Admittance dependence of the infinite cylindrical antenna upon exciting gap thickness.
Infinite cylindrical antenna admittance dependence on exciting frequency and gap thickness
Miller, E. K.↗
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Quantification of LEU Holdup using gamma ray imaging and inverse transport solver
Holdup is the residual amount of special nuclear material (SNM) remaining in a processing facility after the bulk materials have been cleaned out. In commercial uranium processing facilities, quantification of holdup is a major challenge because of the highly variable shapes and sizes of the deposits. Any method that attempts to generalize and calibrate deposit shapes in order to quantify holdup will be prone to high uncertainties. Uncertainties on the order of ±50% are typical in holdup results. In international safeguards applications, a ±50% uncertainty can result in a large amount of material unaccounted for (MUF) thereby increasing the difficulty of detecting material diversion and facility misuse. An imaging-based methodology has been developed with the objective of significantly reducing this uncertainty by using the true deposit shape, instead of relying on oversimplified geometric assumptions. The project is a collaboration between ORNL, Y-12, and the University of Tennessee, Knoxville, TN. Uranium sources of known masses were measured using the Germanium Gamma-ray Imager (GeGI), a high-resolution imaging spectrometer, creating a pixelated map for each spectral bin. Two different gamma imaging methods are employed in this work: coded aperture imaging and Compton imaging. A validated MonteCarlo model of the detector has been developed using the GEANT4 code for determining the intrinsic response of the detector, its enclosure, and the coded aperture mask. An inverse transport solver based on the Markov Chain Monte-Carlo approach known as Differential Evolution Adaptive Metropolis (DREAM) is employed to use the measurement data from the image pixels (coded aperture or Compton) to solve for the mass of 235 U in the deposit. A reliable method based on the DREAM solver has been developed to flag the infinite thickness condition of a uranium deposit. The project team is working towards improving the image reconstruction for Compton imaging so that a better localization of the source can be achieved. Besides treating the coded aperture and Compton imaging methods independently, the project is also evaluating a combined method that uses the Compton scatter data from a coded aperture measurement. GEANT4 simulations are being performed to evaluate the combined approach. The impact on the DREAM optimization as the source thickness progressively approaches infinite thickness is being evaluated. A number of uranium sources available at ORNL have been measured, and the DREAM results have been tested and validated for the coded aperture imaging. A similar effort will be carried out to validate the Compton based method once the development of algorithms for better localization are complete. The imaging based quantification is very amenable to unattended monitoring of holdup accumulation at key measurement points. A proof of concept measurement has been completed to demonstrate this capability The current work used the high energy resolution imager GeGI. However, the approach and methodologies are applicable to other imagers such as the cadmium zin telluride (CZT) based imager manufactured by H3D, Inc.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Analysis of interlaminar stresses in thick composite laminates with and without edge delamination
The effect of laminate thickness on the interlaminar stresses in rectangular quasi-isotropic laminates under uniform axial strain was studied. Laminates from 8-ply to infinitely thick were analyzed. Thick laminates were synthesized by stacking (45/0/-45/90) ply groups, rather than grouping like plies. Laminates with and without delaminations were studied. In laminates without delaminations, the free-edge interlaminar normal stress distribution in the outer ply groups was insensitive to total laminate thickness. The interlaminar normal stress distribution for the interior ply groups was nearly the same as for an infinitely thick laminate. In contrast, the free-edge inter-laminar shear stress distribution was nearly the same for inner and outer ply groups and was insensitive to laminate thickness. In laminates with delaminations those delaminations near the top and bottom surfaces of a thick laminate have much larger total strain-energy-release rates (G sub t) and mode I-to-total (G sub t/G sub t) ratios than delaminations deep in the interior. Therefore, delaminations can be expected to grow more easily near the surfaces of a laminate than in the interior.
Whitcomb, J. D.↗
Analysis of interlaminar stresses in thick composite laminates with and without edge delamination
The effect of laminate thickness on the interlaminar stresses in rectangular quasi-isotropic laminates under uniform axial strain was studied. Laminates from 8-ply to infinitely thick were analyzed. Thick laminates were synthesized by stacking (45/0/-45/90) ply groups, rather than grouping like plies. Laminates with and without delaminations were studied. In laminates without delaminations, the free-edge interlaminar normal stress distribution in the outer ply groups was insensitive to total laminate thickness. The interlaminar normal stress distribution for the interior ply groups was nearly the same as for an infinitely thick laminate. In contrast, the free-edge inter-laminar shear stress distribution was nearly the same for inner and outer ply groups and was insensitive to laminate thickness. In laminates with delaminations those delaminations near the top and bottom surfaces of a thick laminate have much larger total strain-energy-release rates (G sub t) and mode I-to-total (G sub t/G sub t) ratios than delaminations deep in the interior. Therefore, delaminations can be expected to grow more easily near the surfaces of a laminate than in the interior.
Whitcomb, J. D.↗
URANIUM HOLDUP MONITORING WITH COMPTON IMAGING AS FUNCTION OF DEPTH AND MASS
Mass quantification using standoff gamma detection is a logical progression for MC&A applications in uranium processing facilities. While obtaining a ground truth from physical collection and weighing of masses is ideal and routine, it poses a logistical problem from both a standpoint of ALARA programs as well as interruptions to operations. The standard approach is the Generalized Geometry in Holdup (GGH) method that can apply for many cases where geometries of the holdup match simulated models; however, there are many cases where a model may not exist or a feature of the holdup geometry is such that it does not match a model particularly well.1 Gamma imaging at standoff distances and outside process equipment has potential to address these shortcomings and improve mass estimations while reducing personnel exposure; however, algorithms still require a significant degree of benchmarking to build sufficient confidence in algorithms before displacing GGH in some procedures. This paper presents the creation of a set of laboratory standards of depleted U3O8 in fixed size containers covering a range of masses and effective thicknesses up to the infinite thickness for the 185-keV line. These blocks are identically sized aluminum boxes loaded such that a thin, flat face is placed towards the imager, while the back side contains closed cell foam to apply pressure to keep the powder in a fixed position at the front face as the sources are manipulated for measurements. Included is an analysis of the mass estimation using a commercially available Compton imaging instrument where multiple geometries are created showing limitations in current methodologies.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
User's manual for CBS3DS, version 1.0
CBS3DS is a computer code written in FORTRAN 77 to compute the backscattering radar cross section of cavity backed apertures in infinite ground plane and slots in thick infinite ground plane. CBS3DS implements the hybrid Finite Element Method (FEM) and Method of Moments (MoM) techniques. This code uses the tetrahedral elements, with vector edge basis functions for FEM in the volume of the cavity/slot and the triangular elements with the basis functions for MoM at the apertures. By virtue of FEM, this code can handle any arbitrarily shaped three-dimensional cavities filled with inhomogeneous lossy materials; due to MoM, the apertures can be of any arbitrary shape. The User's Manual is written to make the user acquainted with the operation of the code. The user is assumed to be familiar with the FORTRAN 77 language and the operating environment of the computer the code is intended to run.
Reddy, C. J.↗
Gravitational effects on flames spreading over thick solid surfaces
A theoretical model for the downward spread of a flame in the gas over a semi-infinitely thick fuel bed is presented. Gas-phase chemistry is assumed to proceed at an infinite rate while the fuel bed is taken to pyrolyze at the surface in an Arrhenius fashion. Spread rates and flame shapes are computed for two different ambient oxygen concentrations for gravitational accelerations both below and above that of the earth. Predicted spread rates decrease and actual flame size increases with decreasing gravity. Results agree favorably with available, experimental results and expected results from reduced gravity experimentation.
Vedha-Nayagam, M.↗
Comparison of gamma-ray spectral analysis methods for thick-walled UF 6 cylinders
Three data analysis methods were compared for gamma ray spectra collected by planar and coaxial high-purity germanium detectors (HPGe) on thick-walled uranium hexafluoride cylinders. The cylinder contents range from natural to low-enriched uranium (4.95% 235 U). Each spectrum was analyzed with the traditional 185.7 keV enrichment meter method, a 185.7/1001 keV ratio method, and the Fixed Energy Response Function Analysis with Multiple Efficiency (FRAM) software that utilizes low- and high-energy gamma rays and X-rays. When results for all cylinders were compared, the enrichment meter method and the 185.7/1001 keV peak ratio method consistently provided the most accurate data for all detector types. The error on the enrichment calculations analyzed with FRAM did not meet the international target value whereas those calculated with the enrichment meter and ratio method did. Enrichments calculated by FRAM were found to skew to higher values on natural uranium and to lower values on low-enriched uranium. FRAM calculated the least-precise enrichments; replicate analyses of single cylinders resulted in 235 U values that varied by as much as 19%. FRAM does have the significant advantages in that it does not require the use of calibration cylinders, infinite thickness criteria are not necessary, and it can be applied to any HPGe detector. Finally, if calibration cylinders are available, the enrichment meter and 185.7/1001 peak ratio are the recommended methods as they are the most accurate and precise.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Photon detector response function methodology using MCNP and shift hybrid radiation transport code for wide-area contamination assay applications
Here, radiation transport modeling using the Monte Carlo N-Particle (MCNP) radiation transport code and Monte Carlo code, Shift, were employed to model detector responses for a variety of wide-area photon contamination scenarios. In this study, 2" × 2" and 3" × 3" cylindrical NaI(Tl) scintillation detector configurations at source detector-distances of 0.5 cm, 1 cm, 2.54 cm, 10 cm, and 30 cm were modeled. Media of soil, concrete, and steel were evaluated for contamination depths ranging from surface to a depth of an infinite thickness in each medium for photon energies ranging from 20 keV to 3 MeV, which correspond to the energies that current detectors can discern. Monoenergetic photon surface contamination detector responses for each of the media, source–detector distances, and detectors were estimated using MCNP v6.2. Shift was harnessed for improved variance reduction of particle transport in highly attenuating media to obtain average cell fluxes in the two MCNP NaI(Tl) scintillation detector configurations. Average cell flux values in Shift were coupled with detector responses from MCNP to convert average cell flux in a void to energy distribution of pulses in the NaI(Tl) scintillation detector crystal of interest. An optimized detector response function methodology was developed by coupling the MCNP radiation transport method with the Consistent Adjoint Driven Importance Sampling (CADIS) hybrid radiation transport method built into Shift to significantly decrease the runtime of thousands of MCNP pulse height simulations. The methodology may be utilized to quickly and accurately facilitate the assessment of a broad range of wide-area environmental contamination assay and decommissioning cleanup applications.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Uranium measurements in the field using high-resolution cadmium zinc telluride detectors
A new generation of cadmium zinc telluride (CZT) detectors has become available and is being evaluated by the International Atomic Energy Agency (IAEA) for safeguards verifications in the field. The new CZT detector, model M400, is a room temperature spectrometer manufactured by H3D, Inc. The M400 demonstrates superior energy resolution, effective isotope identification capabilities, and convenient usability features when tested in a controlled laboratory environment. These characteristics define the M400 as a potential platform for IAEA field detection applications, which could become suitable for nuclear material characterization (e.g., enrichment verification) and nuclear safeguards missions. The capabilities of gamma spectrometry codes including Fixed energy, Response function Analysis with Multiple efficiencies (FRAM) from Los Alamos National Laboratory, CZT for Uranium (CZTU) from Lawrence Livermore National Laboratory, and Gamma Detector Response and Analysis Software (GADRAS) from Sandia National Laboratories were adapted for M400 spectra, and the performance of the codes has been validated. This was reported in a prior work. To further validate the performance of the high-energy resolution CZT detector and the isotopic analysis codes, a field measurement campaign consisting of uranium hexafluoride (UF 6 ) cylinder measurements was conducted at a fuel fabrication facility. A total of 34 Type 30B cylinders containing UF6 were measured using three different M400 CZT detectors. Each detector was outfitted with a custom rectangular collimator and shield made out T-Flex®, a tungsten-impregnated polymer. Measurements were performed at three different locations of the cylinder, ensuring that the measurement geometry satisfied the infinite thickness criterion. The spectra from the M400 CZT were analyzed using the code General Enrichment Meter (GEM). For analyzing the gamma-ray spectra from UF 6 cylinder, the GEM code is the appropriate tool since it relies only on the gamma-ray emissions from 235 U and not from other isotopes. Results from the spectral analysis were compared with the known abundance of 235 U in the cylinders, as well as with the International Target Values 2020 (ITV2020). The suitability of the different underlying techniques used by the various codes for UF 6 analysis is discussed. The challenges of measuring UF 6 contained in cylinders and mitigation strategies are highlighted.
46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
Robust method for broadband efficiency enhancement of electron photocathodes using optical interferences
In this work, we demonstrate the key features of an interference cathode using both simulations and experiments. We deposit Cs 3 Sb photocathodes on Ag to produce an interference enhanced photocathode with 2–5× quantum efficiency (QE) enhancement using a robust procedure that requires only a smooth metal substrate and QE monitoring during growth. We grow both an interference cathode (Ag substrate) and a typical photocathode (Si reference substrate) simultaneously to confirm that the effects are due to optical interactions with the substrate rather than photocathode composition or surface electron affinity differences. Growing the cathodes until the QE converges shows both the characteristic interference peaks during growth and the identical limiting case where the cathode is “infinitely thick,” in agreement with simulations. We also grow a cathode until the QE on Ag peaks and then stop the growth, demonstrating broadband QE enhancement.
36 MATERIALS SCIENCE↗
The Dirac equation as a model of topological insulators
The Dirac equation with a spatially dependent mass can be used as a simple, exactly soluble, continuum model of a three-dimensional Topological Insulator. For a bulk system, the sign of the mass determines the parity at the only time-reversal point ( k _ = 0 ) and, thus, leads to the designation of the bulk as being topologically trivial or non-trivial. Since the mass changes sign at the interface between a topologically trivial and non-trivial materials, topological surface states appear on that boundary. We present that electron scattering experiments may provide an alternate probe of the topological character of the surface states. For infinitely thick slabs, the states on the opposite sides of the slab decouple. The spatial decoupling results in the surface states become gapless, non-degenerate and, due to the Rashba spin–orbit coupling generated by the loss of inversion symmetry, exhibit spin-momentum locking. We review several characteristic properties of the topological surface states which are dependent on the topological quantum numbers and show that, using this model, they can be calculated exactly using simple approaches.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Two-beam Bragg diffraction, filtering, and delays
We summarize transmission and reflection amplitudes of Bragg-crystals based on two-beam Bragg diffraction theory. Then, we consider a specific case of infinitely thick and symmetrical Bragg-crystal and its reflective properties in spectral and angular domain. We obtain analytical expressions for filtering width and respective delay amplitudes, temporal delay from spectral phase shift and spatial displacement from angular phase shift.
43 PARTICLE ACCELERATORS↗
Fitting the RESRAD External Dose Rate Coefficients Model to the FGR 15 Data
FGR15 (Bellamy et al. 2025) lists external dose rate coefficients for radionuclides in soil, water and air. It has five tables of coefficients for contaminated soil; one for radionuclides on the surface of the soil and one each for radionuclides in soil layers of 1 cm, 5 cm, 15 cm and infinite thickness. Each table contains 7512 coefficients, quantifying the external dose rate from each of the 1252 ICRP107 radionuclides, to each of the six reference persons of different ages.
54 ENVIRONMENTAL SCIENCES↗
A nonhomogeneous boundary-value problem for the linear transport equation for a slab geometry
Finite thickness infinite slab with radiation from time dependent source, solving nonhomogeneous boundary value problem for linear transport equation
Hintz, G. R.↗
Further calculations based upon a theory of flame spread across solid fuels
A theory of flame spread above solid fuel beds of finite or infinite thickness is considered. Heat transfer ahead of the flame is allowed through both the solid and gas phases. The simplifying assumption of a surface reaction is made. Temperature profiles in both phases, concentration profiles in the gas phase, heat transfer at the surface, and flame spreading rates are determined. It is found that chemical kinetic parameters together with transport properties strongly influence the spreading rate. Heat transfer through the gas phase is the dominant mechanism for energy transfer ahead of the spreading flame over a wide range of Peclet numbers for the gas and solid phases.
Feng, C. C.↗
A Model of Radiative and Conductive Energy Transfer in Planetary Regoliths
The thermal regime in planetary regoliths involves three processes: propagation of visible radiation, propagation of thermal radiation, and thermal conduction. The equations of radiative transfer and heat conduction are formulated for particulate media composed of anisotropically scattering particles. Although the equations are time dependent, only steady state problems are considered in this paper. Using the two-stream approximation, solutions are obtained for two cases: a layer of powder heated from below and an infinitely thick regolith illuminated by visible radiation. Radiative conductivity, subsurface temperature gradients, and the solid state greenhouse effect all appear intrinsically in the solutions without ad hoc additions. Although the equations are nonlinear, approximate analytic solutions that are accurate to a few percent are obtained. Analytic expressions are given for the temperature distribution, the optical and thermal radiance distributions, the hemispherical albedo, the hemispherical emissivity, and the directional emissivity. Additional applications of the new model to three problems of interest in planetary regoliths are presented by Hapke.
Hapke, Bruce↗
Mutual coupling between parallel columns of periodic slots in a ground plane surrounded by dielectric slabs
Arrays of slots with arbitrary orientation in a conducting plane which are infinitely periodic in one dimension and finitely periodic in another dimension are considered. The perfect conducting plane extends infinitely and is bounded on each side by dielectric slabs of finite thickness and infinite extent. Single columns of slots are represented by equivalent magnetic scattering currents, which are solved for via the moment method. The mutual coupling (admittance) between slot columns in the presence of the stratified media is found by the array scanning method (ASM), which expresses the admittance as the average of the scan admittance of an artificially constructed doubly infinite array of slots over all real scan angles. The technique avoids the use of Sommerfeld integrals, but still gives rise to singularities at scan angles corresponding to the resonant excitation of surface waves. An analytical approximation is made to remove these surface wave singularities, thus making numerical implementation of the method practical. The method is quite general and may be extended to thin slot elements of arbitrary shape and orientation.
Skinner, J. P.↗