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DOE OSTI2023

On the statistical theory of self-gravitating collisionless dark matter flow

Dark matter, if it exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale-dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e., correlation, structure, dispersion, and spectrum functions, are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share the same kinematic relations for even order correlations. The limiting correlation of velocity $\mathrm{ρ_{L}=1/2}$ on the smallest scale ( r = 0) is a unique feature of collisionless flow (⁠$\mathrm{ρ_{L}=1}$ for incompressible flow). On large scale, transverse velocity correlation has an exponential form $T_{2}∝e^{–r/r_2}$ with a constant comoving scale r 2 =21.3 Mpc/h that may be related to the horizon size at matter–radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of ${S}_{2}^{1}∝r^{1/4}$. All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale r between 1 and 7 Mpc/h. Divergence is negatively correlated for r > 30 Mpc/h that leads to a negative density correlation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2019

Causal hydrodynamic fluctuations in non-static and inhomogeneous backgrounds

Highlights: •The fluctuation–dissipation relation is modified by inhomogeneous backgrounds. •The constitutive equations are restricted by causality and fluctuation properties. •The structure of constitutive equation gives a natural cutoff scale of the theory. •The memory function with tensor structures in inhomogeneous backgrounds is obtained. -- Abstract: To integrate hydrodynamic fluctuations, namely thermal fluctuations of hydrodynamics, into dynamical models of high-energy nuclear collisions based on relativistic hydrodynamics, the property of the hydrodynamic fluctuations given by the fluctuation–dissipation relation should be carefully investigated. The fluctuation–dissipation relation for causal dissipative hydrodynamics with the finite relaxation time is naturally given in the integral form of the constitutive equation by the linear-response theory. While, the differential form of the constitutive equation is commonly used in analytic investigations and dynamical calculations for practical reasons. We give the fluctuation–dissipation relation for the general linear-response differential form and discuss the restrictions to the structure of the differential form, which comes from the causality and the positive semi-definiteness of the noise autocorrelation, and also the relation of those restrictions to the cutoff scale of the hydrodynamic fluctuations. We also give the fluctuation–dissipation relation for the integral form in non-static and inhomogeneous background by introducing new tensors, the pathline projectors. We find new modification terms to the fluctuation–dissipation relation for the differential form in non-static and inhomogeneous background which are particularly important in dynamical models to describe rapidly expanding systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Radial oscillations of viscous neutron stars: Zero diffusion case

In this article, the spectrum of radial oscillations of neutron stars is systematically studied within two frameworks of viscous relativistic hydrodynamics: the relativistic Navier-Stokes and Israel-Stewart theories. A correspondence is established between the discrete stellar eigenmodes and the continuous dispersion relation of perturbations around a homogeneous fluid, providing a basis for interpreting our numerical results. We analyze the Newtonian limit and assess the impact of relativistic corrections, such as the gravitational redshifting of microscopic relaxation timescales. We show that bulk viscosity can significantly affect the behavior of both hydrodynamic and nonhydrodynamic fundamental modes, and that, depending on the magnitude of the viscous effects, it is the nonhydrodynamic mode that becomes unstable beyond the turning point in a sequence of equilibrium configurations. These results provide a useful step toward systematic studies of neutron star quasinormal modes in the presence of viscosity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Know the enemy: 2D Fermi liquids

Highlights: • Regime of validity of the Fermi liquid theory in 2D interacting Fermi systems has been investigated. • Phase diagram for hydrodynamic and ballistic regimes in the frequency–temperature space has been obtained. • Temperature correction to quasiparticle effective mass has been calculated. • 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation have been discussed. We describe an analytical theory investigating the regime of validity of the Fermi liquid theory in interacting, via the long-range Coulomb coupling, two-dimensional Fermi systems comparing it with the corresponding 3D systems. We find that the 2D Fermi liquid theory and 2D quasiparticles are robust up to high energies and temperatures of the order of Fermi energy above the Fermi surface, very similar to the corresponding three-dimensional situation. We calculate the phase diagram in the frequency–temperature space separating the collisionless ballistic regime and the collision-dominated hydrodynamic regime for 2D and 3D interacting electron systems. We also provide the temperature corrections up to third order for the renormalized effective mass, and comment on the validity of 2D Wiedemann–Franz law and 2D Kadawoki–Woods relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

The MFiX Particle-in-Cell Method (MFiX-PIC) Theory Guide

MFiX (Multiphase Flow with Interphase eXchanges) is an open-source multiphase flow solver developed at the National Energy Technology Laboratory. Within the code, users have access to a single phase or interpenetrating continua-based multiphase two-fluid model (TFM), a discrete element model (DEM), and a particle-in-cell model (PIC). TFM, DEM, and PIC can all be used to create multiphase simulations that include hydrodynamics, chemical reactions, and heat transfer.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRS1993

Nearly incompressible fluids. II - Magnetohydrodynamics, turbulence, and waves

The theory of nearly incompressible (NI) fluid dynamics developed previously for hydrodynamics is extended to magnetohydrodynamics (MHD). Based on a singular expansion technique, modified systems of fluid equations are obtained for which the effects of compressibility are admitted only weakly in terms of the different possible incompressible solutions. NI MHD represents the interface between the compressible and incompressible magnetofluid descriptions in the subsonic regime. It is shown that three distinct NI descriptions exist corresponding to each of the three possible plasma beta regimes. The detailed theory of weakly compressible corrections to the various incompressible MHD descriptions is presented, and the implications for the solar wind are discussed.

Zank, G. P.↗

DOE OSTI2020

Theory of ignition and burn propagation in inertial fusion implosions

A detailed analytic model is presented here to investigate the physics of burn propagation in inertially confined plasmas. The onset of ignition and burn propagation occurs when alpha heating of the hot spot causes rapid ablation of shell mass into the hot spot. This allows large energy gains to be achieved since most of the fuel mass is located in the shell. Here, we first present a comprehensive review of previous analytic models that have been used to describe the physics of hot-spot evolution and ignition; we then show that a proper description of a propagating burn wave requires a comprehensive model of hot spot and shell evolution that includes proper mass conservation in the shell, fusion reactivity, and fuel depletion. The analytic theory is in good agreement with detailed radiation-hydrodynamic simulations that predict the onset of burn propagation as occurring when the yield enhancement caused by alpha heating is between 15- and 25-fold, $f_α$ ~ 1.4, where $f_α$ = alpha energy deposited/hot-spot energy at bang time, and the hot-spot burnup fraction is approximately 2%. We show that the definition of ignition is not sensitive to the alpha-particle stopping power nor asymmetries provided that the absorbed fraction of alpha particles $θ_α$ is correctly accounted for. Finally, we use the results of 2-D simulations to show that even when $θ_α$ is small and unknown (as is true in hot spots with mid modes that have significant leakage of alpha particles into the surrounding cold bubbles), one can still relate the experimentally measureable parameter $\chi^{53}_α$ to the yield amplification and the burning-plasma parameter $Q^{\text{hs}}_α$ = alpha energy deposited/total input work delivered to the hot spot

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Exploring the parameter space of MagLIF implosions using similarity scaling. II. Current scaling

Magnetized liner inertial fusion (MagLIF) is a magneto-inertial-fusion (MIF) concept, which is presently being studied on the Z pulsed power facility. The MagLIF platform has achieved interesting plasma conditions at stagnation and produced significant fusion yields in the laboratory. Given the relative success of MagLIF, there is a strong interest to scale the platform to higher peak currents. However, scaling MagLIF is not entirely straightforward due to the large dimensionality of the experimental input parameter space and the numerous physical processes involved in MIF implosions. Here, in this work, we propose a novel method to scale MagLIF loads to higher currents. Our method is based on similarity (or similitude) scaling and attempts to preserve much of the physics regimes already known or being studied on today's Z pulsed-power driver. By avoiding significant deviations into unexplored and/or less well-understood regimes, the risk of unexpected outcomes on future scaled-up experiments is reduced. Using arguments based on similarity scaling, we derive the scaling rules for the experimental input parameters characterizing a MagLIF load (as functions of the characteristic current driving the implosion). We then test the estimated scaling laws for various metrics measuring performance against results of 2D radiation–magneto-hydrodynamic hydra simulations. Agreement is found between the scaling theory and the simulation results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Experimental and computational study of phase space dynamics in strongly coupled plasmas with steep density gradients

Understanding how plasmas thermalize when density gradients are steep remains a fundamental challenge in plasma physics, with direct implications for fusion experiments and astrophysical phenomena. Standard hydrodynamic models break down in these regimes, and kinetic theories make predictions that have never been directly tested. Here, we present the first detailed phase-space measurements of a strongly coupled plasma as it evolves from sharp density gradients to thermal equilibrium. Using laser-induced fluorescence imaging of an ultracold calcium plasma, we track the complete ion distribution function f(x,v,t). We discover that commonly used kinetic models (Bhatnagar–Gross–Krook and Lenard–Bernstein) overpredict thermalization rates, even while correctly capturing the initial counterstreaming plasma formation. Our measurements reveal that the initial ion acceleration response scales linearly with electron temperature, and that the simulations underpredict the initial ion response. In our geometry we demonstrate the formation of well-controlled counterpropagating plasma beams. This experimental platform enables precision tests of kinetic theories and opens new possibilities for studying plasma stopping power and flow-induced instabilities in strongly coupled systems.

Bergeson, Scott (ORCID:0000000231249226)↗

DOE OSTI2025

Measurement and Modeling of Electron Temperature in Laboratory Photoionized Plasmas Relevant to Astrophysics

The electron temperature of photoionized plasmas characterizes the thermalization of photoelectrons, impacts the charge-state distribution, emissivity, and opacity through atomic recombination processes, and is needed to perform detailed comparisons with theory predictions. We discuss temperature measurements in laboratory photoionized plasmas and a comparison with model calculations done with several theory approximations and codes. These include a radiation-hydrodynamics simulation and two nonequilibrium heating and ionization models that tracked the evolution of the internal energy of the electrons. Furthermore, for the same physics model and X-ray flux time history, calculations were performed assuming steady-state or time-dependent conditions. The time history of steady-state results correlates with that of the X-ray flux, while that of the time-dependent cases does not, and it is qualitatively and quantitatively different from the steady-state case. Steady-state results significantly overestimated temperature measurements, while time-dependent results produced better approximations, which suggests the importance of transient effects in the experiment and also the need for time-resolved measurements.

Laboratory astrophysics↗

NASA NTRS1974

Keynote address

The requirements for a conference on turbomachinery aerodynamics and hydrodynamics are examined. The subject range of the conference is identified as basic fluid mechanics, propulsion aspects of the field, and design applications to turbomachines using gases and liquids. Background information is provided on the field of hydrodynamic and aerodynamic applications. The investigation of boundary layer theory and acoustics in the area of unsteady fluid mechanics is reported. The remaining challenge to synthesize the disciplines into the design of process of turbomachinery is explained.

Horlock, J. H.↗

DOE OSTI2020

Enhanced hydrodynamic transport in near magic angle twisted bilayer graphene

Using the semiclassical quantum Boltzmann theory and employing the Dirac model with twist angle-dependent Fermi velocity, we obtain results for the electrical resistivity, the electronic thermal resistivity, the Seebeck coefficient, and the Wiedemann-Franz ratio in near magic angle twisted bilayer graphene, as functions of doping density (around the charge-neutrality point) and modified Fermi velocity $\tilde{v}$. The $\tilde{v}$ dependence of the relevant scattering mechanisms, i.e., electron-hole Coulomb, long-range impurities, and acoustic gauge phonons, is considered in detail. We find a range of twist angles and temperatures, where the combined effect of momentum-nonconserving collisions (long-range impurities and phonons) is minimal, opening a window for the observation of strong hydrodynamic transport. In this work, several experimental signatures are identified, such as a sharp dependence of the electric resistivity on doping density and a large enhancement of the Wiedemann-Franz ratio and the Seebeck coefficient.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Hydrodynamic expansion and near-infrared absorption of x-ray heated aluminum plasmas

We use x-ray pulses from dense argon plasmas at the Z Machine (Sandia National Laboratories) to generate hypersonic aluminum plasmas akin to material ejecta during proposed planetary defense missions, fusion reactor wall excursions, and other high-energy density processes. Near-infrared absorption is used to diagnose the controlled expansion of the plasmas through cylindrical cavities following their generation from x-ray heating of solid aluminum 7075 alloy. The data are compared to multidimensional radiation hydrodynamics simulations utilizing the ALEGRA multiphysics code, accounting for the dynamics of radiation scattering, material phase change, plasma expansion, thermal re-irradiation, and interactions with the cavity and with the infrared beams. To allow for accurate simulation, density functional theory is used to apply the Hagen–Rubens relation for the far-infrared and is adjoined with a detailed configuration accounting model using the Propaceos code, producing opacities spanning 10 −1 –10 4 eV photon energy for aluminum 7075 alloy, and in comparison with pure aluminum. The model is found to agree with experimental data in the higher-fluence regime when the Hagen–Rubens relation is applied. The ejected material, which is observed to travel up to 55 km/s, is comprised of a strongly ionized, non-LTE plasma front at ∼10 eV temperature followed by a weakly ionized LTE gas at higher density. The present findings lend some confidence to the broad-range equation of state and infrared opacity models for weakly ionized aluminum plasmas while demonstrating an approach to their future refinement, with potential application to astrophysical plasmas and other extreme processes.

Adiabatic process↗

DOE OSTI2025

Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation

We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of 2+1-dimensional SU(2) lattice gauge theory on a quasi-one-dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about 20 with the local Hilbert space truncated at 𝑗 max = $\frac{1}{2}$. Because of the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width approximately proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law 𝑡 −$\frac{1}{2}$ decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusionlike spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes.

Hamiltonian systems↗

NASA NTRS1991

The flow of plasma in the solar terrestrial environment

The overall goal of our NASA Theory Program is to study the coupling, time delays, and feedback mechanisms between the various regions of the solar-terrestrial system in a self-consistent, quantitative, manner. To accomplish this goal, it will eventually be necessary to have time-dependent macroscopic models of the different regions of the solar-terrestrial system and we are continually working toward this goal. However, our immediate emphasis is on the near-earth plasma environment, including the ionosphere, the plasmasphere, and the polar wind. In this area, we have developed unique global models that allow us to study the coupling between the different regions. These results are highlighted. Another important aspect of our NASA Theory Program concerns the effect that localized structure has on the macroscopic flow in the ionosphere, plasmasphere, thermosphere and polar wind. The localized structure can be created by structured magnetospheric inputs (i.e., structured plasma convection, particle precipitation or Birkeland current patterns) or time variations in these inputs due to storms and substorms. Also, some of the plasma flows that we predict with our macroscopic models may be unstable. Another one of our goals is to examine the stability of our predicted flows. Because time-dependent three-dimensional numerical models of the solar-terrestrial environment generally require extensive computer resources, they are usually based on relatively simple mathematical formulations (i.e., simple MHD or hydrodynamic formulations). Therefore, another long-range goal of our NASA Theory Program is to study the conditions under which various mathematical formulations can be applied to specific solar-terrestrial regions. This may involve a detailed comparison of kinetic, semikinetic, and hydrodynamic predictions for a given polar wind scenario or it may involve the comparison of a small-scale particle-in-cell (PIC) simulation of a plasma expansion event with a similar macroscopic expansion event. The different mathematical formulations have different strengths and weaknesses and a careful comparison of model predictions for similar geophysical situations will provide insight into when the various models can be used with confidence.

Schunk, Robert W.↗

NASA NTRS1992

The flow of plasma in the solar terrestrial environment

The overall goal of our NASA Theory Program is to study the coupling, time delays, and feedback mechanisms between the various regions of the solar-terrestrial system in a self-consistent, quantitative manner. To accomplish this goal, it will eventually be necessary to have time-dependent macroscopic models of the different regions of the solar-terrestrial system and we are continually working toward this goal. However, our immediate emphasis is on the near-earth plasma environment, including the ionosphere, the plasmasphere, and the polar wind. In this area, we have developed unique global models that allow us to study the coupling between the different regions. Another important aspect of our NASA Theory Program concerns the effect that localized structure has on the macroscopic flow in the ionosphere, plasmasphere, thermosphere, and polar wind. The localized structure can be created by structured magnetospheric inputs (i.e., structured plasma convection, particle precipitation or Birkeland current patterns) or time variations in these inputs due to storms and substorms. Also, some of the plasma flows that we predict with our macroscopic models may be unstable, and another one of our goals is to examine the stability of our predicted flows. Because time-dependent, three-dimensional numerical models of the solar-terrestrial environment generally require extensive computer resources, they are usually based on relatively simple mathematical formulations (i.e., simple MHD or hydrodynamic formulation). Therefore, another long-range goal of our NASA Theory Program is to study the conditions under which various mathematical formulations can be applied to specific solar-terrestrial regions. This may involve a detailed comparison of kinetic, semikinetic, and hydrodynamic predictions for a given polar wind scenario or it may involve the comparison of a small-scale particle-in-cell (PIC) simulation of a plasma expansion event with a similar macroscopic expansion event. The different mathematical formulations have different strengths and weaknesses and a careful comparison of model predictions for similar geophysical situations will provide insight into when the various models can be used with confidence.

Schunk, R. W.↗

DOE OSTI2020

Atomic kinetics of laboratory photoionized plasmas relevant to astrophysics. Final report

The major goal of this project was to study the atomic and radiation physics of photoionized plasmas driven by a broadband x-ray flux and its impact on plasma x-ray heating and ionization, emissivity and opacity, and radiation-hydrodynamics. This problem is relevant to the physics of accretion disks surrounding black holes, x-ray binaries, and active galactic nuclei in astrophysics. In addition, it is also important for understanding non-equilibrium laboratory plasmas driven by a distribution of photons. To this end, and motivated by previous and ongoing gas-cell experiments performed by the PI at the Z facility of Sandia National Laboratories, we developed a new experimental platform at the 1MA Zebra pulsed power accelerator of the University of Nevada, Reno based on using a gas jet produced by a supersonic nozzle. The gas jet is turned into a photoionized plasma driven by the x- ray flux from a wire-array z-pinch. Establishing this new experimental platform at Zebra was a major goal of this project. In addition, we have also dedicated effort to continue complementary experiments at the Z facility using the gas-cell photoionized plasma set up with support from the Fundamental Science Program at Z as well as to perform data processing and analysis, and theory and modeling simulations, including electron kinetics and radiation-hydrodynamics. Since we seek to test and establish what physics models are needed to describe photoionized plasma guided by experimental observation, these complementary experimental efforts were central to achieving the goals of this project.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Pivotal Roles of Triple Screening-Topological, Electrostatic, and Hydrodynamic-On Dynamics in Semidilute Polyelectrolyte Solutions

For semidilute polyelectrolyte solutions, it is generally assumed that topological, electrostatic, and hydrodynamic interactions are screened (called triple screening). Despite a large body of research focused on polyelectrolyte solutions, the concept of triple screening has never been rigorously verified. In this work, we test the concept by probing concentration fluctuations in aqueous solutions containing a well-studied polyelectrolyte, sodium poly(styrenesulfonate) (NaPSS) with neutron scattering, theory, and molecular dynamics simulations. Neutron spin–echo (NSE) and small-angle neutron scattering (SANS) data from semidilute solutions of NaPSS are presented at different polymer and salt (NaCl) concentrations. A combined theory for structure (J. Chem. Phys. 105, 5183 (1996)) and dynamics (J. Chem. Phys. 107, 2619 (1997)), which captures effects of hydrodynamic, topological, and electrostatic screening, is used to interpret the experimental results. Here, the theory quantitatively predicts the decay rate obtained from the NSE measurements while capturing the shape and concentration dependencies of the polyelectrolyte peak observed in the SANS spectra. Detailed comparisons of the theory and the experiments reveal that the wavevector-dependent decay rate of concentration fluctuations in semidilute solutions of polyelectrolytes is dictated by the screening of hydrodynamic, topological, and electrostatic interactions. This conclusion is corroborated by coarse-grained molecular dynamics simulations, executed without any hydrodynamic interactions, which fail to capture the correct wavevector dependence of the decay rate. These results highlight that the theories based on the concept of triple screening provide a quantitative framework for predicting a relation between the structure and dynamics of polyelectrolyte solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗