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DOE OSTI2015

Measurements of SNAC2 area dosimeters placed in different configurations around the PROSPERO reactor and comparison with TRIPOLI-4 calculations

In the context of criticality accident alarm system tests, several experiments were carried out in 2013 on the PROSPERO reactor to study the response to neutron and gamma of different devices and dosimeters, particularly on the SNAC2 dosimeter. This article presents the results of this criticality dosimeter in different configurations, and compares the experimental measurements with the results of calculation performed with the TRIPOLI-4 Monte-Carlo Neutral Particles transport code. PROSPERO is a metallic critical assembly managed by the Criticality, Neutron Science and Measurement Department located at the French CEA Research Center of Valduc. The core, surrounded by a reflector of depleted uranium, is composed of 2 horizontal cylindrical blocks made of a highly enriched uranium alloy which can be placed in contact, and of 4 depleted uranium control rods which allow the reactor to be driven. This reactor, placed in a cell 10 m x 8 m x 6 m high, with 1.4-meter-thick concrete walls, is used as a fast neutron spectrum source and is operated at stable power level in delayed critical state, which can vary from 3 mW to 3 kW. PROSPERO is extensively used for electronic hardening or to study the effect of the neutrons on various materials. The SNAC2 criticality dosimeter is a zone dosimeter allowing the off line measurement of criticality accident neutron doses. This dosimeter consists of the pile up of seven activation foils embedded into a 23 mm diameter x 21 mm height cadmium container. The activation measurement of each foil, using a gamma spectroscopy technique, gives information about the neutron reaction rates. The SNAC2 software allows the spectrum unfolding from these values, taking into account the hypothesis of a particular spectrum shape, in three components: a Maxwell spectrum component for the thermal range, a 1/E component for the epithermal range, and a Watt spectrum component for the high energy range. Moreover, from the neutron spectrum, the SNAC software can calculate the neutron fluence integrated by the dosimeter and the neutron dose. During the 3 weeks measurement campaign many radioprotection devices were used. To modify the spectrum seen by these devices, several shields of various thicknesses made of concrete or polyethylene, with or without cadmium covers, were placed in the PROSPERO cell. These devices allow the study of criticality accident spectra in several environments: from metal to pseudo liquid. The fluxes measured by the SNAC2 devices were compared with TRIPOLI-4 calculations. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2011

3D Monte Carlo Modeling of the EEDF in Negative Hydrogen Ion Sources

For optimization and accurate prediction of the amount of H{sup -} ion production in negative ion sources, analysis of electron energy distribution function (EEDF) is necessary. We are developing a numerical code which analyzes EEDF in tandem-type arc-discharge sources. It is a three-dimensional Monte Carlo simulation code with the realistic geometry and magnetic configuration. Coulomb collision between electrons is treated with 'Binary Collision' model and collisions with hydrogen species are treated with 'Null-collision (NC)' method. We have applied this code to the analysis of the JAEA 10 ampere negative ion source. The numerical result shows that the obtained EEDFs reasonably agree with experimental results.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2015

penORNL: a parallel Monte Carlo photon and electron transport package using PENELOPE

The parallel Monte Carlo photon and electron transport code package penORNL was developed at Oak Ridge National Laboratory to enable advanced scanning electron microscope (SEM) simulations on high-performance computing systems. This paper discusses the implementations, capabilities and parallel performance of the new code package. penORNL uses PENELOPE for its physics calculations and provides all available PENELOPE features to the users, as well as some new features including source definitions specifically developed for SEM simulations, a pulse-height tally capability for detailed simulations of gamma and x-ray detectors, and a modified interaction forcing mechanism to enable accurate energy deposition calculations. The parallel performance of penORNL was extensively tested with several model problems, and very good linear parallel scaling was observed with up to 512 processors. penORNL, along with its new features, will be available for SEM simulations upon completion of the new pulse-height tally implementation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Design and validation of a gamma-ray scanning system for measuring irradiated nuclear fuel

We report a prototype gamma-ray scanning system was designed to perform post-irradiation measurements of nuclear fuel at Idaho National Laboratory (INL). The system is composed of a coaxial high-purity germanium (HPGe) detector, a collimator, and mechanical positioning stages that translate the fuel sample across the front of the collimator. This paper documents the design process, modeling and the laboratory characterization performed to validate the system. The modeling of the system was done using the Monte Carlo N-Particle code with vendor-supplied design specifications, dimensional measurements, and x-ray radiographs of the HPGe detector. The characterization included measurements of calibrated radiation sources in different geometries, and calculations for absolute efficiency and dead time. Benchmark measurements were performed scanning an irradiated fuel rodlet containing ten pellets of 4.9% enriched UO2 in zirconium alloy. These results were compared to simulated spectra to further help characterize the detector model. One goal of the system is to determine the number of fissions per gram of UO2 in the fuel; comparison of the results from this prototype system's assay of the irradiated fuel rodlet are in agreement with previously estimated results.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2024

Software stewardship and advancement of a high-performance computing scientific application: QMCPACK

Here, we provide an overview of the software engineering efforts and their impact in QMCPACK, a production-level ab-initio Quantum Monte Carlo open-source code targeting high-performance computing (HPC) systems. Aspects included are: (i) strategic expansion of continuous integration (CI) targeting CPUs, using GitHub Actions own runners, and NVIDIA and AMD GPUs used in pre-exascale systems, (ii) incremental reduction of memory leaks using sanitizers, (iii) incorporation of Docker containers for CI and reproducibility, and (iv) refactoring efforts to improve maintainability, testing coverage, and memory lifetime management. We quantify the value of these improvements by providing metrics to illustrate the shift towards a predictive, rather than reactive, maintenance approach. Our goal, in documenting the impact of these efforts on QMCPACK, is to contribute to the body of knowledge on the importance of research software engineering (RSE) for the stewardship and advancement of community HPC codes to enable scientific discovery at scale.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Direction-Modulated Brachytherapy for High-Dose-Rate Treatment of Cervical Cancer. I: Theoretical Design

Purpose: To demonstrate that utilization of the direction-modulated brachytherapy (DMBT) concept can significantly improve treatment plan quality in the setting of high-dose-rate (HDR) brachytherapy for cervical cancer. Methods and Materials: The new, MRI-compatible, tandem design has 6 peripheral holes of 1.3-mm diameter, grooved along a nonmagnetic tungsten-alloy rod (ρ = 18.0 g/cm{sup 3}), enclosed in Delrin tubing (polyoxymethylene, ρ = 1.41 g/cm{sup 3}), with a total thickness of 6.4 mm. The Monte Carlo N-Particle code was used to calculate the anisotropic {sup 192}Ir dose distributions. An in-house-developed inverse planning platform, geared with simulated annealing and constrained-gradient optimization algorithms, was used to replan 15 patient cases (total 75 plans) treated with a conventional tandem and ovoids (T and O) applicator. Prescription dose was 6 Gy. For replanning, we replaced the conventional tandem with that of the new DMBT tandem for optimization but left the ovoids in place and kept the dwell positions as originally planned. All DMBT plans were normalized to match the high-risk clinical target volume V100 coverage of the T and O plans. Results: In general there were marked improvements in plan quality for the DMBT plans. On average, D2cc for the bladder, rectum, and sigmoid were reduced by 0.59 ± 0.87 Gy (8.5% ± 28.7%), 0.48 ± 0.55 Gy (21.1% ± 27.2%), and 0.10 ± 0.38 Gy (40.6% ± 214.9%) among the 75 plans, with best single-plan reductions of 3.20 Gy (40.8%), 2.38 Gy (40.07%), and 1.26 Gy (27.5%), respectively. The high-risk clinical target volume D90 was similar, with 6.55 ± 0.96 Gy and 6.59 ± 1.06 Gy for T and O and DMBT, respectively. Conclusions: Application of the DMBT concept to cervical cancer allowed for improved organ at risk sparing while achieving similar target coverage on a sizeable patient population, as intended, by maximally utilizing the anatomic information contained in 3-dimensional imaging. A series of mechanical and clinical validations are to be followed.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2025

Accelerating detector simulations with Celeritas: Profiling and performance optimizations

Celeritas is a GPU-optimized Monte Carlo (MC) particle transport code designed to meet the growing computational demands of next-generation high energy physics (HEP) experiments. It provides efficient simulation of electromagnetic (EM) physics processes in complex geometries with magnetic fields, detector hit scoring, and seamless integration into Geant4-driven applications to offload EM physics to GPUs. Recent efforts have focused on performance optimizations and expanding profiling capabilities. This paper presents some key advancements, including the integration of the Perfetto system profiling tool for detailed performance analysis and the development of track-sorting methods to improve computational efficiency.

Lund, Amanda [Argonne National Laboratory (ANL)]↗

DOE OSTI2014

Comparative studies of actinide and sub-actinide fission cross section calculation from MCNP6 and TALYS

Comparative studies of actinide and sub-actinide fission cross section calculation from MCNP6 and TALYS have been conducted. In this work, fission cross section resulted from MCNP6 prediction will be compared with result from TALYS calculation. MCNP6 with its event generator CEM03.03 and LAQGSM03.03 have been validated and verified for several intermediate and heavy nuclides fission reaction data and also has a good agreement with experimental data for fission reaction that induced by photons, pions, and nucleons at energy from several ten of MeV to about 1 TeV. The calculation that induced within TALYS will be focused mainly to several hundred MeV for actinide and sub-actinide nuclides and will be compared with MCNP6 code and several experimental data from other evaluator.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Gamma-ray dose from an overhead plume

Standard plume models can underestimate the gamma-ray dose when most of the radioactive material is above the heads of the receptors. Typically, a model is used to calculate the air concentration at the height of the receptor, and the dose is calculated by multiplying the air concentration by a concentration-to-dose conversion factor. Models indicate that if the plume is emitted from a stack during stable atmospheric conditions, the lower edges of the plume may not reach the ground, in which case both the ground-level concentration and the dose are usually reported as zero. However, in such cases, the dose from overhead gamma-emitting radionuclides may be substantial. Such underestimates could impact decision making in emergency situations. The Monte Carlo N-Particle code, MCNP, was used to calculate the overhead shine dose and to compare with standard plume models. At long distances and during unstable atmospheric conditions, the MCNP results agree with the standard models. As a result, at short distances, where many models calculate zero, the true dose (as modeled by MCNP) can be estimated with simple equations.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2017

Induced Radioactivity in Lead Shielding at the National Synchrotron Light Source

The National Synchrotron Light Source (NSLS) at Brookhaven National Laboratory was shut down in September 2014. Lead bricks used as radiological shadow shielding within the accelerator were exposed to stray radiation fields during normal operations. The FLUKA code, a fully integrated Monte Carlo simulation package for the interaction and transport of particles and nuclei in matter, was used to estimate induced radioactivity in this shielding and stainless steel beam pipe from known beam losses. The FLUKA output was processed using MICROSHIELD® to estimate on-contact exposure rates with individually exposed bricks to help design and optimize the radiological survey process. This entire process can be modeled using FLUKA, but use of MICROSHIELD® as a secondary method was chosen because of the project’s resource constraints. Due to the compressed schedule and lack of shielding configuration data, simple FLUKA models were developed in this paper. FLUKA activity estimates for stainless steel were compared with sampling data to validate results, which show that simple FLUKA models and irradiation geometries can be used to predict radioactivity inventories accurately in exposed materials. During decommissioning 0.1% of the lead bricks were found to have measurable levels of induced radioactivity. Finally, post-processing with MICROSHIELD® provides an acceptable secondary method of estimating residual exposure rates.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

DOE OSTI2018

Production of Th 229 for medical applications: Excitation functions of low-energy protons on Th 232 targets

As a part of a general program to evaluate production routes for 229 Th, we studied production of 229 Th via proton-induced reactions on 232 Th targets bombarded with low-energy protons, E p ≤ 40MeV. The reported excitation functions include those for proton-induced reactions on natural thorium yielding to 228,229,230&232 Pa isotopes; 232 Th( p,xn ) reactions, where x=1, 3, 4, and 5, at proton energy ranges of 12–40 MeV. Although the data for 232 Th(p,n) 228 Pa, 232 Th(p,3n) 230 Pa, and 232 Th(p,5n) 232 Pa reactions were deduced by direct analysis of the thorium foils after irradiation, the data for 232 Th(p,4n) 229 Pa were obtained by radiochemical techniques. The half-life of 229 Pa was evaluated and determined to be 1.55 ± 0.01 d. Further, the α-branching ratio, α/(α + EC) of 229 Pa was evaluated to be 0.53 ± 0.10% by allowing 229 Pa to decay for ~7d, then chemically extracting and quantifying the 225 Ac (t 1/2 = 10.0±0.1d) from 229 Pa samples. In addition, we report the effective production cross section of 229 Th in a thick 232 Th target in the proton energy range of 23–33 MeV. The peak of the excitation function for the 232 Th(p,4n) 229 Pa reaction occurs at 162 ± 14 mb and E p =29.7±0.5MeV. This is only slightly larger than the effective cross section for the 232 Th(p,x) 229 Th reaction (obtained from a thick target experiment). This data indicates that the 232 Th(p,4n) 229 Pa reaction is the major reaction pathway for the cumulative 232 Th(p,x) 229 Th reaction cross section in this energy range. The measured cross sections were compared with theoretical cross sections using the simulation codes Particle and Heavy Ion Transport code System (PHITS) and Monte Carlo Neutral Particle 6 (MCNP6). Furthermore, at proton energy ranges of 12–33 MeV, the cumulative excitation function predicted by PHITS for the reactions leading to 229 Th was in close agreement with the experimental function, whereas the function predicted by MCNP6 was a factor of two higher at the peak of the excitation function.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

First Industrial Tests of a Matrix Monitor Correction for the Differential Die-away Technique of Historical Waste Drums

The fissile mass in radioactive waste drums filled with compacted metallic residues (spent fuel hulls and nozzles) produced at AREVA NC La Hague reprocessing plant is measured by neutron interrogation with the Differential Die-away measurement Technique (DDT). In the next years, old hulls and nozzles mixed with Ion-Exchange Resins will be measured. The ion-exchange resins increase neutron moderation in the matrix, compared to the waste measured in the current process. In this context, the Nuclear Measurement Laboratory (LMN) of CEA Cadarache has studied a matrix effect correction method, based on a drum monitor, namely a 3He proportional counter located inside the measurement cavity. After feasibility studies performed with LMN's PROMETHEE 6 laboratory measurement cell and with MCNPX simulations, this paper presents first experimental tests performed on the industrial ACC (hulls and nozzles compaction facility) measurement system. A calculation vs. experiment benchmark has been carried out by performing dedicated calibration measurements with a representative drum and {sup 235}U samples. The comparison between calculation and experiment shows a satisfactory agreement for the drum monitor. The final objective of this work is to confirm the reliability of the modeling approach and the industrial feasibility of the method, which will be implemented on the industrial station for the measurement of historical wastes. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2011

Evaluation of brachytherapy lung implant dose distributions from photon-emitting sources due to tissue heterogeneities

Purpose: Photon-emitting brachytherapy sources are used for permanent implantation to treat lung cancer. However, the current brachytherapy dose calculation formalism assumes a homogeneous water medium without considering the influence of radiation scatter or tissue heterogeneities. The purpose of this study was to determine the dosimetric effects of tissue heterogeneities for permanent lung brachytherapy. Methods: The MCNP5 v1.40 radiation transport code was used for Monte Carlo (MC) simulations. Point sources with energies of 0.02, 0.03, 0.05, 0.1, 0.2, and 0.4 MeV were simulated to cover the range of pertinent brachytherapy energies and to glean dosimetric trends independent of specific radionuclide emissions. Source positions from postimplant CT scans of five patient implants were used for source coordinates, with dose normalized to 200 Gy at the center of each implant. With the presence of fibrosis (around the implant), cortical bone, lung, and healthy tissues, dose distributions and {sub PTV}DVH were calculated using the MCNP *FMESH4 tally and the NIST mass-energy absorption coefficients. This process was repeated upon replacing all tissues with water. For all photon energies, 10{sup 9} histories were simulated to achieve statistical errors (k = 1) typically of 1%. Results: The mean PTV doses calculated using tissue heterogeneities for all five patients changed (compared to dose to water) by only a few percent over the examined photon energy range, as did PTV dose at the implant center. The {sub PTV}V{sub 100} values were 81.2%, 90.0% (as normalized), 94.3%, 93.9%, 92.7%, and 92.2% for 0.02, 0.03, 0.05, 0.1, 0.2, and 0.4 MeV source photons, respectively. Relative to water, the maximum bone doses were higher by factors of 3.7, 5.1, 5.2, 2.4, 1.2, and 1.0 The maximum lung doses were about 0.98, 0.94, 0.91, 0.94, 0.97, and 0.99. Relative to water, the maximum healthy tissue doses at the mediastinal position were higher by factors of 9.8, 2.2, 1.3, 1.1, 1.1, and 1.1. However, the maximum doses to these healthy tissues were only 3.1, 7.2, 11.3, 10.9, 9.0, and 8.1 Gy while maximum bone doses were 66, 177, 236, 106, 49, and 39 Gy, respectively. Similarly, maximum lung doses were 55, 66, 73, 74, 73, and 73 Gy, respectively. Conclusions: The current brachytherapy dose calculation formalism overestimates PTV dose and significantly underestimates doses to bone and healthy tissue. Further investigation using specific brachytherapy source models and patient-based CT datasets as MC input may indicate whether the observed trends can be generalized for low-energy lung brachytherapy dosimetry.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2019

Precision Description of Processes at Colliders in the SANC System

A review of the SANC computer system intended for theoretical support of experiments at colliders is presented. The system allows the precision predictions to be obtained semiautomatically for a wide class of particle interaction processes within the Standard Model. In this case, one considers total contributions of one-loop radiative corrections. Basic elements of the computer system are described, and examples of using the system for the high-precision description of certain processes of the Standard Model particle interactions are given. The MCSANC code developed using the Monte Carlo simulation is presented, which is used to calculate cross sections of a number of processes, investigated at the Large Hadron Collider. The prospects of research development in this field for theoretical support at future hadron and lepton colliders are discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

lanl/jaybenne

Monte Carlo thermal radiation transport code

Ryan, Ben↗

DOE OSTI2023

Fully Implicit Conjugate Heat Transfer Analysis of the ARC-Class Vacuum Vessel

The coupled simulation of fusion reactor blankets including neutronics, thermal-hydraulics and thermo-mechanics is expected to speed up the design cycle of fusion reactor design concepts. In this work we demonstrate tight implicit coupling of conjugate heat transfer using the open-source Computational Fluid Dynamics software OpenFOAM for thermo-fluid mechanics and Diablo for thermo-solid mechanics. The heat transfer analysis is augmented by volumetric energy deposition from neutronic calculations using the Monte Carlo N-particle code on both solid and fluid parts of the vacuum vessel. An additional heat flux is imposed on the first wall estimated from the design power of the reactor. The tight coupling is realized through the open-source coupling library, preCICE, and tested on the vacuum vessel of the affordable, robust, compact reactor design by Commonwealth Fusion Systems. The features of the coupling and the influence of different coupling parameters such as coupling schemes, acceleration techniques and convergence criterion are discussed. The coupled simulation results are compared to a thermal-hydraulics simulation which includes only the fluid domains (the liquid immersion molten salt blanket and cooling channel) to demonstrate usefulness of a coupled simulation. Further analysis is performed to identify regions of hot spots for subsequent design improvement. This introduces the outline for integrating conjugate electromagnetics and fluid/solid mechanics (e.g., allow for deformation of the cooling channel walls) with our present approach for future analysis.

Sircar, Arpan↗

DOE OSTI2021

Sensitivity-based Similarity Metrics for New Experiment Design Optimization

The nuclear data used in advanced reactor simulations requires validation. Data from nuclear criticality experiments can provide this validation. New nuclear criticality experiment design requires extensive knowledge and expert judgement such that the experimental design parameters are selected in such a way to keep the experiment subcritical. To aide in this experimental design process, professionals can utilize sensitivity and uncertainty analysis. Sensitivity and uncertainty analysis relies on matching new application experiments with currently existing benchmark experiments. Currently, there is functionality in the Whisper 1.1 software package to calculate a similarity metric based on neutron multiplication factor sensitivity coefficients between a new application designed by the user and existing International Criticality Safety Benchmark Experiment Project (ICSBEP) benchmarks. The Whisper 1.1 software package is included in Monte Carlo N-Particle ® Code Version 6.21 (MCNP ® 6.2). This work is geared toward expanding this capability to new similarity metrics based on beta-effective sensitivity coefficients and reactivity coefficient sensitivity coefficients. While the investigation of these sensitivity coefficients is presented in detail in separate works at this same conference, this work will be primarily focused on studying the similarity metrics in more detail. These similarity metrics will then be incorporated into the optimization algorithms used for experiment design in EUCLID (Experiments Underpinned by Computational Learning for Improvements in nuclear Data), which is a Los Alamos National Laboratory (LANL) project designed to constrain nuclear data of interest, such that adjustments can be made to possible inaccuracies. A more detailed optimization can be subsequently performed by breaking down these similarity metrics by isotope, reaction, and energy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2012

2012 SARA Students Technical Report

The Service Academy Research Associates (SARA) program provides an opportunity for Midshipmen and Cadets from US Service Academies to participate in research at Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), and Sandia National Laboratory for several weeks during the summer as part of their summer training assignments. During the summer of 2012, three Midshipmen were assigned to work with the XCP Division at LANL for approximately 5-6 weeks. As one of the nation's top national security science laboratories, LANL stretches across 36 square miles, has over 2,100 facilities, and employs over 9,000 individuals including a significant number of students and postdocs. LANL's mission is to 'apply science and technology to: ensure the safety, security, and reliability of the US nuclear deterrent, reduce global threats, and solve other emerging national security challenges.' While LANL officially operates under the US Department of Energy (DoE), fulfilling this mission requires mutual cooperation with the US Department of Defense (DoD) as well. LANL's high concentration of knowledge and experience provides interns a chance to perform research in many disciplines, and its connection with the DoD in both operation and personnel gives SARA students insight to career possibilities both during and after military service. SARA students have plenty of opportunity to enjoy hiking, camping, the Los Alamos YMCA, and many other outdoor activities in New Mexico while staying at the Buffalo Thunder Resort, located 20 miles east of the lab. XCP Division is the Computational Physics division of LANL's Weapons Department. Working with XCP Division requires individuals to be Q cleared by the DoE. This means it is significantly more convenient for SARA students to be assigned to XCP Division than their civilian counterparts as the DoD CNWDI clearance held by SARA students is easily transferred to the lab prior to the students arriving at the start of the summer. SARA students working with XCP Division were given a comprehensive introduction into nuclear engineering and physics, nuclear weapons, and radiation transport and detection via texts and lectures at various classification levels. Students also attended tours of several prominent facilities at LANL including TA-41 Ice House, TA-55 PF-4 plutonium facility, the Nicholas C. Metropolis Center for Modeling and Simulation, also known as the Secure Computing Center (SCC), and the Dual-Axis Radiological Hydro Test (DARHT) facility; in addition, SARA students accompanied by LANL staff traveled to Minot AFB in North Dakota for tours of the 5th Bomb Wing and 91st Missile Wing facilities. Students participated in a week long class on the Monte Carlo N Particle (MCNP) code to supplement their understanding of radiation transport simulations. SARA students were then tasked with using this knowledge to model radiation detectors and use MCNP to compare their models to experimental data and previously accepted models.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗