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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.

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At least 631 records · Page 35
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Tuning the thermal activation atmosphere breaks the activity–stability trade-off of Fe–N–C oxygen reduction fuel cell catalysts

Fe–N–C catalysts are the most promising platinum group metal-free oxygen-reduction catalysts, but they suffer from a low density of active metal sites and the so-called activity–stability trade-off. Here we report an Fe–N–C catalyst prepared by adding an optimal amount of H 2 to the traditional inert atmosphere during the thermal activation. The presence of H 2 significantly increases the total density of FeN 4 sites, suppressing the unstable pyrrolic-N-coordinated S1 sites and favouring the stable pyridinic-N-coordinated S2 sites with shortened Fe–N bond lengths. Here, we propose that the intrinsically stable S2 sites are probably arranged in well-graphitized carbon layers, and the S1 sites exist in less-graphitized carbon. H 2 could remove unstable S1 sites and retain stable S2 sites during the pyrolysis to break the challenging activity–stability trade-off. The Fe–N–C catalyst in membrane electrode assemblies maintains a current density of 67 mA cm -2 at 0.8 V (H 2 –air) after 30,000 voltage cycles (0.60 to 0.95 V under H 2 –air), achieving encouraging durability and performance simultaneously.

25 ENERGY STORAGE↗
DOE OSTI2018

Fabrication, Assembly, and Metrology of the Neutron Imaging Pinhole

The neutron imaging pinhole is a complex aperture that is designed to have its image plane at the center of a laser fusion capsule implosion. The aperture’s high-Z materials of tungsten and gold block the neutrons so that only the neutrons passing through the machined apertures make it to the image plane and detector. The pinhole assembly consists of 11 layers of gold in between two layers of tungsten and gold. These 64 triangular pinholes and six penumbra apertures provide a matrix image that can be reconstructed to image complex deuterium-tritium neutron burn details in laser fusion capsules. The gold layers were diamond turned flat before the profiles were cut into their faces. Four of the layers were profiled with penumbral profile arrays that tapered from a radius of 250 to 150 µm. Three gold layers were just diamond turned to wedges to set the tilt of the whole aperture. Three gold layers were profiled on both sides with triangle groove arrays that consist of eight equilateral triangles with the depth of 200 to 15 µm over the 200-mm length, with a tolerance of 2 µm. Custom software programming routines were written using Labview to move the diamond-turning profiler through the required X-Y-Z movements to cut the penumbral and grooved profiles of the pinhole into the varying tilted arrays of features. The software is optimized to push the profile of the whole part into the face while eliminating any unneeded passes that do not cut any material. Each layer was thoroughly inspected on both sides using an optical coordinate measuring machine and white-light interferometer to validate each of the profiles. The pinhole assembly was inspected on a rotary stage so that both ends of the assembly can be inspected and presented in a single point cloud. The process of machining, programming, assembly, and inspection of the neutron imaging pinhole is covered.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

MASK3 for Advanced WEC Dynamics and Controls

This report outlines the "MASK3" wave tank test within the Advanced WEC Dynamics and Controls (AWDC) project. This test represents the final test in the AWDC project. The focus of the MASK3 test was to consider coordinated 3-degree-of-freedom (3DOF) control of a WEC in a realistic ocean environment. A key aspect of this test was the inclusion of a "self-tuning" mechanism which uses an optimization algorithm to update controller gains based on a changing sea state. The successful implementation of the self-tuning mechanism is the last crucial step required for such a controller to be implemented in real ocean environments.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

STOCHASTIC OPTIMAL POWER FLOW FOR REAL-TIME MANAGEMENT OF DISTRIBUTED RENEWABLE GENERATION AND DEMAND RESPONSE (Final Report)

To meet the grand challenge of a sustainable energy future, there has been a surge of interest in renewable energy. Today, the uncertainty associated with renewable resources is handled by using operating reserves. The high penetration of renewable resources, however, introduces difficult-to-control dynamics and challenges for power system operation. Decision support tools are necessary at the bulk system operational level to recognize and efficiently utilize renewable resources and distributed demand response products in concert with traditional grid resources. It is envisaged that responsive load can potentially have very significant cost advantages over either spinning or non-spinning ramping reserve. Critical decisions are made during hour(s)-ahead and real-time power system operation regarding the commitment and dispatch of generators to ensure power delivery is both reliable and economic. These decisions are typically made by a security constrained optimal flow, which determines future generator commitments, dispatches, and ensures adequate reserves are available in the event of a contingency (unexpected outage) or if future system conditions deviate from forecasts. However, security has been always based on a pre-specified subset of contingency constraints whose enforcement does not guarantee security under all possible future possibilities while also giving little or no weight to the likelihood of each contingent event or the severity of its consequences. Existing tools, which are based exclusively on deterministic optimization models, do not yield optimal operational decisions to address these new challenges, in terms of both reliability and cost-effectiveness. This project has focused on developing a stochastic optimal power flow (SOPF) framework, which integrates renewable resource uncertainty, load uncertainty, distributed storage (DS), demand response (DR) products, in a holistic manner to address the uncertainty associated with ever-increasing renewable resources, along with the inclusion of distributed demand response products in future power systems. A proof-of-concept problem was created using the Pennsylvania-Jersey-Maryland (PJM) power system network. Synthetic wind generation was added to the system to simulate 50% wind penetration. A 1-hour test of SOPF operation indicated more than 6% operational cost savings. The project continued by adding the Midwestern Independent System Operator (MISO) as a partner, with focus shifting from SOPF to Stochastic Look-Ahead Unit Commitment (SLAC). Unlike PJM, MISO is faced with significant renewable energy resources within its footprint and is challenged with substantial uncertainty in its operations. The SLAC distinguishes itself from existing tools that operators use. At best, today’s tools solve two to three cases independently, where one or two system parameters, such as forecasted load level (e.g., a low, base, and high forecast), are varied and the resulting scenarios are analyzed independently. The stochastic-based optimization of SLAC leverages statistical information from an ensemble of potential operational scenarios and their respective likelihood. The SLAC output can be translated into valuable information to the operator such as suggested commitments, optimal scheduling and dispatch of resources, reserve requirements at both locational and zonal resolutions, ramping availability and requirements, availability of demand response including operational guidance concerning the near-term and real-time coordination between distributed energy resources, and utilization of distributed storage resources. The developed SOPF/SLAC tool, a stand-alone tool compatible with existing EMSs, will provide system operators with unprecedented visibility, flexibility and predictability to these resources and operational guidance concerning the real-time coordination between DERs and DR/DS products. The game changing and practical impact of this disruptive technology will be dramatic and will usher in a new era in the electric power industry, wherein green energy concepts are fully embraced, and electric power costs are lowered throughout the nation.

42 ENGINEERING↗
DOE OSTI2019

Hierarchical Management of Distributed Energy Resources Using Chance-Constrained OPF and Extremum Seeking Control

Distributed energy resources (DERs) are becoming an important part of distribution systems, because of their economic and environmental benefits. Although their inherent intermittency and volatility introduce uncertainties into the electric power system, they have the potential to provide controllability to the system under proper coordination. In this paper, we propose a hierarchical control algorithm for distribution systems with DERs so that they have controllability similar to a generator bus. The upper level scheduler solves a chance-constrained optimal power flow (OPF) problem to plan the operation of the DERs based on forecasts, and the lower level distributed DER controllers leverage the extremum seeking approach to deliver the planned power at the feeder head. The proposed algorithm is tested on a modified IEEE 13-node feeder, demonstrating its effectiveness.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Coordination Sphere of Lanthanide Aqua Ions Resolved with Ab Initio Molecular Dynamics and X-ray Absorption Spectroscopy

To resolve the fleeting structures of lanthanide Ln 3+ aqua ions in solution, we (i) performed the first ab initio molecular dynamics (AIMD) simulations of the entire series of Ln 3+ aqua ions in explicit water solvent using pseudopotentials and basis sets recently optimized for lanthanides and (ii) measured the symmetry of the hydrating waters about Ln 3+ ions (Nd 3+ , Dy 3+ , Er 3+ , Lu 3+ ) for the first time with extended X-ray absorption fine structure (EXAFS). EXAFS spectra were measured experimentally and generated from AIMD trajectories to directly compare simulation, which concurrently considers the electronic structure and the atomic dynamics in solution, with experiment. In this study, we performed a comprehensive evaluation of EXAFS multiple-scattering analysis (up to 6.5 Å) to measure Ln–O distances and angular correlations (i.e., symmetry) and elucidate the molecular geometry of the first hydration shell. This evaluation, in combination with symmetry-dependent L 3 - and L 1 -edge spectral analysis, shows that the AIMD simulations remarkably reproduces the experimental EXAFS data. The error in the predicted Ln–O distances is less than 0.07 Å for the later lanthanides, while we observed excellent agreement with predicted distances within experimental uncertainty for the early lanthanides. Our analysis revealed a dynamic, symmetrically disordered first coordination shell, which does not conform to a single molecular geometry for most lanthanides. This work sheds critical light on the highly elusive coordination geometry of the Ln 3+ aqua ions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

The Challenges of Modeling Distributed Energy Resources (DERs) as Blackstart Resources and for Volt-VAR Optimality

Modeling, testing and instituting Distributed Energy Resources (DERs) as Blackstart Resoucrces presents several challenges due to the fundamental differences between traditional black start resources (e.g., large generators) versus DERs like solar PV systems with battery storage. This paper addresses some of these key challenges. These include intermittency of coordinating DERs to provide continuous power during a black start event, especially during extended periods of cloud cover or when battery energy storage is depleted. This paper additionally addresses the collapsing voltage and stability control challenges specific to maintaining bulk power system stability during black start synchronization These physical and engineering limitations require careful engineering design, modeling and engineering to ensure that DERs can support critical loads and substations during black start events. A variety of additional challenges also exist. Additionally, there are challenges associated with feeder location and low voltage secondary system impacts on DER functions and settings. We compare typical functions and settings for DERs for power factor control and correction. We also demonstrate how voltag control via Volta-VAR power factor correction can be done

Mukherjee, Srijib↗
DOE OSTI2019

Advanced WEC Dynamics and Controls MASK3 Test

Sandia National Laboratories and the Department of Energy (DOE) have completed on a multi-year program to examine the effects of control theory on increasing power produced by resonant wave energy conversion (WEC) devices. The tank tests have been conducted at the Naval Surface Warfare Center Carderock Division (NSWCCD) Maneuvering and Sea Keeping Basin (MASK) in West Bethesda, MD. This report outlines the "MASK 3 " wave tank test within the Advanced WEC Dynamics and Controls (AWDC) project. This test represents the final test in the AWDC project. The focus of the MASK 3 test was to consider coordinated 3 -degree-of-freedom ( 3 DOF) control of a WEC in a realistic ocean environment. A key aspect of this test was the inclusion of a "self-tunine mechanism which uses an optimization algorithm to update controller gains based on a changing sea state. The successful implementation of the self-tuning mechanism is the last crucial step required for such a controller to be implemented in real ocean environments.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

Control system for multi-system coordination via a single reference governor

This report describes the improvements to the Feasible Actuator Range Modifier (FARM) component of the RAVEN-based HYBRID framework for analysis of Integrated Energy Systems (IES). FARM supports the HERON plug-in that solves the power dispatch problem. The solution involves economically optimal dispatches that satisfy the limits on production variables and corresponding rates of variation (explicit constraints) as well as the limits on the process variables tied to the service life of equipment (implicit constraints). The problem can be addressed as a two-stage process, i.e., HERON power dispatcher estimates a solution that meets explicit constraints (low-resolution physics), whereas FARM uses the simulation outcomes of HYBRID high-fidelity model to capture the system dynamic response and enforce implicit constraints (high-resolution physics). The initial version of the code (FARM-Alpha) was released by Argonne National Laboratory in January 2021 followed by FARM-Beta (January 2022) and FARM-Gamma (April 2022).

42 ENGINEERING↗
DOE OSTI2024

Review of In Situ Sensing for Directed Energy Deposition for Industrial Part Quality Assessment

As the use additive manufacturing (AM) processes continues to grow in critical industries, improved quality assurance methods are becoming increasingly sought after for qualification and certification of AM components. Traditional nondestructive evaluation of printed components is often unable to supply the required confidence in print quality to justify qualification and certification, but the layer-by-layer nature of AM provides unprecedented opportunities for in situ quality inspection. This document summarizes recent developments in process monitoring research specifically related to Directed Energy Deposition (DED). Particular attention is given to three aspects of the highlighted manuscripts: (1) the type of sensors used, (2) features extracted from each sensor modality, and (3) analysis of extracted features for AM quality assessment. Based on the review of the state-of-the-art, several observations have been made. First, none of the reviewed works have applied their trained models to real part geometries, with many of the works relying on single track experiments, thin-walled structures, and cubes. Similarly, there have not been any works demonstrating model generalizability, i.e., a model trained on data from one build allows for fruitful analysis of data from another build. Many works used machine learning techniques to distinguish different process regimes (i.e., normal, keyholing, lack-of-fusion), but very few papers have investigated stochastic variation in an already “optimized” process. Sensor fusion approaches are also limited in the DED sensing literature, but the few works that have employed such techniques have demonstrated the benefits. Finally, registration of in situ data to the build coordinate system is of paramount importance to producing industrially relevant in situ monitoring systems. Data registration allows direct correlations between process anomalies detected in the process monitoring data to localized departures in part quality, but such techniques are generally lacking in the current literature.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Does practice make perfect? Lessons learned from full-scale power system incident response exercise

While threats to the energy sector occur daily, few utilities get the opportunity to fully test out their detection and response mechanisms to advanced threats in the real world. With the high demand for reliability, few grid operators would allow execution of simulated cyber-attacks on their live systems. The DOE-funded Liberty Eclipse project offers a unique opportunity for small and large utilities and coops to practice their combined IT/OT responses to a live red team executing attacks against an isolated power system on an island in New York. Both cyber teams and power operations teams must work together to detect and respond to attacks, even restoring the power system against extreme impacts. Lessons learned from these exercises reveal key takeaways for understanding what a real attack against the electric sector will look like, gaps in execution of the best-laid plans when the pressure of a real event is bearing down, and how organizations can better prepare for advanced attacks by optimizing participation in exercises. This presentation will discuss successes and opportunities for improvement both in how utilities can prepare for and respond to events, as well as how full-scale IT/OT exercises can be coordinated.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Tools and Methods for Optimization of Nuclear Plant Outages

Refueling outages are one of the most challenging phases in a nuclear power plants (NPP) operating cycle. Refueling outages are extremely costly for a NPP due to the large amount of required resources and because of lost revenue due to plant being off the grid. Outage durations have steadily decreased across the industry over that last few decades primarily due to improved planning and coordination, but there are still many plants that struggle to meet the performance metrics accomplished by other utilities. Schedule resilience is one of the issues. NPP outages require scheduling thousands of activities in a duration of around 30 days on average. Outage staff begin working on the schedule more than a year ahead of the outage start and make every effort to build a robust schedule. Despite the robust and detailed planning, once the outage starts, numerous emergent issues typically appear along with schedule delays requiring continuous replanning and adjusting. When schedule disruption occurs during an outage, plant staff make urgent efforts to recover but often not able to maintain the planned outage duration. These outage delays can cost a utility several million dollars per day. Tools that could help outage schedulers create a more resilient schedule and allow them to optimally reschedule emergent work could significantly reduce outage delays. One key aspect of creating a resilient schedule is to have accurate estimates for activity duration. Another important outage scheduling capability is the ability to schedule emergent work with minimal disruption. The Optimization of Outage Activities project under the Risk-Informed Systems Analysis Pathway (RISA) sponsored by Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) program focuses on developing tools and methods to support nuclear power plants with optimization of outage schedules. The goal of the outage optimization is the completion of all planned and emergent outage activities as fast as possible while maintaining highest level of safety. This report describes the initial development of tools to support outage management that leverage computational and machine learning methods developed in other RISA and LWRS projects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Optimizing first- and last-mile public transit services leveraging transportation network companies (TNC)

First-mile last-mile (FMLM) mobility services that connect riders to public transit can lead to improved transit accessibility and network efficiency if such services are convenient and reliable. However, many current FMLM services are inefficient and costly because they are inflexible (e.g., fixed supply of shuttles) and do not leverage collected data for optimized decision making. At the same time, new forms of shared mobility can provide added flexibility and real-time analytics to FMLM systems when carefully integrated. This study evaluates performance and cost implications of public/private coordination between transit shuttles and transportation network companies (TNC) in the FMLM context. A real-time operations model was developed to simulate daily operations for an existing FMLM system using real-world demand data. Three supply strategies were tested with varying levels of flexibility: (1) Status Quo (two 23-passenger on-demand shuttles), (2) Hybrid (one 23-passenger on-demand shuttle + TNC), and (3) TNC Only (exclusively use TNC services). Results indicated that the added flexibility of the Hybrid service design (using shuttles and TNCs) improved service performance (a 7.7% improvement), reduced daily operating costs (– 6.0%), and improved service reliability (95th percentile travel times decreased by up to 40% during peak periods). In addition, the Hybrid service design was more robust to variations in demand. Here, the Hybrid service was significantly cheaper to operate (– 31.6%) at reduced demand levels (50% of normal), and improved service performance (a 10.2% improvement) when demand levels were increased (150% of normal). These findings emphasize the importance of flexibility in FMLM service designs, especially when demand is sparse and variable.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

A method for assessing economic, environmental, and reliability tradeoffs of interregional transmission connecting ERCOT (the Texas grid) to the eastern and western grids

Reliable development of the power grid is an evolving concern for humanity due to extreme weather that frequently threatens power sector infrastructure. The state of Texas is a uniquely structured testbed for grid planners to study when looking for solutions to development, innovation, and overcoming such challenges. Because of its size and islanded structure, Texas is small enough to model, but big enough to matter. Texas is a global leader in energy production, energy consumption, and maintains an unusually diverse fuel mix. In addition, the state has experienced winter freezes, heat waves, wind storms, droughts and floods that have threatened power sector infrastructure or caused recent blackouts and calls for demand side conservation. One of the most devastating of these events was the North American winter storm, dubbed “Winter Storm Uri” by the Weather Channel, that froze the region in February 2021 and led to an extended power outage event that put the majority of Texan residents in darkness for days. While preparing to avoid such outage events in the future, various tools have been proposed to improve grid reliability, including energy efficiency, demand response, and distributed energy resources. An additional option would be to develop interregional transmission that connects the Texas grid to other national grids. To assess the merits of this idea, we developed a novel, universally-applicable and internationally-relevant framework to study how the Texas grid would evolve alongside access to various interregional ties. This method allows us to stress the synthetic grid structure and analyze how it would respond to the shock of a simulated winter storm event. Our method leverages open-source modeling tools, such as PowerGenome, pyGRETA, and GenX to synthesize unique zonal grid data, construct a consolidated network of model regions, and simulate different developmental pathways of capacity expansion and operational dispatch. We demonstrate our method with an analysis connecting the Electric Reliability Council of Texas (ERCOT), the grid that serves most of Texas, the Western Electricity Coordinating Council (WECC), the grid that serves the western half of the contiguous U.S., and the Eastern Interconnect, the grid that serves the eastern half of the contiguous U.S. Our results indicate that the cost-optimal capacity of interregional transmission connecting the ERCOT grid to other grids lies between 9–13 GW assuming baseline conditions. Building this amount of connecting capacity in one or multiple directions lowers the costs and emissions of development and operation by up to $16 billion and 257 million metric tonnes (MMT) respectively. Additionally, our results show that the interregional connections between ERCOT and other national grids reduce the amount of total load shed required through mild winter storm events. However, our results also show that there is a threshold of very extreme winter storm conditions, spanning multiple service areas, above which the connections exacerbate resource adequacy problems. Therefore, the results indicate that the connections need to be carefully planned alongside the rest of the grid infrastructure to avoid over-reliance on specific resources or technology options.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Trajectory design via unsupervised probabilistic learning on optimal manifolds

Abstract This article illustrates the use of unsupervised probabilistic learning techniques for the analysis of planetary reentry trajectories. A three-degree-of-freedom model was employed to generate optimal trajectories that comprise the training datasets. The algorithm first extracts the intrinsic structure in the data via a diffusion map approach. We find that data resides on manifolds of much lower dimensionality compared to the high-dimensional state space that describes each trajectory. Using the diffusion coordinates on the graph of training samples, the probabilistic framework subsequently augments the original data with samples that are statistically consistent with the original set. The augmented samples are then used to construct conditional statistics that are ultimately assembled in a path planning algorithm. In this framework, the controls are determined stage by stage during the flight to adapt to changing mission objectives in real-time.

42 ENGINEERING↗
DOE OSTI2019

Unraveling Confined Dynamics of Guests Trapped in Self-Assembled Pd 6 L 4 Nanocages by Ultrafast Mid-IR Polarization-Dependent Spectroscopy

Self-assembled coordination cages form host–guest complexes through weak noncovalent interactions. Knowledge of how these weak interactions affect the structure, reactivity, and dynamics of guest molecules is important to further the design principles of current systems and optimize their specific functions. We apply ultrafast mid-IR polarization-dependent pump–probe spectroscopy to probe the effects of two Pd 6 L 4 self-assembled nanocages on the properties and dynamics of fluxional group-VIII metal carbonyl guest molecules. We find that the interactions between the Pd 6 L 4 nanocages and guest molecules act to alter the ultrafast dynamics of the guests, restricting rotational diffusional motion and decreasing the vibrational lifetime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Atlas of putative minima and low-lying energy networks of water clusters n = 3 - 25

We report a database consisting of the putative minima and ~3.2 million local minima lying within 5 kcal/mol from the putative minima for water clusters of sizes n = 3 – 25 using an improved version of the Monte Carlo Temperature Basin Paving (MCTBP) global optimization procedure in conjunction with the ab-initio based, flexible, polarizable Thole-Type Model (TTM2.1-F, version 2.1) interaction potential for water. Several of the low-lying structures, as well as lowlying penta-coordinated water networks obtained with the TTM2.1-F potential, were further refined at the Møller-Plesset second order perturbation MP2/aug-cc-pVTZ level of theory. In total, we have identified 3,138,303 networks corresponding to local minima of the clusters n = 3 – 25, whose Cartesian coordinates and relative energies can be obtained from the webpage https://sites.uw.edu/wdbase/. Networks containing penta-coordinated water molecules start to appear at n = 11 and, quite surprisingly, are energetically close (within 1 – 3 kcal/mol) to the putative minima, a fact that has been confirmed from the MP2 calculations. This large database of water cluster minima spanning quite dissimilar hydrogen bonding networks is expected to influence the development and assessment of the accuracy of interaction potentials for water as well as lower scaling electronic structure methods (such as different density functionals). Furthermore, it can also be used in conjunction with data science approaches (including but no limited to neural networks, machine and deep learning) to understand the properties of water, nature’s most important substance.

Rakshit, Avijit↗
DOE OSTI2020

Generalized Grad–Shafranov equation for non-axisymmetric MHD equilibria

The structure of static MHD equilibria that admit continuous families of Euclidean symmetries is well understood. Such field configurations are governed by the classical Grad–Shafranov equation, which is a single elliptic partial differential equation in two space dimensions. By revealing a hidden symmetry, here we show that in fact all smooth solutions of the equilibrium equations with non-vanishing pressure gradients away from the magnetic axis satisfy a generalization of the Grad–Shafranov equation. In contrast to solutions of the classical Grad–Shafranov equation, solutions of the generalized equation are not automatically equilibria, but instead only satisfy force balance averaged over the one-parameter hidden symmetry. We then explain how the generalized Grad–Shafranov equation can be used to reformulate the problem of finding exact three-dimensional smooth solutions of the equilibrium equations as finding an optimal volume-preserving symmetry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗