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At least 163 records · Page 9

Data Center Market Report

The data center market is poised to explode in the coming decade due to undeniable drivers such as continued adoption of generative AI, increased data storage needs, and enterprise integration of AI in numerous industries [1] [2] [3]. Scalable power and increased computational capacity are at the forefront of considerations for hyperscalers, the major cloud service providers in this space. Lawrence Livermore National Laboratory is uniquely poised to help with informed decision making for data center market leaders during this phase of explosive expansion. National grid modeling expertise and cutting edge innovations in computer cooling systems place LLNL in an enviable position for creating economic impact in the data center industry by leveraging its expertise in these areas which can help the data center market keep up with growing demand.

97 MATHEMATICS AND COMPUTING↗

Future Generation High Performance Computing Center (FG-HPCC): RFI Technical Considerations

Lawrence Livermore National Security, LLC (LLNS) is interested in receiving information about technologies that could be available in the 2029-2030 timeframe that may serve to enable the vision for a Future Generation High Performance Computing (HPC) Center (FG-HPCC) described in this document. The future HPC Center vision has been conceived to meet the future mission needs of the Advanced Simulation and Computing (ASC) Program within the National Nuclear Security Administration (NNSA). LLNS envisions a center composed not of many independent clusters, but of heterogeneous elements accessible to users as a single system. The capabilities will be integrated to create a scalable, flexible, yet tightly coupled computing center capable of integrated HPC, AI, and cloud-like workloads.

97 MATHEMATICS AND COMPUTING↗

Notes on Array Antenna Phase Center

The location of an antenna, and indeed the radar system it serves, is typically presumed to be its phase center. This is the point from which a far-field apparent spherical wavefront seems to be centered. Even when a true phase center doesn’t exist, an ‘apparent’ phase center can still be calculated for the neighborhood of some direction of interest, often the mainlobe of the beam. Such calculations are especially necessary for non-symmetric arrays, or sub-arrays.

42 ENGINEERING↗

Automated tape-target centering based on template matching for construction measurement tasks using robotic total station

Robotic total stations have transformed surveying and construction mapping through precise, efficient, and automated measurements. These instruments integrate a theodolite, which measures horizontal and vertical angles, with an electronic distance measurement (EDM) unit to determine distances, allowing accurate 3D measurement of observable points. Traditionally, users manually aimed the total station at a target. Recent advancements in robotic motor control and integration of cameras now enable automatic rotation and aiming, typically requiring only a single operator to position the target. Automated aiming is commonly performed using retroreflector prisms, which reflect light back to the source with minimal scattering, enabling high-precision measurements over long distances. However, retroreflectors, especially those designed for 360 degree, can be expensive and impractical for certain applications. This paper presents an algorithm for automating the center detection of low-cost disposable tape targets using the total station's onboard camera and a template matching algorithm. The algorithm identifies the target's center pixel in the image, and the instrument is commanded to aim at that location. We evaluated the performance of this template-matching-based centering method under various distances, angles, lighting conditions, and field environments, comparing its results to both manual aiming and conventional automated aiming of tape targets. Manual aiming was used as the baseline operational reference in the absence of an independent ground-truth measurement. The proposed approach achieves target centering results comparable to the manual baseline. This method provides a cost-effective alternative for high-precision applications where retroreflector targets are constrained by budget or logistics.

Harrington, Joshua [ORNL]↗

Real-Time Identification of Oxygen Vacancy Centers in LiNbO 3 and SrTiO 3 during Irradiation with High Energy Particles

Oxygen vacancies are known to play a central role in the optoelectronic properties of oxide perovskites. A detailed description of the exact mechanisms by which oxygen vacancies govern such properties, however, is still quite incomplete. The unambiguous identification of oxygen vacancies has been a subject of intense discussion. Interest in oxygen vacancies is not purely academic. Precise control of oxygen vacancies has potential technological benefits in optoelectronic devices. In this review paper, we focus our attention on the generation of oxygen vacancies by irradiation with high energy particles. Irradiation constitutes an efficient and reliable strategy to introduce, monitor, and characterize oxygen vacancies. Unfortunately, this technique has been underexploited despite its demonstrated advantages. This review revisits the main experimental results that have been obtained for oxygen vacancy centers (a) under high energy electron irradiation (100 keV–1 MeV) in LiNbO 3 , and (b) during irradiation with high-energy heavy (1–20 MeV) ions in SrTiO 3 . In both cases, the experiments have used real-time and in situ optical detection. Moreover, the present paper discusses the obtained results in relation to present knowledge from both the experimental and theoretical perspectives. Our view is that a consistent picture is now emerging on the structure and relevant optical features (absorption and emission spectra) of these centers. One key aspect of the topic pertains to the generation of self-trapped electrons as small polarons by irradiation of the crystal lattice and their stabilization by oxygen vacancies. What has been learned by observing the interplay between polarons and vacancies has inspired new models for color centers in dielectric crystals, models which represent an advancement from the early models of color centers in alkali halides and simple oxides. The topic discussed in this review is particularly useful to better understand the complex effects of different types of radiation on the defect structure of those materials, therefore providing relevant clues for nuclear engineering applications.

36 MATERIALS SCIENCE↗

Unraveling Electronic and Vibrational Coherences Following a Charge Transfer Process in a Photosystem II Reaction Center

A reaction center is a unique biological system that performs the initial charge separation within a Photosystem II (PSII) multiunit enzyme, which eventually drives the catalytic water-splitting in plants and algae. The possible role of quantum coherences coinciding with the energy and charge transfer processes in PSII reaction center is one of the active areas of research. Here, we study these quantum coherences by using a numerically exact method on an excitonic dimer model, including linear vibronic coupling and employing optimal parameters from experimental two-dimensional coherent spectroscopic measurements. This enables us to precisely capture the excitonic interaction between pigments and the dissipation of the energy from electronic and charge-transfer (CT) states to the protein environment. We employ the time nonlocal (TNL) quantum master equation to calculate the population dynamics, which yields numerically reliable results. The calculated results show that, due to the strong dissipation, the lifetime of electronic coherence is too short to have direct participation in the charge transfer processes. However, there are long-lived vibrational coherences present in the system at frequencies close to the excitionic energy gap. These are strongly coupled with the electronic coherences, which makes the detection of the electronic coherences with conventional techniques very challenging. Additionally, we unravel the strong excitonic interaction of radical pair (PD1 and PD2) in the reaction center, which results in a long-lived electronic coherence of >100 fs, even at room temperature. Our work provide important physical insight to the charge separation process in PSII reaction center, which may be helpful for better understanding of photophysical processes in other natural and artificial light-harvesting systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Package Data for CERF-Data Centers

This dataset contains sample input 100m resolution raster files for running the CERF-DC python package (see https://github.com/IMMM-SFA/cerf_data_centers) at the state level across the CONUS. Due to data availability constraints, some of the items included in this dataset are proxies or assumptions for siting factors used in the model. These are individually noted in the item descriptions and can be exchanged with more detailed information upon availability. Data Descriptions The following raster files are included in the data download: state_siting_region.tif — State areas identified by state FIPS code composite_siting_suitability.tif — Value of 1 indicates suitable siting location, 0 otherwise. The following areas are excluded from siting: Areas within 300m of a federal airport runway Waterbodies Areas with slope >16% Areas susceptible to sinkholes High coastal or inland flood risk areas Local, state, and federal parks, leisure areas, and cemeteries Areas >2 km away from electric substations Areas >5 km away from a municipal water supplier service area Areas >2 km away from high-speed fiber provider service territory Protected Areas Database of the United States (PAD-US) areas Railroads, major roadways, and minor roadways Military areas and training grounds Developed lands Areas >0.8 km (0.5 miles) from developed lands land_value_dollar_per_sqft.tif — USD per square foot (sqft) derived from USDA $/acre land cost personal_property_tax_rate.tif — Personal property tax rate by state. Uses an assumed 0.0125 personal property tax rate for states with personal property tax, 0 for states without personal property tax. real_property_tax_rate.tif — Real property tax rate. Based on county level residential real estate property tax rates. sales_tax_rate.tif — Sales tax rate by state. mechanical_cooling_fraction.tif — Fraction of year (values between 0 and 1, inclusive) that the data center would be cooled through mechanical processes based on local water stress and humidity levels. water_cooling_fraction.tif — Fraction of year (values between 0 and 1, inclusive) that the data center would be cooled through evaporative (water cooled) processes based on local water stress and humidity levels. distance_to_substation.tif — Distance to nearest substation in hundreds of meters (i.e., value of 1 equals a distance of 100m). Offshore areas have a value of 0. industrial_electricity_rates_dollar_per_kwh.tif — USD/kWh industrial electricity rates. Represents the average industrial rate across all utilities that operate within a given county. Values are derived from the US Utility Rate Database. commercial_electricity_rates_dollar_per_kwh.tif — USD/kWh commercial electricity rates. Represents the average commercial rate across all utilities that operate within a given county. Values are derived from the US Utility Rate Database. data_center_market_locations.tif — Grid cells with positive values represent the centroid of existing data center market clusters. The value of non-zero grid cells represents the number of data centers in the market cluster. All other grid cells have a value of 0. Geospatial Metadata CRS: Albers Equal Area Conic (ESRI:102003) Extent: -2415585.0000000023283064,-1441981.2605773280374706 : 2384414.9999999976716936,1708018.7394226719625294 Dimensions: X: 48000 Y: 31500 Bands: 1 Origin: -2415585.0000000023283064,1708018.7394226719625294 Pixel Size: 100,-100 Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. License This data is made available under a CCBY4.0 License Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Mongird, Kendall↗

Package Data for CERF-Data Centers

This dataset contains sample input 100m resolution raster files for running the CERF-DC python package (see https://github.com/IMMM-SFA/cerf_data_centers) at the state level across the CONUS. Due to data availability constraints, some of the items included in this dataset are proxies or assumptions for siting factors used in the model. These are individually noted in the item descriptions and can be exchanged with more detailed information upon availability. Data Descriptions The following raster files are included in the data download: state_siting_region.tif — State areas identified by state FIPS code composite_siting_suitability.tif — Value of 1 indicates suitable siting location, 0 otherwise. The following areas are excluded from siting: Areas within 300 m of a federal airport runway or within an airport area boundary Waterbodies Areas with slope >16% Areas susceptible to sinkholes High coastal or inland flood risk areas Local, state, and federal parks, leisure areas, and cemeteries Areas >2 km away from electric substations Areas >5 km away from a municipal water supplier service area Areas >2 km away from high-speed fiber provider service territory USGS Protected Areas Database of the United States (PAD-US) GAP status 1, 2, or 3 areas US National Parks Wetlands USFWS critical habitats BIA land areas Railroads, major roadways, and minor roadways Military areas and training grounds NLCD developed lands Areas >0.8 km (0.5 miles) from NLCD developed lands land_value_dollar_per_sqft.tif — USD per square foot (sqft) derived from USDA $/acre land cost personal_property_tax_rate.tif — Personal property tax rate by state. Uses an assumed 0.0125 personal property tax rate for states with personal property tax, 0 for states without personal property tax. real_property_tax_rate.tif — Real property tax rate. Based on county level residential real estate property tax rates. sales_tax_rate.tif — Sales tax rate by state. mechanical_cooling_fraction.tif — Fraction of year (values between 0 and 1, inclusive) that the data center would be cooled through mechanical processes based on local water stress and humidity levels. water_cooling_fraction.tif — Fraction of year (values between 0 and 1, inclusive) that the data center would be cooled through evaporative (water cooled) processes based on local water stress and humidity levels. distance_to_substation.tif — Distance to nearest substation in hundreds of meters (i.e., value of 1 equals a distance of 100m). Offshore areas have a value of 0. industrial_electricity_rates_dollar_per_kwh.tif — USD/kWh industrial electricity rates. Represents the average industrial rate across all utilities that operate within a given county. Values are derived from the US Utility Rate Database. commercial_electricity_rates_dollar_per_kwh.tif — USD/kWh commercial electricity rates. Represents the average commercial rate across all utilities that operate within a given county. Values are derived from the US Utility Rate Database. data_center_market_locations.tif — Grid cells with positive values represent the centroid of existing data center market clusters. The value of non-zero grid cells represents the number of data centers in the market cluster. All other grid cells have a value of 0. Geospatial Metadata CRS: Albers Equal Area Conic (ESRI:102003) Extent: -2415585.0000000023283064,-1441981.2605773280374706 : 2384414.9999999976716936,1708018.7394226719625294 Dimensions: X: 48000 Y: 31500 Bands: 1 Origin: -2415585.0000000023283064,1708018.7394226719625294 Pixel Size: 100,-100 Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. License This data is made available under a CCBY4.0 License Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Mongird, Kendall↗

Integrating AI Data Centers with the Power Grid

The rapid expansion of artificial intelligence (AI) has triggered an unprecedented surge in electricity demand, with US data center energy use projected to double or triple 2023 levels by 2028. This exponential growth places strain on grid infrastructure, which can hinder timely construction of desired computing capacity. To bridge this supply-demand gap, utilities and AI developers are increasingly turning to demand flexibility, a strategy that incentivizes shifting or reducing power use during peak periods of grid stress. Data centers are uniquely equipped for flexible operations due to their digital workloads, built-in redundancy, and onsite energy assets. This article outlines four primary mechanisms to enable data center flexibility: computational load flexibility (shifting tasks temporally or geographically), flexible use of core facility infrastructure adjustments, energy storage utilization, and onsite electricity generation. To encourage adoption, utilities are deploying new tariff designs, including voluntary interruptible service riders, mandated flexibility requirements, and streamlined interconnection processes for flexible loads. For the highly capitalized and rapidly growing AI industry, the primary motivators for embracing these strategies are expediting facility interconnection, satisfying emerging regulatory mandates, and mitigating community resistance. While demand flexibility cannot substitute the long-term need for new bulk power generation, it serves as an essential, immediate solution for enabling near-term deployment. By transforming data centers from grid stressors into stabilizing assets, flexible operations can ensure reliable grid integration, ease market pressures, and support a resilient power system.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Purcell-Enhanced Emissions from Diamond Color Centers in Slow Light Photonic Crystal Waveguides

Diamond color centers are promising candidates for optically addressable quantum memories, which motivates the development of efficient photonic interfaces, often using nanophotonic cavities with narrow spectral line widths and small mode volumes. However, they require perfect spectral and spatial overlap between the cavity mode and quantum emitter, which is challenging. This is especially true for solid-state quantum emitters that are often randomly positioned and suffer from inhomogeneous broadening. Another approach to enhance light-matter interaction across large optical bandwidths and areas is using slow light waveguides. Here, in this study, we demonstrate diamond slow light photonic crystal (PhC) waveguides optically coupled to embedded silicon-vacancy (SiV) color centers. We use the recently developed thin-film diamond approach to fabricate fully suspended two-dimensional PhC waveguides. We demonstrate waveguide modes with high group indices up to 70 and observe Purcell-enhanced emissions of the SiVs. Our approach represents a practical diamond platform for robust spin-photon interfaces with color centers.

2D photonic crystal waveguide↗

Neutral Silicon Vacancy Centers in Undoped Diamond via Surface Control

Neutral silicon vacancy centers (SiV 0 ) in diamond are promising candidates for quantum applications; however, stabilizing SiV 0 requires high-purity, boron-doped diamond, which is not a readily available material. Here, we demonstrate an alternative approach via chemical control of the diamond surface. We use low-damage chemical processing and annealing in a hydrogen environment to realize reversible and highly stable charge state tuning in undoped diamond. The resulting SiV 0 centers display optically detected magnetic resonance and bulklike optical properties. Controlling the charge state tuning via surface termination offers a route for scalable technologies based on SiV 0 centers, as well as charge state engineering of other defects.

74 ATOMIC AND MOLECULAR PHYSICS↗

FINAL TECHINICAL REPORT THUNDERING BUFFALO HEALTH AND WELLNESS CENTER

This U.S. Department of Energy, Office of Indian Energy supported project consists of energy conservation measures (ECMs) and a solar photovoltaic (PV) system to reduce cost of utility bills in a newly constructed Fort Peck Wellness Center, for use by tribal members in improving their physical and mental wellness. Construction of the building was outside the scope of the DOE supported project. A new 2-story wellness center was designed and constructed in Poplar, Montana. The wellness center is comprised of fitness areas, gymnasium, pool and spa, offices, and BOH support areas. The building was completed and has been operational for more than a year. A final measurement and verification of energy savings was completed after one year of operation and the results are presented herein, showing an energy savings 20% higher than the originally models indicated.

14 SOLAR ENERGY↗

Unlocking Synergistic Benefits of Colocation of Data Centers at Airports

This white paper evaluates the potential of a new energy system configuration: Strategic colocation of data centers - on airport property or adjacent to airports - in order to realize significant operational, economic, and environmental benefits to airports, data centers, and the communities they serve. While increasing demand from both airports and data centers requires both parties to make significant infrastructure investments, colocation can mitigate some of the energy, land use, permitting, and connectivity challenges of siting and powering these industries.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Wide-field microwave magnetic field imaging with nitrogen-vacancy centers in diamond

Non-invasive imaging of microwave (MW) magnetic fields with microscale lateral resolution is pivotal for various applications, such as MW technologies and integrated circuit failure analysis. Diamond nitrogen-vacancy (NV) center magnetometry has emerged as an ideal tool, offering micrometer-scale resolution, millimeter-scale field of view, high sensitivity, and non-invasive imaging compatible with diverse samples. However, up until now, it has been predominantly used for imaging of static or low-frequency magnetic fields or, concerning MW field imaging, to directly characterize the same microwave device used to drive the NV spin transitions. In this work, we leverage an NV center ensemble in diamond for wide-field imaging of MW magnetic fields generated by a test device employing a differential measurement protocol. The microscope is equipped with a MW loop to induce Rabi oscillations between NV spin states, and the MW field from the device-under-test is measured through local deviations in the Rabi frequency. This differential protocol yields magnetic field maps of a 2.57 GHz MW field with a sensitivity of ∼9 μT Hz −1/2 for a total measurement duration of T=357 s, covering a 340 × 340 μm 2 field of view with a micrometer-scale spatial resolution and a device-under-test input power dynamic range of 30 dB. This work demonstrates a novel NV magnetometry protocol, based on differential Rabi frequency measurement, that extends NV wide-field imaging capabilities to imaging of weak MW magnetic fields that would be difficult to measure directly through standard NV Rabi magnetometry.

crystallographic defects↗

Human readiness levels and Human Views as tools for user-centered design

The Human Readiness Level (HRL) scale is a simple nine-level scale that brings structure and consistency to the real-world application of user-centered design. It enables multidisciplinary consideration of human-focused elements during the system development process. Use of the standardized set of questions comprising the HRL scale results in a single human readiness number that communicates system readiness for human use. The Human Views (HVs) are part of an architecture framework that provides a repository for human-focused system information that can be used during system development to support the evaluation of HRL levels. Here, this paper illustrates how HRLs and HVs can be used in combination to support user-centered design processes. A real-world example for a U.S. Army software modernization program is described to demonstrate application of HRLs and HVs in the context of user-centered design.

42 ENGINEERING↗

Organizational and psychological measures for data center energy efficiency: barriers and mitigation strategies

Abstract It was last estimated that in 2020, data centers comprised approximately 2% of total US electricity consumption, with an estimated annual growth rate of 4%. As our country increasingly relies on information technology (IT), our data centers (DCs) will need to increase their energy efficiency (EE) to stabilize their energy consumption. The task of studying EE in DCs is complicated by the interconnected nature of humans and mission-critical technical systems. Moreover, the literature tends to focus on technology solutions such as improvements to IT equipment, cooling infrastructure, and software, without addressing organizational and psychological drivers. Our research demystifies the complex interactions between humans and DCs, by asking What non-technical barriers impede EE investment decision-making and/or implementing energy management strategies? To begin to answer this question, we perform a literature review of 86 resources, ranging from peer-reviewed journal publications to handbooks. We also consider related fields such as organizational behavioral management and energy intensive buildings. We develop a public Zotero library, perform content coding, and complete a rudimentary network analysis. Our findings from the literature review suggest that (1) technological solutions are abundant in the literature but fall short of providing practical guidance on the pitfalls of implementation, (2) making energy efficiency a priority at the executive level of organizations will be largely ineffective if the IT and facilities staff are not directly incentivized to increase EE, and (3) there is minimal current understanding of how the individual psychologies of IT and facilities staff affect EE implementation in DCs. In the next phase of our research, we plan to interview data center operators/experts to ground-truth our literature findings and collaboratively design decarbonization policy solutions that target organizational structure, empower individual staff, and foster a supportive external market.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Expert and operator perspectives on barriers to energy efficiency in data centers

Abstract It was last estimated in 2016 that data centers (DCs) comprise approximately 2% of total US electricity consumption. However, this estimate is currently being updated to account for the massive increase in computing needs due to streaming, cryptocurrency, and artificial intelligence (AI). To prevent energy consumption that tracks with increasing computing needs, it is imperative we identify energy efficiency strategies and investments beyond the low-hanging fruit solutions. In a two-phased research approach, we ask: What non-technical barriers still impede energy efficiency (EE) practices and investments in the data center sector, and what can be done to overcome these barriers? In particular, we are focused on social and organizational barriers to EE. In Phase I, we performed a literature review and found that technical solutions are abundant in the literature, but fail to address the top-down cultural shifts that need to take place in order to adapt new energy efficiency strategies. In Phase II, reported here, we interviewed 16 data center operators/experts to ground-truth our literature findings. Our interview protocols focus on three aspects of DC decision-making: procurement practices, metrics and monitoring, and perceived barriers to energy efficiency. We find that vendors are the key drivers of procurement decisions, advanced efficiency metrics are facility-specific, and there is convergence in the design of advanced facilities due to the heat density of parallelized infrastructure. Our ultimate goals for our research are to design DC decarbonization policies that target organizational structure, empower individual staff, and foster a supportive external market.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Slow manifolds of classical Pauli particle enable structure-preserving geometric algorithms for guiding center dynamics

Since variational symplectic integrators for the guiding center was proposed, structure-preserving geometric algorithms have become an active research field in plasma physics. We found that the slow manifolds of the classical Pauli particle enable a family of structure-preserving geometric algorithms for guiding center dynamics with long-term stability and accuracy. This discovery overcomes the difficulty associated with the unstable parasitic modes for variational symplectic integrators when applied to the degenerate guiding center Lagrangian. It is a pleasant surprise that Pauli's Hamiltonian for electrons, which predated the Dirac equation and marks the beginning of particle physics, reappears in classical physics as an effective algorithm for solving an important plasma physics problem. This technique is applicable to other degenerate Lagrangians reduced from regular Lagrangians.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗