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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Final Report - Subcontract B629114

During my visits to LLNL August 20-24, 2018, and September 10-14, 2018, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from $hp$ adaptive finite element calculations, and is implemented in the PLTMG software package, version 13. This preconditioner typically requires 3 – 20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive definite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent of the polynomial degree $p$ as $p → ∞$, but but remains strong for $p ≤$ 9, which is the highest polynomial degree allowed in PLTMG , due to limitations of the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Radiogenic lead with dominant content of {sup 208}Pb: New coolant and neutron moderator for innovative nuclear reactors

The advantages of radiogenic lead with dominant content of {sup 208}Pb as a reactor coolant with respect to natural lead are caused by unique nuclear properties of {sup 208}Pb which is a double-magic nucleus with closed proton and neutron shells. This results in significantly lower micro cross section and resonance integral of radiative neutron capture by {sup 208}Pb than those for numerous light neutron moderators. The extremely weak ability of {sup 208}Pb to absorb neutrons results in the following effects. Firstly, neutron moderating factor (ratio of scattering to capture cross sections) is larger than that for graphite and light water. Secondly, age and diffusion length of thermal neutrons are larger than those for graphite, light and heavy water. Thirdly, neutron lifetime in {sup 208}Pb is comparable with that for graphite, beryllium and heavy water what could be important for safe reactor operation. The paper presents some results obtained in neutronics and thermal-hydraulics evaluations of the benefits from the use of radiogenic lead with dominant content of {sup 208}Pb instead of natural lead as a coolant of fast breeder reactors. The paper demonstrates that substitution of radiogenic lead for natural lead can offer the following benefits for operation of fast breeder reactors. Firstly, improvement of the reactor safety thanks to the better values of coolant temperature reactivity coefficient and, secondly, improvement of some thermal-hydraulic reactor parameters. Radiogenic lead can be extracted from thorium sludge without isotope separation as {sup 208}Pb is a final isotope in the decay chain of {sup 232}Th. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

SIMULATION OF ENERGETIC PARTICLE TRANSPORT AND ACCELERATION AT SHOCK WAVES IN A FOCUSED TRANSPORT MODEL: IMPLICATIONS FOR MIXED SOLAR PARTICLE EVENTS

We use numerical solutions of the focused transport equation obtained by an implicit stochastic differential equation scheme to study the evolution of the pitch-angle dependent distribution function of protons in the vicinity of shock waves. For a planar stationary parallel shock, the effects of anisotropic distribution functions, pitch-angle dependent spatial diffusion, and first-order Fermi acceleration at the shock are examined, including the timescales on which the energy spectrum approaches the predictions of diffusive shock acceleration theory. We then consider the case that a flare-accelerated population of ions is released close to the Sun simultaneously with a traveling interplanetary shock for which we assume a simplified geometry. We investigate the consequences of adiabatic focusing in the diverging magnetic field on the particle transport at the shock, and of the competing effects of acceleration at the shock and adiabatic energy losses in the expanding solar wind. We analyze the resulting intensities, anisotropies, and energy spectra as a function of time and find that our simulations can naturally reproduce the morphologies of so-called mixed particle events in which sometimes the prompt and sometimes the shock component is more prominent, by assuming parameter values which are typically observed for scattering mean free paths of ions in the inner heliosphere and energy spectra of the flare particles which are injected simultaneously with the release of the shock.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

RADIATION TRANSPORT FOR EXPLOSIVE OUTFLOWS: OPACITY REGROUPING

Implicit Monte Carlo (IMC) and Discrete Diffusion Monte Carlo (DDMC) are methods used to stochastically solve the radiative transport and diffusion equations, respectively. These methods combine into a hybrid transport-diffusion method we refer to as IMC-DDMC. We explore a multigroup IMC-DDMC scheme that in DDMC, combines frequency groups with sufficient optical thickness. We term this procedure ''opacity regrouping''. Opacity regrouping has previously been applied to IMC-DDMC calculations for problems in which the dependence of the opacity on frequency is monotonic. We generalize opacity regrouping to non-contiguous groups and implement this in SuperNu, a code designed to do radiation transport in high-velocity outflows with non-monotonic opacities. We find that regrouping of non-contiguous opacity groups generally improves the speed of IMC-DDMC radiation transport. We present an asymptotic analysis that informs the nature of the Doppler shift in DDMC groups and summarize the derivation of the Gentile-Fleck factor for modified IMC-DDMC. We test SuperNu using numerical experiments including a quasi-manufactured analytic solution, a simple 10 group problem, and the W7 problem for Type Ia supernovae. We find that opacity regrouping is necessary to make our IMC-DDMC implementation feasible for the W7 problem and possibly Type Ia supernova simulations in general. We compare the bolometric light curves and spectra produced by the SuperNu and PHOENIX radiation transport codes for the W7 problem. The overall shape of the bolometric light curves are in good agreement, as are the spectra and their evolution with time. However, for the numerical specifications we considered, we find that the peak luminosity of the light curve calculated using SuperNu is ∼10% less than that calculated using PHOENIX.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Irradiation effects on microstructure change in nanocrystalline ceria – Phase, lattice stress, grain size and boundaries

With a wide variety of applications in numerous industries, ranging from biomedical to nuclear, ceramics such as ceria are key engineering materials. It is possible to significantly alter the materials functionality and therefore its applications by reducing the grain size to the nanometer size regime, at which point the unique varieties of grain boundaries and associated interfaces begin to dominate the material properties. Nanocrystalline films of cubic ceria deposited onto Si substrates have been irradiated with 3 MeV Au+ ions at temperatures of 300 and 400 K to evaluate their response to irradiation. It was observed that the films remained phase stable. Following a slight stress relief stage at low damage levels, the overall lattice is extremely stable up to high irradiation dose of ~34 displacements per atom. The grains were also observed to undergo a temperature-dependent grain growth process upon ion irradiation. This is attributed to a defect-driven mechanism in which the diffusion of defects from the collision cascade is critical. Formation of dislocations that terminate and stabilize at symmetric grain boundaries may be the limiting factor in the grain growth and overall energy reduction of the system. Utilizing ion modification, possible improvement of the adhesion of thin films and reduction of the probability of detrimental effects of stress-induced problems are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Hierarchical calibration and validation for modeling bench-scale solvent-based carbon capture. Part 1: Non-reactive physical mass transfer across the wetted wall column

A hierarchical model calibration and validation are proposed here for quantifying the confidence level of mass transfer prediction using a computational fluid dynamics (CFD) model, where the solvent-based carbon dioxide (CO 2 ) capture is simulated and the predicted results are compared to the corresponding bench-scale experimental data. Two unit problems with an increasing level of complexity are proposed to break down the complex physical/chemical processes of solvent-based CO 2 capture into relatively simpler problems to separate the effects of physical transport and chemical reaction. This paper focuses on the calibration and validation of the first unit problem, i.e., the CO 2 mass transfer across a falling ethanolamine (MEA) film in the absence of chemical reaction. This problem is investigated both experimentally and numerically using non-reactive nitrous oxide (N 2 O) as a surrogate for CO 2 . To capture motion of the gas-liquid interface, a volume of fluid method is employed with a one-fluid formulation to compute the mass transfer between the two phases. Parallel bench-scale experiments are designed and conducted to validate and calibrate the CFD models using a general Bayesian calibration approach. Two important transport parameters, Henry's constant and gas diffusivity, are calibrated to produce the posterior distributions, which will be used as input for the second unit problem to address the chemical absorption of CO 2 across the MEA falling film, where both mass transfer and chemical reaction are involved. Finally, mass transfer coefficients predicted by CFD are also compared with those predicted by the traditional/empirical correlations under both steady and wavy falling film conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Dielectric-barrier-discharge plasma-assisted hydrogen diffusion flame. Part 1: Temperature, oxygen, and fuel measurements by one-dimensional fs/ps rotational CARS imaging

One-dimensional hybrid fs/ps CARS imaging provides single-laser-shot measurements of temperature, oxygen, and hydrogen in a plasma-assisted hydrogen diffusion flame. The coaxial dielectric-barrier-discharge burner collapses the Re ~50 hydrogen diffusion flame to within ~5 mm of the burner surface at an applied AC potential of 8.75 kV at 18 kHz, coinciding nicely with the full spatial extent of the 1D CARS measurements. Translating the burner through the measurement volume allowed for measurements at numerous radial locations in increments of 1 mm with a resolution of 140 µm × 30 µm × 600 µm, sufficient to resolve spatial gradients in this unsteady flame. Longer probe delays, required for improved dynamic range in regions of high temperature fluctuations, proved difficult to model as a result of a nontrivial decay in the O 2 Raman coherence arising from complexities associated with the triplet ground electronic state of the O 2 molecule. Oxygen linewidths were treated empirically using the observed O 2 coherence decay in spectra acquired from the product gases of lean, near-adiabatic H 2 /air flames stabilized on a Hencken flat-flame burner. While still leading to errors up to 10% at worst, the empirically determined Raman linewidth factors eliminated any systematic error in the O 2 /N 2 measurements with probe delay. Temperature measurements in the Hencken Burner flames proved to be insensitive to probe pulse delay, providing robust thermometry. Here, demonstration of this technique in both the canonical Hencken burner flames and a new DBD burner validates its effectiveness in producing multiple spatially resolved measurements in combustion environments. Measurements in the DBD burner revealed an unsteady, counterflow flattened flame structure near the fuel orifice which became unsteady as the reaction zone curves towards the surface for larger radial positions. Lastly, fluctuations in the fuel concentration were largest at the source, as the large, plasma-generated, unsteady external toroidal vortex that dominates the transport in this flame provides enhanced ventilation of the flame surface in close proximity to the fuel tube.

42 ENGINEERING↗
DOE OSTI2015

Exploring stellar evolution models of sdB stars using MESA

Stellar evolution calculations have had great success reproducing the observed atmospheric properties of different classes of stars. Recent detections of g-mode pulsations in evolved He burning stars allow a rare comparison of their internal structure with stellar models. Asteroseismology of subdwarf B (sdB) stars suggests convective cores of 0.22–0.28 M{sub ⊙}, ≳45% of the total stellar mass. Previous studies found significantly smaller convective core masses (≲0.19 M{sub ⊙}) at a comparable evolutionary stage. We evolved stellar models with Modules for Experiments in Stellar Astrophysics (MESA) to explore how well the interior structures inferred from asteroseismology can be reproduced by standard algorithms. Our qualitative evolutionary paths, position in the logg−T{sub eff} diagram, and model timescales are consistent with previous results. The sdB masses from our full evolutionary sequences fall within the range of the empirical sdB mass distribution, but are nearly always lower than the median. Using standard MLT with atomic diffusion we find convective core masses of ∼0.17–0.18 M{sub ⊙}, averaged over the entire sdB lifetime. We can increase the convective core sizes to be as large as those inferred from asteroseismology, but only for extreme values of the overshoot parameter (overshoot gives numerically unstable and physically unrealistic behavior at the boundary). High resolution three-dimensional simulations of turbulent convection in stars suggest that the Schwarzschild criterion for convective mixing systematically underestimates the actual extent of mixing because a boundary layer forms. Accounting for this would decrease the errors in both sdB total and convective core masses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Final Report - Subcontract B6183769

During my visit to LLNL during July 5{15, 2016, we worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear system arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12 [1]. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive definite elliptic equations, convection dominated convection-diffusion equations, and highly inde nite Helmholtz equations, among others). The convergence rate is not independent of the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of numerical quadrature formulae. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in [2]. Like traditional geometric multilevel methods, this scheme relies on extensive knowledge of the underlying finite element space in order to construct both the smoother and the coarse grid correction components.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Final Report - Subcontract B623760

During my visit to LLNL during July 17{27, 2017, I worked on linear system solvers. The two level hierarchical solver that initiated our study was developed to solve linear systems arising from hp adaptive finite element calculations, and is implemented in the PLTMG software package, version 12. This preconditioner typically requires 3-20% of the space used by the stiffness matrix for higher order elements. It has multigrid like convergence rates for a wide variety of PDEs (self-adjoint positive de nite elliptic equations, convection dominated convection-diffusion equations, and highly indefinite Helmholtz equations, among others). The convergence rate is not independent of the polynomial degree p as p ! 1, but but remains strong for p 9, which is the highest polynomial degree allowed in PLTMG, due to limitations of the numerical quadrature rules implemented in the software package. A more complete description of the method and some numerical experiments illustrating its effectiveness appear in. Like traditional geometric multilevel methods, this scheme relies on knowledge of the underlying finite element space in order to construct the smoother and the coarse grid correction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Assessing the ASME Section III, Division 5, Class A Primary Load Design Rules Against Creep Notch Effects

This report assesses the ASME Section III, Division 5, Subsection HB, Subpart B rules covering the design and construction of high temperature Class A nuclear reactor components for their robustness against creep notch effects. The creep notch effect combines the effect of multiaxial stresses on material creep deformation and damage. This report considers both effects, including the potential for creep mechanism shifts affecting the extrapolation of design data from high stress, short-time experimental data to low stress, long time operating component conditions. The report summarizes the history of and literature on multiaxial creep and surveys the current ASME design rules dealing with multiaxial effects. The report then describes the results of two dedicated numerical studies, one assessing the robustness of the ASME rules against uncertainty in extrapolating from uniaxial creep test data to multiaxial component conditions and a second study examining the potential effects of a mechanism shift from high stress, dislocation-mediated creep to diffusion-dominated creep at lower stresses. The final conclusion of the report is that the ASME rules adequately guard against multiaxial creep failure, though there are several aspects of the Code that could be optimized to provide less over-conservative design predictions or to provide a more consistent design margin as a function of temperature and stress. In a few areas, particularly the potential for mechanism shifts outside the currently-available experimental data, the Code rules should be revaluated as additional experimental data and new modeling and simulation results become available

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Code Coverage Status of ARC Code-DIF3D

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. DIF3D plays a pivotal role in the ARC system as the primary homogenized assembly neutronic calculation methodology for fast reactor problems. Over its 40 years history, ARC software usage with DIF3D has been applied to numerous fast and thermal spectrum reactor analysis projects with good to excellent comparison against experiments. With continued improvement of computation resources, many of the geometry modeling capabilities in DIF3D that were primarily used in low order schemes are not really needed anymore. Today, the diffusion and transport capabilities of DIF3D-VARIANT are primarily used in the reactor design process with some scattered usage of DIF3D-FD and DIF3D-Nodal. In recent work, the DIF3D software verification was completed for DIF3D-FD and DIF3D-VARIANT on the geometry options used in the Versatile Test Reactor project. While we can be confident that these capabilities of DIF3D are well used and thus trusted, it does not demonstrate that all possible input options of DIF3D are actually working, but just those that were tested as part of VTR are and that they are correct. Thus, the purpose of the present work is to identify a set of test problems for DIF3D and assess the code coverage of DIF3D for those test problems. The goal is to document what parts of the existing DIF3D code are touched by the set of test problems and which are not. Because the verification work done on DIF3D-VARIANT and DIF3D-FD was focused on the most common uses of DIF3D for fast reactor analysis, the code coverage assessment of those capabilities is the highest priority. This will ensure that nothing is being missed by the existing verification test problems that DIF3D relies upon. The DIF3D-Nodal capability will also be inspected for code coverage as part of this work to further ensure that regular regression testing of DIF3D will trap any likely errors the end user might experience with the DIF3D software. The code coverage analysis of DIF3D was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of DIF3D. The detailed coverage tables are given for each submodule of DIF3D separately, and for the submodules which are primarily developed for DIF3D, most of the source files could be at least partially touched. Most of the uncovered parts/files could be easily ignored, because they are either for error message and debugging output or obviously not needed by DIF3D. Out of the entire source codes of DIF3D, only a few uncovered modules deserve further investigation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Code Coverage Status of the ARC Code DIF3D

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. DIF3D plays a pivotal role in the ARC system as the primary homogenized assembly neutronic calculation methodology for fast reactor problems. Over its 40 years history, ARC software usage with DIF3D has been applied to numerous fast and thermal spectrum reactor analysis projects with good to excellent comparison against experiments. With continued improvement of computation resources, many of the geometry modeling capabilities in DIF3D that were primarily used in low order schemes are not really needed anymore. Today, the diffusion and transport capabilities of DIF3D-VARIANT are primarily used in the reactor design process with some scattered usage of DIF3D-FD and DIF3D-Nodal. In recent work, the DIF3D software verification was completed for DIF3D-FD and DIF3D-VARIANT on the geometry options used in the Versatile Test Reactor project. While we can be confident that these capabilities of DIF3D are well used and thus trusted, it does not demonstrate that all possible input options of DIF3D are actually working, but just those that were tested as part of VTR are and that they are correct. Thus, the purpose of the present work is to identify a set of test problems for DIF3D and assess the code coverage of DIF3D for those test problems. The goal is to document what parts of the existing DIF3D code are touched by the set of test problems and which are not. Because the verification work done on DIF3D-VARIANT and DIF3D-FD was focused on the most common uses of DIF3D for fast reactor analysis, the code coverage assessment of those capabilities is the highest priority. This will ensure that nothing is being missed by the existing verification test problems that DIF3D relies upon. The DIF3D-Nodal capability will also be inspected for code coverage as part of this work to further ensure that regular regression testing of DIF3D will trap any likely errors the end user might experience with the DIF3D software. The code coverage analysis of DIF3D was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of DIF3D. The detailed coverage tables are given for each submodule of DIF3D separately, and for the submodules which are primarily developed for DIF3D, most of the source files could be at least partially touched. Most of the uncovered parts/files could be easily ignored, because they are either for error message and debugging output or obviously not needed by DIF3D. Out of the entire source codes of DIF3D, only a few uncovered modules deserve further investigation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Developing a laser shockwave model for characterizing diffusion bonded interfaces

The US National Nuclear Security Agency has a Global Threat Reduction Initiative (GTRI) with the goal of reducing the worldwide use of high-enriched uranium (HEU). A salient component of that initiative is the conversion of research reactors from HEU to low enriched uranium (LEU) fuels. An innovative fuel is being developed to replace HEU in high-power research reactors. The new LEU fuel is a monolithic fuel made from a U-Mo alloy foil encapsulated in Al-6061 cladding. In order to support the fuel qualification process, the Laser Shockwave Technique (LST) is being developed to characterize the clad-clad and fuel-clad interface strengths in fresh and irradiated fuel plates. LST is a non-contact method that uses lasers for the generation and detection of large amplitude acoustic waves to characterize interfaces in nuclear fuel plates. However, because the deposition of laser energy into the containment layer on a specimen's surface is intractably complex, the shock wave energy is inferred from the surface velocity measured on the backside of the fuel plate and the depth of the impression left on the surface by the high pressure plasma pulse created by the shock laser. To help quantify the stresses generated at the interfaces, a finite element method (FEM) model is being utilized. This paper will report on initial efforts to develop and validate the model by comparing numerical and experimental results for back surface velocities and front surface depressions in a single aluminum plate representative of the fuel cladding.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2013

Laser thermoelastic generation in metals above the melt threshold

An approach is presented for calculating thermoelastic generation of ultrasound in a metal plate exposed to nanosecond pulsed laser heating, sufficient to cause melting but not ablation. Detailed consideration is given to the spatial and temporal profiles of the laser pulse, penetration of the laser beam into the sample, the appearance and subsequent growth and then contraction of the melt pool, and the time dependent thermal conduction in the melt and surrounding solid throughout. The excitation of the ultrasound takes place during and shortly after the laser pulse and occurs predominantly within the thermal diffusion length of a micron or so beneath the surface. It is shown how, because of this, the output of the thermal simulations can be expressed as axially symmetric transient radial and normal surface force distributions. The epicentral displacement response to these force distributions is obtained by two methods, the one based on the elastodynamic Green's functions for plate geometry determined by the Cagniard generalized ray method and the other using a finite element numerical method. The two approaches are in very close agreement. Numerical simulations are reported on the epicentral displacement response of a 3.12 mm thick tungsten plate irradiated with a 4 ns pulsed laser beam with Gaussian spatial profile, at intensities below and above the melt threshold.

36 MATERIALS SCIENCE↗
DOE OSTI2012

A GENERAL CIRCULATION MODEL FOR GASEOUS EXOPLANETS WITH DOUBLE-GRAY RADIATIVE TRANSFER

We present a new version of our code for modeling the atmospheric circulation on gaseous exoplanets, now employing a 'double-gray' radiative transfer scheme, which self-consistently solves for fluxes and heating throughout the atmosphere, including the emerging (observable) infrared flux. We separate the radiation into infrared and optical components, each with its own absorption coefficient, and solve standard two-stream radiative transfer equations. We use a constant optical absorption coefficient, while the infrared coefficient can scale as a power law with pressure; however, for simplicity, the results shown in this paper use a constant infrared coefficient. Here we describe our new code in detail and demonstrate its utility by presenting a generic hot Jupiter model. We discuss issues related to modeling the deepest pressures of the atmosphere and describe our use of the diffusion approximation for radiative fluxes at high optical depths. In addition, we present new models using a simple form for magnetic drag on the atmosphere. We calculate emitted thermal phase curves and find that our drag-free model has the brightest region of the atmosphere offset by {approx}12 Degree-Sign from the substellar point and a minimum flux that is 17% of the maximum, while the model with the strongest magnetic drag has an offset of only {approx}2 Degree-Sign and a ratio of 13%. Finally, we calculate rates of numerical loss of kinetic energy at {approx}15% for every model except for our strong-drag model, where there is no measurable loss; we speculate that this is due to the much decreased wind speeds in that model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Lyα heating of inhomogeneous high-redshift intergalactic medium

The intergalactic medium (IGM) prior to the epoch of reionization consists mostly of neutral hydrogen gas. Lyman-α (Lyα) photons produced by early stars resonantly scatter off hydrogen atoms, causing energy exchange between the radiation field and the gas. This interaction results in moderate heating of the gas due to the recoil of the atoms upon scattering, which is of great interest for future studies of the pre-reionization IGM in the H I 21 cm line. We investigate the effect of this Lyα heating in the IGM with linear density, temperature, and velocity perturbations. Perturbations smaller than the diffusion length of photons could be damped due to heat conduction by Lyα photons. The scale at which damping occurs and the strength of this effect depend on various properties of the gas, the flux of Lyα photons, and the way in which photon frequencies are redistributed upon scattering. To find the relevant length scale and the extent to which Lyα heating affects perturbations, we calculate the gas heating rates by numerically solving linearized Boltzmann equations in which scattering is treated by the Fokker-Planck approximation. We find that (1) perturbations add a small correction to the gas heating rate, and (2) the damping of temperature perturbations occurs at scales with comoving wavenumber k ≳ 10{sup 4} Mpc{sup –1}, which are much smaller than the Jeans scale and thus unlikely to substantially affect the observed 21 cm signal.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Fast penetration of megagauss fields into metallic conductors

Megagauss magnetic-field penetration into a conducting material is studied via a simplified but representative model, wherein the magnetic-diffusion equation is coupled with a thermal-energy balance. The specific scenario considered is that of a prescribed magnetic field rising (in proportion to an arbitrary power r of time) at the surface of a conducting half-space whose electric conductivity is assumed proportional to an arbitrary inverse power γ of temperature. We employ a systematic asymptotic scheme in which the case of a strong surface field corresponds to a singular asymptotic limit. In this limit, the highly magnetized and hot “skin” terminates at a distinct propagating wave-front. Employing the method of matched asymptotic expansions, we find self-similar solutions of the magnetized region which match a narrow boundary-layer region about the advancing wave front. The rapidly decaying magnetic-field profile in the latter region is also self similar; when scaled by the instantaneous propagation speed, its shape is time-invariant, depending only on the parameter γ. The analysis furnishes a simple asymptotic formula for the skin-depth (i.e., the wave-front position), which substantially generalizes existing approximations. It scales with the power γr + 1∕2 of time and the power γ of field strength, and is much larger than the field-independent skin depth predicted by an athermal model. The formula further involves a dimensionless O(1) pre-factor which depends on r and γ. It is determined by solving a nonlinear eigenvalue problem governing the magnetized region. Another main result of the analysis, apparently unprecedented, is an asymptotic formula for the magnitude of the current-density peak characterizing the wave-front region. Complementary to these systematic results, we provide a closed-form but ad hoc generalization of the theory approximately applicable to arbitrary monotonically rising surface fields. Our results are in excellent agreement with numerical simulations of the model, and compare favourably with detailed magnetohydrodynamic simulations reported in the literature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗