Search NASA⌕ Search

SEARCH · Search NASA

Results for “THEORIES - FLOW LINEAR”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quasi-linear theory of forced magnetic reconnection for the transition from the linear to the Rutherford regime

Abstract Using the in-viscid two-field reduced magneto-hydrodynamic (MHD) model, a new analytical theory is developed to unify the Hahm–Kulsrud–Taylor (HKT) linear solution and the Rutherford quasi-linear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in the Taylor problem. An integral form of an analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford quasi-linear solution. In particular, the quasi-linear effect can be described by a single coefficient K s ∝ S 8 / 5 ψ c 2 , where S = τ R τ A and ψ c are the Lundquist number and amplitude of external magnetic perturbation, respectively. The HKT linear solution for the response can be recovered when the index K s → 0. On the other hand, the quasi-linear effect plays a key role in the island growth when K s ~ 1. Our new analytical solution has also been compared with reduced MHD simulations with agreement.

Physics↗
DOE OSTI2022

Linear Theory of Electromagnetic Ion Beam Instabilities in the Earth’s Forshock: Peter Gary’s Contributions (1981–1991)

We discuss Peter Gary’s contributions to the understanding of the origin and properties of ultra-low frequency (ULF) waves in the Earth’s foreshock during the period when the International Sun Earth Explorer spacecraft (ISEE-1 and -2) provided unique data about the plasma and wave environment in this region. Peter’s work concerning the linear theory of electromagnetic ion beam instabilities is contained in five journal articles and then summarized in a review article, all of which are discussed here. Brief summaries of observations and theory prior to ISEE as well as to later work are also included.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Hybrid Simulation and Quasi-linear Theory of Bi-Kappa Proton Instabilities

The quasi-steady states of collisionless plasmas in space (e.g., in the solar wind and planetary environments) are governed by the interactions of charged particles with wave fluctuations. These interactions are responsible not only for the dissipation of plasma waves but also for their excitation. The present analysis focuses on two instabilities, mirror and electromagnetic ion cyclotron instabilities, associated with the same proton temperature anisotropy T ⊥ > T ∥ (where ⊥, ∥ are directions defined with respect to the local magnetic field vector). Theories relying on standard Maxwellian models fail to link these two instabilities (i.e., predicted thresholds) to the proton quasi-stable anisotropies measured in situ in a completely satisfactory manner. Here we revisit these instabilities by modeling protons with the generalized bi-Kappa (bi-κ power-law) distribution, and by a comparative analysis of a 2D hybrid simulation with the velocity-moment-based quasi-linear (QL) theory. It is shown that the two methods feature qualitative and, even to some extent, quantitative agreement. The reduced QL analysis based upon the assumption of a time-dependent bi-Kappa model thus becomes a valuable theoretical approach that can be incorporated into the present studies of solar wind dynamics.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Expansion-driven Weibel instability in magnetohydrodynamics: Linear theory for static systems

The Weibel dispersion relation is obtained in the magnetohydrodynamic (MHD) approximation by including a tensor expression for temperature. MHD gives an upper cutoff wavenumber for Weibel growth identical to kinetic theory if the electron drift velocity is included in the evolution of the electron temperature. MHD overestimates growth rates compared to kinetic theory and gives maximum growth at larger wavenumbers, but it only leads to divergent results as temperature anisotropy tends to infinity. Thermal conduction in MHD lowers the growth rates and shifts maximum growth to smaller wavenumbers, but flux-limited or nonlocal thermal conduction is found to significantly limit these effects. The results are used as a first step in evaluating the potential of MHD to simulate expansion-driven Weibel instability, which occurs due to the temperature tensor only cooling in the direction of expansion. Finally, the small temperature anisotropy found in expansion-driven Weibel instability means that MHD could be an adequate model because growth rates are much less than the electron plasma frequency, and wavelengths are much greater than the Debye length.

Davies, J. R. [Univ. of Rochester, NY (United Stat↗
DOE OSTI2020

Measurement of Ehrlich-Schwoebel barrier contribution to the self-organized formation of ordered surface patterns on Ge(001)

Normal-incidence 1-keV Ar + ion bombardment leads to amorphization and ultrasmoothing of Ge at room temperature, but at elevated temperatures the Ge surface remains crystalline and is unstable to the formation of self-organized nanoscale patterns of ordered pyramid-shaped pits. The physical phenomenon distinguishing the high-temperature patterning from room-temperature ultrasmoothing is believed to be a surface instability due to the Ehrlich-Schwoebel barrier for diffusing vacancies and adatoms, which is not present on the amorphous material. This real-time grazing-incidence small-angle x-ray scattering study compares smoothing of a prepatterned Ge sample at room temperature with patterning of an initially flat Ge sample at an elevated temperature. In both experiments, when the nanoscale structures are relatively small in height, the average kinetics can be explained by a linear theory. Furthermore, the linear theory coefficients, indicating surface stability or instability, were extracted for both experiments. A comparison between the two measurements allows estimation of the contribution of the Ehrlich-Schwoebel barrier to the self-organized formation of ordered nanoscale patterns on crystalline Ge surfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Second Linear Response Theory and the Analytic Calculation of Excited-State Properties

We present a method based on second linear response time-dependent density func- tional theory (TDDFT) to calculate permanent and transition multipoles of excited states, which are required to compute excited-state absorption/emission spectra, multi- photon optical processes, among others. In previous work, we examined computations based on second linear response theory in which linear response TDDFT was employed twice. In contrast, the present methodology only requires information from a single linear response calculation to compute the excited-state properties. These are eval- uated analytically through various algebraic operations involving electron repulsion integrals and excitation vectors. The present derivation focuses on full many-body wave functions instead of single orbitals, as in our previous approach. Here, we test the proposed method by applying it to several diatomic and triatomic molecules. This shows that the computed excited-state dipoles are consistent with respect to reference equation-of-motion coupled cluster calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Parameterized anomalous transport model for current-carrying collisionless plasmas in pulsed power inertial confinement fusion

Current delivery in pulsed power inertial confinement fusion is influenced by collisionless current-carrying microturbulent plasmas, which are sourced from electrode surfaces. In this setting, the lower hybrid drift instability—triggered by plasma acceleration—is a leading candidate driver of difficult-to-predict momentum and energy transport. To characterize the nonlinear state of the microturbulent plasma, a parameterized anomalous transport model is developed for the instability, with analytic formulas for anomalous collision frequency, resistivity, and species heating rates. The formulas are expressed in terms of linear-theory variables and four dimensionless parameters that characterize the macroscopic plasma state. The model is built on linear theory analysis, power law analysis, and quasilinear theory analysis, and is validated using a series of nonlinear continuum kinetic Vlasov–Poisson simulations. The theoretical and computational investigation demonstrates that the anomalous collision frequency associated with the instability can be reliably approximated, within about a factor of five or better, by the unscaled linear theory growth rate of the fastest-growing wavenumber mode. This finding enables efficient calculation of anomalous resistivity and species heating rates over a wide range of plasma conditions, resulting in improved predictive capabilities.

Complex functions↗
DOE OSTI2022

Double cylinder target design for study of hydrodynamic instabilities in multi-shell ICF

Cylindrical implosions are used to study hydrodynamic instability growth for inertial confinement fusion (ICF) applications, as the cylindrical geometry allows for easier diagnostic access while retaining convergence effects. In this work, we use the established cylindrical implosion platform [Palaniyappan et al., Phys. Plasmas 27, 042708 (2020)] to inform the double shell ICF campaign [Montgomery et al., Phys. Plasmas 25, 092706 (2018)]. We present a design for a double cylindrical target as an analogue to the double shell ICF capsule in order to study hydrodynamic instability growth on the high-Z inner shell. Our design work is done with two-dimensional (2D) Eulerian radiation-hydrodynamics simulations, considering the axial uniformity of the implosion and feasibility of measuring the instability growth of pre-seeded single mode sinusoidal perturbations. We discuss in depth the design for a target to be directly driven at the OMEGA laser facility [Boehly et al., Opt. Commun. 133, 495 (1997)]. We evaluate the design for axial implosion symmetry and visibility of instability growth using synthetic radiographs constructed from the simulations, as the instability growth on the inner cylinder is experimentally measured using x-ray radiography of the implosion. We find that the seeded perturbation growth on the inner cylinder should be visible in an experiment, even with axial implosion asymmetry and preheat. We compare our 2D simulations with linear theory predictions for perturbation growth and show that a cylinder with lower azimuthal mode number (mode-20) perturbations compares more favorably with linear theory, while a cylinder with higher azimuthal mode number (mode-40) perturbations at the same starting amplitude saturates and is over-predicted by linear theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Microphysics of shock-grain interaction for inertial confinement fusion ablators in a fluid approach

Ablator materials used for inertial confinement fusion, such as high-density carbon (HDC) and beryllium, have grain structure which may lead to small-scale density nonuniformity and the generation of perturbations when the materials are shocked and compressed. Here, we use a combination of a linear theory of shock interaction with density nonuniformity [Velikovich et al., Phys. Plasmas 14, 072706 (2007)] and numerical simulations to study shock interaction with a model representation of HDC grains. While the shock-grain interaction is nonlinear, the linear theory shows some key features of the shock-grain interaction, which also hold for the (nonlinear) simulations. The postshock perturbations are made up of sonic reflections off of grain boundaries and vorticity deposition along them, with the latter dominating the perturbed energy content. The mean (per mass) postshock perturbed kinetic energy decreases with increasing grain size, but energy will be deposited at increasing spatial scale. From the perspective of the postshock perturbed energy, the detailed linear theory largely supports a proposed method [S. Davidovits et al., Phys. Plasmas 29, 112708 (2022)] for deresolving the grains (in a similar grains model) that treats the grains statistically. Finally, our simulation results highlight the influence of thermal conduction on the perturbation dynamics at grain scales.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth

The response of the cross-beam energy transfer instability (CBET) to laser bandwidth is investigated through a combination of theory and simulation. Existing linear theory is generalized to treat broadband lasers, demonstrating that CBET is most effectively suppressed when the bandwidth exceeds the ion-acoustic wave (IAW) frequency. It is shown that for such bandwidths, reverse (seed to pump) transfer becomes possible, which reduces the net energy transfer rapidly as bandwidth is increased. The CBET gain exponent in this regime scales with bandwidth (Δω) as Δω−3 for Gaussian or Lorentzian laser spectra with different scalings possible for other spectra. Comparison of our theory with linearized fluid and particle-in-cell simulations, performed with the laser-plasma simulation environment (LPSE) and vector particle in cell (VPIC) codes, respectively, finds that the model is accurate in the absence of nonlinear processes. However, linear analysis also finds that the IAW energy density scales as Δω−1, implying that nonlinear effects may be more difficult to control than the CBET scaling would suggest. Indeed, nonlinear effects are found to be present in VPIC simulations with high-intensity lasers, despite minimal apparent CBET. Nonlinear processes in the VPIC cases include particle trapping, the two-ion wave decay, and ion wave self-focusing. In some high intensity VPIC cases, these effects lead to net energy transfer from seed to pump and increases to backscatter stimulated Brillouin scattering reflectivities. Finally, for a given bandwidth, we show that improved control of nonlinear processes can be achieved via smoothing by spectral dispersion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

An intrinsic ductility parameter derived from anisotropic linear elasticity theory

A new indicator of intrinsic ductility (κ) is introduced based on linear elasticity. In the limit of elastic isotropy this parameter is equal to the Pugh ratio ( B / G ) plus a constant; but unlike the Pugh ratio, κ incorporates anisotropy and crystallography to improve predictive value. We identify a single ductile-to-brittle transition setpoint for κ that predicts crack-tip plasticity in atomistic simulations, experimental elongation to failure of polycrystalline elemental metals pulled in tension, and fracture energy measurements of glasses, suggesting commonality in the relationship between plasticity and fracture across all three of these cases. Statistical analysis supports the superiority of κ over B / G at predicting crack-tip plasticity in atomistic simulations and elongation to failure of polycrystalline elemental metals.

Winter, Ian S.↗
DOE OSTI2023

Anomalous cross-field transport in a Hall thruster inferred from direct measurement of instability growth rates

The contribution of the electron drift instability to anomalous electron transport is experimentally assessed in a Hall effect discharge. The transport is represented by an anomalous collision frequency, which is related through quasilinear theory to the energy and growth rate of the instability. The wave energy is measured directly with ion saturation probes, while estimates of the growth rate are employed based on both linearized theory and direct measurement. The latter measurement is performed with a bispectral analysis method. The wave-driven collision frequency is compared to measurements of the actual collision frequency inferred from a method based on laser- induced fluorescence. It is found that estimates for transport using linearized theory for the growth differ by over an order of magnitude from the actual anomalous collision frequency in the plasma. The wave-driven anomalous collision frequency with measured growth, however, is shown to agree with the electron collision frequency in magnitude and capture aspects of the trends in spatial variation. This result demonstrates experimentally that wave-driven effects ultimately can explain the observed cross-field transport in these devices. As a result, the implications of this finding are discussed in the context of the key lengthscales that drive the transport as well as the implications identifying reduced fidelity models that could be used to predict anomalous collision frequency.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Accurate effective fluid approximation for ultralight axions

Ultralight axions are theoretically interesting and phenomenologically rich dark sector candidates, but they are difficult to track across cosmological timescales because of their fast oscillations. We resolve this problem by developing a novel method to evolve them efficiently and accurately. We first construct an exact effective fluid which at late times matches the axion but which evolves in a simple way. We then approximate this evolution with a carefully chosen equation of state and sound speed. With our scheme we find that we can obtain subpercent accuracy for the linear theory suppression of axion density fluctuations relative to that of cold dark matter without tracking even a single complete oscillation of the axion field. Furthermore, we use our technique to test other approximation schemes and to provide a fitting formula for the transfer function for the matter power spectrum in linear theory in axion models. Implementing our approach in existing cosmological axion codes is straightforward and will help unleash the potential of high-precision next-generation experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Ring Formation in Protoplanetary Disks Driven by an Eccentric Instability

We find that, under certain conditions, protoplanetary disks may spontaneously generate multiple, concentric gas rings without an embedded planet through an eccentric cooling instability. Using both linear theory and nonlinear hydrodynamics simulations, we show that a variety of background states may trap a slowly processing, one-armed spiral mode that becomes unstable when a gravitationally stable disk rapidly cools. The angular momentum required to excite this spiral comes at the expense of nonuniform mass transport that generically results in multiple rings. For example, one long-term hydrodynamics simulation exhibits four long-lived, axisymmetric gas rings. We verify the instability evolution and ring-formation mechanism from first principles with our linear theory, which shows remarkable agreement with the simulation results. Dust trapped in these rings may produce observable features consistent with observed disks. Additionally, direct detection of the eccentric gas motions may be possible when the instability saturates, and any residual eccentricity left over in the rings at later times may also provide direct observational evidence of this mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Revealing the Drag Instability in One-fluid Nonideal Magnetohydrodynamic Simulations of a 1D Isothermal C-shock

C-type shocks are believed to be ubiquitous in turbulent molecular clouds thanks to ambipolar diffusion. We investigate whether the drag instability in 1D isothermal C-shocks, inferred from the local linear theory of Gu & Chen, can appear in nonideal magnetohydrodynamic simulations. Two C-shock models (with narrow and broad steady-state shock widths) are considered to represent the typical environment of star-forming clouds. The ionization-recombination equilibrium is adopted for the one-fluid approach. In the 1D simulation, the inflow gas is continuously perturbed by a sinusoidal density fluctuation with a constant frequency. The perturbations clearly grow after entering the C-shock region until they start being damped at the transition to the post-shock region. We show that the profiles of a predominant Fourier mode extracted locally from the simulated growing perturbation match those of the growing mode derived from the linear analysis. Moreover, the local growth rate and wave frequency derived from the predominant mode generally agree with those from the linear theory. Therefore, we confirm the presence of the drag instability in simulated 1D isothermal C-shocks. We also explore the nonlinear behavior of the instability by imposing larger-amplitude perturbations to the simulation. We find that the drag instability is subject to wave steepening, leading to saturated perturbation growth. Issues concerning local analysis, nonlinear effects, one-fluid approach, and astrophysical applications are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

First-principles characterization of the magnetic properties of Cu 2 (OH) 3 Br

Low-dimensional spin-1/2 transition metal oxides and oxyhalides continue to be at the forefront of research investigating nonclassical phases such as quantum spin liquids. In this work, we examine the magnetic properties of the oxyhalide Cu 2 (OH) 3 Br in the botallackite structure using first-principles density functional theory, linear spin-wave theory, and exact diagonalization calculations. This quasi-two-dimensional system consists of Cu 2+ S = 1/2 moments arranged on a distorted triangular lattice. Our exact diagonalization calculations, which rely on a first-principles-based magnetic model, generate spectral functions consistent with inelastic neutron scattering data. By performing computational experiments to disentangle the chemical and steric effects of the halide ions, we find that the dominant effect of the halogen ions is steric in the Cu 2 (OH) 3 X series of compounds.

36 MATERIALS SCIENCE↗