The dispersion relation for a 1D1V electrostatic plasma whose fast particles are speed-limited is derived and analyzed. By examining the normal modes of this dispersion relation, we show that the imposed speed-limiting substantially reduces the frequency of fast electron plasma oscillations while preserving the correct physics of lower-frequency plasma dynamics (e.g. ion acoustic wave dispersion and damping). We then demonstrate how the timestep constraints of conventional electrostatic particle-in-cell methods are relaxed by the speed-limiting approach, thus enabling larger timesteps and faster simulations. Here, these results indicate that the SLPIC method is a fast, accurate, and powerful technique for modeling plasmas wherein electron kinetic behavior is nontrivial (such that a fluid/Boltzmann representation for electrons is inadequate) but evolution is on ion timescales.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗