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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Reionization in a cold dark matter universe: The feedback of galaxy formation on the intergalactic medium

We study the coupled evolution of the intergalactic medium (IGM) and the emerging structure in the universe in the context of the cold dark matter (CDM) model, with a special focus on the consequences of imposing reionization and the Gunn-Peterson constraint as a boundary condition on the model. We have calculated the time-varying density of the IGM by coupling our detailed, numerical calculations of the thermal and ionization balance and radiative transfer in a uniform, spatially averaged IGM of H and He, including the mean opacity of an evolving distribution of gas clumps which correspond to quasar absorption line clouds, to the linearized equations for the growth of density fluctuations in both the gaseous and dark matter components in a CDM universe. We use the linear growth equations to identify the fraction of the gas which must have collapsed out at each epoch, an approach similar in spirit to the so-called Press-Schechter formalism. We identify the IGM density with the uncollapsed baryon fraction. The collapsed fraction is postulated to be a source of energy injection into the IGM, by radiation or bulk hydrodynamical heating (e.g., via shocks) or both, at a rate which is marginally enough to satisfy the Gunn-Peterson constraint at z less than 5. Our results include the following: (1) We find that the IGM in a CDM model must have contained a substantial fraction of the total baryon density of the universe both during and after its reionization epoch. (2) As a result, our previous conclusion that the observed Quasi-Stellar Objects (QSOs) at high redshift are not sufficient to ionize the IGM enough to satisfy the Gunn-Peterson constraint is confirmed. (3) We predict a detectable He II Gunn-Peterson effect at 304(1 + z) A in the spectra of quasars at a range of redshift z greater than or approx. 3, depending on the nature of the sources of IGM reionization. (4) We find, moreover, that a CDM model with high bias parameter b (i.e., b greater than or approx. 2) cannot account for the baryon content of the universe at z approximately 3 observed in quasar absorption line gas unless Omega (sub B) significantly exceeds the maximum value allowed by big bang nucleocynthesis. (5) For a CDM model with bias parameter within the allowed range of (lower) values, the lower limit to Omega(sub B) imposed by big bang nucleosynthesis (Omega(sub B) h(sup 2) greater than or equal to 0.01) combines with our results to yield the minimum IGM density for the CDM fodel. For CDM with b = 1 (Cosmic Background Explorer (COBE) normalization), we find Omega(sub IGM)(sup min) (z approximately 4) approx. equal 0.02-0.03, and Omega(sub IGM)(sup min)(z approximately 0) approx. equal 0.005-0.03, depending upon the nature of the sources of IGM reionization. (6) In general, we find that self-consistent reionization of the IGM by the collapsed baryon fraction has a strong effect on the rate of collapse. (7) As a further example, we show that the feedback effect on the IGM of energy release by the collapsed baryon fraction may explain the slow evolution of the observed comoving QSO number density between z = 5 and z = 2, followed by the sharp decline after z = 2.

Shapiro, Paul R.↗
NASA NTRS1994

A simulation of the intracluster medium with feedback from cluster galaxies

We detail method and report first results from a three-dimensional hydrodynamical and N-body simulation of the formation and evolution of a Coma-sized cluster of galaxies, with the intent of studying the history of the hot, X-ray emitting intracluster medium. Cluster gas, galaxies, and dark matter are included in the model. The galaxies and dark matter fell gravitational forces; the cluster gas also undergoes hydrodynamical effects such as shock heating and PdV work. For the first time in three dimensions, we include modeling of ejection of processed gas from the simulated galaxies by winds, including heating and heavy element enrichment. For comparison, we employ a `pure infall' simulation using the same initial conditions but with no galaxies or winds. We employ an extreme ejection history for galactic feedback in order to define the boundary of likely models. As expected, feedback raises the entropy of the intracluster gas, preventing it from collapsing to densities as high as those attained in the infall model. The effect is more pronounced in subclusters formed at high redshift. The cluster with feedback is always less X-ray luminous, but experiences more rapid luminosity evolution, than the pure infall cluster. Even employing an extreme ejection model, the final gas temperature is only approximately 15% larger than in the infall model. The radial temperature profile is very nearly isothermal within 1.5 Mpc. The cluster galaxies in the feedback model have a velocity dispersion approximately 15% lower than the dark matter. This results in the true ratio of specific energies in galaxies to gas being less than one, beta(sub spec) approximately 0.7. The infall model predicts beta(sub spec) approximately 1.2. Large excursions in these values occur over time, following the complex dynamical history of the cluster. The morphology of the X-ray emission is little affected by feedback. The emission profiles of both clusters are well described by the standard beta-model with beta(sub fit) approximately equal to 0.7 - 0.9. X-ray mass estimates based on the assumptions of hydrostatic equilibrium and the applicability of the beta-model are quite accurate in both cases. A strong, radial iron abundance gradient is present, which develops as a consequence of the steepening of the galaxy density profile over time. Spectroscopic observations using nonimaging detectors with wide (approximately 45 min) fields of view dramatically smear the gradient. Observations with arcminute resolution, made available with the ASCA satellite, would readily resolve the gradient.

Metzler, Christopher A.↗
NASA NTRS2011

Simulation of Relativistic Shocks and Associated Radiation from Turbulent Magnetic Fields

Using our new 3-D relativistic particle-in-cell (PIC) code, we investigated long-term particle acceleration associated with a relativistic electron-positron jet propagating in an unmagnetized ambient electron-positron plasma. The simulations were performed using a much longer simulation system than our previous simulations in order to investigate the full nonlinear stage of the Weibel instability and its particle acceleration mechanism. Cold jet electrons are thermalized and ambient electrons are accelerated in the resulting shocks. Acceleration of ambient electrons leads to a maximum ambient electron density three times larger than the original value as predicted by hydrodynamic compression. Behind the bow shock, in the jet shock, strong electromagnetic fields are generated. These fields may lead to time dependent afterglow emission. In order to go beyond the standard synchrotron model used in astrophysical objects we have used PIC simulations and calculated radiation based on first principles. We calculated radiation from electrons propagating in a uniform parallel magnetic field to verify the technique. We also used the technique to calculate emission from electrons based on simulations with a small system. We obtain spectra which are consistent with those generated from electrons propagating in turbulent magnetic fields. This turbulent magnetic field is similar to the magnetic field generated at an early nonlinear stage of the Weibel instability. A fully developed shock within a larger system may generate a jitter/synchrotron spectrum.

Nishikawa, K.-I.↗
NASA NTRS1988

Multistream hydrodynamic modeling of interhemispheric plasma flow

Interhemispheric plasma flow was simulated using one-stream and two-stream hydrodymic models in order to test the suggestion of Banks et al. (1971) and others that the collision of high-speed flows originating from the conjugate hemispheres will cause the formation of a pair of shocks. The single-fluid hydrodynamic equations were modified to include multiple ion streams, allowing for the possibility of counterstreaming flow. It was found that a counterstreaming of ion streams from conjugate hemispheres does occur during the early stages of the refilling of plamaspheric flux tubes, and that a pair of reverse shocks does form. These shocks form away from the equator, and their subsequent motion creates conditions similar to those predicted by the single-stream hydrodynamic models. The findings support the conclusion of earlier studies that the refilling of the plasmasphere occurs from the equatorial region downward.

Rasmussen, C. E.↗
DOE OSTI2024

A hybrid finite volume method and smoothed particle hydrodynamics approach for efficient and accurate blast simulations

Modeling strong shock waves in fluids remains a persistent challenge in computational physics. Essential to research efforts in industry and defense, numerous methods have been devised to improve the accuracy and efficiency of shock simulations. A novel, hybrid Finite Volume Method (FVM)-Smoothed Particle Hydrodynamics (SPH) approach is capable of further improving efficiency and retaining accuracy by exploiting the favorable characteristics of each respective method. This hybrid approach is presented for shock capturing in compressible fluids. The Python framework Pyro2 is employed to simulate a coarse FVM mesh, while the Python framework PySPH is utilized to model the fluid in regions with high gradients through SPH particles. The performance of the hybrid FVM-SPH scheme, compared to the individual FVM and SPH methods, is assessed in 1 kt and 10 kt blast simulations. Our results indicate that the hybrid approach offers higher computational efficiency than SPH while preserving its accuracy and characteristics. The hybrid approach had a relative speedup of 11.3x and 22.3x over the FVM and SPH approaches for the 1 kt simulation and a relative speedup of 14.7x and 20.9x over the FVM and SPH approaches for the 10 kt simulation. The hybrid SPH algorithm enables future compressible fluid simulations with more extensive capabilities than grid-based methods alone, presenting potential applications in modeling fluid-structure interactions and solid deformation and fracturing in blast simulations.

Myers, Conner↗
NASA NTRS1985

Persistence of shocks to large distances in the solar wind

Present hydrodynamic models of solar wind streams predict that interactions will cause interplanetary shocks to decay and large-scale structures to coalesce and smooth out, with a decay length of 10-15 AU for moderate or small-amplitude shocks. The Pioneer 10 plasma data, extending 1-30 AU, are examined in the light of such predictions. It is found that coalescence of streams into a single stream per solar rotation does occur, in general, but that considerable structure remains by 30 AU. The leading edge of a stream often exhibits a velocity jump of greater than 20 km/s; many of these may be shocks. There is a characteristic velocity-density-temperature signature of these distant streams which differs from the close-in double-shock signature. A unique transient was seen in July 1982, at 28 AU, with a velocity jump of about 235 km/s.

Kayser, S. E.↗
DOE OSTI2021

Reduced order models for Lagrangian hydrodynamics

It is reported, as a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp gradients. These challenges hinder the existing projection-based model reduction schemes from being practical. We develop several variations of projection-based reduced order model techniques for Lagrangian hydrodynamics by introducing three different reduced bases for position, velocity, and energy fields. A time-windowing approach is also developed to address the challenge imposed by the advection-dominated solutions. Lagrangian hydrodynamics is formulated as a nonlinear problem, which requires a proper hyper-reduction technique. Therefore, we apply the over-sampling DEIM and SNS approaches to reduce the complexity due to the nonlinear terms. Finally, we also present both a posteriori and a priori error bounds associated with our reduced order model. We compare the performance of the spatial and time-windowing reduced order modeling approaches in terms of accuracy and speed-up with respect to the corresponding full order model for several numerical examples, namely Sedov blast, Gresho vortices, Taylor-Green vortices, and triple-point problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Collapsing white dwarfs

The results of the hydrodynamic collapse of an accreting C + O white dwarf are presented. Collapse is induced by electron captures in the iron core behind a conductive deflagration front. The shock wave produced by the hydrodynamic bounce of the iron core stalls at about 115 km, and thus a neutron star formed in such a model would be formed as an optically quiet event.

Baron, E.↗
DOE OSTI2020

Modeling radiative-shocks created by laser–cluster interactions

Radiative-shocks induced by laser–cluster interactions are modeled using radiation-hydrodynamic simulations. A good agreement—in both shock velocity and density profiles—is obtained between experiment and simulations, indicating that non-local thermodynamic equilibrium (NLTE) radiative effects are important in the experimental regime examined, particularly at early times (≤30 ns) due to the elevated temperatures (≥35 eV). The enhanced NLTE radiative emission causes the shock to be reduced in amplitude, increased in width, and reduced in propagation velocity, while the amplitude of the radiative precursor is increased. As the density and temperature conditions are relatively modest, this potentially has important implications for the scalings that are used in laboratory–astrophysics to transform between laboratory and astrophysical scales, which do not hold for non-LTE systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Time-dependent cosmic ray shocks with injection - A progress report

The study presents preliminary results of a two-fluid hydrodynamical simulation of cosmic-ray-modified shock structure by extending the steady-state calculations of Zank et al. (1991) to the time-dependent case. The present simulations model diffusive shock acceleration of the energetic particle component at planar shocks. A new model for the injection of cosmic ray particles is presented. The quadratic artificial viscosity algorithm is found to be numerically unstable and therefore unusable for strong cosmic ray shocks. There is visible ringing and overshoot in the various profiles. A large enhancement in the fluid density appears downstream of the subshock. This 'overcompression' results from the upstream fluid being compressed in the precursor, then traversing a strong shock with compression ratio near the adiabatic limit of four.

Donohue, D. J.↗
DOE OSTI2026

Passive Freeze-Out of the Richtmyer-Meshkov Instability

The Richtmyer-Meshkov instability (RMI) poses a major challenge in inertial confinement fusion (ICF) due to its role in mixing and performance degradation. We report the first experimental observation of passive freeze-out of RMI in a low-pressure surrogate regime, an instability stagnation effect induced without modifying the driving pressure pulse or the target surface geometry. Using additively manufactured subsurface voids in a sinusoidal target, we convert a single shock into a sequence of weaker shocks that suppress instability growth upstream of the surface by over 70%. High-speed x-ray imaging and hydrodynamic simulations suggest that this suppression arises primarily from temporal shaping, with lesser contributions from spatial curvature and shock weakening. Our results demonstrate a driver-independent pathway for controlling shock-driven hydrodynamic instabilities relevant to ICF and other high energy density systems.

Materials science↗
NASA NTRS1972

Model development of supersonic trough wind with shocks.

The time-dependent one dimensional hydrodynamic equations describe the evolution of the thermal plasma flow along closed magnetic field lines outside of the plasmasphere. The convection of the supersonic polar wind onto a closed field line results in the assumed formation of collisionless plasma shocks. These shocks move earthward as the field line with its 'frozen-in' plasma remains fixed or contracts with time to smaller L coordinates. The high equatorial plasma temperature (of the order of electron volts) produced by the shock process decreases with time if the flow is isothermal, but it will increase if the contraction is under adiabatic conditions. Assuming adiabaticity a peak in the temperature forms at the equator in conjunction with a depression in the ion density. After an initial contraction, if the flux tube drifts to higher L coordinates, the direction of the shock motion can be reversed so that the supersonic region will expand along the field line toward the state characterizing the supersonic polar wind.

Grebowsky, J. M.↗
DOE OSTI2025

Shock propagation in aerogel and TPP foams for inertial fusion energy target design

Achieving practical inertial fusion energy (IFE) requires the development of target designs with well-characterized microstructure and compression response. We measured shock dynamics in low-density (17.5–500 mg/cm 3 ) aerogel and two-photon polymerization (TPP) foams using x-ray phase contrast imaging (XPCI) methods and the Velocity Interferometer System for Any Reflector. By analyzing shock front evolution, we examined how target type and density influence shock propagation and energy dissipation. Talbot-XPCI shows that aerogels support a smooth, bowed shock front due to their homogeneous nanometer-scale pore network. In contrast, TPP foams exhibit irregular, stepwise propagation driven by interactions with their periodic micrometer-scale lattice. Shock velocity follows a power-law relation: aerogels deviate from classical ρ −1/2 scaling due to pore-collapse dissipation, while TPP foams follow the trend with larger uncertainties from density variations. Comparisons with xRAGE simulations reveal systematic underestimation of shock speeds. These results provide the first experimental constraints on shock propagation in TPP foams over a wide density range and highlight the influence of internal structure on anisotropic shock behavior. Our findings support improved benchmarking of EOS and hydrodynamic models and inform the design of foam architectures that promote implosion symmetry in IFE capsules.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Hot electron preheat effects in two-photon polymerization plastic lattice laser-driven shock-tube experiments on the OMEGA laser

We present simulations of Omega shock tube experiments designed to investigate hot electron preheat effects in 3D-printed, two-photon polymerization (2PP) plastic lattices. Preheat is inferred in the experiments from the expansion of a plastic witness disk embedded in the lattice. Using the Eulerian radiation-hydrodynamics code xRAGE, we model shock propagation and preheat from both radiative and hot electron energy sources to evaluate their relative impact. To simulate the transport of laser-generated hot electrons, the nonlocal electron heat transport model proposed by Schurtz, Nicolaï, and Busquet (SNB) is extended with a hot electron source term and an energy cascade algorithm. We explore how variations in ablator, lattice geometry, and laser drive affect the shock velocity and witness disk expansion. Simulations show that the inclusion of a 5 μm gold layer reduces shock pressure by 60% and shock speeds by 30%–40% but does not significantly reduce the hot electron preheat, and that different lattice geometries lead to enhanced shock velocities—up to 40% faster than in homogeneous foams. However, radiative and conductive preheat from classical mechanisms alone fail to match experiment. By including a hot electron source term, we reproduce experimental observables such as disk expansion rates and spatial radiographic features. We find that a hot electron population corresponding to 4%–8% of the incident laser energy with T hot = 50 keV produces expansion which agrees with the experimental data, suggesting hot electron preheat is the most plausible explanation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

Effects of equatorially trapped ions on refilling of the plasmasphere

The kinetic aspects of shock formation in response to the equatorial heating of ions are reported by means of small-scale kinetic simulations of countersteaming plasma flows along a spatially varying magnetic field having the features of the dipolar magnetic field lines. Attention is given to the trapping of the field-aligned flowing ions in response to the simulated equatorial heating of ions and the associated self-consistent structures in the electric potentials and the f-plasma flow pattern. Trapping is found to lead to the formation of electrostatic shocks, which propagate away from the 'equator' as seen in the hydrodynamic model of Singh and Torr (1990). The shocks form near the mirror points of the 'equatorially' heated ions. The second stage of the refilling with equatorially trapped ions is reported. A variety of structures in density and temperature distributions as the refilling proceeds slowly is found.

Singh, Nagendra↗
NASA NTRS1995

Motion of the Termination Shock in Response to an 11 Year Variation in the Solar Wind

A two-dimensional hydrodynamic numerical model has been used to study the motion of the termination shock in response to an 11 year variation in the solar wind ram pressure. For a total variation in the ram pressure by a factor of 2, a termination shock at 89 AU moves inward and outward about +/- 8 percent of its distance with a typical velocity of 12 km/s.

solar↗
NASA NTRS1994

Shock propagation and the generation of magnetohydrodynamic wave fields in inhomogeneous molecular clouds

We develop a simple one-dimensional model for the interaction of a steady, thin, planar shock wave with a nonrigid cloud which may be in motion relative to the surrounding medium, and we apply the model to shocks impinging on, and propagating through, molecular clouds. Both 'adiabatic' (gamma = 5/3) and radiative (gamma = 1) shocks are considered and we allow for the presence of a uniform magnetic field directed either parallel or perpendicular to the shock normal. The former field orientation is equivalent to the hydrodynamic case, and the latter involves only fast MHD shocks. We focus on the manner in which such shocks can generate internal kinetic motions in the cloud on a range of size and density scales through the direct acceleration of cores and clumps by shocks transmitted into them and through the generation of an MHD wavefield via the reflection of the incident shock at clump boundaries. We find that stronger incident Mach numbers and smaller density contrasts lead to more efficient cloud acceleration, as do isothermal intercloud shocks and small intercloud magnetic field strengths. The acceleration efficiency is insensitive to the adiabatic index and the magnetic field strength in the cloud itself. For typical parameter choices, the direct acceleration of clouds and clumps by strong shocks is found to be substantial and could at least in part account for their observed velocity dispersions. If the shocks are moderately weak, the final velocity of the cloud is linearly related to its initial velocity, with higher acceleration giving shallower slopes (i.e., final velocity distributions which are less sensitive to the initial distribution). Compared to the kinetic energy of the postshock cloud, the energy given to the wavefield at each encounter is small, and the heating of the interclump medium by the dissipation of this wavefield is found to be insufficient to balance the cooling rate in the cloud as a whole (although it may be important in particular regions), even if this medium is warm, unless it is also extremely tenuous (n approximately less than 0.1/cu cm). Nevertheless, the correction for the velocity imparted to the cloud leads to a substantial increase in the critical incident Mach numner for wave emission over that reported by Spitzer for the rigid case. The implications of our model for shock-induced star formation are discussed briefly.

Miesch, Mark S.↗
DOE OSTI2020

A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics

The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.

97 MATHEMATICS AND COMPUTING↗