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Fast Time Response Electromagnetic Disruption Mitigation Concept

An important and urgent issue for ITER is predicting and controlling disruptions. Tokamaks and spherical tokamaks have the potential to disrupt. Methods to rapidly quench the discharge after an impending disruption is detected are essential to protect the vessel and internal components. The warning time for the onset of some disruptions in tokamaks could be <10 ms, which poses stringent requirements on the disruption mitigation system for reactor systems. In this proposed method, a cylindrical boron nitride projectile containing a radiative payload composed of boron, boron nitride, or beryllium particulate matter and weighing similar to 15 g is accelerated to velocities on the order of 1 to 2 km/s in <2 ms in a linear rail gun accelerator. A partially fragmented capsule is then injected into the tokamak discharge in the 3- to 6-ms timescale, where the radiative payload is dispersed. The device referred to as an electromagnetic particle injector has the potential to meet the short warning timescales for which a reactor disruption mitigation system must be built. The system is fully electromagnetic, with no mechanical moving parts, which ensures high reliability after a period of long standby.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Gamma-Ray Simulated Spectrum Deconvolution of a LaBr₃ 1-in. x 1-in. Scintillator for Nondestructive ATR Fuel Burnup On-Site Predictions

A deconvolution method for a LaBr₃ 1"x1" detector for nondestructive Advanced Test Reactor (ATR) fuel burnup applications was developed. The method consisted of obtaining the detector response function, applying a deconvolution algorithm to 1”x1” LaBr₃ simulated, data along with evaluating the effects that deconvolution have on nondestructively determining ATR fuel burnup. The simulated response function of the detector was obtained using MCNPX as well with experimental data. The Maximum-Likelihood Expectation Maximization (MLEM) deconvolution algorithm was selected to enhance one-isotope source-simulated and fuel- simulated spectra. The final evaluation of the study consisted of measuring the performance of the fuel burnup calibration curve for the convoluted and deconvoluted cases. The methodology was developed in order to help design a reliable, high resolution, rugged and robust detection system for the ATR fuel canal capable of collecting high performance data for model validation, along with a system that can calculate burnup and using experimental scintillator detector data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Post-processing of phase change material in a zero-change commercial silicon photonic process

Integration of phase change material (PCM) with photonic integrated circuits can transform large-scale photonic systems by providing non-volatile control over phase and amplitude. The next generation of commercial silicon photonic processes can benefit from the addition of PCM to enable ultra-low power, highly reconfigurable, and compact photonic integrated circuits for large-scale applications. Despite all the advantages of PCM-based photonics, today’s commercial foundries do not provide them in their silicon photonic processes yet. We demonstrate the first-ever electrically programmable PCM device that is monolithically post-processed in a commercial foundry silicon photonics process using a few fabrication steps and coarse-resolution photolithography. These devices achieved 1.4 dB/μm of amplitude switching contrast using a thin layer of 12.5 nm GeSbTe in this work. We have also characterized the reconfiguration speed as well as repeatability of these devices over 20,000 switching cycles. Our solution enables non-volatile photonic VLSI systems that can be fabricated at low cost and high reliability in a commercial foundry process, paving the way for the development of non-volatile programmable photonic integrated circuits for a variety of emerging applications.

Optics↗

Root Causes of Field Emitters in SRF Cavities Placed in CEBAF Tunnel

It has been suspected that appearance of new field emitters can occur in SRF cavities after their placement in accelerator tunnel for long term beam operation. This apparently has been the case for CEBAF. However, no physical evidence has been shown in the past. In this contribution, we will report on the recent results concerning the root cause of field emitters in SRF cavities placed in CEBAF tunnel. We will discuss these results in the context of high-reliability and low-cryogenic-loss operation of CEBAF.

Geng, Rongli↗

Progress towards the completion of the proton power upgrade project

The Proton Power Upgrade project at the Spallation Neutron Source at Oak Ridge National Laboratory will increase the proton beam power capability from 1.4 to 2.8 MW. Upon completion in early 2025, 2 MW of beam power will be available for neutron production at the existing first target station (FTS) with the remaining beam power available for the future second target station (STS). The project has installed seven superconducting radio-frequency (RF) cryomodules and supporting RF power systems to increase the beam energy by 30% to 1.3 GeV, and the beam current will be increased by 50%. The injection and extraction region of the accumulator ring are being upgraded, and a new 2 MW mercury target has been developed along with supporting equipment for high-flow gas injection to mitigate cavitation and fatigue stress. The first four cryomodules and supporting systems were commissioned in 2022-2023 and supported neutron production at 1.05 GeV, 1.7 MW with high reliability. The first-article 2 MW target was operated successfully for approximately 4400 MW-Hours over two run periods. The long outage began in August 2023 for installation of the remaining technical equipment and construction of the Ring-to-Target Beam Transport tunnel stub that will enable connection to the STS without interrupting operation of the FTS. The upgrade is proceeding on-schedule and on-budget, and resumption of neutron production for the user program is planned for July 2024.

43 PARTICLE ACCELERATORS↗

FY2011 Oak Ridge National Laboratory Annual Progress Report for the Power Electronics and Electric Machinery Program

The U.S. Department of Energy (DOE) announced in May 2011 a new cooperative research effort comprising DOE, the U.S. Council for Automotive Research (composed of automakers Ford Motor Company, General Motors Company, and Chrysler Group), Tesla Motors, and representatives of the electric utility and petroleum industries. Known as U.S. DRIVE (Driving Research and Innovation for Vehicle efficiency and Energy sustainability), it represents DOE's commitment to developing public-private partnerships to fund high risk-high reward research into advanced automotive technologies. The new partnership replaces and builds upon the partnership known as FreedomCAR (derived from 'Freedom' and 'Cooperative Automotive Research') that ran from 2002 through 2010 and the Partnership for a New Generation of Vehicles initiative that ran from 1993 through 2001. The Oak Ridge National Laboratory's (ORNL's) Power Electronics and Electric Machines (PEEM) subprogram within the DOE Vehicle Technologies Program (VTP) provides support and guidance for many cutting-edge automotive technologies now under development. Research is focused on developing revolutionary new power electronics (PE), electric motor (EM), and traction drive system technologies that will leapfrog current on-the-road technologies. The research and development (R&D) is also aimed at achieving a greater understanding of and improvements in the way the various new components of tomorrow's automobiles will function as a unified system to improve fuel efficiency. In supporting the development of advanced vehicle propulsion systems, the PEEM subprogram has enabled the development of technologies that will significantly improve efficiency, costs, and fuel economy. The PEEM subprogram supports the efforts of the U.S. DRIVE partnership through a three phase approach intended to: (1) identify overall propulsion and vehicle related needs by analyzing programmatic goals and reviewing industry's recommendations and requirements and then develop the appropriate technical targets for systems, subsystems, and component R&D activities; (2) develop and validate individual subsystems and components, including EMs and PE; and (3) determine how well the components and subsystems work together in a vehicle environment or as a complete propulsion system and whether the efficiency and performance targets at the vehicle level have been achieved. The research performed under this subprogram will help remove technical and cost barriers to enable the development of technology for use in such advanced vehicles as hybrid electric vehicles (HEVs), plug-in HEVs (PHEVs), battery electric vehicles, and fuel-cell-powered automobiles that meet the goals of the VTP. A key element in making these advanced vehicles practical is providing an affordable electric traction drive system. This will require attaining weight, volume, efficiency, and cost targets for the PE and EM subsystems of the traction drive system. Areas of development include: (1) novel traction motor designs that result in increased power density and lower cost; (2) inverter technologies involving new topologies to achieve higher efficiency with the ability to accommodate higher temperature environments while achieving high reliability; (3) converter concepts that use methods of reducing the component count and integrating functionality to decrease size, weight, and cost; (4) new onboard battery charging concepts that result in decreased cost and size; (5) more effective thermal control through innovative packaging technologies; and (6) integrated motor-inverter traction drive system concepts. ORNL's PEEM research program conducts fundamental research, evaluates hardware, and assists in the technical direction of the VTP Advanced Power Electronics and Electric Motors (APEEM) program. In this role, ORNL serves on the U.S. DRIVE Electrical and Electronics Technical Team, evaluates proposals for DOE, and lends its technological expertise to the direction of projects and evaluation of developing technologies. ORNL also executes specific projects for DOE. DOE's continuing R&D into advanced vehicle technologies for transportation offers the possibility of reducing the nation's dependence on foreign oil and the negative economic impacts of crude oil price fluctuations. It also supports the Administration's goal of deploying 1 million PHEVs by 2015.

02 PETROLEUM↗

Advanced Fuels Campaign Execution Plan (Revision 1)

The purpose of the Advanced Fuels Campaign (AFC) Execution Plan is to communicate the structure and management of research, development, and demonstration (RD&D) activities within the Fuel Cycle Research and Development (FCRD) program. Included in this document is an overview of the FCRD program, a description of the difference between revolutionary and evolutionary approaches to nuclear fuel development, the meaning of science-based development of nuclear fuels, and the "Grand Challenge" for the AFC that would, if achieved, provide a transformational technology to the nuclear industry in the form of a high performance, high reliability nuclear fuel system. The activities that will be conducted by the AFC to achieve success towards this grand challenge are described and the goals and milestones over the next 20 to 40 year period of research and development are established.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Hydrogen Fueling Station in Honolulu, Hawaii Feasibility Analysis

The Department of Energy Hydrogen & Fuel Cells Program Plan (September 2011) identifies the use of hydrogen for government and fleet electric vehicles as a key step for achieving “reduced greenhouse gas emissions; reduced oil consumption; expanded use of renewable power…; highly efficient energy conversion; fuel flexibility…; reduced air pollution; and highly reliable grid-support.” This report synthesizes several pieces of existing information that can inform a decision regarding the viability of deploying a hydrogen (H2) fueling station at the Fort Armstrong site in Honolulu, Hawaii.

08 HYDROGEN↗

ECH Technology Development

Electron Cyclotron Heating (ECH) is needed for plasma heating, current drive, plasma stability control, and other applications in fusion energy sciences research. The program of fusion energy sciences supported by U. S. DOE, Office of Science, Fusion Energy Sciences relies on the development of ECH technology to meet the needs of several plasma devices working at the frontier of fusion energy sciences research. The largest operating ECH system in the world is at DIII-D, consisting of six 1 MW, 110 GHz gyrotrons capable of ten second pulsed operation, plus two newer gyrotrons. The ECH Technology Development research program investigated the options for upgrading the DIII-D 110 GHz ECH system. Options included extending present-day 1 MW technology to 1.3 – 1.5 MW power levels or developing an entirely new approach to achieve up to 2 MW of power per gyrotron. The research consisted of theoretical research and designs conducted by Communication and Power Industries of Palo Alto, CA working with MIT. Results of the study would be validated in a later phase by research on short pulse length gyrotrons at MIT and long pulse / cw gyrotrons in industry. This research follows a highly successful program of development that has led to the highly reliable, six megawatt ECH system at the DIII-D tokamak. Eventually, gyrotrons at the 1.5 megawatt to multi-megawatt power level will be needed for heating and current drive in large scale plasmas including ITER and DEMO.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Materials compatibility and aging for flux and cleaner combinations

A materials study of high reliability electronics cleaning is presented here. In Phase 1, mixed type substrates underwent a condensed contaminants application to view a worst- case scenario for unremoved flux with cleaning agent residue for parts in a silicone oil filled environment. In Phase 2, fluxes applied to copper coupons and to printed wiring boards underwent gentle cleaning then accelerated aging in air at 65% humidity and 30 O C. Both sets were aged for 4 weeks. Contaminants were no-clean (ORL0), water soluble (ORH1 liquid and ORH0 paste), and rosin (RMA; ROL0) fluxes. Defluxing agents were water, solvents, and engineered aqueous defluxers. In the first phase, coupons had flux applied and heated, then were placed in vials of oil with a small amount of cleaning agent and additional coupons. In the second phase, pairs of copper coupons and PWB were hand soldered by application of each flux, using tin-lead solder in a strip across the coupon or a set of test components on the PWB. One of each pair was cleaned in each cleaning agent, the first with a typical clean, and the second with a brief clean. Ionic contamination residue was measured before accelerated aging. After aging, substrates were removed and a visual record of coupon damage made, from which a subjective rank was applied for comparison between the various flux and defluxer combinations; more corrosion equated to higher rank. The ORH1 water soluble flux resulted in the highest ranking in both phases, the RMA flux the least. For the first phase, in which flux and defluxer remained on coupons, the aqueous defluxers led to worse corrosion. The vapor phase cleaning agents resulted in the highest ranking in the second phase, in which there was no physical cleaning. Further study of cleaning and rinsing parameters will be required.

36 MATERIALS SCIENCE↗

Results for Phase I of the IAEA Coordinated Research Program on HTGR Uncertainties

The quantification of uncertainties in design and safety analysis of reactors is today not only broadly accepted, but in many cases became the preferred way to replace traditional conservative analysis for safety and licensing analysis. The use of a more fundamental methodology is also consistent with the reliable high fidelity physics models and robust, efficient, and accurate codes available today. To facilitate uncertainty analysis applications a comprehensive approach and methodology must be developed and applied. High Temperature Gas-cooled Reactors (HTGR) has its own peculiarities, coated particle design, large graphite quantities, different materials and high temperatures that also require other simulation requirements. The IAEA has therefore launched a Coordinated Research Project (CRP) on the HTGR Uncertainty Analysis in Modeling (UAM) in 2013 to study uncertainty propagation specifically in the HTGR analysis chain. Two benchmark problems are defined, with the prismatic design represented by the General Atomics (GA) MHTGR-350 and a 250 MW modular pebble bed design similar to the HTR-PM (INET, China). This report summarizes the contributions of the HTGR Methods Simulation group at Idaho National Laboratory (INL) up to this point of the CRP. The activities at INL have been focused so far on creating the problem specifications for the prismatic design, as well as providing reference solutions for the exercises defined for Phase I. An overview is provided of the HTGR UAM objectives and scope, and the detailed specifications for Exercises I-1, I-2, I-3 and I-4 are also included here for completeness. The main focus of the report is the compilation and discussion of reference results for Phase I (i.e. for input parameters at their nominal or best-estimate values), which is defined as the first step of the uncertainty quantification process. These reference results can be used by other CRP participants for comparison with other codes or their own reference results. The status on the Monte Carlo modeling of the experimental VHTRC facility is also discussed. Reference results were obtained for the neutronics stand-alone cases (Ex. I-1 and Ex. I-2) using the (relatively new) Monte Carlo code Serpent, and comparisons were performed with the more established Monte Carlo codes MCNP and KENO-VI. For the thermal-fluids stand-alone cases (Ex. I-3 and I-4) the commercial CFD code CFX was utilized to obtain reference results that can be compared with lower fidelity tools.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Summary. “Materials Challenges in Nuclear Energy,” S.J. Zinkle, 2013

Nuclear energy continues to grow in abundance and importance. It offers a future electric grid based entirely off of green energy, and it has numerous applications. Nuclear power has capabilities to desalinate water, deliver process heat or steam, affordably crack hydrogen from water, and extract unconventional fossil fuel sources. Current light water reactors demonstrate high reliability under normal operating conditions. Researchers have shown significant interest and investigating how to extend reactor lifespans and into other possible reactor designs. Further understanding of mechanisms responsible for corrosion and stress corrosion cracking, radiation hardening and degradation, and nuclear fuels innovations can lead to safer, more reliable, and cost-effective water-cooled nuclear reactors for electricity production.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Exe-Guard Project

The exe-Guard Project is an alliance between Dominion Virginia Power (DVP), Sandia National Laboratories (SNL), Dartmouth University, and Schweitzer Engineering Laboratories (SEL). SEL is primary recipient on this project. The exe-Guard project was selected for award under DE-FOA-0000359 with CFDA number 81.122 to address Topic Area of Interest 4: Hardened platforms and Systems. The exe-Guard project developed an antivirus solution for control system embedded devices to prevent the execution of unauthorized code and maintain settings and configuration integrity. This project created a white list antivirus solution for control systems capable of running on embedded Linux® operating systems. White list antivirus methods allow only credible programs to run through the use of digital signatures and hash functions. Once a system’s secure state is baselined, white list antivirus software denies deviations from that state because of the installation of malicious code as this changes hash results. Black list antivirus software has been effective in traditional IT environments but has negative implications for control systems. Black list antivirus uses pattern matching and behavioral analysis to identify system threats while relying on regular updates to the signature file and recurrent system scanning. Black list antivirus is vulnerable to zero day exploits which have not yet been incorporated into a signature file update. System scans hamper the performance of high availability applications, as revealed in NIST special publication 1058 which summarizes the impact of blacklist antivirus on control systems: Manual or “on-demand” scanning has a major effect on control processes in that they take CPU time needed by the control process (Sometimes close to 100% of CPU time). Minimizing the antivirus software throttle setting will reduce but not eliminate this effect. Signature updates can also take up to 100% of CPU time, but for a much shorter period than a typical manual scanning process. Control systems are vulnerable to performance losses if off-the-shelf blacklist antivirus solutions aren’t implemented with care. This investment in configuration in addition to constant decommissioning to perform manual signature file updates is unprecedented and impractical. Additionally, control systems are often disconnected or islanded from the network making the delivery of signature updates difficult. Exe-Guard project developed a white list antivirus solution that mitigated the above drawbacks and allows control systems to cost-effectively apply malware protection while maintaining high reliability. The application of security patches can also be minimized since white listing maintains constant defense against unauthorized code execution. Security patches can instead be applied in less frequent intervals where system decommissioning can be scheduled and planned for. Since control systems are less dynamic than IT environments, the feasibility of maintaining a secure baselined state is more practical. Because upgrades are performed in infrequent, calculated intervals, it allows a new security baseline to be established before the system is returned to service. Exe-Guard built on the efforts of SNL under the Code Seal project. SNL demonstrated prototype Trust Anchors on the project which are independent monitoring and control devices that can be integrated into untrustworthy components. The exe-Guard team started with the lessons learned under this project then designed commercial solution for white list malware protection. Malware is a real threat, even on islanded or un-networked installations, since operators can unintentionally install infected files, plug in infected mass storage devices, or infect a piece of equipment on the islanded local area network that can then spread to other connected equipment. Protection at the device level is one of the last layers of defense in a security-in-depth defense model before an asset becomes compromised. This project provided non-destructive intrusion, isolation and automated response solution, achieving a goal of the Department of Energy (DOE) Roadmap to Secure Control Systems. It also addressed CIP-007-R4 which requires asset owners to employ malicious software prevention tools on assets within the electronic security perimeter. In addition, the CIP-007-R3 requirement for security patch management is minimized because white listing narrows the impact of vulnerabilities and patch releases. The exe-Guard Project completed all tasks identified in the statement of project objective and identified additional tasks within scope that were performed and completed within the original budget. The cost share was met and all deliverables were successfully completed and submitted on time. Most importantly the technology developed and commercialized under this project has been adopted by the Energy sector and thousands of devices with exe-Guard technology integrated in them have now been deployed and are protecting our power systems today

24 POWER TRANSMISSION AND DISTRIBUTION↗

Applying DER-CAM for IIT Microgrid Explansion Planning

The Distributed Energy Resources Customer Adoption Model (DER-CAM) is an economic and environmental model of customer DER adoption. This model has been in development at the Lawrence Berkeley National Laboratory since 2000. The objective of the model is to find optimal DER investments while minimizing total energy costs or carbon dioxide (CO2) emissions, or achieving a weighted objective that simultaneously considers both criteria. The Illinois Institute of Technology (IIT) Microgrid project started in August 2008, and the majority of the project was completed in May 2013. IIT Microgrid, funded mostly by a grant from the U.S. Department of Energy as well as State and philanthropic contributions, empowers the campus consumers with the objective of establishing a smart microgrid that is highly reliable, economically viable, environmentally friendly, fuel-efficient, and resilient in extreme circumstances with a self-healing capability. In this project, we apply DER-CAM to study the expansion planning of the IIT Microgrid. First, the load data, environmental data, utility data, and technology data for the IIT Microgrid are gathered and organized to follow the DER-CAM input requirements. Then, DERCAM is applied to study the expansion planning of the IIT Microgrid for different cases, where different objectives in DER-CAM and different utility conditions are tested. Case 1 considers the objective of minimizing energy costs with fixed utility rates and 100% electric utility availability. Case 2 considers the objective of minimizing energy costs with real-time utility rates and 4 emergency weeks when the IIT Microgrid does not have access to the electric utility grid and has to operate in island mode. In Case 3, the utility rates are restored to fixed values and 100% electric utility availability is assumed, but a weighted multi-objective (Obj: a × costs + b × CO2 emissions, where a and b are weights for cost minimization and CO2 emissions minimization) is utilized to consider both energy costs and CO2 emissions. On the basis of the test results, the IIT Microgrid has the potential to benefit from investments in more DER technologies. The current annual energy costs and CO2 emissions for the IIT Microgrid are 6,495.1 k$ and 39,838.5 metric tons, respectively. This represents the baseline for this project.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Solar PV O&M Standards and Best Practices - Existing Gaps and Improvement Efforts

As greater numbers of photovoltaic (PV) systems are being installed, operations & maintenance (O&M) activities will need to be performed to ensure the PV system is operating as designed over its useful lifetime. To mitigate risks to PV system availability and performance, standardized procedures for O&M activities are needed to ensure high reliability and long-term system bankability. Efforts are just getting underway to address the need for standard O&M procedures as PV gains a larger share of U.S. generation capacity. Due to the existing landscape of how and where PV is installed, including distributed generation from small and medium PV systems, as well as large, centralized utility-scale PV, O&M activities will require different levels of expertise and reporting, making standards even more important. This report summarizes recent efforts made by solar industry stakeholders to identify the existing standards and best practices applied to solar PV O&M activities, and determine the gaps that have yet to be, or are currently being addressed by industry.

14 SOLAR ENERGY↗

Solar PV O&M Standards and Best Practices – Existing Gaps and Improvement Efforts

As greater numbers of photovoltaic (PV) systems are being installed, operations & maintenance (O&M) activities will need to be performed to ensure the PV system is operating as designed over its useful lifetime. To mitigate risks to PV system availability and performance, standardized procedures for O&M activities are needed to ensure high reliability and long-term system bankability. Efforts are just getting underway to address the need for standard O&M procedures as PV gains a larger share of U.S. generation capacity. Due to the existing landscape of how and where PV is installed, including distributed generation from small and medium PV systems, as well as large, centralized utility-scale PV, O&M activities will require different levels of expertise and reporting, making standards even more important. This report summarizes recent efforts made by solar industry stakeholders to identify the existing standards and best practices applied to solar PV O&M activities, and determine the gaps that have yet to be, or are currently being addressed by industry.

14 SOLAR ENERGY↗

Testing the Feasibility of a Low-Cost Network Performance Measurement Infrastructure

Todays science collaborations depend on reliable, high performance networks, but monitoring the end-to-end performance of a network can be costly and difficult. The most accurate approaches involve using measurement equipment in many locations, which can be both expensive and difficult to manage due to immobile or complicated assets. The perfSONAR framework facilitates network measurement making management of the tests more reasonable. Traditional deployments have used over-provisioned servers, which can be expensive to deploy and maintain. As scientific network uses proliferate, there is a desire to instrument more facets of a network to better understand trends. This work explores low cost alternatives to assist with network measurement. Benefits include the ability to deploy more resources quickly, and reduced capital and operating expenditures. Finally, we present candidate platforms and a testing scenario that evaluated the relative merits of four types of small form factor equipment to deliver accurate performance measurements.

97 MATHEMATICS AND COMPUTING↗

A Complex Systems Approach to More Resilient Multi-Layered Security Systems

In July 2012, protestors cut through security fences and gained access to the Y-12 National Security Complex. This was believed to be a highly reliable, multi-layered security system. This report documents the results of a Laboratory Directed Research and Development (LDRD) project that created a consistent, robust mathematical framework using complex systems analysis algorithms and techniques to better understand the emergent behavior, vulnerabilities and resiliency of multi-layered security systems subject to budget constraints and competing security priorities. Because there are several dimensions to security system performance and a range of attacks that might occur, the framework is multi-objective for a performance frontier to be estimated. This research explicitly uses probability of intruder interruption given detection (P I ) as the primary resilience metric. We demonstrate the utility of this framework with both notional as well as real-world examples of Physical Protection Systems (PPSs) and validate using a well-established force-on-force simulation tool, Umbra.

97 MATHEMATICS AND COMPUTING↗