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DOE OSTI2023

Linearization of an Electron Beam’s Longitudinal Phase Space Using a Hollow-Channel Plasma

The removal of undesired beam nonlinear energy chirp (time-energy correlation) or linearization of the beam longitudinal phase space (LPS) is crucial for high-brightness linac-based scientific applications, such as x-ray free-electron lasers. In this paper, we propose that a low-density hollow channel plasma can be used as a near-ideal passive linearizer to significantly linearize the beam LPS and, at the same time, preserve the beam emittance. Physically, the passage of the beam through the hollow plasma channel excites a strong quasicosinoidal longitudinal wakefield that acts to mitigate the beam nonlinear energy chirp by superimposing a reverse chirp on the beam. The theoretical analyses and large-scale three-dimensional start-to-end simulations confirm that the beam longitudinal phase space can be almost completely linearized without noticeable beam emittance growth. In conclusion, application of such a near-ideal linearizer may significantly improve the performance of numerous accelerator-based applications.

43 PARTICLE ACCELERATORS↗

DOE OSTI2021

Example of exponentially enhanced magnetic reconnection driven by a spatially bounded and laminar ideal flow

In laboratory and natural plasmas of practical interest, the spatial scale Δ d at which magnetic field lines lose distinguishability differs enormously from the scale a of magnetic reconnection across the field lines. In the solar corona, plasma resistivity gives a/Δ d ~ 10 12 , which is the magnetic Reynold number R m . The traditional resolution of the paradox of disparate scales is for the current density j associated with the reconnecting field Brec to be concentrated by a factor of Rm by the ideal evolution, so j ~ B rec /µ 0 Δ d . A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrarily chosen magnetic field lines, Δ max /Δ min , when calculated at various points in time. Reconnection becomes inevitable where Δ max /Δ min ~ R m . A simple model of the solar corona will be used for a numerical illustration that the natural rate of increase in time is linear for the current density but exponential for Δ max /Δ min . Reconnection occurs on a time scale and with a current density enhanced by only ln(a/Δ d ) from the ideal evolution time and from the current density B rec /µ 0 a. In both resolutions, once a sufficiently wide region, Δ r , has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfv´enic time scale. The Alfv´enic evolution is intrinsically ideal but expands the region in which Δ max /Δ min is large.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Multiscale formulation of frictional contact mechanics at the pore scale

Direct numerical simulation (DNS) yields the highest fidelity predictions of mechanical deformation at the pore scale, but is prohibitively expensive for analyzing large or many samples. Discrete element methods (DEM) are an efficient alternative, but are limited to granular media and incapable of estimating or controlling prediction errors. We present a pore-level multiscale method (PLMM) that approximates DNS efficiently and with controllable accuracy. We focus on the linear elastic response of a consolidated geologic porous medium with arbitrary microstructure, heterogeneous mineralogy, containing cracks or defects. PLMM decomposes the solid phase into non-overlapping subdomains, on which local basis functions are constructed. The bases are then coupled with a global interface problem that accounts for slip or stick contact conditions between the subdomains. PLMM produces an initial, but accurate, approximation to DNS that can be iteratively improved. It is amenable to parallelism and allows for different mesh, models, and physics in each subdomain. An algebraic interpretation of PLMM as a preconditioner is also presented to allow non-intrusive implementation into existing solvers. Lastly, this work extends previous developments of PLMM in fluid dynamics to solid mechanics and enables future extensions towards modeling coupled flow and mechanics problems.

42 ENGINEERING↗

NASA NTRS1976

An iterative decoupling solution method for large scale Lyapunov equations

A great deal of attention has been given to the numerical solution of the Lyapunov equation. A useful classification of the variety of solution techniques are the groupings of direct, transformation, and iterative methods. The paper summarizes those methods that are at least partly favorable numerically, giving special attention to two criteria: exploitation of a general sparse system matrix structure and efficiency in resolving the governing linear matrix equation for different matrices. An iterative decoupling solution method is proposed as a promising approach for solving large-scale Lyapunov equation when the system matrix exhibits a general sparse structure. A Fortran computer program that realizes the iterative decoupling algorithm is also discussed.

Athay, T. M.↗

NASA NTRS1989

Galaxy clustering and the origin of large-scale flows

Peebles's 'cosmic virial theorem' is extended from its original range of validity at small separations, where hydrostatic equilibrium holds, to large separations, in which linear gravitational stability theory applies. The rms pairwise velocity difference at separation r is shown to depend on the spatial galaxy correlation function xi(x) only for x less than r. Gravitational instability theory can therefore be tested by comparing the two up to the maximum separation for which both can reliably be determined, and there is no dependence on the poorly known large-scale density and velocity fields. With the expected improvement in the data over the next few years, however, this method should yield a reliable determination of omega.

Juszkiewicz, R.↗

NASA NTRS1984

Large-scale stationary and turbulent flow over topography

The contributions made to the formation of stationary features of flow over topography by linear and nonlinear dynamics were examined with an integrated quasi-geostrophic model with idealized topographic forcing. The simulation was run out to several months and generated time-averaged values which were compared with those obtained with linear theory. Linear predictions were converted to turbulent features through the addition of stationary, nonlinear thermodynamic and transient vorticity fluxes. The turbulence features matched atmospheric data on energy spectra, the direction and magnitude of energy transfers, and the spatial magnitudes involved. Transient flow transferred the majority of energy absorbed by the upscale flow and, by absorbing energy, reduced the energy of stationary flow while retaining resonance signatures. Instability was a pervasive feature of the topographically forced flow except at high wavenumbers. The results confirm that transient eddies are interactive with both asymmetric and zonal flow and cannot be adequately described by linear theory.

Vallis, G. K.↗

NASA NTRS1993

Spatial structure, sampling design and scale in remotely-sensed imagery of a California savanna woodland

This article describes research related to sampling techniques for establishing linear relations between land surface parameters and remotely-sensed data. Predictive relations are estimated between percentage tree cover in a savanna environment and a normalized difference vegetation index (NDVI) derived from the Thematic Mapper sensor. Spatial autocorrelation in original measurements and regression residuals is examined using semi-variogram analysis at several spatial resolutions. Sampling schemes are then tested to examine the effects of autocorrelation on predictive linear models in cases of small sample sizes. Regression models between image and ground data are affected by the spatial resolution of analysis. Reducing the influence of spatial autocorrelation by enforcing minimum distances between samples may also improve empirical models which relate ground parameters to satellite data.

Mcgwire, K.↗

NASA NTRS1985

Does orientation affect the smoothness of parsec-scale radio jets?

The compact, nonthermal radio sources which are studied with very-long-baseline interferometry (VLBI) are often found to have a linear structure with a bright, nearly unresolved component at one end. This asymmetric structure is usually referred to as a 'core-jet' morphology. In some sources there are bright bumps or knots - regions of enhanced radio emission - along the 'jets', while other sources have relatively smooth, featureless jets. This paper reports the result of a study of the differences between compact radio sources with bumpy and smooth jets. It is concluded that most, if not all, of the difference in jet smoothness can be attributed to the orientation of the radio axis with respect to the line of sight. Thus, the VLBI observations do not necessarily imply that there are intrinsic differences in the smoothness of parsec-scale radio jets.

Jones, D. L.↗

NASA NTRS1988

Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flows

The physical problem of large-scale coherent structures in real, developing free turbulent shear flows are discussed from the point of view of a broader interpretation of the nonlinear aspects of hydrodynamic stability. Variations on the Amsden and Harlow problem are considered, and the role of linear theory in nonlinear problems is addressed. Spatially developing two-dimensional coherent structures and three-dimensional nonlinear effects in large-scale coherent mode interactions are considered.

Liu, J. T. C.↗

DOE OSTI2022

Optically induced changes in the band structure of the Weyl charge-density-wave compound (TaSe 4 ) 2 I

Collective modes are responsible for the emergence of novel quantum phases in topological materials. In the quasi-one dimensional (1D) Weyl semimetal (TaSe 4 ) 2 I , a charge density wave (CDW) opens band gaps at the Weyl points, thus turning the system into an axionic insulator. Melting the CDW would restore the Weyl phase, but 1D fluctuations extend the gapped regime far above the 3D transition temperature (T CDW = 263 K), thus preventing the investigation of this topological phase transition with conventional spectroscopic methods. Here we use a non-equilibrium approach: we perturb the CDW phase by photoexcitation, and we monitor the dynamical evolution of the band structure by time- and angle-resolved photoelectron spectroscopy. We find that, upon optical excitation, electrons populate the linearly dispersing states at the Fermi level (E F ), and fill the CDW gap. The dynamics of both the charge carrier population and the band gap renormalization (BGR) show a fast component with a characteristic time scale of a few hundreds femtoseconds. However, the BGR also exhibits a second slow component on the µs time scale. The combination of an ultrafast response and of persistent changes in the spectral weight at E$_\mathrm{F}$, and the resulting sensitivity of the linearly dispersing states to optical excitations, may explain the high performances of (TaSe 4 ) 2 I as a material for broadband infrared photodetectors.

36 MATERIALS SCIENCE↗

NASA NTRS1986

The topology of the large-scale structure of the universe

It has been suggested recently that the topology of a distribution of galaxies can be characterized by the mean Gaussian curvature per unit volume of surfaces of constant density. An expression is derived which relates the mean curvature of isodensity surfaces to the power spectrum of density fluctuations in the linear regime of Gaussian fluctuations with random phases. The result may be compared to real galaxy catalogs if the galaxy density is smoothed over scales larger than a correlation length. The implications of the result for understanding the large-scale structure of the universe are discussed.

Hamilton, A. J. S.↗

NASA NTRS2015

Comparison of the Tangent Linear Properties of Tracer Transport Schemes Applied to Geophysical Problems.

A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.

4DVAR↗

NASA NTRS1990

Electrostatic lower hybrid waves excited by electromagnetic whistler mode waves scattering from planar magnetic-field-aligned plasma density irregularities

This paper presents a theoretical model for electrostatic lower hybrid waves excited by electromagnetic whistler mode waves propagating in regions of the magnetosphere and the topside ionosphere, where small-scale magnetic-field-aligned plasma density irregularities are thought to exist. In this model, the electrostatic waves are excited by linear mode coupling as the incident electromagnetic whistler mode waves scatter from the magnetic-field-aligned plasma density irregularities. Results indicate that high-amplitude short-wavelength (5 to 100 m) quasi-electrostatic whistler mode waves can be excited when electromagnetic whistler mode waves scatter from small-scale planar magnetic-field-aligned plasma density irregularities in the topside ionosphere and magnetosphere.

Bell, T. F.↗

DOE OSTI2021

A first principles framework to predict the transient performance of latent heat thermal energy storage

Thermal energy storage (TES) is increasingly recognized as an essential component of efficient Combined Heat and Power (CHP), Concentrated Solar Power (CSP), Heating Ventilation and Air Conditioning (HVAC), and refrigeration as it reduces peak demand while helping to manage intermittent availability of energy (e.g., from solar or wind). Latent Heat Thermal Energy Storage (LHTES) is a viable option because of its high energy storage density. Parametric analysis of LHTES in terms of dimensionless numbers is highly desired as a tool to model LHTES systems. One approach is to develop a model equation so as to minimize the error between the model and data obtained from experiments or simulations. While this approach can produce an accurate correlation applicable within the range of data used for its creation, it does not provide physical understanding of the rate-limiting process controlling the transient behavior of the device. In this paper we present an alternative approach whereby the potential rate-limiting processes are identified from first principles and then the key process is determined as a function of time as a LHTES device is charged. For example, in a simple geometry, the melt-fraction can be expected to vary linearly in time if the heat transfer rate is limited by natural convection of the phase changing material and we show it scales with the PCM Grashof number as $Gr^1_p$ and PCM Prandtl number as $Pr_p^{(1/3)}$. On the other hand, if surface area of solid PCM limits the heat transfer rate, the melt fraction increases asymptotically to reach full melting. The existence of these linear and asymptotic regions and the $Gr^1_pP r^{1/3}_p$ shape of the melt fraction curve is verified using our database of 64 simulations. Of practical importance in designing LHTES devices is the melt fraction at which the heat transfer rate ceases to be limited by convection, after which the heat storage rate deteriorates. For our geometry, this is found to be about 90%. This test case of our methodology shows the value of our approach, that predicting heat storage rate based on the rate-limiting physical phenomenon as a function of time is an effective approach to modeling LHTES devices.

25 ENERGY STORAGE↗

NASA NTRS1993

Lee waves: Benign and malignant

The flow of an incompressible fluid over an obstacle will produce an oscillation in which buoyancy is the restoring force, called a gravity wave. For disturbances of this scale, the atmosphere may be treated as dynamically incompressible, even though there exists a mean static upward density gradient. Even in the linear approximation - i.e., for small disturbances - this model explains a great many of the flow phenomena observed in the lee of mountains. However, nonlinearities do arise importantly, in three ways: (1) through amplification due to the decrease of mean density with height; (2) through the large (scaled) size of the obstacle, such as a mountain range; and (3) from dynamically singular levels in the fluid field. These effects produce a complicated array of phenomena - large departure of the streamlines from their equilibrium levels, high winds, generation of small scales, turbulence, etc. - that present hazards to aircraft and to lee surface areas. The nonlinear disturbances also interact with the larger-scale flow in such a manner as to impact global weather forecasts and the climatological momentum balance. If there is no dynamic barrier, these waves can penetrate vertically into the middle atmosphere (30-100 km), where recent observations show them to be of a length scale that must involve the coriolis force in any modeling. At these altitudes, the amplitude of the waves is very large, and the phenomena associated with these wave dynamics are being studied with a view to their potential impact on high performance aircraft, including the projected National Aerospace Plane (NASP). The presentation shows the results of analysis and of state-of-the-art numerical simulations, validated where possible by observational data, and illustrated with photographs from nature.

Wurtele, M. G.↗

DOE OSTI2022

Spontaneous magnetization of collisionless plasma

Here we study within a fully kinetic framework the generation of “seed” magnetic fields through the Weibel instability, driven in an initially unmagnetized plasma by a large-scale shear force. We develop an analytical model that describes the development of thermal pressure anisotropy via phase mixing, the ensuing exponential growth of magnetic fields in the linear Weibel stage, and the saturation of the Weibel instability when the seed magnetic fields become strong enough to instigate gyromotion of particles and thereby inhibit their free-streaming. The predicted scaling dependencies of the saturated fields on key parameters (e.g., ratio of system scale to electron skin depth and forcing amplitude) are confirmed by two-dimensional and three-dimensional particle-in-cell simulations of an electron–positron plasma. This work demonstrates the spontaneous magnetization of a collisionless plasma through large-scale motions as simple as a shear flow and therefore has important implications for magnetogenesis in dilute astrophysical systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Nonperturbative bounds on scattering of massive scalar particles in d ≥ 2

We study two-to-two scattering amplitudes of a scalar particle of mass m. For simplicity, we assume the presence of Z 2 symmetry and that the particle is Z 2 odd. We consider two classes of amplitudes: the fully nonperturbative ones and effective field theory (EFT) ones with a cut-off scale M. Using the primal numerical method which allows us to impose full non-linear unitarity, we construct novel bounds on various observables in 2 ≤ d ≤ 4 space-time dimensions for both classes of amplitudes. We show that our bounds are much stronger than the ones obtained by using linearized unitarity or positivity only. We discuss applications of our bounds to constraining EFTs. Finally, we compare our bounds to the amplitude in Φ 4 theory computed perturbatively at weak coupling, and find that they saturate the bounds.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Designing order–disorder transformation in high-entropy ferritic steels

Order–disorder transformations hold an essential place in chemically complex high-entropy ferritic steels (HEFSs) due to their critical technological application. The chemical inhomogeneity arising from mixing of multi-principal elements of varying chemistry can drive property altering changes at the atomic scale, in particular short-range order. Using density-functional theory-based linear-response theory, we predict the effect of compositional tuning on the order–disorder transformation in ferritic steels—focusing on Cr–Ni–Al–Ti–Fe HEFSs. We show that Ti content in Cr–Ni–Al–Ti–Fe solid solutions can be tuned to modify short-range order that changes the order–disorder path from BCC-B2 (Ti atomic-fraction = 0) to BCC-B2-L2 1 (Ti atomic-fraction > 0) consistent with existing experiments. Our study suggests that tuning degree of SRO through compositional variation can be used as an effective means to optimize phase selection in technologically useful alloys.

36 MATERIALS SCIENCE↗