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At least 541 records · Page 30

Gas-Gap Calorimeter Sizing and Rating Tools for Heat Pipe Experimentation

Effective gas-gap calorimeter sizing and rating tools are required to design calorimeters that enable well-defined operating conditions, high cooling powers, and accurate calorimetry. The present report describes two tools utilizing Microsoft Excel and MathWorks MATLAB that enable the sizing and rating of gas-gap calorimeters with a He-Ar binary gas mixture in the gap. The Excel tools are two easy-to-use spreadsheets for calculating heat pipe operating temperature or He-Ar mole fractions given the required inputs. The MATLAB tool includes similar models with more robust solution algorithms along with sub-options for full-vacuum, static gas-gap, and forced circulation in the gas-gap. The accuracy of the developed tools were demonstrated by comparing with existing work in literature. The MATLAB tool was used for a parametric study to determine the gas-gap thickness, coolant gap thickness, coolant flow rate, and coolant inlet temperatures for the testing of a 3/4 in outer diameter heat pipe up to powers of 10 kW and temperatures of 1,000°C. The effects of heat pipe and calorimeter inner shell surface emissivities were investigated, considering the inability to control or accurately measure surface emissivities in most applications. It was found that controlling the He-Ar mole fractions provides a wide operating range for gas-gap thicknesses around ~ 0.042--0.090 in (~ 1.07--2.29 mm) for a surface emissivity range of 0.4--0.8, since conduction heat transfer is a significant fraction of the heat transfer across the gas-gap. In addition, it was found that turbulent flow in the coolant gap is needed at high input powers to prevent shell temperatures from approaching the boiling temperature of the water coolant. The parametric study resulted in choosing stainless steel tubes with an outer diameter and thickness of 1 x 0.065 in as the inner shell, and a 1-1/2 x 0.156 in as the outer shell of the calorimeter. Overall, this report presents the necessary information for the sizing and rating of gas-gap calorimeters with He-Ar mixtures for the testing of high-temperature heat pipes (~ 500--1,000°C).

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Optimizing Power Reclamation of Micro Hydro Turbines in WWTPs Aeration Basins

Abstract This study investigates the optimum operating conditions and design configurations that can optimize the power reclaimed by small hydro turbines derived by the rising water-bubble current. The rising current is generated by the compressed air introduced by the diffusers at the bottom of aeration basins of Wastewater Treatment Plants (WWTPs). While optimizing the power production, the standard oxygen transfer efficiency (SOTE) is monitored since it is a significant parameter that cannot be sacrificed in the operation of WWTPs. Using one set of turbine blades, it was found out that the highest velocity is obtained in the upper half of the water column (70% - 80%). In contrast, the lowest velocities were obtained just above the air diffuser and at the water surface. Testing started with using a single turbine (ST) to determine the location of the optimum power reclaimed at each tested airflow (1.18, 1.42, 1.65, and 1.89 L/s). Then using double turbine (DT) and triple turbine (TT) to compare their performance to the ST’s maximum power increased power reclamation. The maximum percentage of increase in power reclamation for DT is 19.59%, while it is 20.24% in the case of TT. At a commonly used airflow in WWTPs (1.42 L/s), the optimum configurations of DTs and TTs were selected to investigate the effect of having the proposed setup on the SOTE. For membrane diffusers, DTs and TTs limited the dispersion of the air bubbles in the tank, therefore, reducing the SOTE (8.3% for DT and 3.7% for the TT). The ceramic and sharp-nub diffusers were also tested versus rubber membrane ones to determine the effect of using the ceramic and sharp-nub diffusers on the power reclamation and SOTE. Ceramic diffusers neither achieve higher power reclamation than the membrane nor increases the SOTE. In contrast, sharp-nub diffusers increase the SOTE for all configurations compared to membranes, but this came into account of power reclamation, where sharp-nub diffusers cause a DT and a TT to produce less power than ST does.

Energy & Fuels↗

Plasma Wall Interaction with 3-D Plasma Boundaries

The interaction of the edge plasma and the material surfaces is one of the most critical challenges on the path to harness fusion power as new, fundamental energy source. This challenge typically combines the thrust to reach high density, low temperature (detached) plasmas in front of the divertor target plates as well as understanding the plasma material interaction (PMI) in particular in this regime. The combination of both research thrusts represents an extraordinarily challenging subject encompassing spatial scales spanning nanometers to meters in all states of matter and across a broad energy range. Modeling capabilities, which help to interpret data from nowadays experiments and enable extrapolation to future devices are urgently required. This is in particular true for toroidal magnetic confinement devices with three-dimensional (3D) plasma boundaries. Such plasma boundary geometries occur in tokamaks, when small amplitude magnetic perturbations are used to stabilize the unruly edge plasma or in stellarators, that are inherently 3D plasma confinement devices. In this project, the impact of 3D plasma boundaries on the plasma material interaction (PMI) was assessed. This work focused on plasma boundary conditions, in which high-density conditions at the material surfaces yield mitigation of the otherwise immense heat and particle loads that these materials would see. These so-called high recycling and eventually detached plasma regimes are of great interest for future reactor operation. In the project, key features that are unique to 3D boundaries were explored in comparison to canonically assumed axisymmetric plasma edge situations in tokamaks. In particular, the relevance of the 3D boundary situation in the extrapolation to the plasma boundary solution at ITER, the next step fusion energy experiment under construction as a multi-national, world-wide large-science experiment in southern France, has been explored. The EMC3-EIRENE plasma edge fluid and kinetic neutral transport code has been advanced to cope with the challenging and unprecedented conditions in the ITER boundary plasma including 3D fields that are planned to be used to suppress harmful edge instabilities, the so-called edge localized modes. This is a vital integration challenge for ITER and the results from this grant have provide a leading capability for this assessment. It was shown that the detachment process in a 3D edge solution for ITER follows the recycling regimes that are known from axisymmetric solutions, but that multiple plasma exhaust channels connected to the material surfaces are established which feature individual recycling characteristics. Because these channels touch the material surfaces in the divertor in a 3D geometry, the compatibility with the plasma material interaction (PMI), including erosion and impurity generation has been found to be an important part of the integration challenge. To address this, the fully 3D plasma material interaction code ERO2 has been adapted to these ITER specific geometries and a homogeneous mixing model was implemented, that allows to consider the mixing of Be and Was used at ITER in the PMI modeling. This model enhancement has been used to study non-local migration of Be in the JET ITER like wall configuration and it has been shown that with this model such complex migration processes in ITER relevant plasma shapes and with ITER relevant plasma boundary conditions can be addressed. The combined modeling approach using EMC3-EIRENE as a plasma boundary transport code and the ERO2 specialized PMI model will be an asset for the continued preparations of ITER operation as well as for Fusion Pilot Plant efforts that have emerged in the U.S. during the evolution of this grant. The predictive capability of this numerical tool has been validated at the DIII-D US national fusion facility. Here, dedicated plasma edge diagnostics were implemented to measure the impurity household around a 3D edge plasma during ELM suppression by 3D fields. Dedicated experiments with local material probes using these diagnostics and the state-of-the-art suite of boundary measurements at DIII-D have shown that the 3D perturbation of the plasma edge that is excreted by such 3D control fields yield a perturbation of the plasma boundary flux structure and hence also of the resulting PMI. The 3D boundary plasma is composed out of helical magnetic flux channels that intersect the divertor targets at an angle relative to the main guiding field, i.e., the toroidal magnetic field component of the tokamak. A similar effect has been measured as well on limiter surfaces during the startup campaign at the new stellarator experiment Wendelstein 7-X. These experiments ad initial analysis with the ERO plasma material interaction model, suggested that the place of erosion for a given particle from the surface and its re-deposition can be different in such 3D field geometries yielding potentially a significant level of net-erosion. This is not the case for axisymmetric solutions, where it was shown in the past that the eroded particles are effectively re-deposited into gaps produced by erosion at the same position and hence the net-erosion levels are small. For ITER, the quest to suppress the ELMs and at the same time maintain the integrity of the divertor is an issue, which these fundamental findings will help to resolve. The coupling of this work to the extrapolation in the ITER program has been addressed by both the PI and the lead numerical scientist being ITER Science Fellows in the duration of the contract and forward. A second focus in the exploration of 3D boundary effects on tokamaks and stellarators has been set on the measurement of helium exhaust features with such 3D fields. This is important because He represents the ash of the fusion process and needs to be exhausted. It was shown that 3D field application compatible with suppression of ELMs yields an increase of the helium exhaust performance. The ratio of the effective helium confinement time over the energy confinement time was reduced by almost 50% which demonstrated that the impact of helium accumulation in the plasma core with respect to the confinement of energy to sustain the fusion reaction is significantly improved with such 3D control fields. It was shown that this is the case for tokamaks as well as stellarators. At the Large helical Device in Japan, a similar enhancement of the helium exhaust features when small amplitude additional 3D fields were applied was measured. This is an important additional function of 3D field application and its impact on ITER is presently being studied in combination with investigations of helium exhaust in 3D field geometries of stellarator devices.

3D plasma edge transport↗

Model-based real-time surface heat flux and temperature estimation for the DIII-D tokamak

A control-oriented model for monitoring of wall power flux densities on the DIII-D tokamak has been successfully implemented and validated experimentally. Future reactors will have to withstand severe steady state high heat flux loads on plasma-facing components (PFCs). Due to the difficulty of directly-measuring local heat fluxes on these components, monitoring and protection of PFCs during the plasma discharge can benefit from simplified physics-based real-time (RT) functional models to estimate and guide heat load control. As a first step into the development, a control-oriented model for monitoring of wall power flux densities and temperatures on DIII-D tokamak has been successfully implemented. The paper discusses the experimental demonstration and comparison of the 2-D model-based wall heat flux algorithm on the DIII-Dinner wall limiter (IWL) against infra-red camera heat flux measurements for limited plasma configurations. The paper also reports on the benchmarking of the field line tracing environment, SMITER, developed at ITER organization on DIII-D tokamak against experimental IR diagnostic data and the derivation of the component shaping weighting factors for the 2-D model-based approach. Here, the extension of the model-based approach for surface temperature estimation on the DIII-D IWL is also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Flexible Fabric-Based IDC Sensors for Conformal Curved Surface Applications

Interdigital capacitor (IDC) sensors are attractive in-situ sensors that can be used to measure permittivity variations in materials. Such sensors could be powerful enablers for cable insulation aging detection. Since insulation aging is correlated with a change in its material permittivity an IDC can measure that change via its measured capacitance. A new thin, flexible fabric-based IDC sensor is introduced for application on conformal curved surfaces such as an electrical cable surface. A multielectrode IDC and its backplane were fabricated using conductive copper polyester taffeta fabrics that were adhesively bonded to nonconductive polyester fabric. The sensor because of its soft flexible structure eliminates the problem of sensor conductor damage which is common for printed circuit board (PCB) type sensors when conformed to the surface of a cable. It also significantly reduces the airgap between the electrodes and the surface that they must contact in order to measure the capacitance. Airgap reduction and consistency are important in order to accurately predict permittivity variations in cable insulation material due to aging. Both PCB-based sensors and the new fabric-based sensors were built and tested on unaged cables and cables that underwent accelerated aging. Results demonstrate the proposed advantages of the novel fabric-based IDC sensor.

interdigital capacitor sensor, IDC, NDE, PCB senso↗

A Review of the Influence of Processing Parameters on ODS Steels Produced via Additive Manufacturing Techniques

Abstract This paper reviews current observations regarding processing conditions for oxide dispersion-strengthened steels consolidated through additive manufacturing techniques. Variations in ODS steels observed across process parameters include changes in grain size, grain texture, oxide size, density of oxides, porosity, melt pool characteristics, and mechanical properties. These properties were then compared across techniques to understand which techniques and processing conditions lead to the highest strength, ductility, and oxide density. Current literature suggests that a mix of grain types, in the form of either morphology or phase, can significantly increase the strength of printed ODS steels. Meanwhile, the most ductile samples, regardless of consolidation technique or matrix material, were made from feedstock with oxide additions located on the powder surface. Reported grain and oxide sizes were plotted against the ratio of laser power to scan speed, volumetric energy density, and normalized enthalpy. No strong correlation between these values and microstructural features was observed. The plots that were made suggest that a larger data set, more in-depth representative equations, and more defined material properties as a function of specific feedstock used are necessary to determine a value that can be correlated to the printed ODS steel microstructure.

deJong, Matthew↗

Optimization of stochastic feature properties in laser powder bed fusion

Process parameter selection in laser powder bed fusion (LPBF) controls the as-printed dimensional tolerances, pore formation, surface quality and microstructure of printed metallic structures. Measuring the stochastic mechanical performance for a wide range of process parameters is cumbersome both in time and cost. As such, in this study, we overcome these hurdles by using high-throughput tensile (HTT) testing of over 250 dogbone samples to examine process-driven performance of strut-like small features, ~1 mm 2 in austenitic stainless steel (316 L). The output mechanical properties, porosity, surface roughness and dimensional accuracy were mapped across the printable range of laser powers and scan speeds using a continuous wave laser LPBF machine. Tradeoffs between ductility and strength are shown across the process space and their implications are discussed. While volumetric energy density deposited onto a substrate to create a melt-pool can be a useful metric for determining bulk properties, it was not found to directly correlate with output small feature performance.

316 L stainless steel↗

DBD plasma-assisted ethanol steam reforming for green H 2 production: Process optimization through response surface methodology (RSM)

Herein this work investigates ethanol steam reforming (ESR) to produce hydrogen (H 2 ) in a dielectric barrier discharge (DBD) plasma reactor. A five-level, three-factor experiment design was performed using a response surface methodology (RSM) to evaluate the combined effects of the three process parameters, including discharge power, total flow rate, and ethanol-to-water (EtOH/H 2 O) molar ratio on the plasma-assisted ESR reaction. Quadratic regression models were employed in RSM to fit the experimental results and present the correlation between process parameters and targeted responses (EtOH conversion, H 2 yield, H 2 selectivity, and specific energy requirement (SER) for H 2 production). The results suggested that the EtOH/H 2 O molar ratio is considered to have the most significant effect on the EtOH conversion and H 2 , H 2 selectivity, while the total flow rate is the most significant parameter determining SER for H 2 production. Process optimization demonstrated the optimal process conditions, including a discharge power of 55.9 W, a total flow rate of 26.7 ml/min, and an EtOH/H 2 O molar ratio equal to 0.34. A validation test was performed and confirmed the feasibility of the optimization process.

08 HYDROGEN↗

Bridging molecular-scale interfacial science with continuum-scale models

Solid–water interfaces are crucial for clean water, conventional and renewable energy, and effective nuclear waste management. However, reflecting the complexity of reactive interfaces in continuum-scale models is a challenge, leading to oversimplified representations that often fail to predict real-world behavior. This is because these models use fixed parameters derived by averaging across a wide physicochemical range observed at the molecular scale. Recent studies have revealed the stochastic nature of molecular-level surface sites that define a variety of reaction mechanisms, rates, and products even across a single surface. To bridge the molecular knowledge and predictive continuum-scale models, we propose to represent surface properties with probability distributions rather than with discrete constant values derived by averaging across a heterogeneous surface. This conceptual shift in continuum-scale modeling requires exponentially rising computational power. By incorporating our molecular-scale understanding of solid–water interfaces into continuum-scale models we can pave the way for next generation critical technologies and novel environmental solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Building a spontaneously formed and self-healing protective layer with an F-rich electrochemically active organic molecule for ultra-stable Li metal batteries

Additives in the electrolyte act as engineers in Li metal batteries. Inspired by the superior cycle performance of organic materials in half cells, tetrafluoro-1,4-benzoquinone (TFBQ), the main structure of which has been widely applied as an organic cathode material, is utilized for the first time as an additive for Li metal protection. By chemical and electrochemical reactions between TFBQ and the Li metal surface, an F-rich interface layer is in situ formed on the Li metal surface during the charge and discharge process. From electrochemical tests and characterization, the powerful self-healing ability of the interface layer enabled by TFBQ is revealed, making an extremely stable Li metal anode. By using a lean electrolyte with 0.1 M TFBQ, the cycle life of Li|Li symmetric cells is increased at least 6 times compared to the control group. Moreover, impressive full cell performance was achieved. Ultra-stable Li–LFP cells showed a 0.026% average degradation for 600 cycles at 1C and Li–NMC622 cells showed a 36.8% higher capacity compared to the control group over 200 cycles at 0.5C, which are among the best results reported. Furthermore, this work efficiently and conveniently provides a new research direction to Li metal protection and Li metal batteries.

25 ENERGY STORAGE↗

Correlation between the temperature evolution of the interfacial region and the growing dynamic cooperativity length scale

Here, we study experimentally the temperature evolution of the thickness of the interfacial layer, L int (T), between bulk matrices and the surface of nanoparticles in nanocomposites through broadband dielectric spectroscopy. Analyses revealed a power-law dependence between the logarithm of structural relaxation time in the interfacial layer, τ int (T), and the L int (T): ln τ i n t ( T ) / τ 0 ∝ L i n t β ( T ) / T , with τ 0 ~ 10 –12 s, and β index ~0.67 at high temperatures and ~1.7 at temperatures close to the glass transition temperature. In addition, our analysis revealed that the L int (T) is comparable to the length scale of dynamic heterogeneity estimated from previous nonlinear dielectric measurements and the four-point NMR [ξ NMR (T)], with L int (T) ~ ξ NMR (T). These observations may suggest a direct correlation between the L int (T) and the size of the cooperatively rearranging regions and have strong implications for understanding the dynamic heterogeneity and cooperativity in supercool liquids and their role in interfacial dynamics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Loss Analysis and Performance Optimization Pathways of 729-mV Voc Si Solar Cells with Poly-Si on Locally-Etched Dielectric Passivating Contacts

In this article, the loss analysis of silicon solar cells with polysilicon on locally-etched dielectric passivating contacts with Voc=729.0 mV and efficiency=22.6% has been presented. Experimentally, nano-pinholes were introduced in SiO x (2.2 nm) and SiO x /SiN y (2.2 nm/8nm) stack using metal-assisted chemical etching (MACE). SunSolve and Quokka3 were used to simulate the experimental solar cell and investigate the optical and electrical power losses. Simulations suggest maximum power loss occurs due to recombination and resistive losses in the bulk (~0.76 mW/cm2) followed by power loss due to rear contact recombination (~0.35 mW/cm2). Recombination at the front surface also contributes to 0.24 mW/cm2. The effect of improving the bulk lifetime and lowering the recombination current density at the rear side on Voc, FF and hence, efficiency has been investigated. Further, advanced structures have been proposed to minimize recombination and parasitic absorption to achieve higher Voc and Jsc of the solar cells with locally-etched dielectric passivating contacts.

contacts↗

Python-Cubit ® Enhancement Scripts: 16.14

The Python-Cubit ® enhancement code base is intended to be used as an extension to already existing Cubit ® functionality. It provides the user with a number of functionalities that are either currently outside the realm of the python functions which Cubit ® supplies internally (such as vector math), or that are comprised of commonly used combinations of already existing python functionalities (such as removing a full round from a slot cut). The foreseen style of use for many of these scripts is to utilize volume names and geometric data such as surface area, surface type, etc. as a way to filter out geometries, and provide a powerful id-less method. These filters combined with a number of already existing python functionalities such as the set() operator and zip() function can be used to operate on many geometries at a single time without a need for the user to manually select them or use their ids. Please refer to the example given in the documents examples section for a demonstration of the work flow.

97 MATHEMATICS AND COMPUTING↗

A Lunar Farside Low Radio Frequency Array for Dark Ages 21-cm Cosmology

An array of low-frequency dipole antennas on the lunar farside surface will probe a unique, unexplored epoch in the early Universe called the Dark Ages. It begins at Recombination when neutral hydrogen atoms formed, first revealed by the cosmic microwave background. This epoch is free of stars and astrophysics, so it is ideal to investigate high energy particle processes including dark matter, early Dark Energy, neutrinos, and cosmic strings. A NASA-funded study investigated the design of the instrument and the deployment strategy from a lander of 128 pairs of antenna dipoles across a 10 kmx10 km area on the lunar surface. The antenna nodes are tethered to the lander for central data processing, power, and data transmission to a relay satellite. The array, named FARSIDE, would provide the capability to image the entire sky in 1400 channels spanning frequencies from 100 kHz to 40 MHz, extending down two orders of magnitude below bands accessible to ground-based radio astronomy. The lunar farside can simultaneously provide isolation from terrestrial radio frequency interference, the Earth's auroral kilometric radiation, and plasma noise from the solar wind. It is thus the only location within the inner solar system from which sky noise limited observations can be carried out at sub-MHz frequencies. Through precision calibration via an orbiting beacon and exquisite foreground characterization, the farside array would measure the Dark Ages global 21-cm signal at redshifts z~35-200. It will also be a pathfinder for a larger 21-cm power spectrum instrument by carefully measuring the foreground with high dynamic range.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

High quality superconducting Nb co-planar resonators on sapphire substrate

We present measurements and simulations of superconducting Nb co-planar waveguide resonators on sapphire substrate down to millikelvin temperature range with different readout powers. In the high temperature regime, we demonstrate that the Nb film residual surface resistance is comparable to that observed in the ultra-high quality, bulk Nb 3D superconducting radio frequency cavities while the resonator quality is dominated by the BCS thermally excited quasiparticles. At low temperature both the resonator quality factor and frequency can be well explained using the two-level system models. Through the energy participation ratio simulations, we find that the two-level system loss tangent is $\sim 10^{-2}$, which agrees quite well with similar studies performed on the Nb 3D cavities.

Zhu, S.↗

Loss Analysis and Performance Optimization Pathways of 729-mV VocSi Solar Cells with Poly-Si on Locally-Etched Dielectric Passivating Contacts

In this article, the performance analysis of a 22.5% efficient polysilicon on silicon oxide (poly-Si/SiOx) passivated contact solar cells with deliberately introduced pinholes using metal-assisted chemical etching (MACE) has been performed with the help of optical analysis using Sunsolve and electrical analysis using Quokka3. The power loss is maximum due to recombination and resistive losses in the bulk (~0.76 mW/cm2 ) followed by power loss due to rear contact recombination (~0.35 mW/cm2 ). Recombination at the front surface also contributes to 0.24 mW/cm2. The effect of improving the bulk lifetime and lowering the recombination current density at the rear side on Voc, FF and efficiency has been investigated.

MACE↗

Thermal Management System for an Electric Machine with Additively Manufactured Hollow Conductors with Integrated Heat Pipes: Preprint

This paper discusses steps taken to size a thermal management system for an aircraft propulsion electric machine containing additively manufactured coils integrated with heat pipes aimed at boosting its specific power. Experimental setups are used to size and characterize heat pipes for the application and 3D thermal FEA is used to determine optimum heat transfer coefficient of convective boundaries. Geometric details of fin-based surface area enhancement required to reach target combined overall heat transfer coefficient (U) and surface area (A) performance (UA) in W/K, is worked out for relevant boundaries and the resulting UA is verified in 3D thermal FEA. Thermal management system's UA (by extension specific power) sensitivity to coolant temperature is explored and temperature distribution plots of optimized machine components are presented and discussed.

additive manufacturing↗

X-Ray Afterglows from the Gamma-Ray Burst “Large-angle” Emission

In this work, we derive basic analytical results for the timing and decay of the gamma-ray burst (GRB) counterpart and delayed afterglow light curves for a brief emission episode from a relativistic surface endowed with angular structure, consisting of a uniform core of size ${\theta }_{c}$ (Lorentz factor ${{\rm{\Gamma }}}_{c}$ and surface emissivity ${i}_{\nu ^{\prime} }^{{\prime} }$ are angle independent) and an axially symmetric power-law envelope (${\rm{\Gamma }}\sim {\theta }^{-g}$). In this "large-angle emission" model, radiation produced during the prompt emission phase (GRB) at angles $\theta \gt {\theta }_{c}$ arrives at the observer well after the burst (delayed emission). The dynamical time range of the very fast decaying GRB "tail" and of the flat afterglow "plateau" and the morphology of the GRB counterpart/afterglow are all determined by two parameters: the core's parameter ${{\rm{\Gamma }}}_{c}{\theta }_{c}$ and the envelope's Lorentz factor index g, leading to three types of light curves that display three post-GRB phases (type 1: tail, plateau/slow decay, post-plateau/normal decay), two post-GRB phases (type 2: tail and fast decay), or just one (type 3: normal decay). We show how X-ray light-curve features can be used to determine core and envelope dynamical and spectral parameters. Testing of the large-angle emission model is done using the Swift/XRT X-ray emission of two afterglows of type 1 (GRB 060607A, GRB 061121), one of type 2 (GRB 061110A), and one of type 3 (GRB 061007). We find that the X-ray afterglows with plateaus require an envelope Lorentz factor ${\rm{\Gamma }}\sim {\theta }^{-2}$ and a comoving-frame emissivity ${i}_{\nu ^{\prime} }^{{\prime} }\sim {\theta }^{2}$; thus, for a typical afterglow spectrum ${F}_{\nu }\sim {\nu }^{-1}$, the lab-frame energy release is uniform over the emitting surface.

79 ASTRONOMY AND ASTROPHYSICS↗