Search NASA⌕ Search

SEARCH · Search NASA

Results for “Integral transforms”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Explainable AI for Multivariate Time Series Pattern Exploration: Latent Space Visual Analytics With Temporal Fusion Transformer and Variational Autoencoders in Power Grid Event Diagnosis

Detecting and analyzing complex patterns in multivariate time-series data is crucial for decision-making in urban and environmental system operations. However, challenges arise from the high dimensionality, intricate complexity, and interconnected nature of complex patterns, which hinder the understanding of their underlying physical processes. Existing AI methods often face limitations in interpretability, computational efficiency, and scalability, reducing their applicability in real-world scenarios. This paper proposes a novel visual analytics framework that integrates two generative AI models, Temporal Fusion Transformer (TFT) and Variational Autoencoders (VAEs), to reduce complex patterns into lower-dimensional latent spaces and visualize them in 2D using dimensionality reduction techniques such as PCA, t-SNE, and UMAP with DBSCAN. These visualizations, presented through coordinated and interactive views and tailored glyphs, enable intuitive exploration of complex multivariate temporal patterns, identifying patterns’ similarities and uncover their potential correlations for a better interpretability of the AI outputs. The framework is demonstrated through a case study on power grid signal data, where it identifies multi-label grid event signatures, including faults and anomalies with diverse root causes. Additionally, novel metrics and visualizations are introduced to validate the models and assess the performance, efficiency, and consistency of latent maps generated by VAE, which have been utilized in prior studies for latent space cartography and used as a benchmark in this study, and the emerging TFT architecture under various configurations. These analyses provide actionable insights for model parameter tuning and reliability improvements. Comparative results highlight that TFT achieves shorter run times and superior scalability to diverse time-series data shapes compared to VAE. This work advances fault diagnosis in multivariate time series, fostering explainable AI to support critical system operations.

Explainable AI↗
DOE OSTI2026

A Discrete Hankel Transform Approach to Nuclear Data Processing for Fusion Applications

This study introduces advancements to the numerical solutions employed in the processing of nuclear data for fusion applications. It leverages the convolution theorem and Fourier transform techniques to enhance computational efficiency and broaden applicability. Building upon a previously reported discrete Hankel transform approach for Doppler broadening, this work refines the solution of convolution integrals central to these applications. The methodology provides a general and unified framework for evaluating any convolution operation, regardless of whether the underlying problem involves temperature effects in nuclear reactions. The applicability to the nuclear data processing for fusion is demonstrated by deriving the convolution integrals for some of the fusion-related quantities. As before, the convolution operation utilizes a Gaussian-based kernel; however, the discrete Hankel transform of order $𝛼$ = $\frac{1}{2}$ is now applied to the forward Fourier transform of the nonkernel argument, rather than the inverse Fourier transform. This modification eliminates the need for the integration of the nonkernel, cross section–based function, which is a step that posed challenges for certain pointwise cross-section representations. It also removes the requirement for cross-section linearization. Optimized for graphics processing unit architectures, the approach significantly improves computational performance. These advancements are currently under evaluation as the foundation for the next-generation thermonuclear data file processing codes being developed at Lawrence Livermore National Laboratory.

Nuclear science and engineering↗
DOE OSTI2026

AstraAI v1

AstraAI is an open-source, structure-aware AI coding agent designed for large scientific and DOE-HPC codebases such as AMReX-based applications. Unlike general-purpose coding assistants, AstraAI combines retrieval-augmented generation (RAG) with compiler-level Abstract Syntax Tree (AST) analysis to perform precise, scope-constrained code modifications. It identifies exact function spans, enforces locality of edits, and maintains cross-file invariants, enabling deterministic and build-safe transformations in complex C++/GPU environments. AstraAI is intended for developers working on large, evolving HPC frameworks where correctness, reproducibility, and structural integrity are critical. Typical use cases include modifying physics kernels, updating GPU device lambdas, and performing multi-file refactors without breaking compilation or runtime semantics. Compared to conventional LLM-based coding agents - even those with repository access - AstraAI provides structural guarantees rather than free-form text patches. It minimizes unintended diffs, prevents scope drift, preserves formatting and build stability, and reduces structural hallucinations. By integrating compiler tooling directly into the generation loop, AstraAI transforms AI-assisted coding from probabilistic text editing into deterministic, structure-preserving program transformation suitable for mission-critical scientific software.

Natarajan, Mahesh [Lawrence Berkeley National Labo↗
DOE OSTI2026

AGFormer: Adaptive Spatiotemporal graph informed transformer for multi-reservoir inflow forecasting

Accurate reservoir inflow forecasting is crucial for effective water resource management, yet most machine learning models focus on single-reservoir prediction and overlook spatial dependencies among hydrologically connected reservoirs. Here, we propose AGFormer (Adaptive Graph-Informed Transformer), an end-to-end framework that integrates adaptive graph learning with temporal sequence modeling for multi-reservoir inflow forecasting. A shared encoder and graph attention mechanism generate reservoir-specific embeddings, which are then processed by the Transformer-based encoder–decoder for multi-step inflow forecasting. We also introduce a pretraining paradigm to learn robust temporal embeddings from misaligned historical records. Evaluated on 30 reservoirs in the Upper Colorado River Basin, AGFormer achieves superior seven-day-ahead forecasts, with NSE > 0.75 for 20 reservoirs—outperforming Encoder–Decoder LSTM, GCN+LSTM, and Transformer baselines. Adaptive graph learning captures dynamic inter-reservoir dependencies, and feature attribution aligns with snowmelt-driven hydrology. Incorporating forecasted meteorological inputs further enhances accuracy, demonstrating AGFormer’s potential to support reservoir management under dynamic hydrological conditions.

Adaptive graph learning↗
DOE OSTI2026

Extreme-scale EV charging infrastructure planning for last-mile delivery using high-performance parallel computing

Here, this paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Capacity allocation↗
DOE OSTI2025

Beyond Optimization: Exploring Novelty Discovery in Autonomous Experiments

Autonomous experiments (AEs) are transforming how scientific research is conducted by integrating artificial intelligence with automated experimental platforms. Current AEs primarily focus on the optimization of a predefined target; while accelerating this goal, such an approach limits the discovery of unexpected or unknown physical phenomena. Here, we introduce a novel framework, INS 2 ANE (Integrated Novelty Score−Strategic Autonomous Non-Smooth Exploration), to enhance the discovery of novel phenomena in autonomous microscopy experimentation. Our method integrates two key components: (1) a novelty scoring system that evaluates the uniqueness of experimental results and (2) a strategic sampling mechanism that promotes exploration of under-sampled regions even if they appear less promising by conventional criteria. We validate this approach on a preacquired data set with a known ground truth comprising of image−spectral pairs. We further implement the process on autonomous scanning probe microscopy experiments. INS 2 ANE significantly increases the diversity of explored phenomena in comparison to conventional optimization routines, enhancing the likelihood of discovering previously unobserved phenomena. These results demonstrate the potential for autonomous microscopy experiments to enhance the scientific discovery by navigating complex experimental spaces to uncover novel phenomena.

Materials↗
DOE OSTI2026

AnisONet: A deep neural operator-based anisotropic permeability upscaler from pore to Darcy scale

Directional permeability variations, which govern directional fluid flow in porous media with anisotropy, are important to accurately predict flow behavior, reactive transport, and fluid–solid interactions for various processes such as enhanced geothermal systems, energy storage devices, and biological systems. However, the intricate architecture of porous media makes it difficult to predict directional permeabilities. In this work, we present a novel machine learning (ML) framework, AnisONet, built upon an integration of a convolutional neural network, Swin transformer, and the deep operator network architecture, designed to predict anisotropic permeability and upscale predictions to larger spatial domains. First, AnisONet was evaluated with three classes of two-dimensional (2D) porous media, including synthetic circular and elliptical grains and natural sandstone grains from micro-computed tomography images. A lattice Boltzmann model (LBM) was used to calculate directional permeabilities at every 10° angle, producing 19 data points per image of porous media. AnisONet is then trained to predict permeability as a function of rotation angle. AnisONet showed strong predictive capability of directional permeability. Second, we tested our model for five upscaling cases with a large image size in the finite-element method (FEM) for 2D Darcy flow with various permeability tensor construction methods. Overall, upscaled permeability tensors in FEM simulations produce a reasonably good match with LBM results, highlighting the importance of selecting appropriate tensor formation strategies for accurate permeability upscaling. AnisONet, as a directional permeability estimator, could be further developed for more complex geometries, with the potential to develop a foundational ML model for various applications in porous media.

42 ENGINEERING↗
DOE OSTI2024

Discovery of highly potent and ALK2/ALK1 selective kinase inhibitors using DNA-encoded chemistry technology

Activin receptor type 1 (ACVR1; ALK2) and activin receptor like type 1 (ACVRL1; ALK1) are transforming growth factor beta family receptors that integrate extracellular signals of bone morphogenic proteins (BMPs) and activins into Mothers Against Decapentaplegic homolog 1/5 (SMAD1/SMAD5) signaling complexes. Several activating mutations in ALK2 are implicated in fibrodysplasia ossificans progressiva (FOP), diffuse intrinsic pontine gliomas, and ependymomas. The ALK2 R206H mutation is also present in a subset of endometrial tumors, melanomas, non-small lung cancers, and colorectal cancers, and ALK2 expression is elevated in pancreatic cancer. Using DNA-encoded chemistry technology, we screened 3.94 billion unique compounds from our diverse DNA-encoded chemical libraries (DECLs) against the kinase domain of ALK2. Off-DNA synthesis of DECL hits and biochemical validation revealed nanomolar potent ALK2 inhibitors. Further structure-activity relationship studies yielded center for drug discovery (CDD)-2789, a potent [NanoBRET (NB) cell IC50: 0.54 μM] and metabolically stable analog with good pharmacological profile. Crystal structures of ALK2 bound with CDD-2281, CDD-2282, or CDD-2789 show that these inhibitors bind the active site through Van der Waals interactions and solvent-mediated hydrogen bonds. CDD-2789 exhibits high selectivity toward ALK2/ALK1 in KINOMEscan analysis and NB K192 assay. In cell-based studies, ALK2 inhibitors effectively attenuated activin A and BMP-induced Phosphorylated SMAD1/5 activation in fibroblasts from individuals with FOP in a dose-dependent manner. Thus, CDD-2789 is a valuable tool compound for further investigation of the biological functions of ALK2 and ALK1 and the therapeutic potential of specific inhibition of ALK2.

Jimmidi, Ravikumar↗
DOE OSTI2025

Hawaii Threat Brief

The Digital Energy Transformation is redefining how power systems operate, integrating physical infrastructure with digital technologies to enhance efficiency, visibility, and resilience. For islanded and digitally modernizing systems like Hawai‘i’s, this shift presents both new opportunities and evolving challenges in cybersecurity, supply chain assurance, and environmental resilience. This brief provides an overview of critical infrastructure dependencies and systemic risks associated with increasing digital integration. It summarizes recent energy-sector threat activity and case studies that illustrate adversary tactics and supply chain vulnerabilities, and identifies pathways to strengthen resilience.

25 - ENERGY STORAGE↗
DOE OSTI2025

Non-Destructive, Three-Dimensional Imaging of Processes in the Rhizosphere Utilizing High Energy Photons

Soil structure, which can be described as the aggregation and distribution of pore spaces, regulates carbon, nutrient, and water cycling across the Earth system. Yet the inability to make quantitative, dynamic, in situ measurements of soil structure and rhizosphere carbon flow has prevented meaningful incorporation of soil structural processes into Earth System Models (ESMs). The key limitations are: (i) Lack of scale integration between micron-scale soil structure and ecosystem-scale models, (ii) Poor functional linkage between soil structural properties and biogeochemical processes, and (iii) Absence of dynamic 3D measurements of rhizosphere structural changes and carbon transformations. To address these challenges, we developed a new integrated positron emission tomography (PET) - microcomputed tomography (CT) imaging platform that enables the first 4D (spatial 3D and time), non-invasive, quantitative imaging of carbon allocation and rhizosphere structural dynamics in living plants and intact soils. The system combines: • Rhizo-PET (R-PET): a high-resolution positron emission tomography scanner optimized for 11 CO 2 tracing in plant roots. • a-Se micro-CT: a high-contrast, high-spatial resolution CT system based on amorphous selenium (a-Se) direct conversion technology, enabling micron-scale visualization of soil structure and root–soil interfaces. Together, these advances allow us to quantify how carbon exudates move, transform, and stabilize within the rhizosphere, directly informing missing processes in BER-relevant carbon cycle models.

42 ENGINEERING↗
DOE OSTI2025

Impact assessment of geomagnetic induced current neutral blocking devices with power electronics sources on distance relay for 230 kV transmission lines

Electrical grids increased the integration of power electronics sources onto transmission lines. In addition, recent reports show a significant rise in geomagnetic storms occurring in 2024. These geomagnetic storms can affect transmission lines by inducing electrical currents within them, potentially causing power outages due to overloaded power transformers. Geomagnetic induced current neutral blocking devices (GIC-NBDs) are capacitors on the ground of wye power transformers, to avoid damage caused by geomagnetic storms. The integration of distance relays and transmission lines with power electronics sources and GIC-NBDs needs to be studied to observe if GIC-NBDs and power electronics sources could adversely affect operation of the electrical grid. In this analysis, the effect of 2 MW power electronics sources and GIC-NBDs on distance relays is assessed for different 230 kV transmission line lengths in radial and nonradial power systems. The simulations measured the apparent impedances, with different electrical faults. Results for a typical 2,650 μF GIC-NBD application were presented on impedance plots, and the distance relay model operations were assessed. In conclusion, the tests for radial and nonradial power systems showed the behavior of the distance elements and source impedance ratios, assessing the effect of power electronics sources and GIC-NBDs on 230 kV transmission lines.

Distance relays↗
DOE OSTI2024

The path to 2060: Saudi Arabia's long-term pathway for GHG emission reduction

Saudi Arabia, as part of its Saudi Green Initiative, has announced its goal to achieve net zero green-house gas emissions by 2060. This ambitious target underscores the nation's dedication to address-ing climate change. However, there is a significant gap in comprehensive analysis regarding the long-term effects of Saudi Arabia's climate policies and their collective contribution towards the net-zero objective. This study endeavors to bridge this gap through a detailed examination using the GCAM-KSA, a specialized version of the Global Change Analysis Model tailored for Saudi Arabia, employing a multi-sectoral methodology that integrates economic, energy, and land use systems within a coherent framework to assess the impact of climate policies on GHG emissions. Our anal-ysis reveals that reaching net-zero GHG emissions by 2060 is a complex challenge requiring con-certed efforts across all sectors of the economy. While transitioning to low-carbon electricity and improving energy efficiency offer considerable emission reductions, fully decarbonizing the indus-trial and transportation sectors poses a significant hurdle. Our findings suggest that Saudi Arabia must triple its emission reduction commitments in its next Nationally Determined Contributions (NDCs) update to align with its 2060 net-zero goal. Early action and increased ambition could avoid the chances of getting locked into the high emission assets and give enough time to transform the energy system. Furthermore, the adoption and integration of Carbon Dioxide Removal (CDR) tech-nologies are identified as crucial for offsetting residual emissions, especially in sectors that might continue to rely on fossil fuels.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Integrated Multiport Conductive and Wireless Architecture for Electric Vehicle Charging

This paper explores the opportunity of integrating conductive and wireless electric vehicle charging architectures and presents an integrated multiport charging architecture suitable for simultaneous conductive and wireless charging of electric vehicles. The architecture successfully integrates the primary side power electronic high frequency inverter and the high frequency transformer with the wireless transmitter and receiver to achieve independent power flow at each port. Design of the integrated magnetics is discussed, and results are presented that demonstrate the decoupled power flow at each port. The proposed integrated architecture increases the utilization of the same charging infrastructure without a proportionate increase in the cost.

Mukherjee, Subho [ORNL] (ORCID:0009000672297925)↗
DOE OSTI2024

Improving streamflow predictions across CONUS by integrating advanced machine learning models and diverse data

Accurate streamflow prediction is crucial to understand climate impacts on water resources and develop effective adaption strategies. A global long short-term memory (LSTM) model, using data from multiple basins, can enhance streamflow prediction, yet acquiring detailed basin attributes remains a challenge. To overcome this, we introduce the Geo-vision transformer (ViT)-LSTM model, a novel approach that enriches LSTM predictions by integrating basin attributes derived from remote sensing with a ViT architecture. Applied to 531 basins across the Contiguous United States, our method demonstrated superior prediction accuracy in both temporal and spatiotemporal extrapolation scenarios. Geo-ViT-LSTM marks a significant advancement in land surface modeling, providing a more comprehensive and effective tool for better understanding the environment responses to climate change.

Tayal, Kshitij↗
DOE OSTI2025

Orientation reversal and the Chern-Simons natural boundary

We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.

Chern-Simons theories↗
DOE OSTI2025

Viral‐mediated delivery of morphogenic regulators enables leaf transformation in Sorghum bicolor (L.)

Recent advancements in monocot transformation, using leaf tissue as explant material, have expanded the number of grass species capable of transgenesis. However, the complexity of vectors and reliance on inducible excision of essential morphogenic regulators have so far limited widespread application. Plant RNA viruses, such as Foxtail Mosaic Virus (FoMV), present a unique opportunity to express morphogenic regulator genes, such as Babyboom (Bbm), Wuschel2 (Wus2), Wuschel-like homeobox protein 2a (Wox2a) and the GROWTH-REGULATING FACTOR 4 (GRF4) GRF-INTERACTING FACTOR 1 (GIF1) fusion protein transiently in leaf explant tissues. Furthermore, altruistic delivery of conventional and viral vectors could provide opportunities to simplify vectors used for leaf transformation—facilitating vector optimization and reducing reliance on morphogenic regulator gene integration. In this study, both viral and conventional T-DNA vectors were tested for their ability to promote the formation of embryonic calli, a critical step in leaf transformation protocols, using Sorghum bicolor leaf explants. Although conventional leaf transformation vectors yielded viable embryonic calli (43.2 ± 2.9%: GRF4-GIF1, 50.2 ± 3%: Bbm/Wus2), altruistic conventional vectors employing the GRF4-GIF1 morphogenic regulator resulted in improved efficiencies (61.3 ± 4.7%). Altruistic delivery was further enhanced with the use of viral vectors employing both GRF4-GIF1 and Bbm/Wus2 regulators, resulting in 75.1 ± 2.3% and 79.2 ± 2.5% embryonic calli formation, respectively. Embryonic calli generated from both conventional and viral vectors produced shoots expressing fluorescent reporters, which were confirmed using molecular analysis. This work provides an important proof-of-concept for the use of both altruistic vectors and viral-expressed morphogenic regulators for improving plant transformation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Data for "Viral-mediated Delivery of Morphogenic Regulators Enables Leaf Transformation in Sorghum bicolor (L.)"

Recent advancements in monocot transformation, using leaf tissue as explant material, have expanded the number of grass species capable of transgenesis. However, the complexity of vectors and reliance on inducible excision of essential morphogenic regulators have so far limited widespread application. Plant RNA viruses, such as Foxtail Mosaic Virus (FoMV), present a unique opportunity to express morphogenic regulator genes, such as Babyboom ( Bbm ), Wuschel2 ( Wus2 ), Wuschel-like homeobox protein 2a ( Wox2a ) and the GROWTH-REGULATING FACTOR 4 (GRF4) GRF-INTERACTING FACTOR 1 (GIF1) fusion protein transiently in leaf explant tissues. Furthermore, altruistic delivery of conventional and viral vectors could provide opportunities to simplify vectors used for leaf transformation—facilitating vector optimization and reducing reliance on morphogenic regulator gene integration. In this study, both viral and conventional T-DNA vectors were tested for their ability to promote the formation of embryonic calli, a critical step in leaf transformation protocols, using Sorghum bicolor leaf explants. Although conventional leaf transformation vectors yielded viable embryonic calli (43.2 ± 2.9%: GRF4-GIF1, 50.2 ± 3%: Bbm/Wus2), altruistic conventional vectors employing the GRF4-GIF1 morphogenic regulator resulted in improved efficiencies (61.3 ± 4.7%). Altruistic delivery was further enhanced with the use of viral vectors employing both GRF4-GIF1 and Bbm/Wus2 regulators, resulting in 75.1 ± 2.3% and 79.2 ± 2.5% embryonic calli formation, respectively. Embryonic calli generated from both conventional and viral vectors produced shoots expressing fluorescent reporters, which were confirmed using molecular analysis. This work provides an important proof-of-concept for the use of both altruistic vectors and viral-expressed morphogenic regulators for improving plant transformation.

gene editing↗
DOE OSTI2025

Dynamics of McMillan mappings II. axially symmetric map

Here, in this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device potentially capable of mitigating collective space charge forces, some of its fundamental properties have not been described yet. The main goal of our work is to close this gap and understand the limitations and potentials of this device. It is worth mentioning that the McMillan axially symmetric map provides the first-order approximations of dynamics for a general linear lattice plus an arbitrary thin lens with motion separable in polar coordinates. Therefore, advancements in its understanding should give us a better picture of more generic and not necessarily integrable round beams. In the first part of the article, we classify all possible regimes with stable trajectories and find the canonical action-angle variables. This provides an evaluation of the dynamical aperture, Poincaré rotation numbers as functions of amplitudes, and thus determines the spread in nonlinear tunes. Also, we provide a parameterization of invariant curves, allowing for the immediate determination of the map image forward and backward in time. The second part investigates the particle dynamics as a function of system parameters. We show that there are three fundamentally different configurations of the accelerator optics causing different regimes of nonlinear oscillations. Each regime is considered in great detail, including the limiting cases of large and small amplitudes. In addition, we analyze the dynamics in Cartesian coordinates and provide a description of observable variables and corresponding spectra.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗