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NASA NTRS2011

Kinetic Monte Carlo Simulation of Oxygen and Cation Diffusion in Yttria-Stabilized Zirconia

Yttria-stabilized zirconia (YSZ) is of interest to the aerospace community, notably for its application as a thermal barrier coating for turbine engine components. In such an application, diffusion of both oxygen ions and cations is of concern. Oxygen diffusion can lead to deterioration of a coated part, and often necessitates an environmental barrier coating. Cation diffusion in YSZ is much slower than oxygen diffusion. However, such diffusion is a mechanism by which creep takes place, potentially affecting the mechanical integrity and phase stability of the coating. In other applications, the high oxygen diffusivity of YSZ is useful, and makes the material of interest for use as a solid-state electrolyte in fuel cells. The kinetic Monte Carlo (kMC) method offers a number of advantages compared with the more widely known molecular dynamics simulation method. In particular, kMC is much more efficient for the study of processes, such as diffusion, that involve infrequent events. We describe the results of kinetic Monte Carlo computer simulations of oxygen and cation diffusion in YSZ. Using diffusive energy barriers from ab initio calculations and from the literature, we present results on the temperature dependence of oxygen and cation diffusivity, and on the dependence of the diffusivities on yttria concentration and oxygen sublattice vacancy concentration. We also present results of the effect on diffusivity of oxygen vacancies in the vicinity of the barrier cations that determine the oxygen diffusion energy barriers.

Good, Brian↗

DOE OSTI2016

On the channel width-dependence of the thermal conductivity in ultra-narrow graphene nanoribbons

The thermal conductivity of low-dimensional materials and graphene nanoribbons, in particular, is limited by the strength of line-edge-roughness scattering. One way to characterize the roughness strength is the dependency of the thermal conductivity on the channel's width in the form W{sup β}. Although in the case of electronic transport, this dependency is very well studied, resulting in W{sup 6} for nanowires and quantum wells and W{sup 4} for nanoribbons, in the case of phonon transport it is not yet clear what this dependence is. In this work, using lattice dynamics and Non-Equilibrium Green's Function simulations, we examine the width dependence of the thermal conductivity of ultra-narrow graphene nanoribbons under the influence of line edge-roughness. We show that the exponent β is in fact not a single well-defined number, but it is different for different parts of the phonon spectrum depending on whether phonon transport is ballistic, diffusive, or localized. The exponent β takes values β < 1 for semi-ballistic phonon transport, values β ≫ 1 for sub-diffusive or localized phonons, and β = 1 only in the case where the transport is diffusive. The overall W{sup β} dependence of the thermal conductivity is determined by the width-dependence of the dominant phonon modes (usually the acoustic ones). We show that due to the long phonon mean-free-paths, the width-dependence of thermal conductivity becomes a channel length dependent property, because the channel length determines whether transport is ballistic, diffusive, or localized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Multiple emission components in the Cygnus cocoon detected from Fermi -LAT observations

Star-forming regions may play an important role in the life cycle of Galactic cosmic rays (CRs), notably as home to specific acceleration mechanisms and transport conditions. Gamma-ray observations of Cygnus X have revealed the presence of an excess of hard-spectrum gamma-ray emission, possibly related to a cocoon of freshly accelerated particles. We seek an improved description of the gamma-ray emission from the cocoon using ~13 yr of observations with the Fermi-Large Area Telescope (LAT) and use it to further constrain the processes and objects responsible for the young CR population. We developed an emission model for a large region of interest, including a description of interstellar emission from the background population of CRs and recent models for other gamma-ray sources in the field. Thus, we performed an improved spectro-morphological characterisation of the residual emission including the cocoon. The best-fit model for the cocoon includes two main emission components: an extended component FCES G78.74+1.56, described by a 2D Gaussian of extension r 68 = 4.4° ± 0.1° -0.1° +0.1° and a smooth broken power law spectrum with spectral indices 1.67 ± 0.05 -0.01 +0.02 and 2.12 ± 0.02 -0.01 +0.00 below and above 3.0 ± 0.6 -0.2 +0.0 GeV, respectively; and a central component FCES G80.00+0.50, traced by the distribution of ionised gas within the borders of the photo-dissociation regions and with a power law spectrum of index 2.19 ± 0.03 -0.01 +0.00 that is significantly different from the spectrum of FCES G78.74+1.56. An additional extended emission component FCES G78.83+3.57, located on the edge of the central cavities in Cygnus X and with a spectrum compatible with that of FCES G80.00+0.50, is likely related to the cocoon. For the two brightest components FCES G80.00+0.50 and FCES G78.74+1.56, spectra and radial-azimuthal profiles of the emission can be accounted for in a diffusion-loss framework involving one single population of non-thermal particles with a flat injection spectrum. Particles span the full extent of FCES G78.74+1.56 as a result of diffusion from a central source, and give rise to source FCES G80.00+0.50 by interacting with ionised gas in the innermost region. For this simple diffusion-loss model, viable setups can be very different in terms of energetics, transport conditions, and timescales involved, and both hadronic and leptonic scenarios are possible. The solutions range from long-lasting particle acceleration, possibly in prominent star clusters such as Cyg OB2 and NGC 6910, to a more recent and short-lived release of particles within the last 10–100 kyr, likely from a supernova remnant. The observables extracted from our analysis can be used to perform detailed comparisons with advanced models of particle acceleration and transport in star-forming regions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

The effect of saturated thermal conduction on clouds in a hot plasma

We numerically investigate the internal evolution of multiphase clouds, which are at rest with respect to an ambient, highly ionized medium (HIM) representing the hot component of the circumgalactic medium. Time-dependent saturated thermal conduction and its implications like condensation rates and mixing efficiency are assessed in multiphase clouds. Our simulations are carried out by using the adaptive mesh refinement code FLASH. The model clouds are initially in both hydrostatic and thermal equilibrium and are in pressure balance with the HIM. Thus, they have steep gradients in both temperature and density at the interface to HIM leading to non-negligible thermal conduction. Several physical processes are considered numerically or semi-analytically: thermal conduction, radiative cooling and external heating of gas, self-gravity, mass diffusion, and dissociation of molecules and ionization of atoms. It turns out that saturated thermal conduction triggers a continuous condensation irrespective of cloud mass. Dynamical interactions with ambient HIM all relate to the radial density gradient in the clouds: (1) mass flux due to condensation is the higher the more homogeneous the clouds are; (2) mixing of condensed gas with cloud gas is easier in low-mass clouds, because of their shallower radial density gradient; and thus (3) accreted gas is distributed more efficiently. A distinct and sub-structured transition zone forms at the interface between cloud and HIM, which starts at smaller radii and is much narrower as deduced from analytical theory.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

Allgood, Daniel C.↗

NASA NTRS1984

Research on gallium arsenide diffused junction solar cells

The feasibility of using bulk GaAs for the fabrication of diffused junction solar cells was determined. The effects of thermal processing of GaAs was studied, and the quality of starting bulk GaAs for this purpose was assessed. These cells are to be made by open tube diffusion techniques, and are to be tested for photovoltaic response under AMO conditions.

Borrego, J. M.↗

NASA NTRS2005

Length dependence of carbon nanotube thermal conductivity and the "problem of long waves"

We present the first calculations of finite length carbon nanotube thermal conductivity that extend from the ballistic to the diffusive regime, throughout a very wide range of lengths and temperatures. The long standing problem of vanishing scattering of the "long wavelength phonf dramatically here, making the thermal conductivity diverge as the nanotube length increases. We show that the divergence disappears if 3-phonon scattering processes are considered to second or higher order. Nevertheless, for defect free nanotubes, the thermal conductivity keeps increasing up to very large lengths (10 gm at 300 K). Defects in the nanotube are also able to remove the long wavelength divergence.

Evaluation Studies↗

DOE OSTI2014

Effects of carbon on phosphorus diffusion in SiGe:C and the implications on phosphorus diffusion mechanisms

The use of carbon (C) in SiGe base layers is an important approach to control the base layer dopant phosphorus (P) diffusion and thus enhance PNP heterojunction bipolar transistor (HBT) performance. This work quantitatively investigated the carbon impacts on P diffusion in Si₀.₈₂Ge₀.₁₈:C and Si:C under rapid thermal anneal conditions. The carbon molar fraction is up to 0.32%. The results showed that the carbon retardation effect on P diffusion is less effective for Si₀.₈₂Ge₀.₁₈:C than for Si:C. In Si₀.₈₂Ge₀.₁₈:C, there is an optimum carbon content at around 0.05% to 0.1%, beyond which more carbon incorporation does not retard P diffusion any more. This behavior is different from the P diffusion behavior in Si:C and the B in Si:C and low Ge SiGe:C, which can be explained by the decreased interstitial-mediated diffusion fraction f{sub I}{sup P,SiGe} to 95% as Ge content increases to 18%. Empirical models were established to calculate the time-averaged point defect concentrations and effective diffusivities as a function of carbon and was shown to agree with previous studies on boron, phosphorus, arsenic and antimony diffusion with carbon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Thermal transport in 2- and 3-dimensional periodic “holey” nanostructures

Understanding thermal transport in two- and three-dimensional periodic “holey” nanostructures is important for realizing applications of these structures in thermoelectrics, photonics and batteries. In terms of continuum heat diffusion physics, the effective medium theory provides the framework for obtaining the effective thermal conductivity of such structures. However, recently measured nanostructures possess thermal conductivities well below these continuum predictions. In some cases, their thermal conductivities are even lower than predictions that account for sub-continuum phonon transport. We analyze current understanding of thermal transport in such structures, discussing the various theories, the measurements and the insights gained from comparing the two.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Towards Energy-Positive Buildings through a Quality-Matched Energy Flow Strategy

Current strategies for net-zero buildings favor envelopes with minimized aperture ratios and limiting of solar gains through reduced glazing transmittance and emissivity. This load-reduction approach precludes strategies that maximize on-site collection of solar energy, which could increase opportunities for net-zero electricity projects. To better leverage solar resources, a whole-building strategy is proposed, referred to as “Quality-Matched Energy Flows” (or Q-MEF): capturing, transforming, buffering, and transferring irradiance on a building’s envelope—and energy derived from it—into distributed end-uses. A mid-scale commercial building was modeled in three climates with a novel Building-Integrated, Transparent, Concentrating Photovoltaic and Thermal fenestration technology (BITCoPT), thermal storage and circulation at three temperature ranges, adsorption chillers, and auxiliary heat pumps. BITCoPT generated electricity and collected thermal energy at high efficiencies while transmitting diffuse light and mitigating excess gains and illuminance. The balance of systems satisfied cooling and heating demands. Relative to baselines with similar glazing ratios, net electricity use decreased 71% in a continental climate and 100% or more in hot-arid and subtropical-moderate climates. Total EUI decreased 35%, 83%, and 52%, and peak purchased electrical demands decreased up to 6%, 32%, and 20%, respectively (with no provisions for on-site electrical storage). Decreases in utility services costs were also noted. These results suggest that with further development of electrification the Q-MEF strategy could contribute to energy-positive behavior for projects with similar typology and climate profiles.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2002

Disentangling X-Ray Emission Processes In Vela-Like Pulsars

This grant is to support analysis of data from the X-ray Multi-mirror Mission (XMM). Specifically, we have been awarded time to observe two young neutron stars, B1823-13 and B1046-58, whose X-ray emission is expected to be a complicated combination of emission from an associated supernova remnant, from a wind-powered synchrotron nebula, from magnetospheric pulsations, and from the surface of the neutron star itself. It is only with XMM's unique combination of spectral, temporal and angular resolution that all these different processes can be separated and studied. Observations of B1823-13 have been conducted and analyzed. We interpret the data as follows: The unpulsed extended non-thermal nature of the central core argues that the extended source of emission corresponds to synchrotron emission from a nebula powered by the pulsar. The temperature of the diffuse component is too high to be interpreted as thermal emission; we rather argue that this extended component is non-thermal emission from a surrounding supernova remnant shell.

Gaensler, Bryan↗

DOE OSTI2022

Tritium diffusion and formation in the bulk and defective surface of γ-LiAlO2 pellets: First-principles investigation

In tritium-producing burnable absorber rods (TPBAR), γ-LiAlO2 is used in the form of an annular ceramic pellet enriched with the 6Li isotope. When irradiated in a pressurized water reactor (PWR), the 6Li pellets absorb neutrons and produce tritium (3H) through 6Li + n 3H + α. The 3H chemically reacts with the metal getter where it is captured and leads to formation of a metal hydride. For TPBARs to enable effective tritium production in PWRs, we investigated the 3H diffusion pathways in the bulk and surface of γ-LiAlO2 with different concentrations of lithium defects. The calculated results for bulk and low-index surfaces, thermal conductivity, 3H activation energy barriers, and the 3H diffusion coefficients in γ-LiAlO2 are in good agreement with the available experimental values. In the bulk, our results show that the smallest activation energy barrier is 0.63 eV for substitutional 3H diffusion with a diffusion coefficient of 3.25x10-12 m2/s. After 3H diffused from bulk to the surface, it could form different species (such as 3H2, 3H2O, C3H4) depending on the surface structure, vacancy types and the impurity carbon. Our results indicate that the 3H2 is the main product from γ-LiAlO2 pellets. As the number of VLi vacancies and 3H atoms increases under irradiation (3H-rich condition), 3H2O release could increase from the surface of γ-LiAlO2 pellets.

Jia, Ting↗

DOE OSTI2012

Effect of superbanana diffusion on fusion reactivity in stellarators

Fusion reactivity is usually obtained using a Maxwellian distribution. However, energy-dependent radial diffusion can modify the energy distribution. Superbanana diffusion is energy-dependent and occurs in nonaxisymmetric magnetic confinement devices, such as stellarators, because of ripple-trapped particles which can take large steps between collisions. In this paper, the D-T fusion reactivity is calculated using a non-Maxwellian energy distribution obtained by solving the Fokker-Planck equation numerically, including radial superbanana diffusion as well as energy scattering. The ions in the tail of the distribution, with energies larger than thermal, which are most needed for fusion, are depleted by superbanana diffusion. In this paper, it is shown that the D-T fusion reactivity is reduced by tail ion depletion due to superbanana diffusion, by roughly a factor of 0.5 for the parameters used in the calculation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Conclusions • Multimaterial and isotopically-labeled specimens were successfully fabricated via FFF-AM • Raman spectroscopy, atomic force microscopy, and neutron scattering show promise for direct measurements of interlayer diffusion in the multimaterial and isotopically-labeled specimens • Although isotopically-labeled specimens offer the greatest potential for experimentally verifying FFF-AM process models, substituting hydrogen with deuterium alters the thermal and rheological properties of the HDPE polymer

Multimaterial and Isotopically Labeled Specimen Fabrication via Material Extrusion Additive Manufacturing for Interlayer Diffusion Analysis

Jones, Haley W. [Savannah River National Laborator↗

DOE OSTI2018

Simulated Microstructural and Compositional Evolution of U-Pu-Zr Alloys Using the Potts-Phase Field Modeling Technique

U-Pu-Zr alloys are considered ideal metallic fuels for Experimental Breeder Reactors because of their superior material properties and potential for increased burnup performance. However, significant constituent redistribution has been observed in these alloys when irradiated, or subject to a thermal gradient, resulting in inhomogeneity of both composition and phase, which, in turn, alters the fuel performance. The hybrid Potts-phase field method is reformulated for ternary alloys in a thermal gradient and utilized to simulate and predict constituent redistribution and phase transformations in the U-Pu-Zr nuclear fuel system. Simulated evolution profiles for the U-16Pu-23Zr (at%) alloy show concentric zones that are compared with published experimental results; discrepancies in zone size are attributed to thermal profile differences and assumptions related to the diffusivity values used. Twenty-one alloys, over the entire ternary compositional spectrum, are also simulated to investigate the effects of alloy composition on constituent redistribution and phase transformations. The U-40Pu-20Zr (at%) alloy shows the most potential for compositional uniformity and phase homogeneity, throughout a thermal gradient, while remaining in the compositional range of feasible alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2025

CO 2 Capture Characteristics of Hyperbranched Poly(alkylene imine): A Molecular Dynamics Simulation Approach

This study explores the CO 2 capture characteristics of hyperbranched poly(ethylenimine) (HB-PEI) and poly- (propyleneimine) (HB-PPI) through molecular dynamics simulations using density functional theory-calibrated force fields. Key features such as density, free volume, glass transition temperature, CO 2 /H 2 O distribution, and molecular diffusion are systematically investigated to elucidate structure−function relationships under dry and hydrated conditions. HB-PEI demonstrates a slightly higher density and lower free volume compared to HB-PPI yet shows superior CO 2 capture due to the high amine concentration. Glass transition analysis indicates a higher thermal mobility in HBPEI, enhancing the CO 2 diffusivity. Pair correlation and coordination analyses confirm a stronger affinity of CO 2 with primary and secondary amines, particularly in hydrated environments where water competes with CO 2 for binding sites. Despite its more compact structure, HB-PEI outperformed HB-PPI in CO 2 and H 2 O transport, as confirmed by higher diffusion coefficients across all hydration levels. These findings highlight a critical balance among polymer architecture, amine accessibility, and hydration in designing next-generation solid amine sorbents for efficient direct air capture applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Thermodiffusion in concentrated ferrofluids: Experimental and numerical results on magnetic thermodiffusion

Ferrofluids consist of magnetic nanoparticles dispersed in a carrier liquid. Their strong thermodiffusive behaviour, characterised by the Soret coefficient, coupled with the dependency of the fluid's parameters on magnetic fields is dealt with in this work. It is known from former experimental investigations on the one hand that the Soret coefficient itself is magnetic field dependent and on the other hand that the accuracy of the coefficient's experimental determination highly depends on the volume concentration of the fluid. The thermally driven separation of particles and carrier liquid is carried out with a concentrated ferrofluid (φ = 0.087) in a horizontal thermodiffusion cell and is compared to equally detected former measurement data. The temperature gradient (1 K/mm) is applied perpendicular to the separation layer. The magnetic field is either applied parallel or perpendicular to the temperature difference. For three different magnetic field strengths (40 kA/m, 100 kA/m, 320 kA/m) the diffusive separation is detected. It reveals a sign change of the Soret coefficient with rising field strength for both field directions which stands for a change in the direction of motion of the particles. This behaviour contradicts former experimental results with a dilute magnetic fluid, in which a change in the coefficient's sign could only be detected for the parallel setup. An anisotropic behaviour in the current data is measured referring to the intensity of the separation being more intense in the perpendicular position of the magnetic field: S{sub T‖} = −0.152 K{sup −1} and S{sub T⊥} = −0.257 K{sup −1} at H = 320 kA/m. The ferrofluiddynamics-theory (FFD-theory) describes the thermodiffusive processes thermodynamically and a numerical simulation of the fluid's separation depending on the two transport parameters ξ{sub ‖} and ξ{sub ⊥} used within the FFD-theory can be implemented. In the case of a parallel aligned magnetic field, the parameter can be determined to ξ{sub ‖} = (2.8; 9.1; 11.2) × 10{sup −11} · D{sub ‖} kg/(A{sup 2}m) for the different field strengths and in dependence on the magnetic diffusion coefficient D{sub ‖}. An adequate fit in the perpendicular case is not possible, by ξ{sub ⊥} = 1 × 10{sup −17} kg/(Am{sup 2}) a rather good agreement between numerical and experimental data can be found for a field strength of 40 kA/m, a change in the coefficient's sign in the perpendicular setup is not numerically determinable via this theory. The FFD-theory is only partly applicable to calculate the concentration profile in concentrated magnetic fluids established due to a temperature gradient and magnetic field applied.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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↗