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At least 199 records · Page 11

Irradiation-Induced Structural Disorder and Its Influence on the Mechanical Response of Polycrystalline MoS2

Molybdenum disulfide (MoS2) thin films are widely used as dry-film lubricants and protective coatings in aerospace and other radiation-exposed environments. Conventional synthesis routes produce polycrystalline films whose grain boundaries and other native defects cause their mechanical and tribological behavior to differ substantially from that of ideal single crystals. Under irradiation, these films progressively evolve from polycrystalline structures, composed of layered MoS2 grains, into highly disordered and eventually amorphous structures, altering both their tribological performance and mechanical integrity. Here, we employ reactive atomistic simulations to investigate irradiation-driven structural evolution in bulk polycrystalline MoS2. Using controlled primary knock-on atom (PKA) events, we characterize the progressive transition from a polycrystalline microstructure to an amorphous network by tracking defect accumulation and structural disorder. We then establish how this transition modifies the dominant deformation mechanisms and the temperature-dependent tensile response. Specifically, irradiation suppresses interlayer sliding and delamination, mechanisms which facilitate the deformation of the pristine polycrystal, resulting in defect-induced hardening. Broadly, our results establish direct process–structure–property relationships linking irradiation-induced defect accumulation, microstructural evolution, deformation mechanisms, and mechanical behavior, providing an atomistic framework for understanding the structural integrity and long-term reliability of irradiated MoS2 coatings.

Moore, Daniel [Sandia National Laboratories (SNL)]↗

Impact of Irradiation on Corrosion Performance of Hybrid Organic/Inorganic Coatings on Austenitic Stainless Steel

The effects of gamma radiation on the performance of two corrosion-resistant coatings applied to stainless-steel 304L (SS304L) surfaces are presented. Specifically, the ability of the coatings to mitigate corrosion of SS304L surfaces as a function of the dose received (0–1300 Mrad) and dose rate (176 compared to 1054 rad/s) is evaluated using electrochemical methods, spectroscopy, and microscopy. Coating A, an organic/inorganic hybrid coating consisting of a two-part silica ceramic component and a polymer linker was evaluated in comparison to Coating B, which utilized Coating A as a topcoat for a commercial, off-the-shelf, Zn-rich primer. Post irradiation, Coating A demonstrated some corrosion protection following exposure to low levels of gamma radiation, but coating degradation occurred with an increased exposure dose and resulted in isolated regions of corrosion initiation. For Coating B, greater corrosion resistance was observed compared to Coating A due to the sacrificial nature of the Zn at elevated doses of gamma radiation. No effect of the dose rate (for the single dose examined) was observed for either coating. It is proposed for Coating B that as the polymer coating thermally degrades above 250 °C (bond scission of the polymer occurs), the remaining Zinc layer adhered to the SS304L post-irradiation enables enhanced corrosion resistance as compared to Coating A, which displays solely polymer degradation. The results presented herein establish an understanding of coating behavior with radiation exposure, specifically the relationship between corrosion coating performance and radiation dose, and can inform ageing and lifetime management for various applications.

degradation↗

Benchmarking MCNP models to support gamma irradiation experiments

Seismic isolators and damping devices have been used for 30+ years to reduce seismic forces and deployed in 10,000+ structures, including bridges, buildings, and mission-critical infrastructure. Studies have shown that seismic isolation of nuclear power plants can reduce the seismic risk by several orders of magnitude and substantially reduce the overnight capital cost. Advanced reactor developers are considering seismic isolation as an integral design feature in their reactor design. It can either be deployed at the building level, isolating the entire reactor building, or at the component level, isolating individual pieces of safety-class equipment, such as a reactor vessel or a steam generator. For equipment isolation, located close to the reactor vessel, the seismic isolators and/or damping devices may be exposed to gamma and neutron radiation, with a possible effect on their mechanical properties which would affect the response of the isolated equipment under earthquake shaking. The Department of Energy, as part of its Nuclear Energy University Program (NEUP), in collaboration with the Idaho National Laboratory (INL), is funding a project at the University at Buffalo (UB) to investigate the effect of gamma radiation on the mechanical properties of various seismic protective devices. (When isolating equipment, the seismic protective devices will be located outside the reactor vessel where the neutron exposure will be insignificant.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

The Maintainable Fusion Pilot Plant

The US fusion community has coalesced around the goal of building an FPP as described by the National Academies of Science, Engineering, and Medicine (NASEM). In addition to demonstrating the viability of the technologies necessary to operate such a plant, including demonstration of net energy and electricity production, NASEM found that a “fusion pilot plant will need to demonstrate the ability to efficiently perform remote maintenance and replacement in support of the design of a power plant, taking into account details of the consequences of the fusion environment, such as material activation and tritium retention in components.” Current designs of fusion demonstration reactors do usually foresee a regular exchange of their first wall modules, including the tritium breeding blankets. In the European Power Plant Conceptual Studies, it is assumed that a fusion reactor will need to change its divertor every 2 years and its first wall blanket module every 5 to 6 years to reach acceptable availability. Underlying this capability are remote-handling technologies to keep the outage for the exchange of these components short. There are many uncertainties in the remote-handling schemes, and most schemes are at a preconceptual level at best. In addition, the exchange of these components would either produce an enormous rad-waste stream or would require an enormous refurbishment activity with huge cost-prohibitive hot-cells. Past Fusion Nuclear Science Facility (FNSF) preconceptual studies have led to hot cell dimensions of an unbelievable size, likely costing tens of billions of dollars. Already at The Way (previously International Thermonuclear Experimental Reactor, ITER), hot-cells have become cost-prohibitive, demanding redesigns of the ITER first wall to reduce the toxic rad-waste/inventory. In this in-situ PFC repair project, a concept for a long-life, maintainable first wall module concept is developed and tested. This first wall concept relies on innovative remote handling to repair the first wall modules in-situ, avoiding costly refurbishments outside of the tokamak vessel. This approach was highlighted in the Fusion Energy Sciences Advisory Committee (FESAC) report on Transformative Enabling Capabilities for Efficient Advance Toward Fusion Energy. In general, the damage of the first wall armor is due to particle and radiation exposures. Load conditions vary from one fusion reactor design to another. In tokamaks, first wall Plasma Facing Components (PFCs) are exposed to far-Scrape-Off-Layer plasma fluxes, electromagnetic radiation, energetic CX neutrals, and potentially runaway electron beams. Protecting the first wall to the worst-case load conditions would require the design of a very thick first wall armor. Transient heat and particle fluxes due to disruptions or edge localized modes can lead to excessive heat loads resulting potentially in melting PFCs down to the cooling channel. Catastrophic events like these need to be avoided by appropriate disruption mitigation systems. However, failure of these systems will still put a first wall at an unacceptable risk. Hence, a first wall design needs to accommodate the occasional transient heat loads by introducing sacrificial limiters, which will absorb these transients.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comprehensive analysis of disruption mitigation methods using gas and pellet-like injections in ITER-like Tokamaks

Abstract Inert-gas shielding could be an effective mechanism for protection of plasma facing surfaces (PFS) against plasma particles impact and photon radiation heat loads during transient events in fusion devices. Neutral gas injection is one promising way to mitigate erosion of tokamak components and contamination. The objective of this work is to study and optimize mitigation methods using neutral gas and pellet-like injections to decrease the heat load to the divertor surfaces and to prevent vaporization of the various internal surfaces due to transient events in ITER-like devices. The integrated self-consistent models implemented in the HEIGHTS package was used for detailed analysis of the potential secondary plasma generation from the injected inert gas, its radiative characteristics, and shielding effectiveness. We varied the density, size, and location of an argon gas cloud to minimize the disruption energy deposited into the divertor components. We also investigated innovative ways for minor changes in ITER-like internal design to mitigate disruptions. We found the optimum parameters to fully protect ITER tokamak surfaces from erosion and vaporization during plasma instabilities. This preliminary analysis showed that using Ar gas injection methods could lead to enhancement in components lifetime in ITER-like and future DEMO devices with minor design changes.

Science & Technology - Other Topics↗

Horn Location Sensors for LBNF

The Horn Location Sensor (HLS) system—named for the magnetic focusing horns it monitors, along with other critical beamline elements – is a high-precision alignment system developed for the Long-Baseline Neutrino Facility (LBNF) to support the Deep Underground Neutrino Experiment (DUNE). With minimal maintenance, the HLS can operate reliably in environments with high radiation, and it ensures that key components such as the protective baffle, focusing horns, and beam position monitors are aligned correctly – each essential for maintaining one of the world’s most intense muon-neutrino beams. A high-precision hydrostatic level sensor, a linear variable differential transformer, and INVAR rods are all used in the system to monitor vertical motion and tilt with sub-millimeter accuracy. A novel Sweep Tracker interferometer enhances calibration fidelity by correcting for non-linearities in laser wavelength and scan rate in real time. A critical part of DUNE’s precision alignment and flux prediction requirements, the HLS system initially supports beam power of up to 1.2 MW and can be upgraded to 2.4 MW.

Frequency scanning interferometry↗

Classifying topology in photonic crystal slabs with radiative environments

Abstract In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. However, the out-of-plane radiative losses in those photonic Chern slabs has been previously neglected, yielding limited accuracy for predictions of these systems’ topological protection. Here, we develop a general framework for measuring the topological protection in photonic systems, such as in photonic crystal slabs, while accounting for in-plane and out-of-plane radiative losses. Our approach relies on the spectral localizer that combines the position and Hamiltonian matrices of the system to draw a real-picture of the system’s topology. This operator-based approach to topology allows us to use an effective Hamiltonian directly derived from the full-wave Maxwell equations after discretization via finite-elements method (FEM), resulting in the full account of all the system’s physical processes. As the spectral FEM-localizer is constructed solely from FEM discretization of the system’s master equation, the proposed framework is applicable to any physical system and is compatible with commonly used FEM software. Moving forward, we anticipate the generality of the method to aid in the topological classification of a broad range of complex physical systems.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

EMP, Attachment 2: Data Management Plan

This Data Management Plan (DMP) is an attachment to the Pacific Northwest National Laboratory Environmental Radiological Air Monitoring Plan (EMP). PNNL is a U.S. Department of Energy Office of Science national laboratory. Radioactive effluent monitoring and environmental surveillance for PNNL operations in Washington State are the responsibility of the PNNL Environmental Protection and Regulatory Programs division and are conducted by the Environmental Radiation Task staff. This DMP describes the data management processes for PNNL radioactive air emissions (stack) monitoring and environmental radiological ambient air surveillance activities.

40 CFR 61 Subpart H↗

Airborne Acoustic Vortex End Effector‐Based Contactless, Multi‐Mode, Programmable Control of Object Surfing

Abstract Tweezers based on optical, electric, magnetic, and acoustic fields have shown great potential for contactless object manipulation. However, current tweezers designed for manipulating millimeter‐sized objects such as droplets, particles, and small animals exhibit limitations in translation resolution, range, and path complexity. Here, a novel acoustic vortex tweezers system is introduced, which leverages a unique airborne acoustic vortex end effector integrated with a three‐degree‐of‐freedom (DoF) linear motion stage, for enabling contactless, multi‐mode, programmable manipulation of millimeter‐sized objects. The acoustic vortex end effector utilizes a cascaded circular acoustic array, which is portable and battery‐powered, to generate an acoustic vortex with a ring‐shaped energy pattern. The vortex applies acoustic radiation forces to trap and spin an object at its center, simultaneously protecting this object by repelling other materials away with its high‐energy ring. Moreover, The vortex tweezers system facilitates contactless, multi‐mode, programmable object surfing, as demonstrated in experiments involving trapping, repelling, and spinning particles, translating particles along complex paths, guiding particles around barriers, translating and rotating droplets containing zebrafish larvae, and merging droplets. With these capabilities, It is anticipated that the tweezers system will become a valuable tool for the automated, contactless handling of droplets, particles, and bio‐samples in biomedical and biochemical research.

Li, Teng↗

Statistical Uncertainty of Inhalation Dose Coefficients: Impact of Particle Deposition in ICRP 66 Human Respiratory Tract Model

Inhaled radioactive materials can pose a long-term health concern, as the material can be incorporated into the body’s metabolic pathways and remain in organs and tissues for extended durations. During the retention period, the radioactive material may localize in a source organ and irradiate adjacent target organs and tissues. Distribution of these materials changes over time, requiring biokinetic modeling to evaluate their movement through various tissues and organs. The evolving distribution depends on multiple inputs characterizing the inhaled material, such as particle size and size distribution, particle density, aspect ratio, specific radionuclide, the chemical form, and solubility. In addition, biological parameters such as breathing rate, breathing type (nasal or nasal/oral), respiratory system morphometry, tidal volume, functional residual capacity, and anatomical dead space all influence material transport. These aerosol properties and physiological characteristics of the respiratory tract jointly define a range of initial conditions that influence the time-dependent distribution of radioactive material. To evaluate both uncertainty in the initial conditions of inhalation exposure and the final output (committed effective dose) from biokinetic models, a Python-based software tool, Radiological Exposure Dose Calculator (REDCAL), was developed to propagate uncertainty within the human respiratory tract model. Focusing on deposition fraction uncertainty, the primary objective was to characterize the initial activity distribution across respiratory regions as a function of anticipated particle sizes and distributions. The impact of the deposition fraction uncertainty was propagated to committed effective dose coefficients for selected radionuclides in a companion publication. For each particle size, a lognormal distribution, characterized by its geometric mean as defined within ICRP Publication 66, serves as the basis for introducing uncertainty into the physical processes governing deposition in various lung regions. Finally, this study addresses the deposition process and examines how uncertainty in deposition mechanisms affects activity distribution in the airways, ultimately presenting the expected range and standard deviation of deposited activity as a function of particle size.

International Commission on Radiological Protectio↗

Space radiation measurements during the Artemis I lunar mission

Space radiation is a notable hazard for long-duration human spaceflight. Associated risks include cancer, cataracts, degenerative diseases and tissue reactions from large, acute exposures. Space radiation originates from diverse sources, including galactic cosmic rays, trapped-particle (Van Allen) belts5 and solar-particle events. Previous radiation data are from the International Space Station and the Space Shuttle in low-Earth orbit protected by heavy shielding and Earth’s magnetic field and lightly shielded interplanetary robotic probes such as Mars Science Laboratory and Lunar Reconnaissance Orbiter. Limited data from the Apollo missions and ground measurements with substantial caveats are also available. Here we report radiation measurements from the heavily shielded Orion spacecraft on the uncrewed Artemis I lunar mission. At differing shielding locations inside the vehicle, a fourfold difference in dose rates was observed during proton-belt passes that are similar to large, reference solar-particle events. Interplanetary cosmic-ray dose equivalent rates in Orion were as much as 60% lower than previous observations. Furthermore, a change in orientation of the spacecraft during the proton-belt transit resulted in a reduction of radiation dose rates of around 50%. These measurements validate the Orion for future crewed exploration and inform future human spaceflight mission design.

79 ASTRONOMY AND ASTROPHYSICS↗

Collaborative Research: Vlasov-Maxwell Simulations to Resolve Electron Heating and Dissipation, in Quasi-Perpendicular Shocks (Final Report)

Collisionless shocks are a grand challenge problem in plasma physics and have been the subject of study for more than six decades. Shocks are ubiquitous phenomena in the universe and are responsible for transforming high energy and momentum flows into thermal energy and energetic particles. Understanding how shocks operate is of primary importance to understand the sun-earth coupling, protecting manned missions and spacecrafts from high energy particles, inertial confinement fusion, and radiation observed from astrophysical plasmas, such as supernova remnants and astrophysical jets. A major unanswered question on this frontier is, how does a collisionless plasma transform flow energy and momentum into electron thermal energy? Many potential mechanisms have been proposed to perform the conversion between flow and thermal energy in a collisionless plasma, but the answer has been elusive. To solve the mystery, non-relativistic perpendicular and quasi-perpendicular shocks are studied via a coordinated approach employing cutting-edge numerical simulations with the continuum kinetic code Gkeyll and spacecraft observations supplied by NASA's Magnetospheric Multiscale (MMS) mission. In both sets of data, we employ novel techniques to identify how and where energy is exchanged between electromagnetic fields and plasma particles. By combining cutting-edge spacecraft data and numerical simulations with these diagnostics, we have been able to identify some of the primary mechanisms responsible electron heating and dissipation in heliospheric shocks. In addition to electron dynamics, we have complete access to proton simulation and in situ data, enabling us to characterize proton heating and acceleration in quasi-perpendicular shocks. Many astrophysical quasi-perpendicular shocks have similar parameters to those in this study, including supernova remnants and shocks in galaxy clusters. Additionally, the simulation code, Gkeyll, and associated analysis scripts are openly available for community use. This award has supported a collaborative effort between Princeton University, the University of Arizona - Tucson, and the University of Maryland - College Park. The award funded three early career scientists, including the funding and training of one female postdoctoral researcher, who was involved in all aspects of the MMS data analysis and some portions of the simulation analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

SPARTAN and IMPROVE Comparison Experiment (SPICE) Interim Campaign Report

SPICE (the SPARTAN and IMPROVE Comparison Experiment) aims to obtain and quantify comparisons between aerosol PM 2.5 mass concentration measurements from the University of Oklahoma (OU) Surface Particulate Matter Network (SPARTAN) station and the U.S. Environmental Protection Agency (EPA) Interagency Monitoring of Protected Visual Environments (IMPROVE) station hosted by the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) User Facility at ARM’s Southern Great Plains (SGP) observatory in Oklahoma. Aerosols—both natural and anthropogenic—affect human populations in multiple ways. Much of ARM’s research focuses on how aerosols influence weather and climate through their optical and radiative effects, as well as their impacts on clouds and precipitation. However, aerosols also pose direct risks to humans and other organisms through inhalation, with the severity of health impacts depending on particle size, chemical composition, and duration of exposure. The IMPROVE network was established by the U.S. EPA to monitor air quality, including visible clarity as well as total and chemically speciated aerosol mass concentrations. The ARM SGP site hosts the IMPROVE SOGP station. Separately, the SPARTAN network operates a globally distributed set of stations similar to IMPROVE but with an emphasis on remote deployment and semi-autonomous operation for use beyond the borders of the United States (IMPROVE only operates within the U.S.). The University of Oklahoma operates a SPARTAN station. To establish confidence in the OU SPARTAN instrumentation and measurement protocol relative to the EPA-certified IMPROVE station, the OU SPARTAN station is currently deployed at SGP in close proximity to the IMPROVE SOGP station. The SPICE campaign was envisioned as a contiguous calendar-year effort for 2025 to capture seasonal variation in mass loading as well as composition. However, independent of the SPICE campaign, the SPARTAN network adopted a new filter construction part-way through the year, interrupting our contiguous data set. Thus, to obtain a contiguous data set with a uniform consistent configuration, SPICE desires an extension through 2026.

54 ENVIRONMENTAL SCIENCES↗

A novel high frequency, high bandwidth, three phase Mach–Zehnder optical data link

In inertial confinement fusion, hydrogen isotopes are fused together under high pressures and temperatures. Typically, the duration of these experiments is incredibly short, on the order of around 60–150 ps. Due to the high radiation environment, a detector’s signal is typically data linked far distances to a protected location. The diagnostic challenge for fusion reaction history measurements is to measure signals of interest maximizing dynamic range while also maintaining time resolution on the order of 10 ps. In this work, we present a new experimental optical data link used to efficiently transport diagnostic signals over great distances to the recording system while not restricting the dynamic range. The concept of a three phase Mach–Zehnder modulator system is introduced as well as a description of the physical prototype. The initial results from testing at the OMEGA facility show that this system is a viable method for signal transportation.

47 OTHER INSTRUMENTATION↗

Testing, Calibration, and UxS Integration of the Kromek GR1 Plus CZT Gamma Spectrometer

Collecting radiation measurements can be a hazardous task, especially in the presence of highly active sources. Various scenarios necessitate source search, classification, and quantification, often with limited or no a priori information. Activities such as disaster mitigation, emergency response, environmental monitoring, and site remediation may involve dangerous radioactive sources. In these situations, there is a pressing need for remote monitoring capabilities that protect human operators from potential harm and enhance adherence to the principle of “As Low as Reasonably Achievable” (ALARA) for radiation doses. The first step toward achieving remote radiation measurement capabilities is the remote operation of a radiation sensor. Once this milestone is reached, the next challenge is to integrate this remote sensing capability into suitable actuation agents, collectively referred to as uncrewed systems (UxS). These systems include familiar platforms such as robotic quadrupeds, aerial multirotor vehicles, and ground vehicles, any of which may be teleoperated, act autonomously, or utilize a combination of both. A critical factor in achieving remote radiation sensing is the availability of data from the appropriate sensor. Many commercially available radiation sensors have closed-source documentation for their communication protocols. Typical end-user products are often self-contained, handheld devices designed for manual measurement scenarios. While there are commercial off-the-shelf (COTS) integrations of radiation sensors with UxS available for purchase, these solutions are typically tailored for specific use cases and may not meet the requirements of different applications. This paper discusses efforts to remotely acquire radiation measurements from a small form-factor CZT gamma spectrometer. Sandia National Laboratories has successfully demonstrated the initial capability to integrate low size, weight, and power (SWaP) gamma spectroscopy into various UxS, alongside co-located GPS data logging and sensor calibration and qualification. With remote gamma spectroscopy achieved, the stage is set for UxS integration of this capability.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Progress Toward Fast Decay Energy Spectroscopy for Actinide Analysis

Decay energy spectroscopy (DES) is an increasingly popular technique for measuring isotopic composition of actinide samples for nuclear safeguards applications. Current approaches for actinide DES utilize milligram-scale external gold absorbers (> 0.1 nJ/K) that are integrated with actinide samples through mechanical kneading and are thermally connected to microcalorimeters using indium or gold wire bonds. This leads to relatively slow sensor rise time and, consequently, limits counting speed to a few counts per second. We are developing faster metallic magnetic calorimeter-based DES by integrating actinide samples with magnetic sensor materials. This reduces signal rise time and enables high counting speed while maintaining the ability to knead the radioactive source with the absorber. We have measured signal rise time of 0.7 μs with a 1.5 mg external gold absorber using this approach. Here, we also demonstrated online DES operation using an Ortec DSPEC 50, a commercially available data acquisition system developed for semiconductor detectors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Review of the Lawrence Livermore Nuclear Accident Dosimeter 1980s-present

A Nuclear Accident Dosimetry program is a federal requirement for all facilities that have the potential to have a criticality accident. Personnel Nuclear Accident Dosimeter (PNAD) theory and analytical procedures are driven by various scientific needs and interacting regulations. A brief history of the status of USA Department of Energy (DOE) nuclear accident dosimetry regulations, recommendations, and performance testing criteria are given. Then, the history of the Lawrence Livermore National Laboratory (LLNL) PNAD is explored, including changes in the physical dosimeter and adjustments of the analysis method through the last four decades. Finally, the performance of LLNL’s PNAD at criticality accident intercomparison training exercises since 2009 is explored. In general, reported neutron doses have been within or close to DOE-STD-1098 performance criteria while reported gamma doses have been outside of DOE-STD-1098 performance criteria. Reported total absorbed doses have varied in meeting ANSI/HPS N13.3 and ANSI/HPS N13.3 (R2019) performance criteria. Dosimetry staff retirement and turnover have left historical knowledge gaps, yet provided opportunities within the NAD program at LLNL. This review paper serves as an overview of the history and status of the NAD program. Brief technical, procedural and programmatic recommendations to improve LLNL’s NAD program are given. Technical recommendations include investigating orientation factors through modeling or empirical experimentation, investigating gamma dosimetry methods for high-dose scenarios, and exploring other dosimetric methods for simpler, quicker NAD analysis. Procedural recommendations include better documentation of conversion factor (activity-to-fluence and fluence-to-dose) derivations and spectrum uses, and updated analysis spreadsheets or simple Graphic User Interfaces for dose calculations. In conclusion, programmatic recommendations include formalized training for NAD analysts, and having multiple SMEs trained on the NAD program.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Classifying photonic topology using the spectral localizer and numerical K -theory

Recently, the spectral localizer framework has emerged as an efficient approach for classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous definitions for concepts such as topological solitons and topological dynamics, where a system’s occupation induces a local change in its topology due to nonlinearity. For systems embedded in radiative environments that do not possess a shared bulk spectral gap, this framework enables the identification of local topology and shows that local topological protection is preserved despite the lack of a common gap. However, as the spectral localizer framework is rooted in the mathematics of C*-algebras, and not vector bundles, understanding and using this framework requires developing intuition for a somewhat different set of underlying concepts than those that appear in traditional approaches for classifying material topology. In this tutorial, we introduce the spectral localizer framework from a ground-up perspective and provide physically motivated arguments for understanding its local topological markers and associated local measure of topological protection. In doing so, we provide numerous examples of the framework’s application to a variety of topological classes, including crystalline and higher-order topology. We then show how Maxwell’s equations can be reformulated to be compatible with the spectral localizer framework, including the possibility of radiative boundary conditions. To aid in this introduction, we also provide a physics-oriented introduction to multi-operator pseudospectral methods and numerical K-theory, two mathematical concepts that form the foundation for the spectral localizer framework. Finally, we provide some mathematically oriented comments on the C*-algebraic origins of this framework, including a discussion of real C*-algebras and graded C*-algebras that are necessary for incorporating physical symmetries. Looking forward, we hope that this tutorial will serve as an approachable starting point for learning the foundations of the spectral localizer framework.

97 MATHEMATICS AND COMPUTING↗