JOWOG 34 High-Order Working Group: Matrix-free methods in SPARC.
Abstract not provided.
Fisher, Travis C.↗
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ATDM AD projects to ECP Report (Q3 FY2020)
The SPARC team has completed much of the workflow development needed for the coupled and uncoupled analyses needed to support our flight test validation work. The SPARC team has continued to make progress on development activities to support unsteady, full reentry vehicle aero analysis, which have focused on turbulence modeling, uniform mesh refinement, in-situ visualization (with the Paraview/Catalyst team), and performance analysis. The SPARC team is making solid progress towards our Q4 goal of demonstrating an improved Wall Modeled Large Eddy Simulation (WMLES) capability for standard geometries using high-order finite difference, discontinuous Galerkin, and low-dissipation finite volume methods. The SPARC team has met the minimum completion criteria for parts of the L1, including documenting performance and scaling of SPARC on Trinity, Sierra and Astra, and performing runs for the flight test validation case.
97 MATHEMATICS AND COMPUTING↗
ARC disruption physics and strategy
Commonwealth Fusion Systems (CFS) plans to operate a tokamak power plant called ARC in the early 2030s. Tokamak plasmas have stability limits that, if crossed, lead to a rapid termination of the plasma, referred to as a disruption. Disruptions pose a melt risk to the first wall resulting from thermal and non-thermal particle heat fluxes, and an electromagnetic loading risk on all metal components within the equilibrium coils. A comprehensive set of models is used herein to provide an assessment of both mitigated and unmitigated ARC disruption loads. A preliminary massive gas injection system is baselined and a runaway electron mitigation coil option is proposed to close possible gaps in the baseline. It is predicted that all ARC disruption loads are within a factor of 2 of the disruption loads in SPARC, a tokamak presently under construction by CFS, and therefore SPARC provides an opportunity to calibrate models, test solutions and inform the design of ARC. The goal for ARC is disruption-free operation, however, the pragmatic design target is to withstand one mitigated disruption per day, and to restart the plasma following mitigation in tens of seconds without interrupting the power output. Unmitigated disruptions must be rare, and experience with unmitigated disruption impacts in SPARC will better define what rare means. The implications of this strategy for plasma disruptivity and disruption prediction are discussed, and operating the ARC scenario on SPARC is expected to refine the ARC final design and operational plan.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Power and particle exhaust for the ARC fusion power plant
To successfully show that fusion is an attractive energy source, the ARCTM fusion power plant will need to operate with a robust, integrated power and particle exhaust solution. To maximise ARC’s fusion power output while avoiding excessive erosion of the plasma-facing components, we will need to radiatively dissipate most of the power crossing the last-closed flux surface, injecting radiating impurities such as argon or neon to access divertor detachment. Divertor detachment will need to be integrated with a high-performance core plasma, and with efficient impurity pumping to prevent the accumulation of helium ash in the core. To access and control detachment in high-performance plasmas, we have designed ARC with up–down-symmetric divertors, with secondary X-points in long, tightly baffled outer legs. Using a core-edge modelling workflow, we predict that with this divertor design, ARC will access detachment with modest argon seeding in the divertor (c Ar,div ∼0.9%), which should have minimal impact on the core ( Z eff,core <0.5) for reasonable argon enrichment (c Ar,div /c Ar,core =6). Due to the high predicted divertor neutral pressure (p div ∼20 Pa), we predict that ARC will sufficiently pump helium to limit ash accumulation in the core (c He,core <2%) for a helium enrichment of c He,div /c He,core =0.4. ARC’s divertor design is expected to increase the stability of a detachment front in the outer divertor leg, helping to prevent divertor reattachment during smaller heat-flux transients such as scrape-off-layer filaments associated with the quasi-continuous exhaust regime. However, this buffering will not be sufficient to prevent divertor reattachment during large type-I edge-localised modes (ELMs), and as such these will need to be avoided on ARC. Experiments on SPARC will be used to select an integrated scenario which avoids or mitigates type-I-ELMs while maintaining access to detachment, good core fusion performance and sufficient impurity exhaust. SPARC experiments will also be used to finalise ARC’s divertor design, by studying the impact of magnetic and first-wall geometry on detachment stability, impurity enrichment and neutral baffling under conditions similar to those expected for ARC. In conclusion, our analysis finds that ARC will have a viable power and particle exhaust solution which is compatible with high-power operations, and this solution will be validated in experiments on SPARC.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Divertor Component Testing
Power exhaust is an immense challenge in tokamaks. Commonwealth Fusion Systems (CFS), in collaboration with MIT and others, is working on the design of a compact (R 0 = 1.85 m), high-field (B 0 = 12 T) tokamak for the demonstration of net fusion energy, called SPARC. Empirical scaling laws indicate that the unmitigated heat flux in the boundary plasma will exceed 10 GW/m 2 . Such high heat fluxes will be a formidable challenge. The scope of this work is to utilize the HHF testing expertise maintained by ORNL, used in support of NSTX-U and to demonstrate the thermal performance of tungsten-coated graphitic foam targets, to help CFS and its collaborators to assess the performance of (1) base materials (tungsten and its alloys) and (2) divertor mockups under SPARC-like divertor heat flux conditions. These activities will be performed by ORNL personnel using electron beam exposure facilities at the Pennsylvania State University’s Applied Research Laboratory (ARL). ARL is a Department of Defense University Affiliated Research Center where ORNL has successfully executed NSTX-U and graphitic foam high heat flux testing using electron beam (e-beam) facilities, which is a nonstandard service. For the assessment of base materials, CFS will do an initial thermal analysis, in consultation with ORNL, to understand under what scenarios the materials are most likely to fail. CFS will supply to ORNL various tungsten-based material samples to test with testing taking 3 weeks. ORNL will thermally stress the samples under SPARC divertor-like conditions to either failure or to a prescribed number of pulses. ORNL will record experimental data, including IR surface temperature and embedded thermocouple readings, and report results to CFS
36 MATERIALS SCIENCE↗
ARC physics basis–magnetohydrodynamics
ARC is designed to produce 400 MW of net electricity and prove the commercial feasibility of a fusion power plant. In order to achieve this goal ARC has to operate with optimal core performance in a stationary scenario that minimises wear on the first wall and divertor. This requires avoiding or mitigating magnetohydrodynamic (MHD) instabilities which have the potential to not only degrade the plasma core but also lead to deleterious transient heat loads on plasma facing components. Therefore, this work aims at characterising the MHD stability of the high performance ARC scenario and inform the design of error field correction coils. Firstly, simulations of vertical displacement events show that an in-vessel coil is not needed and instead the poloidal shaping coils can be used to control vertical stability. These simulations also inform the demands on the corresponding coil power supplies. Stability analysis of the ideal kink mode with or without a conducting wall and kinetic effects suggests that the ARC baseline scenario operates deeply in the stable region. Using RDCON, tearing modes at the 𝑚/𝑛 =2/1 and 3/2 surfaces (with poloidal mode number 𝑚, and toroidal mode number 𝑛) are shown to be linearly stable, and including thermal transport effects in the rational surfaces lead to further stabilisation. However, other transient plasma instabilities can seed neoclassical tearing modes (NTMs). The marginally stable width of NTMs in ARC strongly depends on the internal inductance and can fall below 0.1% of the normalised poloidal flux. Furthermore, an empirical cross-machine model of the 𝑛 =1 error field leading to a disruption predicts a critical error field larger than SPARC but smaller than ITER. Three-dimensional coils can be designed with the Generalised Purturbed Equilbium Code based on a simple model that calculates the maximum correctable error field that is limited by the neoclassical toroidal viscosity torque. Broad scans of different coil geometries identify a set of 2 rows of off-midplane coils to be a suitable solution. It is also determined that such a set of three-dimensional coils is capable of correcting 𝑛 =2 error fields to some degree and creating strong enough 𝑛 =2 or 𝑛 =3 edge resonant perturbation fields for the suppression of edge-localised modes at reasonable coil currents. The final design of the first ARC will be further informed by results from SPARC.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Performance and transport in the ARC tokamak
The ARC TM tokamak, a high-field (𝐵 𝑇 = 11.4 T) fusion power plant, under development by Commonwealth Fusion Systems, is studied using a suite of integrated modelling tools to predict its fusion power generation (𝑃𝑓𝑢𝑠), transport and confinement properties. Analysis is based off an ARC operational point scoped first with zero-dimensional (0-D) plasma operational contour (POPCON) modelling to produce 1.13 GW of fusion power. A suite of integrated modelling tools (TRANSP, ASTRA and TORAX) were applied to predict the performance and kinetic profiles of the ARC design point, yielding a range of predicted performance spanning from ∼900 to 1300 MW in rough quantitative agreement with POPCON predictions. The sensitivity of these results to uncertain modelling inputs was probed using scans of pedestal boundary conditions around EPED-predicted values (total pressure and temperature ratios), tungsten concentration and seperatrix density around their nominal assumptions. Pedestal pressure and pedestal top (𝑇 𝑖 /𝑇 𝑒 ) play a large role in 1.5-dimensional performance predictions, able to modify the predicted 𝑃 𝑓𝑢𝑠 by a factor of 2 within reasonable assumptions. High-fidelity core nonlinear gyrokinetic profile predictions, performed using CGYRO (Candy et al. 2016 J. Comput. Phys., vol. 324, pp. 73–93) coupled with the PORTALS (Rodriguez-Fernandez et al. 2024 Nucl. Fusion, vol. 64, 076034; Phys. Plasmas, vol. 31, 2024, 062501) framework, yield substantially lower performance (𝑃 𝑓𝑢𝑠 =677 MW) compared with 0-D and medium-fidelity modelling for nominal assumptions, showing that there is non-negligible uncertainty between models and that future work on SPARC may help resolve discrepancies. Lower overall performance results from significantly reduced volume-averaged densities and temperatures, along with reduced levels of density and temperature peaking. Turbulence and transport are largely dominated by ion temperature gradient across the profile, confirmed by both linear stability and the response of the nonlinear fluxes to changes in gradients, with some impact of kinetic ballooning modes in the deep core. This work represents one of the most complete scoping of potential fusion power plant conditions performed to date. The extensive integrated modelling provides confidence in ARC performance approaching 1 GW, while nonlinear gyrokinetic modelling results in open questions into the physics of density and temperature peaking in fusion-power-plant-relevant operational space. A discussion of results and the role that the SPARC tokamak (Creely et al. 2020 J. Plasma Phys., vol. 86, 865860502) will play in informing ARC design, performance and operation is presented.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Overview of the physics basis for the ARC fusion power plant
Commonwealth Fusion Systems plans to build ARC as the first fusion power plant at a site in Chesterfield County, Virginia, USA by the early 2030s. We present an overview of analysis comprising the physics basis of the ARC V3A design, a high-magnetic-field tokamak with 𝐵 0 =11.4 T, 𝐼 𝑝 =12.0 MA, 𝑅 0 =4.62 m, 𝑎 =1.18 m. ARC V3A is designed to produce 𝑃 𝑓𝑢𝑠 ≈1.13 GW DT fusion power and deliver ⩾400 MW net electric power to the grid. This overview includes quantitative analysis of fundamental issues for design of and operational plasma scenarios for a tokamak power plant, and lays out the design targets and strategic choices for ARC, including empirical fusion performance projections, assessment of H-mode access, ion cyclotron resonance heating simulations, alpha particle physics and time-dependent full-pulse simulations. This is complemented by topical papers on fusion performance and transport, disruption physics, boundary physics and magnetohydrodynamic stability. Critically, these studies identify key model uncertainties and physics risks to be retired through SPARC operation. Due to the modular nature of ARC, early results from SPARC can be incorporated into the design of the first ARC as well as subsequent replacements of the ARC vacuum vessel.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A critical assessment of solutions to the galaxy diversity problem
Galactic rotation curves exhibit a diverse range of inner slopes. Observational data indicates that explaining this diversity may require a mechanism that correlates a galaxy's surface brightness with the central-most region of its dark matter halo. Here, in this work, we compare several concrete models that capture the relevant physics required to explain the galaxy diversity problem. We focus specifically on a Self-Interacting Dark Matter (SIDM) model with an isothermal core and two Cold Dark Matter (CDM) models with/without baryonic feedback. In contrast to the CDM case, the SIDM model can lead to the formation of an isothermal core in the halo, and is also mostly insensitive to baryonic feedback processes, which act on longer time-scales. Using rotation curves from 90 galaxies in the Spitzer Photometry & Accurate Rotation Curves (SPARC) catalog, we perform a comprehensive model comparison that addresses issues of statistical methodology from prior works. The best-fit halo models that we recover are consistent with standard CDM concentration-mass and abundance matching relations. We find that both the SIDM and feedback-affected CDM models are better than a CDM model with no feedback in explaining the rotation curves of low and high surface brightness galaxies in the sample. However, when compared to each other, there is no strong statistical preference for either the SIDM or the feedback-affected CDM halo model as the source of galaxy diversity in the SPARC catalog.
79 ASTRONOMY AND ASTROPHYSICS↗
Design of passive and structural conductors for tokamaks using thin-wall eddy current modeling
Abstract A new three-dimensional electromagnetic modeling tool ( ThinCurr ) has been developed using the existing PSI-Tet finite-element code in support of conducting structure design work for both the SPARC and DIII-D tokamaks. Within this framework a 3D conducting structure model was created for both the SPARC and DIII-D tokamaks in the thin-wall limit. This model includes accurate details of the vacuum vessel and other conducting structural elements with realistic material resistivities. This model was leveraged to support the design of a passive runaway electron mitigation coil (REMC), studying the effect of various design parameters, including coil resistivity, current quench duration, and plasma vertical position, on the effectiveness of the coil. The REMC is a non-axisymmetric coil designed to passively drive large non-axisymmetric fields during the plasma disruption thereby destroying flux surfaces and deconfining RE seed populations. These studies indicate that current designs should apply substantial 3D fields at the plasma surface during future plasma current disruptions as well as highlight the importance of having the REMC conductors away from the machine midplane in order to ensure they are robust to off-normal disruption scenarios.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
3D radiated power analysis of JET SPI discharges using the Emis3D forward modeling tool
Abstract Precise values for radiated energy in tokamak disruption experiments are needed to validate disruption mitigation techniques for burning plasma tokamaks like ITER and SPARC. Control room analysis of radiated power ( P rad ) on JET assumes axisymmetry, since fitting 3D radiation structures with limited bolometry coverage is an under-determined problem. In mitigated disruptions, radiation is toroidally asymmetric and 3D, due to fast-growing 3D MHD modes and localized impurity sources. To address this problem, Emis3D adopts a physics motivated forward modeling (‘guess and check’) approach, comparing experimental bolometry data to synthetic data from user-defined radiation structures. Synthetic structures are observed with the Cherab modeling framework and a best fit chosen using a reduced χ 2 statistic. 2D tomographic inversion models are tested, as well as helical flux tubes and 3D MHD simulated structures from JOREK. Two nominally identical pure neon shattered pellet injection (SPI) mitigated discharges in JET are analyzed. 2D tomographic inversions with added toroidal freedom are the best fits in the thermal quench (TQ) and current quench (CQ). In the pre-TQ, 2D reconstructions are statistically the best fits, but are likely over-optimized and do not capture the 3D radiation structure seen in fast camera images. The next-best pre-TQ fits are helical structures that extend towards the high-field side, consistent with an impurity flow under the magnetic nozzle effect also observed in JOREK simulations. Whole-disruption radiated fractions of 0.98 + 0.03 / − 0.29 and 1.01 + 0.02 / − 0.17 are found, suggesting that the stored energy may have been fully mitigated by each SPI, although mitigation efficiencies well below ITER and SPARC requirements for high energy pulses are still within the large uncertainties. Emis3D is also used to validate JOREK SPI simulations, and confirms improvements in matching experiment from changes to impurity modeling. Time-dependent toroidal peaking factors are calculated and discussed.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Development and validation of non-axisymmetric heat flux simulations with 3D fields using the HEAT code
A new comprehensive module to simulate heat fluxes from three-dimensional (3D) magnetic fields has been implemented in the HEAT code. Especially compact tokamaks like SPARC require tools to predict and manage large heat fluxes. Existing release versions of HEAT can only simulate axisymmetric heat flux on 3D plasma facing components. The new module uses an M3D-C1 perturbed equilibrium and the MAFOT code to trace field lines of the perturbed 3D magnetic field. Heat flux is then assigned to the resulting footprints via a 3D layer model. The model distinguishes between the scrape-off layer, the magnetic lobes and the private flux region, and employs only 0D parameters like the layer width, diffusive spread and the last closed flux surface position in the perturbed edge to generate a heat flux profile. The magnitude is normalized to the total input power. Resulting heat flux simulations are compared and validated against infrared measurements in the DIII-D tokamak with applied 3D fields; good agreement is found for several cases. The new module can now be applied to the SPARC tokamak; a preliminary result for applied rotating 3D fields is shown.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Feedforward equilibrium trajectory optimization with GSPulse
One of the common tasks required for designing new plasma scenarios or evaluating capabilities of a tokamak is to design the desired equilibria using a Grad-Shafranov (GS) equilibrium solver. However, most standard equilibrium solvers are time-independent and do not include dynamic effects such as plasma current flux consumption, induced vessel currents, or voltage constraints. Another class of tools, plasma equilibrium evolution simulators, do include time-dependent effects. These are generally structured to solve the forward problem of evolving the plasma equilibrium given feedback-controlled voltages. In this work, we introduce GSPulse, a novel algorithm for equilibrium trajectory optimization, that is more akin to a pulse planner than a pulse simulator. GSPulse includes time-dependent effects and solves the inverse problem: given a user-specified set of target equilibrium shapes, as well as limits on the coil currents and voltages, the optimizer returns trajectories of the voltages, currents, and achievable equilibria. This task is useful for scoping performance of a tokamak and exploring the space of achievable pulses. The computed equilibria satisfy both Grad-Shafranov force balance and axisymmetric circuit dynamics. The optimization is performed by restructuring the free-boundary equilibrium evolution equations into a form where it is computationally efficient to optimize the entire dynamic sequence. GSPulse can solve for hundreds of equilibria simultaneously within a few minutes. GSPulse has been validated against NSTX-U and MAST-U experiments and against SPARC feedback control simulations, and is being used to perform scenario design for SPARC. The computed trajectories can be used as feedforward inputs that are connected to the feedback controller to inform and improve feedback performance. The code for GSPulse is available open-source at github.com/jwai-cfs/GSPulse_public.
equilibrium↗
Radiation modeling and experimental validation of sub-cyclotron frequency microwave synchrotron radiation as a diagnostic tool for runaway electrons in present and future tokamaks
The microwave synchrotron radiation in the sub-cyclotron frequency region has been systematically validated as a diagnostic method for runaway electrons (>1 MeV) with radiation modeling and experiments on the DIII-D tokamak. Experimental observations reveal that sub-cyclotron frequency microwave radiation emerges only after runaway electrons are excited during plasma disruptions. Electron gyro-magnetic radiation modeling confirms that only runaway electrons with energies exceeding 1 MeV can emit radiation in the observed sub-cyclotron frequency band on DIII-D. The synchrotron Razin and Beaming effects are modeled in both the sub-cyclotron and standard Electron Cyclotron Emission (ECE) frequency region. Due to the pronounced beaming effect, the modeling supports that a standard ECE system is insensitive to synchrotron radiation from beamed runaway electrons (p ∥ >> p ⟂ ), but very sensitive to ECE radiation from isotropic suprathermal electrons (100 keV or less). DIII-D experiments further show that combining ECE and sub-cyclotron receivers reveals new insights into transient runaway dynamics during the plateau phase. Certain transient crash events appear only in the sub-cyclotron band or lead to opposite changes on the sub-cyclotron and standard ECE signals, supporting models where transient MHD events can exert a different effect on electrons of different energy levels. This novel diagnostic technique offers a powerful tool for studying and detecting runaway electron dynamics in both present-day and high-field future tokamaks. The diagnostic approach has been extrapolated to the SPARC tokamak, where sub-cyclotron radiation is predicted to respond sensitively and solely to runaway electrons during SPARC’s L-mode startup phase.
Yu, Guanying [Hefei Comprehensive National Science↗
A regional inter-disciplinary partnership focusing on the development of a carinata-centered bioeconomy
Brassica carinata or Ethiopian mustard, a non-edible oilseed brassica, is a low carbon, purpose-grown, and none-to-low indirect land-use change bioenergy feedstock for the production of drop-in sustainable aviation fuel, biodiesel, renewable diesel, and a suite of value-added coproducts. Carinata oil converted to drop-in fuel using an American Society for Testing and Materials approved Catalytic Hydrothermolysis process has been successfully tested in commercial and military aviation. Carinata meal, the residue after oil extraction, is a high-protein feed supplement for livestock, poultry, and swine, and can also yield specialty products. The Southeast Partnership for Advanced Renewables from Carinata (SPARC) is a public–private partnership formed with a twofold mission: (1) Removing physical, environmental, social, and economic constraints that prevent regional intensification of carinata production as a low-carbon feedstock for renewable fuel and coproducts and (2) demonstrating enhanced value across the entire value chain by mitigating risk to farmers and other stakeholders. The partnership's goal is to energize the US bioeconomy through sustainable agriculture and thus contribute to energy security and economic diversification. SPARC relies on a combination of cutting-edge multidisciplinary research and active industry engagement to facilitate adoption of the crop. This involves informing stakeholders along the entire supply chain, from producers to end-users, policymakers, influencers, and the public, about the opportunities and best practices related to carinata. This article provides context and background concerning carinata commercialization as a winter cash crop in the Southeast US for renewable fuels and bioproducts. The advances made to date in the areas of feedstock development, fuel and coproduct development, meal valorization, supply chain logistics, and stakeholder engagement are outlined.
09 BIOMASS FUELS↗
ATDM AD Projects to ECP (FY20 Q1 Report)
The SPARC and SPARC V&V teams successfully presented their work at the Dec 11-12 L1 milestone mid-year review. The teams received overwhelmingly positive feedback at the review.
97 MATHEMATICS AND COMPUTING↗