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At least 55 records · Page 3

Analytic insights into nonlocal energy transport. III. steady state Fokker Planck theory in spherical and planar geometry

This paper develops an approximate steady state Fokker Planck theory for energetic electron transport in a spherical laser fusion target. First, we apply the theory to only a small population of electrons, which is specified at the outset. Then, one determines the nonlocal electron energy flux of these electrons at a particular position. These energetic electrons may either come from the tail of the thermal distribution function or be generated by an instability. This paper develops two approximate methods of solution, which we call the “characteristic method” and “sparse eigenfunction.” The former works only in planar geometry and the latter in both planar and spherical geometry. Comparison of the two methods in planar geometry shows that even though the approximations are very different, they give about the same result, increasing their credibility. For the example we have chosen, spherical effects are not important for electrons from the tail of the distribution function but may well be for instability generated electrons, which have much higher energy. Comparing planar to spherical, one finds an additional spherical barrier protecting the fuel. It turns out that the associated fuel preheat a Fokker Planck model predicts is considerably less than that predicted by the Krook models as developed at both NRL and other places.

Manheimer, Wallace (ORCID:0000000163342591)↗

Stellarator fusion systems enabled by arrays of planar coils

We present an overview of a novel electromagnetic coil configuration for stellarators and its application to two near-term fusion systems. The novel coil configuration is the planar coil stellarator, able to implement precisely-quasisymmetric 3D magnetic fields using a set of planar, plasma-encircling coils and a set of planar, field-shaping coils situated on a surface surrounding the plasma. This configuration combines the stellarator’s advantages of steady-state operation, stability, low recirculating power fraction, and a mature physics basis, with the benefits of using simpler, planar coils which allow for a maintenance scheme leveraging large ports, and the ability to control magnets individually. The initial near-term use case considered is a steady state deuterium–deuterium stellarator neutron source, called Eos. The second near-term use case considered is a deuterium–tritium stellarator fusion pilot plant, called Helios, that would be approximately twice the linear dimension of the Eos design.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A New Route Toward Atomically Flat and Defect-Free Ge/SiGe Planar Heterostructures

Germanium-based planar heterostructures are emerging as versatile platforms for realizing quantum devices. In particular, planar Ge/SiGe quantum wells (QWs) host hole states with exceptionally high mobility and strong, electrically tunable spin–orbit interactions, enabling full electrical control of quantum information. A key requirement for these systems is the growth of microscopic, defect-free, atomically flat Ge QW heterostructures on relaxed or reverse-graded SiGe buffer layers, as well as on commercial Ge substrates. While several physical deposition techniques have demonstrated high-quality planar Ge/SiGe QWs, a major challenge remains: minimizing defect density typically requires high growth temperatures, which are incompatible with standard CMOS process flows. Here, we present a convenient low-temperature process for realizing high-quality planar SiGe/Ge heterostructures using a combination of thermal and electron-beam evaporation. We systematically map the effects of ex-situ and in-situ substrate preparation protocols, growth temperature, and post-deposition annealing conditions, and correlate these parameters with surface roughness and defect density. We find that in-situ oxide desorption conditions and post-annealing parameters have the most pronounced impact on improving surface quality. Under optimized conditions, we achieve atomically smooth surfaces with root-mean-square roughness σrms​ ≤ 10 Å and negligible defect density. Interestingly, thermally evaporated Ge layers exhibit oriented triangular crystallites that elongate upon post-annealing in the presence of high Ge vapor pressure. These results demonstrate that this simple, low-temperature deposition approach is a viable and effective route for achieving high-quality Ge QW heterostructures, with strong potential for scalable quantum computing and sensing applications.

Tripathi, Malvika [Fermilab] (ORCID:00000001989251↗

A New Route Toward Atomically Flat and Defect-Free Ge/SiGe Planar Heterostructures

Germanium-based planar heterostructures are emerging as versatile platforms for realizing quantum devices. In particular, planar Ge/SiGe quantum wells (QWs) host hole states with exceptionally high mobility and strong, electrically tunable spin–orbit interactions, enabling full electrical control of quantum information. A key requirement for these systems is the growth of microscopic, defect-free, atomically flat Ge QW heterostructures on relaxed or reverse-graded SiGe buffer layers, as well as on commercial Ge substrates. While several physical deposition techniques have demonstrated high-quality planar Ge/SiGe QWs, a major challenge remains: minimizing defect density typically requires high growth temperatures, which are incompatible with standard CMOS process flows. Here, we present a convenient low-temperature process for realizing high-quality planar SiGe/Ge heterostructures using a combination of thermal and electron-beam evaporation. We systematically map the effects of ex-situ and in-situ substrate preparation protocols, growth temperature, and post-deposition annealing conditions, and correlate these parameters with surface roughness and defect density. We find that in-situ oxide desorption conditions and post-annealing parameters have the most pronounced impact on improving surface quality. Under optimized conditions, we achieve atomically smooth surfaces with root-mean-square roughness σrms​ ≤ 10 Å and negligible defect density. Interestingly, thermally evaporated Ge layers exhibit oriented triangular crystallites that elongate upon post-annealing in the presence of high Ge vapor pressure. These results demonstrate that this simple, low-temperature deposition approach is a viable and effective route for achieving high-quality Ge QW heterostructures, with strong potential for scalable quantum computing and sensing applications.

Tripathi, Malvika [Fermilab] (ORCID:00000001989251↗

Numerical method to calculate the induced drag or optimum loading for arbitrary non-planar aircraft

A simple unified numerical method applicable to non-planar subsonic aircraft has been developed for calculating either the induced drag for an arbitrary loading or the optimum aircraft loading which results in minimum induced drag. The method utilizes a vortex lattice representation of the aircraft lifting surfaces coupled with the classic equations and theorems for computing and minimizing induced drag. Correlation of results from the numerical method with non-planar solutions obtained from other more complex theories indicates very good agreement. Comparison of the induced-drag computations using the numerical method with experimental data for planar and non-planar configurations was also very good.

Blackwell, J. A., Jr.↗

Planar GaAs diodes for THz frequency mixing applications

Schottky barrier diodes for terahertz applications are typically fabricated as a micron to sub-micron circular anode metallization on GaAs which is contacted with a sharp wire (whisker). This structure has the benefits of the simplicity of the fabrication of the diode chip, the minimal shunt capacitance of the whisker contact and the ability of the whisker wire to couple energy to the diode. However, whisker-contacted diodes are costly to assembly and difficult to qualify for space applications. Also, complex receiver systems which require many diodes are difficult to assemble. The objective of this paper is to discuss the advantages of planar Schottky diodes for high frequency receiver applications and to summarize the problems of advancing the planar technology to the terahertz frequency range. Section 2 will discuss the structure, fabrication and performance of state-of-the-art planar Schottky diodes. In Section 3 the problems of designing and fabricating planar diodes for terahertz frequency operation are discussed along with a number of viable solutions. Section 4 summarizes the need for further research and cooperation between diode designers and RF engineers.

Bishop, William L.↗

Interplanetary planar magnetic structures associated with expanding active regions

Planar magnetic structures are interplanetary objects whose magnetic field cannot be explained by Parker's solar wind model. They are characterized by two-dimensional structure of magnetic field that are highly variable and parallel to a plane which is inclined to the ecliptic plane. They appeared independently of interplanetary compression, solar flares, active prominences nor filament disappearances, but the sources often coincided with active regions. On the other hand, it has been discovered by the Yohkoh Soft X-ray telescope that active-region corona expand outwards at speeds of a few to a few tens of km/s near the Sun. The expansions occurred repeatedly, almost continually, even in the absence of any sizable flares. In the Yohkoh Soft X-ray images, the active-region corona seems to expand out into interplanetary space. Solar sources of interplanetary planar magnetic structures observed by Sakigake were examined by Yohkoh soft X-ray telescope. During a quiet period of the Sun from January 6 to November 11, 1993, there found 5 planar magnetic structures according to the criteria (absolute value of Bn)/(absolute value of B) less than 0.1 for planarity and (dB)/(absolute value of B) greater than 0.7 for variability of magnetic field, where Bn, dB, and the absolute value of B are field component normal to a plane, standard deviation, and average of the magnitude of the magnetic field, respectively. Sources of 4 events were on low-latitude (less than 5 degrees) active regions from which loop-like structures were expanding. The coincidence, 80%, is extremely high with respect to accidental coincidence, 7%, of Sakigake windows of solar wind observation with active regions. The last source was on loop-like features which seemed to be related with a mid-latitude (20 degrees) active region.

Nakagawa, Tomoko↗

Planar Strain-Rate-Free Diffusion Flames: Initiation, Properties, and Extinction

An effectively strain-rate-free diffusion flame constitutes the most vigorous laminar combustion of initially unmixed reactive gases. Such a diffusion flame is characterized by a relatively long residence time and by a relatively large characteristic length scale. If such a flame were also planar, providing high symmetry, it would be particularly suitable for experimental and theoretical investigations of key combustion phenomena, such as multicomponent diffusion, chemical kinetics, and soot inception, growth, and oxidation. Unfortunately, a planar strain-rate-free diffusion flame is highly disrupted in earth-gravity (e.g., in a counterflow-diffusion-flame apparatus) because of the very rapid onset (approx. 100 ms) of gravity-induced instability. Accordingly, a specially dedicated apparatus was designed, fabricated, and initially checked out for the examination of a planar strain-rate-free diffusion flame in microgravity. Such a diffusion flame may be formed within a hollowed-out squat container (initially configured as 25 cm x 25 cm x 9 cm), with isothermal, noncatalytic, impervious walls. At test initiation, a thin metallic sheet (approx. 1 mm in thickness) that separates the internal volume into two equal portions, each of dimensions 25 cm x 25 cm x 4.5 cm, is withdrawn, by uniform translation (approx. 50 cm/s) in its own plane, through a tightly fitting slit in one side wall. Thereupon, diluted fuel vapor (initially confined to one half-volume of the container) gains access to diluted oxygen (initially with the same pressure, density, and temperature as the fuel, but initially confined to the other half-volume). After a brief delay (approx. 10 ms), to permit limited but sufficient-for-flammability diffusional interpenetration of fuel vapor and oxidizer, burning is initiated by discharge of a line igniter, located along that side wall from which the trailing edge of the separator withdraws. The ignition spawns a triple-flame propagation across the 25 cm x 25 cm centerplane. When a diffusion flame is emplaced in the centerplane, any subsequent travel, and change in temperature, of that planar diffusion flame may be tracked, along with the effectively spatially uniform but temporally evolving pressure within the container. Eventually, nearly complete depletion of the stoichiometrically deficient reactant, along with heat loss to the container surfaces, effects extinction. These data afford an opportunity to check theoretical models of diffusion and chemical kinetics under conditions ranging from intense burning to flame out, or, alternatively, to evolve simple empirical representations of these phenomena. Thus, the project sought to utilize microgravity testing to elucidate commonly encountered phenomenology, arising in the commonly-encountered mode of combustion (whether related to heating, manufacturing, boiling, and propulsion, or to uncontrolled, free-burning fire in structures and wildland vegetation), of those commonly utilized fuels usually categorized as gaseous fuels (such as hydrogen, natural gas, and propane, which are gaseous under atmospheric conditions).

Fendell, Francis↗

Piecewise-Planar Parabolic Reflectarray Antenna

The figure shows a dual-beam, dualpolarization Ku-band antenna, the reflector of which comprises an assembly of small reflectarrays arranged in a piecewise- planar approximation of a parabolic reflector surface. The specific antenna design is intended to satisfy requirements for a wide-swath spaceborne radar altimeter, but the general principle of piecewise-planar reflectarray approximation of a parabolic reflector also offers advantages for other applications in which there are requirements for wideswath antennas that can be stowed compactly and that perform equally in both horizontal and vertical polarizations. The main advantages of using flat (e.g., reflectarray) antenna surfaces instead of paraboloidal or parabolic surfaces is that the flat ones can be fabricated at lower cost and can be stowed and deployed more easily. Heretofore, reflectarray antennas have typically been designed to reside on single planar surfaces and to emulate the focusing properties of, variously, paraboloidal (dish) or parabolic antennas. In the present case, one approximates the nominal parabolic shape by concatenating several flat pieces, while still exploiting the principles of the planar reflectarray for each piece. Prior to the conception of the present design, the use of a single large reflectarray was considered, but then abandoned when it was found that the directional and gain properties of the antenna would be noticeably different for the horizontal and vertical polarizations.

Hodges, Richard↗

Theory of a Traveling Wave Feed for a Planar Slot Array Antenna

Planar arrays of waveguide-fed slots have been employed in many radar and remote sensing applications. Such arrays are designed in the standing wave configuration because of high efficiency. Traveling wave arrays can produce greater bandwidth at the expense of efficiency due to power loss in the load or loads. Traveling wave planar slot arrays may be designed with a long feed waveguide consisting of centered-inclined coupling slots. The feed waveguide is terminated in a matched load, and the element spacing in the feed waveguide is chosen to produce a beam squinted from the broadside. The traveling wave planar slot array consists of a long feed waveguide containing resonant-centered inclined coupling slots in the broad wall, coupling power into an array of stacked radiating waveguides orthogonal to it. The radiating waveguides consist of longitudinal offset radiating slots in a standing wave configuration. For the traveling wave feed of a planar slot array, one has to design the tilt angle and length of each coupling slot such that the amplitude and phase of excitation of each radiating waveguide are close to the desired values. The coupling slot spacing is chosen for an appropriate beam squint. Scattering matrix parameters of resonant coupling slots are used in the design process to produce appropriate excitations of radiating waveguides with constraints placed only on amplitudes. Since the radiating slots in each radiating waveguide are designed to produce a certain total admittance, the scattering (S) matrix of each coupling slot is reduced to a 2x2 matrix. Elements of each 2x2 S-matrix and the amount of coupling into the corresponding radiating waveguide are expressed in terms of the element S11. S matrices are converted into transmission (T) matrices, and the T matrices are multiplied to cascade the coupling slots and waveguide sections, starting from the load end and proceeding towards the source. While the use of non-resonant coupling slots may provide an additional degree of freedom in the design, resonant coupling slots simplify the design process. The amplitude of the wave going to the load is set at unity. The S11 parameter, r of the coupling slot closest to the load, is assigned an arbitrary value. A larger value of r will reduce the power dissipated in the load while increasing the reflection coefficient at the input port. It is now possible to obtain the excitation of the radiating waveguide closest to the load and the coefficients of the wave incident and reflected at the input port of this coupling slot. The next coupling slot parameter, r , is chosen to realize the excitation of that radiating waveguide. One continues this process moving towards the source, until all the coupling slot parameters r and hence the S11 parameter of the 4-port coupler, r, are known for each coupling slot. The goal is to produce the desired array aperture distribution in the feed direction. From an interpolation of the computed moment method data for the slot parameters, all the coupling slot tilt angles and lengths are obtained. From the excitations of the radiating waveguides computed from the coupling values, radiating slot parameters may be obtained so as to attain the desired total normalized slot admittances. This process yields the radiating slot parameters, offsets, and lengths. The design is repeated by choosing different values of r for the last coupling slot until the percentage of power dissipated in the load and the input reflection coefficient values are satisfactory. Numerical results computed for the radiation pattern, the tilt angles and lengths of coupling slots, and excitation phases of the radiating waveguides, are presented for an array with uniform amplitude excitation. The design process has been validated using computer simulations. This design procedure is valid for non-uniform amplitude excitations as well.

Rengarajan, Sembiam↗

PRINTED, PLANAR MICROWAVE CONNECTOR WITH MULTIPLE SIGNAL LINES

Microwave connectors with a planar geometry have been demonstrated using additive manufacturing techniques. This planar form factor is expected to enable connectors to be integrated directly with other components onto a printed circuit board. The connectors were developed with multiple signal lines that will increase the density of signal connections to PCBs, eliminating the physical constraints of single-signal COTS microwave connectors. This work developed electromagnetic models (using Ansys HFSS) of these planar connectors to predict performance and optimize connector design. Materials and printing processes were developed to fabricate the connectors based on high-temperature PEEK thermoplastics. The multiple signal connectors were designed to operate over the 1-6GHz band and are built upon the single signal printed planar geometry connector introduced in a previous paper [1].

Additive Manufacturing↗

Planar, curved and twisted molecular nanographenes: Reduction-induced alkali metal coordination

Planar and curved polycyclic aromatic hydrocarbons (PAHs) attract significant attention as molecular models of fullerenes, carbon nanotubes, and graphene, thus stimulating broad investigation of chemical reactivity and materials applications of designed nanocarbon π-systems. Non-planar molecular nanographenes (NGs) recently emerge as advanced anode materials in energy storage, showing high reduction limits and enhanced alkali metal intercalation levels. However, the lack of direct structure–property correlations in such complex hybrid systems impedes their further development and utilization. With a focus on alkali-metal-induced reduction of selected PAHs, we herein review original metal binding and intercalation trends, site specific coordination, and distinct carbon framework responses to stepwise electron uptake. Small planar graphene fragments, like triphenylene and coronene, are compared to π-expanded hexabenzocoronenes, followed by the discussion of bowl-shaped corannulene, sumanene and other carbon bowls, as well as bent, warped, and twisted molecular nanographenes. The effect of size, symmetry, and framework topology along with the structural deformation of carbon backbones upon reduction are analyzed, using recent crystallographic examples of alkali-metal intercalated products. In conclusion, the revealed insights into the structures, binding, and metal intercalation in molecular nanographenes should stimulate their future applications as new functional materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigation on gate oxide reliability under gate bias screening for commercial SiC planar and trench MOSFETs

This paper evaluates the impact of the fast high gate-voltage screening technique on gate oxide reliability of commercial 1.2 kV 4H-SiC power metal-oxide-semiconductor field-effect transistors (MOSFETs) with planar and trench gate structures. The measurements are conducted on packaged devices with the intent that the results will be applicable to wafer-level screening. The threshold voltage (V th ) of SiC MOSFETs is measured before and after various screening treatments and recovery process. In addition, constant-voltage time-dependent dielectric breakdown (TDDB) measurements are performed on SiC MOSFETs to obtain the intrinsic lifetime of gate oxide. The objective of this study is to determine the optimal screening conditions and improve screening efficiency without degradation of gate oxide reliability, such as V th shift and reduced oxide intrinsic lifetime. Due to the differences in the gate oxidation process and structural design of SiC planar and trench MOSFETs, the two types of devices exhibit different oxide reliability in the screening process. The recommended screening conditions obtained in this paper reveal that SiC trench MOSFETs can accept higher screening voltages compared to SiC planar MOSFETs. Hence, it can be concluded that more efficient screening techniques can be adopted for SiC MOSFETs with thicker gate oxide to meet the requirements of industrial applications.

36 MATERIALS SCIENCE↗

Planar defect-driven electrocatalysis of CO 2 -to-C 2 H 4 conversion

The selectivity towards a specific C 2+ product, such as ethylene (C 2 H 4 ), is sensitive to the surface structure of copper (Cu) catalysts in carbon dioxide (CO 2 ) electro-reduction. The fundamental understanding of such sensitivity can guide the development of advanced electrocatalysts, although it remains challenging at the atomic level. In this work, we demonstrated that planar defects, such as stacking faults, could drive the electrocatalysis of CO 2 -to-C 2 H 4 conversion with higher selectivity and productivity than Cu(100) facets in the intermediate potential region (–0.50 ~ –0.65 V vs. RHE). The unique right bipyramidal Cu nanocrystals containing a combination of (100) facets and a set of parallel planar defects delivered 67% faradaic efficiency (FE) for C 2 H 4 and a partial current density of 217 mA cm –2 at –0.63 V vs. RHE. In contrast, Cu nanocubes with exclusive (100) facets exhibited only 46% FE for C 2 H 4 and a partial current density of 87 mA cm –2 at an identical potential. Both ex situ CO temperature-programmed desorption and in situ Raman spectroscopy analysis implied that the stronger *CO adsorption on planar defect sites facilitates CO generation kinetics, which contributes to a higher surface coverage of *CO and in turn an enhanced reaction rate of C–C coupling towards C 2+ products, especially C 2 H 4 .

36 MATERIALS SCIENCE↗

Analysis of Crystalline Defects Caused by Growth on Partially Planarized Spalled (100) GaAs Substrates

We analyze the effect of growth on non-(100) surfaces resulting from incomplete planarization of spalled GaAs wafers on the defect structure of GaAs solar cell layers grown by hydride vapor phase epitaxy (HVPE). Controlled spalling of (100)-oriented GaAs has the potential to reduce substrate costs for III-V epitaxy; however, it creates regularly faceted surfaces that may complicate the growth of high-quality III-V optoelectronic devices. We leverage the anisotropic growth rate of HVPE to planarize these faceted GaAs substrates, reducing the surface roughness and degree of faceting. We observe degraded solar cell performance and material quality in sample areas where facets are not completely removed. We used dark lock-in thermography and photoluminescence to identify recombination in areas that were not fully planarized. We used cathodoluminescence to identify the presence of extended defects in these regions, which are correlated with bandgap fluctuations in the material. We hypothesize that these defects were created by strain from compositional fluctuations in ternary alloys grown on the faceted surfaces. This work elucidates the potential issues of solar cells grown on faceted surfaces and builds understanding toward realizing high performance III-V photovoltaics with the cost-reduction potential of controlled spalling.

14 SOLAR ENERGY↗

Trigonal Planar Bis (carbene)Cu(I) Complexes Enable Divergent H 2 Activation with H 2 O for Accelerated Olefin Hydrogenation

CuH-catalyzed olefin hydrogenation is rare compared to those of carbonyl-derived substrates. Olefin insertion into Cu–H to form Cu-alkyl is ubiquitous; however, subsequent H 2 activation remains unknown to our knowledge. Herein, we investigated the transformations of β-H elimination, H 2 cleavage, and catalytic olefin hydrogenation in a series of linear and trigonal planar Cu(I)-alkyl complexes supported by monodentate N-heterocyclic carbene and bidentate naphthyridine- bis (carbene) ligands, respectively. Contrary to unreactive linear species, trigonal planar variants promote β-H elimination, hydrogenolysis, and catalytic hydrogenation of unactivated alkenes at mild temperatures and H 2 pressure. The rare isolation of a naphthyridine- bis (carbene)CuH monomer further affirms two predominant competing pathways for H 2 cleavage of metal–ligand cooperativity at Cu(I)-alkyl or internal electrophilic substitution at Cu(I)-OH. Employing either isolated or in situ generated Cu(I)-OH complex, via protonolysis of alkyl precatalyst by adventitious water, significantly accelerated catalysis compared to that operating primarily by the metal–ligand cooperativity pathway. DFT calculations and energy decomposition analysis on the disparate β-H elimination reactivity between linear and trigonal planar tert-butyl complexes and the mechanism of H 2 activation at a hydroxide complex, indicate that coordination geometry at Cu(I) and properties of the naphthyridine- bis (carbene) ligand are integral to the transformations reported here.

ALMO-EDA↗

Cover Feature: New Noncentrosymmetric Tetrel Pnictides Composed of Square-Planar Gold(I) with Peculiar Bonding (Chem. Eur. J. 26/2021)

Compared to common types of Au(I) coordination, such as linear, trigonal planar, and tetrahedral units observed in extended solids, the square planar coordination is rare. Au(I)relia, shown in the cover image, exhibits the 3-centered bonding of Au-Tt-Au and Au-Pn-Au (on her feathers), square planar cis-[AuTt2Pn2] units (her pendant), and linear …-Au-Au-Au-… chains (her legs) that are characteristic of the novel equiatomic AuSiAs, AuGeP, and AuGeAs compounds. The image was created by designer Grant Luhmann.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Emulation of radiation transport in 3D stochastic media using 1D planar Monte Carlo stochastic media radiation transport algorithms

A subset of stochastic media radiation transport problems involves those in which radiation is incident on a thin slab of stochastic material. Particle tracking in 3D for such problems is expensive, and 1D planar models lack accuracy because they only allow the material to change in one dimension. Therefore, we propose dimensional emulation, which through a slight modification allows existing 1D planar geometry stochastic media radiation transport models to reproduce results from the equivalent 3D models by allowing the material to change in all three dimensions, reproducing the fidelity of the 3D model for the low computational cost of the 1D planar model. In this work, we apply dimensional emulation to three Monte Carlo stochastic media radiation transport models: Chord Length Sampling (CLS), the Local Realization Preserving method (LRP), and a variant of Conditional Point Sampling (CoPS). For a common Markovian benchmark set, the 3D emulation variants of these algorithms are numerically verified to reproduce the results of the 3D variants within statistics while running 1.3 to 2 times faster in the implementation within Sandia National Laboratories open-source research code PlaybookMC. The 3D emulation variants are also shown to yield a 72%–92% reduction in error for the thin slab problems in comparison to the 1D benchmark. As a result, the 3D emulation variant of CLS and CoPS-1 are shown to reproduce 3D CLS results that were used to approximate results for a 3D spherical inclusion geometry benchmark set.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗