Results for “discrete surface” — Page 4

DOE OSTI2022

A consistent and conservative Phase-Field method for multiphase incompressible flows

In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the “optimal” coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient-based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Finally, numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Particle scale impacts on deconstruction energy of pine residues

The goal of this Case Study was to quantify the impacts of variable moisture and ash on hammer mill throughput and energy consumption and on generation of fines that are not able to be fed to conversion, as compared to a status quo Base Case system. Also considered was convertible carbon content (minimum carbon specification) and maximum ash content and the delivered feedstock cost impacts of not being able to feed residue not meeting both specifications to the conversion reactor. Laboratory data on the impacts of input particle size and moisture content on the exit particle size were received from FCIC Subtask 5.2 from their single particle impact population balance modeling study. Additional throughput and energy consumption data were obtained from FCIC Subtask 5.2 for the same grinder with a 6 mm screen in place. These data were utilized to develop the necessary response surface equations to perform throughput analysis using discrete event simulation. Because the ash contents in the separated fines had not been analyzed in the laboratory at the time of the model runs, we chose to assume that the ash distributed proportionally with total mass into the overs and unders in the disk screen following grinding. Key takeaways from this Case Study are that it is significantly more cost effective to hammer mill the residue prior to drying, even though the grinder throughput is lower and energy consumption is higher versus drying first before grinding. An effect of dry grinding versus high moisture grinding is the production of higher amounts of fines during dry grinding, leading to significantly more of the ground feedstock being rejected by conversion for being below a minimum particle size. With wet grinding the system is still able to produce more preprocessed feedstock meeting the minimum particle size specification even though the instantaneous throughput is lower than for the case of grinding dry feedstock. Additionally, even without the higher fines production from dry grinding, the status quo would still be more costly than wet grinding because the material is rejected after the drying energy has already been input for the dry grinding case. Finally, significant reductions in drying energy are obtained by drying after grinding, and those reductions are of far greater magnitude than the grinding energy increase.

09 BIOMASS FUELS↗

DOE OSTI2022

Air classification of forest residue for tissue and ash separation efficiency

The goal of this Case Study was to evaluate the performance of air classification of logging residues toward meeting conversion CMAs for carbon and ash contents, as compared to the static status quo Base Case system in which the residues are first dried and then ground in a hammer mill with a 6 mm screen and fines < 1.18 mm are removed. Also considered were moisture and ash impacts on throughput and Overall Operating Effectiveness (OOE), as well as delivered feedstock cost and minimum fuel selling price (MFSP). Laboratory data on the impacts of fan speed and moisture content on the separation efficiency of soil ash, needles and bark from white wood were received from FCIC Subtask 5.2. Average throughput and energy consumption data were obtained from the Bioenergy Feedstock National User Facility (BFNUF) for the same air classifier. These data were utilized to develop the necessary response surface equations to perform throughput analysis using discrete event simulation. Because the Base Case status quo system utilizes drying prior to grinding, we modeled the Case Study with drying prior to air classification and subsequent grinding of the separated white wood to isolate the individual quality and cost impacts of air classification relative to the Base Case system. Key takeaways from this Case Study are that air classification improves the quality of the final material, but increases the production cost, especially when lights are disposed; this becomes a tradeoff between increased conversion yield and the extra cost. Removing material should be done as early in the process as possible. Each operation that occurs prior to removing the material increases the cost of the disposed material and leads to wasted energy expenditures. As processes are included or modified, the impact on monetary and energy cost should be included in the decision process. Identifying alternative uses and the associated value for material that is separated from the feedstock stream will have a significant impact on the delivered cost of the material. Although there was an increase in production cost by adding air classification, there was a resulting benefit to the MFSP when meeting or exceeding all of the conversion CMAs; this was an important finding that should be explored further with FCIC Subtask 8.3 and potentially FCIC Task 6.

09 BIOMASS FUELS↗

DOE OSTI2022

Impact of anatomical fractionation of corn stover on hammer mill throughput and energy consumption

The goal of this Case Study was to quantify the impacts of variable moisture and ash on hammer mill throughput and energy consumption and on loss of very wet stover that causes failures in the first stage grinder and that are not able to be fed to conversion, as compared to a status quo Base Case system. Also considered was convertible carbohydrate content (minimum total carbohydrate specification) and maximum ash content and the delivered feedstock cost impacts of not being able to feed stover not meeting the total carbohydrate specification to the conversion reactor. Laboratory data on the impacts of moisture content and tissue fraction on throughput and energy consumption in a stage 2 hammer mill were received from FCIC Subtask 5.1. Additional air classifier throughput, energy consumption and separation efficiency data were obtained from FCIC Subtask 5.1 for the new air classifier, which has three exit streams (lights, middle and heavies). These data were utilized to develop the necessary response surface equations to perform throughput analysis using discrete event simulation. Because the ash contents and particle sizes had not been analyzed in the laboratory at the time of the model runs, we assumed that the ash distributed proportionally with total mass into the lights and heavies in an air classifier having two exit streams (lights and heavies) and that the lights fraction from the air classifier was not removed. Key takeaways from this Case Study are that due to lower energy consumption, it is more cost effective to hammer mill fractionated corn stover tissues than whole stover. Reduction of grinding energy was significant and may possibly be connected to particle-particle interactions in the grinder that lead to increased residence time of leaves and husks, resulting in decreased throughput and higher generation of fines when milling whole stover. While we did not see significant impacts to throughput, this was due to moisture failures of the first stage grinder in each system dominating failures and downtime. The operating cost savings of reduced grinding energy savings in the second stage hammer mills alone was high enough to offset the added capital cost of the air classifier and extra grinding line.

09 BIOMASS FUELS↗

DOE OSTI2025

Fault Tolerant Decoding of QLDPC-GKP Codes with Circuit Level Soft Information

Concatenated bosonic-stabilizer codes have recently gained prominence as promising candidates for achieving low-overhead fault-tolerant quantum computing in the long term. In such systems, analog information obtained from the syndrome measurements of an inner bosonic code is used to inform decoding for an outer code layer consisting of a discrete-variable stabilizer code such as a surface code. The use of Quantum Low-Density Parity Check (QLDPC) codes as an outer code is of particular interest due to the significantly higher encoding rates offered by these code families, leading to a further reduction in overhead for large-scale quantum computing. Recent works have investigated the performance of QLDPC-GKP codes in detail, and the use of analog information from the inner code significantly boosts decoder performance. However, the noise models assumed in these works are typically limited to depolarizing or phenomenological noise. In this paper, we investigate the performance of QLDPC-GKP concatenated codes under circuit-level noise, based on a model introduced by Noh et al. in the context of the surface-GKP code. To demonstrate the performance boost from analog information, we investigate three scenarios: (a) decoding without soft information, (b) decoding with precomputed error probabilities but without real-time soft information, and (c) decoding with real-time soft information obtained from round-to-round decoding of the inner GKP code. Results show minimal improvement between (a) and (b), but a significant boost in (c), indicating that real-time soft information is critical for concatenated decoding under circuit-level noise. We also study the effect of measurement schedules with varying depths and show that using a schedule with minimum depth is essential for obtaining reliable soft information from the inner code.

Borah, Shantom K. [Arizona U. (main)]↗

DOE OSTI2023

Impact of Anatomical Fractionation of Corn Stover on Hammer Mill Throughput and Energy Consumption

The goal of this Case Study was to quantify the impacts of variable moisture and ash on hammer mill throughput and energy consumption and on loss of very wet stover that causes failures in the first stage grinder and that are not able to be fed to conversion, as compared to a status quo Base Case system. Also considered was convertible carbohydrate content (minimum total carbohydrate specification), maximum ash content and the delivered feedstock cost impacts of not being able to feed stover that did not meet the total carbohydrate specification to the conversion reactor. Laboratory data on the impacts of moisture content and tissue fraction on throughput and energy consumption in a stage 2 hammer mill were received from FCIC Subtask 5.1: Preprocessing, Corn Stover Preprocessing (Neal Yancey and Sergio Hernandez, INL). Additional air classifier throughput, energy consumption and separation efficiency data were obtained from FCIC Subtask 5.1 (Neal Yancey, INL) for the new air classifier, which has three exit streams (lights, middle and heavies). These data were utilized to develop the necessary response surface equations to perform throughput analysis using discrete event simulation. Because the ash contents and particle sizes had not been analyzed in the laboratory at the time of the model runs, we assumed that the ash distributed proportionally with total mass into the lights and heavies in an air classifier having two exit streams (lights and heavies) and that the lights fraction from the air classifier was not removed.

ash content↗

DOE OSTI2023

Particle Scale Impacts on Deconstruction Energy of Pine Residues

The goal of this Case Study was to quantify the impacts of variable moisture and ash on hammer mill throughput and energy consumption and on generation of fines that are not able to be fed to conversion, as compared to a status quo Base Case system. Also considered was convertible carbon content (minimum carbon specification) and maximum ash content and the delivered feedstock cost impacts of not being able to feed residue not meeting both specifications to the conversion reactor. Laboratory data on the impacts of input particle size and moisture content on the exit particle size were received from FCIC Subtask 5.2: Preprocessing, High Temperature Conversion Preprocessing from their single particle impact population balance modeling study (Tiasha Bhattacharjee, INL). Additional throughput and energy consumption data were obtained from FCIC Subtask 5.2 (Jordan Klinger, INL) for the same grinder with a 6 mm screen in place. These data were utilized to develop the necessary response surface equations to perform throughput analysis using discrete event simulation. Because the ash contents in the separated fines had not been analyzed in the laboratory at the time of the model runs, we chose to assume that the ash distributed proportionally with total mass into the overs and unders in the disk screen following grinding.

energy consumption↗

DOE OSTI2023

Air Classification of Forest Residue for Tissue and Ash Separation Efficiency

The goal of this Case Study was to evaluate the performance of air classification of logging residues toward meeting conversion CMAs for carbon and ash contents, as compared to the static status quo Base Case system in which the residues are first dried and then ground in a hammer mill with a 6 mm screen and fines less than 1.18 mm are removed. Also considered were moisture and ash impacts on throughput and Overall Operating Effectiveness (OOE), as well as delivered feedstock cost and minimum fuel selling price (MFSP). Laboratory data on the impacts of fan speed and moisture content on the separation efficiency of soil ash, needles and bark from white wood were received from FCIC Subtask 5.2: Preprocessing, High Temperature Conversion Preprocessing (Jordan Klinger and Tiasha Bhattacharjee, INL). Average throughput and energy consumption data were obtained from the Bioenergy Feedstock National User Facility (BFNUF) (Neal Yancey, INL) for the same air classifier. These data were utilized to develop the necessary response surface equations to perform throughput analysis using discrete event simulation. Feedstock-Conversion Interface Consortium. Because the Base Case status quo system utilizes drying prior to grinding, we modeled the Case Study with drying prior to air classification and subsequent grinding of the separated white wood to isolate the individual quality and cost impacts of air classification relative to the Base Case system.

CMA↗

DOE OSTI2021

Quasi-periodic travelling gravity–capillary waves

We present a numerical study of spatially quasi-periodic travelling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wavenumbers satisfying the dispersion relation is irrational. We propose a conformal mapping formulation of the water wave equations that employs a quasi-periodic variant of the Hilbert transform to compute the normal velocity of the fluid from its velocity potential on the free surface. We develop a Fourier pseudo-spectral discretization of the travelling water wave equations in which one-dimensional quasi-periodic functions are represented by two-dimensional periodic functions on the torus. This leads to an overdetermined nonlinear least-squares problem that we solve using a variant of the Levenberg–Marquardt method. We investigate various properties of quasi-periodic travelling waves, including Fourier resonances, time evolution in conformal space on the torus, asymmetric wave crests, capillary wave patterns that change from one gravity wave trough to the next without repeating and the dependence of wave speed and surface tension on the amplitude parameters that describe a two-parameter family of waves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A mapped dataset of surface ocean acidification indicators in large marine ecosystems of the United States

Mapped monthly data products of surface ocean acidification indicators from 1998 to 2022 on a 0.25° by 0.25° spatial grid have been developed for eleven U.S. large marine ecosystems (LMEs). The data products were constructed using observations from the Surface Ocean CO 2 Atlas, co-located surface ocean properties, and two types of machine learning algorithms: Gaussian mixture models to organize LMEs into clusters of similar environmental variability and random forest regressions (RFRs) that were trained and applied within each cluster to spatiotemporally interpolate the observational data. The data products, called RFR-LMEs, have been averaged into regional timeseries to summarize the status of ocean acidification in U.S. coastal waters, showing a domain-wide carbon dioxide partial pressure increase of 1.4 ± 0.4 μatm yr -1 and pH decrease of 0.0014 ± 0.0004 yr -1 . RFR-LMEs have been evaluated via comparisons to discrete shipboard data, fixed timeseries, and other mapped surface ocean carbon chemistry data products. Regionally averaged timeseries of RFR-LME indicators are provided online through the NOAA National Marine Ecosystem Status web portal.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗

DOE OSTI2025

Effect of 3D-printed surface textures on wear mechanism in 3-body abrasion of soil

This study systematically investigates the enhancement of wear resistance in 3D printed surface textures through both experimental and theoretical approaches. Three distinct surface morphologies (Smooth Surface, Surface with uniformly distributed Pits, and Surface with uniformly distributed Bumps) were fabricated using High-Impact Polystyrene, where the meso-scale textures were precisely controlled through the 3D printing process. Wear behavior was evaluated using a 3-body wear tester in an abrasive particle environment, analyzing the influence of surface textures under various operating conditions. Systematic wear tests revealed that optimally designed surface textures achieved a remarkable 77 % reduction in wear compared to the worst-performing sample. The wear mechanisms were comprehensively characterized through weight loss measurements, Scanning Electron Microscopy (SEM), and Energy Dispersive Spectroscopy (EDS) analyses, elucidating the surface morphology changes and their interaction with wear particles. Notably, the study identified how the geometric characteristics of surface textures influence the movement of wear particles and the distribution of contact stresses. Discrete element method simulations corroborated the experimental findings, providing theoretical validation for the enhanced wear resistance of the optimal structure. The high correlation between simulated wear patterns and experimental results validates the reliability of the proposed design methodology. In conclusion, these results demonstrate that 3D printed surface texturing offers a cost-effective and scalable approach to significantly improve wear resistance in engineering applications, presenting a practical alternative to conventional, high-cost surface engineering methods.

3-body abrasion↗

DOE OSTI2021

An asymptotically compatible treatment of traction loading in linearly elastic peridynamic fracture

Meshfree discretizations of state-based peridynamic models are attractive due to their ability to naturally describe fracture of general materials. However, two factors conspire to prevent meshfree discretizations of state-based peridynamics from converging to corresponding local solutions as resolution is increased: quadrature error prevents an accurate prediction of bulk mechanics, and the lack of an explicit boundary representation presents challenges when applying traction loads. Herein, we develop a reformulation of the linear peridynamic solid (LPS) model to address these shortcomings, using improved meshfree quadrature, a reformulation of the nonlocal dilatation, and a consistent handling of the nonlocal traction condition to construct a model with rigorous accuracy guarantees. In particular, these improvements are designed to enforce discrete consistency in the presence of evolving fractures, whose a priori unknown location render consistent treatment difficult. In the absence of fracture, when a corresponding classical continuum mechanics model exists, our improvements provide asymptotically compatible convergence to corresponding local solutions, eliminating surface effects and issues with traction loading which have historically plagued peridynamic discretizations. When fracture occurs, our formulation automatically provides a sharp representation of the fracture surface by breaking bonds, avoiding the loss of mass. We provide rigorous error analysis and demonstrate convergence for a number of benchmarks, including manufactured solutions, free-surface, nonhomogeneous traction loading, and composite material problems. Finally, we validate simulations of brittle fracture against a recent experiment of dynamic crack branching in soda-lime glass, providing evidence that the scheme yields accurate predictions for practical engineering problems.

42 ENGINEERING↗

DOE OSTI2023

Reaction Chemistry at Discrete Organometallic Fragments on Black Phosphorus

Abstract Black phosphorus (bP) is a two‐dimensional van der Waals material unique in its potential to serve as a support for single‐site catalysts due to its similarity to molecular phosphines, ligands quintessential in homogeneous catalysis. However, there is a scarcity of synthetic methods to install single metal centers on the bP lattice. Here, we demonstrate the functionalization of bP nanosheets with molecular Re and Mo complexes. A suite of characterization techniques, including infrared, X‐ray photoelectron and X‐ray absorption spectroscopy as well as scanning transmission electron microscopy corroborate that the functionalized nanosheets contain a high density of discrete metal centers directly bound to the bP surface. Moreover, the supported metal centers are chemically accessible and can undergo ligand exchange transformations without detaching from the surface. The steric and electronic properties of bP as a ligand are estimated with respect to molecular phosphines. Sterically, bP resembles tri(tolyl)phosphine when monodentate to a metal center, and bis(diphenylphosphino)propane when bidentate, whereas electronically bP is a σ‐donor as strong as a trialkyl phosphine. This work is foundational in elucidating the nature of black phosphorus as a ligand and underscores the viability of using bP as a basis for single‐site catalysts.

Mitra, Kendahl L. Walz↗

DOE OSTI2023

Reaction Chemistry at Discrete Organometallic Fragments on Black Phosphorus

Abstract Black phosphorus (bP) is a two‐dimensional van der Waals material unique in its potential to serve as a support for single‐site catalysts due to its similarity to molecular phosphines, ligands quintessential in homogeneous catalysis. However, there is a scarcity of synthetic methods to install single metal centers on the bP lattice. Here, we demonstrate the functionalization of bP nanosheets with molecular Re and Mo complexes. A suite of characterization techniques, including infrared, X‐ray photoelectron and X‐ray absorption spectroscopy as well as scanning transmission electron microscopy corroborate that the functionalized nanosheets contain a high density of discrete metal centers directly bound to the bP surface. Moreover, the supported metal centers are chemically accessible and can undergo ligand exchange transformations without detaching from the surface. The steric and electronic properties of bP as a ligand are estimated with respect to molecular phosphines. Sterically, bP resembles tri(tolyl)phosphine when monodentate to a metal center, and bis(diphenylphosphino)propane when bidentate, whereas electronically bP is a σ‐donor as strong as a trialkyl phosphine. This work is foundational in elucidating the nature of black phosphorus as a ligand and underscores the viability of using bP as a basis for single‐site catalysts.

Chemistry↗

DOE OSTI2025

A 3D helical filament surrogate model for 3D tokamak equilibria

A novel approach for efficient representation of three-dimensional (3D) tokamak equilibria is investigated, where a set of helical current filaments occupying the plasma region are employed to resolve deviations from the two-dimensional (2D) axi-symmetric state. A discrete set of 3D filaments, located at rational surfaces for a given toroidal mode number n and following the 2D equilibrium field lines (thus forming closed current loops), are found to provide a surrogate model of 3D equilibria with reasonable accuracy. Specifically, application of the filament model to 3D perturbed equilibria, due to the resonant magnetic perturbation (RMP) in DIII-D and MAST-U discharges, reveals that (1) a single helical filament per rational surface is sufficient; (2) 21 such helical filaments are capable of representing the n = 2 3D response field in MAST-U with less than 10% relative error as compared to that computed by a full magnetohydrodynamic code; (3) optimizing currents (both amplitude and phase) flowing in 3D filaments with fixed geometry, the highest accuracy fitting is found to depend on the characteristics of the 3D equilibria such as the coil current phasing of the RMP coils in our case studies. Here, whis filament approach is also applicable for generating surrogate models of other type of 3D tokamak equilibria, including those during the initial phase of the plasma disruption.

MARS-F↗

DOE OSTI2020

Threadsafe Dynamic Neighbor Lists for Monte Carlo Ray Tracing

Monte Carlo (MC) transport codes offer high-fidelity modeling of particle transport physics, but their high computational cost makes them impractical for many applications. For some applications such as multiphysics and depletion that use finely discretized geometries, a large portion of this computational cost is attributable to ray tracing. Neighbor lists are a well-known method for accelerating ray-tracing calculations in a MC code, but despite their prevalence, little work has been published on the details of their implementation. The fine details can have a significant impact on performance, particularly when using shared-memory parallelism. This paper addresses these details of implementation with a discussion of different neighbor list schemes and their impact on software runtime. Performance tests were run by using OpenMC on a pin-cell problem discretized with up to 200 axial regions. The results demonstrate that switching from surface-based to cell-based neighbor lists leads to a 10 faster calculation rate for the most fine discretization. Finally, using a threadsafe shared-memory data structure results in a 20% faster calculation rate versus simple threadprivate neighbor lists. Results here show that a data structure that is contiguous in memory improves performance by only 1% to 2% over noncontiguous linked lists.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Computing the shape gradient of stellarator coil complexity with respect to the plasma boundary

Coil complexity is a critical consideration in stellarator design. The traditional two-step optimization approach, in which the plasma boundary is optimized for physics properties and the coils are subsequently optimized to be consistent with this boundary, can result in plasma shapes which cannot be produced with sufficiently simple coils. To address this challenge, we propose a method to incorporate considerations of coil complexity in the optimization of the plasma boundary. Coil complexity metrics are computed from the current potential solution obtained with the REGCOIL code (Landreman, Nucl. Fusion , vol. 57, 2017, 046003). While such metrics have previously been included in derivative-free fixed-boundary optimization (Drevlak et al. , Nucl. Fusion , vol. 59, 2018, 016010), we compute the local sensitivity of these metrics with respect to perturbations of the plasma boundary using the shape gradient (Landreman & Paul, Nucl. Fusion , vol. 58, 2018, 076023). We extend REGCOIL to compute derivatives of these metrics with respect to parameters describing the plasma boundary. In keeping with previous research on winding surface optimization (Paul et al. , Nucl. Fusion , vol. 58, 2018, 076015), the shape derivatives are computed with a discrete adjoint method. In contrast with the previous work, derivatives are computed with respect to the plasma surface parameters rather than the winding surface parameters. To further reduce the resolution required to compute the shape gradient, we present a more efficient representation of the plasma surface which uses a single Fourier series to describe the radial distance from a coordinate axis and a spectrally condensed poloidal angle. This representation is advantageous over the standard cylindrical representation used in the VMEC code (Hirshman & Whitson, Phys. Fluids , vol. 26, 1983, pp. 3553–3568), as it provides a uniquely defined poloidal angle, eliminating a null space in the optimization of the plasma surface. In comparison with previous spectral condensation methods (Hirshman & Breslau, Phys. Plasmas , vol. 5, 1998, p. 2664), the modified poloidal angle is obtained algebraically rather than through the solution of a nonlinear optimization problem. The resulting shape gradient highlights features of the plasma boundary that are consistent with simple coils and can be used to couple coil and fixed-boundary optimization.

Physics↗