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At least 433 records · Page 24

Development of combined function dipole-quadrupole PMQs magnets for NSLS-II upgrade

This paper focuses on the R&D performed for the development of permanent magnets-based dipoles-quadrupoles combined function magnets (PMQs) for the future NSLSII upgrade “complex bend” lattice (CB). This new lattice uses PMQs that provide both bending (dipole) and strong focusing (quadrupole) magnetic field on the electron beam. The permanent magnet (PM) technology is suitable for the high magnetic field strengths (0.5 T, 130 T/m) required for such combine function magnets. PM technology leads to a compact magnet design that is essential in realizing the complex bend lattice concept, as well as a passive magnet solution which does not require electrical power supply reducing power consumption by ~ 80% (from 1.7 MW to 0.3 MW for NSLS-II). Two PMQs magnets designs are under consideration: A hybrid design that use both PM and soft iron poles, and Halbach type that is a pure PM design. Both PMQs designs present challenges in achieving the specified magnetic field quality due to their higher sensitivity to errors (mechanical tolerances and PM properties). This paper presents cost-effective designs and prototypes results for hybrid and Halbach PMQs, addressing various technical challenges while meeting the field requirements of the complex bend lattice for the NSLS-II upgrade.

N'gotta, Patrick [Brookhaven]↗

Portable diagnostic package for Thomson scattering and optical emission spectroscopy on Princeton field-reversed configuration 2 (PFRC 2)

An Advanced Research Projects Agency-Energy funded diagnostic system has been deployed to the Princeton field-reversed configuration 2 (PFRC-2) device, located at Princeton Plasma Physics Laboratory. The Portable Diagnostic Package (PDP), designed at Oak Ridge National Laboratory, allows for the measurement of Thomson Scattering (TS) for electron density and temperature and Optical Emission Spectroscopy (OES) for ion temperature, impurity density, and ion velocity. A tunable spectrometer on the PDP with three gratings provides the flexibility to measure low (1 eV) and high (1000 eV) electron temperature ranges from TS. Additionally, using a second spectrometer, the OES diagnostic can survey light emission from various ion excitation levels for wide wavelength ranges. The electron density (<2 × 10 19 m –3 ) of plasmas generated in PFRC-2 has been below the PDP TS discrimination threshold, which has made TS signal detection challenging against a high-background of laser stray light. The laser stray light was iteratively reduced by making modifications to the entrance and exit geometry on PFRC-2. Rayleigh scattering experiments on PFRC have yielded the TS discrimination sensitivity to be >1 × 10 20 m –3 for the PDP. A recently implemented narrow-band notch spectral filter that masks the second harmonic 532 nm Nd:YAG laser wavelength has increased the system’s TS light discrimination sensitivity 65 times compared to the instance when the notch filter was not implemented. The hardware implementation including design changes to the flight tubes and Brewster windows will be discussed, along with results from Rayleigh and rotational Raman scattering sensitivity analyses, which were used to establish a quantitative figure of merit on the system performance. Further, the Raman scattering calibration with the notch filter has improved the PDP electron density threshold to 1 ± 0.5 × 10 18 m –3 .

47 OTHER INSTRUMENTATION↗

Highly excited electron cyclotron for QCD axion and dark-photon detection

We propose using highly excited cyclotron states of a trapped electron to detect meV axion and dark-photon dark matter, marking a significant improvement over our previous proposal and demonstration [One-electron quantum cyclotron as a milli-ev dark-photon detector, .]. When the axion mass matches the cyclotron frequency ω c , the cyclotron state is resonantly excited, with a transition probability proportional to its initial quantum number, n c . The sensitivity is enhanced by taking n c ∼ 10 6 ( 0.1 meV ω c ) 2 . By optimizing key experimental parameters, we minimize the required averaging time for cyclotron detection to t ave ∼ 10 − 6 s, permitting detection of such a highly excited state before its decay. An open–end-cap trap design enables the external photon signal to be directed into the trap, rendering our background-free detector compatible with large focusing cavities, such as the BREAD proposal, while capitalizing on their strong magnetic fields. Furthermore, the axion conversion rate can be coherently enhanced by incorporating layers of dielectrics with alternating refractive indices within the cavity. Collectively, these optimizations enable us to probe the QCD axion parameter space from 0.1 to 2.3 meV (25–560 GHz), covering a substantial portion of the predicted postinflationary QCD axion mass range. This sensitivity corresponds to probing the kinetic mixing parameter of the dark photon down to ε ≈ 2 × 10 − 16 . Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Reducing the Susceptibility of Lumped-Element KIDs to Two-Level System Effects

Arrays of lumped-element kinetic inductance detectors (LEKIDs) optically coupled through an antenna-coupled transmission line are a promising candidate for future cosmic microwave background experiments. However, the dielectric materials used for the microstrip architecture are known to degrade the performance of superconducting resonators. In this paper, we investigate the feasibility of microstrip coupling to a LEKID, focusing on a systematic study of the effect of depositing amorphous silicon nitride on a LEKID. The discrete and spatially separated inductive and capacitive regions of the LEKID allow us to vary the degree of dielectric coverage and determine the limitations of the microstrip coupling architecture. We show that by careful removal of dielectric from regions of high electric field in the capacitor, there is minimal degradation in dielectric loss tangent of a partially covered lumped-element resonator. We present the effects on the resonant frequency and noise power spectral density and, using the dark responsivity, provide an estimate for the resulting detector sensitivity.

47 OTHER INSTRUMENTATION↗

On the Nature of Field-Enhanced Water Dissociation in Bipolar Membranes

Bipolar membranes (BPMs) possess the potential to optimize pH environments for electrochemical synthesis applications when employed in reverse bias. Unfortunately, the performance of BPMs in reverse bias has long been limited by the rate of water dissociation (WD) occurring at the interface of the BPM. Herein, we develop a continuum model of the BPM that agrees with experiment to understand and enhance WD catalyst performance by considering multiple kinetic pathways for WD in the BPM junction catalyst layer. Here, the model reveals that WD catalysts with a more highly alkaline or acidic pH at the point of zero charge (pH PZC ) exhibit accelerated WD kinetics because the more acidic or alkaline pH PZC catalysts possess greater surface charge, enhancing the local electric field and rate of WD. The model is then employed to explore the sensitivity of the BPM performance to various BPM physical parameters. Finally, the model is used to simulate the operation of bimetallic WD catalysts, demonstrating that an optimal bimetallic catalyst has an acidic pH PZC catalyst matched with the cation-exchange layer and an alkaline pH PZC catalyst matched with the anion-exchange layer. The study provides insight into the operation of BPM WD catalysts and gives direction toward the development of next-generation WD catalysts for optimal BPM performance under water-splitting and related conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Improving Cycling Performance of Anode-Free Lithium Batteries by Pressure and Voltage Control

The anode-free lithium (Li) batteries (AFLBs) have great potential to provide higher energy density than most other batteries. However, the performance of AFLBs is very sensitive to pressure and other operating parameters, especially for coin cells widely used in AFLB investigations. Therefore, optimizing cell assembly parameters and test protocol is critical to get reliable and comparable results in this field. In this work, the operating voltage range of AFLBs using a localized high concentration electrolyte has been optimized. The morphology of the deposited Li in AFLBs is much more indicting to the pressure than other type of batteries due to the absence of anode active material (i.e. Li) as a pressure cushion layer in the as prepared cells. With an optimized cycling protocol, a thin layer of uniform nucleation sites can be formed in the initial cycle which will facilitate smooth Li desposition/stripping in the subsequent cycles of AFLBs. The solid electrolyte interphase layer formed under optimized pressure and uniform pressure distribution exhibits a good mechanical stability even after long-term cycling. In conclusion, with an optimized cell configuration, the internal pressure in the coin cells has been optimized to improve the cycling performance of AFLBs (Cu||NMC811) with 72% of capacity retention in 100 cycles.

25 ENERGY STORAGE↗

Deep-ultraviolet ptychographic pocket-scope (DART): mesoscale lensless molecular imaging with label-free spectroscopic contrast

The mesoscale characterization of biological specimens has traditionally required compromises between resolution, field-of-view, depth-of-field, and molecular specificity, with most approaches relying on external labels. Here we present the Deep-ultrAviolet ptychogRaphic pockeT-scope (DART), a handheld platform that transforms label-free molecular imaging through intrinsic deep-ultraviolet spectroscopic contrast. By leveraging biomolecules’ natural absorption fingerprints and combining them with lensless ptychographic microscopy, DART resolves down to 308-nm linewidths across centimeter-scale areas while maintaining millimeter-scale depth-of-field. The system’s virtual error-bin methodology effectively eliminates artifacts from limited temporal coherence and other optical imperfections, enabling high-fidelity molecular imaging without lenses. Through differential spectroscopic imaging at deep-ultraviolet wavelengths, DART quantitatively maps nucleic acid and protein distributions with femtogram sensitivity, providing an intrinsic basis for explainable virtual staining. We demonstrate DART’s capabilities through imaging of tissue sections, cytopathology specimens, blood cells, and neural populations, revealing detailed molecular contrast without external labels. The combination of high-resolution molecular mapping and broad mesoscale imaging in a portable platform opens new possibilities from rapid clinical diagnostics, tissue analysis, to biological characterization in space exploration.

60 APPLIED LIFE SCIENCES↗

Detection and Aggregation of Listeria Monocytogenes Using Polyclonal Antibody Gold-Coated Magnetic Nanoshells Surface-Enhanced Raman Spectroscopy Substrates

Magnetic nanoshells with tailored surface chemistry can enhance bacterial detection and separation technologies. This work demonstrated a simple technique to detect, capture, and aggregate bacteria with the aid of end-functionalized polyclonal antibody gold-coated magnetic nanoshells (pAb-Lis-AuMNs) as surface-enhanced Raman spectroscopy (SERS) probes. Listeria monocytogenes were used as the pathogenic bacteria and the pAb-LisAuMNs, 300 nm diameter, were used as probes allowing facile magnetic separation and aggregation. An optimized covalent bioconjugation procedure between the magnetic nanoshells and the polyclonal antibody was performed at pH six via a carbodiimide crosslinking reaction. Spectroscopic and morphological characterization techniques confirmed the fabrication of stable pAb-Lis-AuMNs. The resulting pAb-Lis-AuMNs acted as a SERS probe for L. monocytogenes based on the targeted capture via surface binding interactions and magnetically induced aggregation. Label-free SERS measurements were recorded for the minimum detectable amount of L. monocytogenes based on the SERS intensity at the 1388 cm -1 Raman shift. L. monocytogenes concentrations exhibited detection limits in the range of 10 4 –10 7 CFU ml -1 , before and after aggregation. By fitting these concentrations, the limit of detection of this method was ~10 3 CFU ml -1 . Using a low-intensity magnetic field of 35 G, pAb-LisAuMNs aggregated L. monocytogenes as demonstrated with microscopy techniques, including SEM and optical microscopy. Overall, this work presents a label-free SERS probe method comprised of a surface-modified polyclonal antibody sub-micron magnetic nanoshell structures with high sensitivity and magnetic induced separation that could lead to the fabrication of multiple single-step sensors.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

The Earth Model Column Collaboratory (EMC 2 ) v1.1: an open-source ground-based lidar and radar instrument simulator and subcolumn generator for large-scale models

Abstract. Climate models are essential for our comprehensive understanding of Earth's atmosphere and can provide critical insights on future changes decades ahead. Because of these critical roles, today's climate models are continuously being developed and evaluated using constraining observations and measurements obtained by satellites, airborne, and ground-based instruments. Instrument simulators can provide a bridge between the measured or retrieved quantities and their sampling in models and field observations while considering instrument sensitivity limitations. Here we present the Earth Model Column Collaboratory (EMC2), an open-source ground-based lidar and radar instrument simulator and subcolumn generator, specifically designed for large-scale models, in particular climate models, but also applicable to high-resolution model output. EMC2 provides a flexible framework enabling direct comparison of model output with ground-based observations, including generation of subcolumns that may statistically represent finer model spatial resolutions. In addition, EMC2 emulates ground-based (and air- or space-borne) measurements while remaining faithful to large-scale models' physical assumptions implemented in their cloud or radiation schemes. The simulator uses either single particle or bulk particle size distribution lookup tables, depending on the selected scheme approach, to perform the forward calculations. To facilitate model evaluation, EMC2 also includes three hydrometeor classification methods, namely, radar- and sounding-based cloud and precipitation detection and classification, lidar-based phase classification, and a Cloud Feedback Model Intercomparison Project Observational Simulator Package (COSP) lidar simulator emulator. The software is written in Python, is easy to use, and can be straightforwardly customized for different models, radars, and lidars. Following the description of the logic, functionality, features, and software structure of EMC2, we present a case study of highly supercooled mixed-phase cloud based on measurements from the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) West Antarctic Radiation Experiment (AWARE). We compare observations with the application of EMC2 to outputs from four configurations of the NASA Goddard Institute for Space Studies (GISS) climate model (ModelE3) in single-column model (SCM) mode and from a large-eddy simulation (LES) model. We show that two of the four ModelE3 configurations can form and maintain highly supercooled precipitating cloud for several hours, consistent with observations and LES. While our focus is on one of these ModelE3 configurations, which performed slightly better in this case study, both of these configurations and the LES results post-processed with EMC2 generally provide reasonable agreement with observed lidar and radar variables. As briefly demonstrated here, EMC2 can provide a lightweight and flexible framework for comparing the results of both large-scale and high-resolution models directly with observations, with relatively little overhead and multiple options for achieving consistency with model microphysical or radiation scheme physics.

58 GEOSCIENCES↗

Warming homogenizes apparent temperature sensitivity of ecosystem respiration

Warming-induced carbon loss through terrestrial ecosystem respiration (Re) is likely getting stronger in high latitudes and cold regions because of the more rapid warming and higher temperature sensitivity of Re (Q 10 ). However, it is not known whether the spatial relationship between Q 10 and temperature also holds temporally under a future warmer climate. Here, we analyzed apparent Q 10 values derived from multiyear observations at 74 FLUXNET sites spanning diverse climates and biomes. We found warming-induced decline in Q 10 is stronger at colder regions than other locations, which is consistent with a meta-analysis of 54 field warming experiments across the globe. We predict future warming will shrink the global variability of Q 10 values to an average of 1.44 across the globe under a high emission trajectory (RCP 8.5) by the end of the century. Therefore, warming-induced carbon loss may be less than previously assumed because of Q 10 homogenization in a warming world.

54 ENVIRONMENTAL SCIENCES↗

From Stoner to local moment magnetism in atomically thin Cr2Te3

Abstract The field of two-dimensional (2D) ferromagnetism has been proliferating over the past few years, with ongoing interests in basic science and potential applications in spintronic technology. However, a high-resolution spectroscopic study of the 2D ferromagnet is still lacking due to the small size and air sensitivity of the exfoliated nanoflakes. Here, we report a thickness-dependent ferromagnetism in epitaxially grown Cr 2 Te 3 thin films and investigate the evolution of the underlying electronic structure by synergistic angle-resolved photoemission spectroscopy, scanning tunneling microscopy, x-ray absorption spectroscopy, and first-principle calculations. A conspicuous ferromagnetic transition from Stoner to Heisenberg-type is directly observed in the atomically thin limit, indicating that dimensionality is a powerful tuning knob to manipulate the novel properties of 2D magnetism. Monolayer Cr 2 Te 3 retains robust ferromagnetism, but with a suppressed Curie temperature, due to the drastic drop in the density of states near the Fermi level. Our results establish atomically thin Cr 2 Te 3 as an excellent platform to explore the dual nature of localized and itinerant ferromagnetism in 2D magnets.

36 MATERIALS SCIENCE↗

Real-Time Monitoring of Gas-Phase and Dissolved CO 2 Using a Mixed-Matrix Composite Integrated Fiber Optic Sensor for Carbon Storage Application

Novel chemical sensors that improve detection and quantification of CO 2 are critical to ensuring safe and cost-effective monitoring of carbon storage sites. Fiber optic (FO) based chemical sensor systems are promising field-deployable systems for real-time monitoring of CO 2 in geological formations for long-range distributed sensing. Here, a mixed-matrix composite integrated FO sensor system was developed with a purely optical readout that reliably operates as a detector for gas-phase and dissolved CO 2 . A mixed-matrix composite sensor coating consisting of plasmonic nanocrystals and hydrophobic zeolite embedded in a polymer matrix was integrated on the FO sensor. The mixed-matrix composite FO sensor showed excellent reversibility/stability in a high humidity environment and sensitivity to gas-phase CO 2 over a large concentration range. This remarkable sensing performance was enabled by using plasmonic nanocrystals to significantly enhance the sensitivity and a hydrophobic zeolite to effectively mitigate interference from water vapor. The sensor exhibited the ability to sense CO 2 in the presence of other geologically relevant gases, which is of importance for applications in geological formations. A prototype FO sensor configuration which possesses a robust sensing capability for monitoring dissolved CO 2 in natural water was demonstrated. Reproducibility was confirmed over many cycles, both in a laboratory setting and in the field. More importantly, we demonstrated on-line monitoring capabilities with a wireless telemetry system, which transferred the data from the field to a website. The combination of outstanding CO 2 sensing properties and facile coating processability makes this mixed-matrix composite FO sensor a good candidate suitable for practical carbon storage applications.

54 ENVIRONMENTAL SCIENCES↗

Alaskan carbon-climate feedbacks will be weaker than inferred from short-term experiments

Climate warming is occurring fastest at high latitudes. Based on short-term field experiments, this warming is projected to stimulate soil organic matter decomposition, and promote a positive feedback to climate change. We show here that the tightly coupled, nonlinear nature of high-latitude ecosystems implies that short-term (<10 year) warming experiments produce emergent ecosystem carbon stock temperature sensitivities inconsistent with emergent multi-decadal responses. We first demonstrate that a well-tested mechanistic ecosystem model accurately represents observed carbon cycle and active layer depth responses to short-term summer warming in four diverse Alaskan sites. We then show that short-term warming manipulations do not capture the non-linear, long-term dynamics of vegetation, and thereby soil organic matter, that occur in response to thermal, hydrological, and nutrient transformations belowground. Our results demonstrate significant spatial heterogeneity in multi-decadal Arctic carbon cycle trajectories and argue for more mechanistic models to improve predictive capabilities.

54 ENVIRONMENTAL SCIENCES↗

Top Yukawa coupling determination at high energy muon collider

The Top Yukawa coupling profoundly influences several core mysteries linked to the electroweak scale and the Higgs boson. We study the feasibility of measuring the Top Yukawa coupling at high energy muon colliders by examining the high energy dynamics of the weak boson fusion to top quark pair processes. A deviation of the Top Yukawa coupling from the Standard Model would lead to a modified VV → t⁢t¯ process, violating unitarity at high energy. Our analysis reveals that utilizing a muon collider with a center-of-mass energy of 10 TeV and an integrated luminosity of 10 ab –1 allows us to investigate the Top Yukawa coupling with a precision surpassing 1.5%, more than one order of magnitude better than the precision from t⁢t¯⁢ℎ channel at muon colliders. This precision represents a notable enhancement compared to the anticipated sensitivities of the High-Luminosity LHC (3.4%) and those at muon colliders derived from the t⁢t¯H process.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Alaskan carbon-climate feedbacks will be weaker than inferred from short-term manipulations: Alaskan Benchmark Data and Model runs

This submission aimed to assess differences in short-term step warming manipulations and long-term chronic response to climate change in Alaskan ecosystems. Briefly, climate warming is occurring fastest at high latitudes. Based on short-term field experiments, this warming is projected to stimulate soil organic matter decomposition, and promote a positive feedback to climate change. We show here that the tightly coupled, nonlinear nature of high-latitude ecosystems implies that short-term (< 10 year) warming experiments produce emergent ecosystem carbon stock temperature sensitivities inconsistent with emergent multi-decadal responses. We first demonstrate that a well-tested mechanistic ecosystem model accurately represents observed carbon cycle and active layer depth responses to short-term summer warming in four diverse Alaskan sites. We then show that short-term warming manipulations do not capture the non-linear, long-term dynamics of vegetation, and thereby soil organic matter, that occur in response to thermal, hydrological, and nutrient transformations belowground. Our results demonstrate significant spatial heterogeneity in multi-decadal Arctic carbon cycle trajectories and argue for more mechanistic models to improve predictive capabilities.The model used in the current study is available publicly (https://github.com/jinyun1tang/ECOSYS), and the current submission contains the python/ matlab codes for analyzing output from the model (includng a readme file to explain the codes). The benchmark data, also enclosed, was collected from a range of published and publicly available sources (extracted using GRABIT: https://www.mathworks.com/matlabcentral/fileexchange/7173-grabit). These sources describe warming induced changes in tundra/ boreal ecosystems.

54 ENVIRONMENTAL SCIENCES↗

Cosmogenic 137 Xe Analysis of Alternatives for nEXO

Neutrinoless double-beta decay is a hypothetical nuclear decay in which two matter particles are produced without corresponding antimatter particles. Observation of neutrinoless double-beta decay would shed light on a potential explanation of matter-antimatter observed in the universe and also indicate the Majorana nature of neutrinos, meaning that the neutrino can act as its own antiparticle. The nEXO experiment is a proposed 5-ton liquid xenon time projection chamber detector with a projected 1.35 × 10 28 yr half-life sensitivity to neutrinoless double-beta decay in 136 Xe [J. Phys. G 49, 015104 (2022)]. While nEXO has a baseline location of SNOLAB, there are several other underground facilities in the world capable of hosting the experiment. The primary change at each site will be cosmogenic 137 Xe backgrounds, caused by varied cosmogenic muon activity at each site. This study finds that while there is a negligible increase in nEXO’s half-life sensitivity at 90% C.L. from improving the cosmogenic 137 Xe veto rejection procedure for SNOLAB, much higher daily muon rates at three other sites will have an adversely negative effect on nEXO’s sensitivity and would likely require further modifications to nEXO’s baseline design to reach nEXO’s scientific goals. Monte Carlo simulations of muons inducing 137 Xe backgrounds were conducted at four underground sites, SNOLAB, SURF, LNGS, and WIPP, each with roughly a factor of 10 times higher daily muon activity than the previous site. There were two primary inputs to these simulations. The first was sample data of cosmogenic muon flight through nEXO’s outer detector, a 12.8m tall and 12.3m wide cylindrical water tank lined with photomultiplier tubes to detect Cerenkov radiation, and all of the secondary interactions produced in the detector. The second input was a parametrization of 137 Xe* production tagging when 137 Xe de-excites and release prompt gammas, as well as accidental tagging caused by neutron capture on 63 Cu, 65 Cu, 19 F, and 1 H throughout the detector. Together, the number of backgrounds relative to the previous 2021 Sensitivity Paper [J. Phys. G 49, 015104 (2022)] was found at each of these four sites across three energy windows, from 400, 1400, and 2600 keV all up to 4600 keV, just above the end point of the prompt gamma spectrum for 137 Xe*. Using level curves for the sensitivity as 137 Xe backgrounds scale relative to baseline calculations, the half-life sensitivity at 90% C.L. for each of trial was found. Even with reduced 137 Xe backgrounds, the results for SNOLAB yielded neglible improvements in nEXO’s predicted sensitivity. On the contrary, the increased backgrounds for the three other considered sites yielded sensitivity estimates below nEXO’s previous projections. This study demonstrates that the shielding from cosmogenic muons at SNOLAB makes it highly preferred even amongst other world leading underground laboratories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Hand Calculation Methods for Nuclear Criticality Safety

This primer provides an overview of the most common hand calculation methods used for criticality safety calculations. The most widely used tools available to a nuclear criticality safety (NCS) practitioner are probably the common Monte Carlo or deterministic criticality safety codes, which can be used to model very complex systems. However, use of these codes can obscure the parameters to which a particular fissile system may be sensitive, whereas the hand calculation methods can be used to delve into the ways each parameter may affect the reactivity of a fissile material system. Furthermore, practitioners must avoid using computer codes as devices that take inputs and simply provide outputs (i.e., a “black box”). Many years ago, pioneers such as Joe Thomas, David Smith, and Hugh Paxton, among others in the field of nuclear criticality safety, took the time before the advent of high-speed desktop computers to create simple hand methods for criticality safety analyses. Some of the methods can be used for single fissile units; others are applicable to fissile units arranged into simple array configurations. This primer discusses the applicability of the various methods, illustrates how they are used, and provides an interpretation of the various results. The NCS practitioner will need to spend time to master the methods that could be most useful; however, they can provide the practitioner with fast and accurate answers to criticality safety problems if they are used correctly and if critical data exist for the problem at hand. Hand calculation methods can be used as a starting point for more advanced calculations, and in many circumstances, they can provide sensitivity and perturbation information more quickly than using a criticality code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗