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DOE OSTI2024

A Spitzer Model-C Stellarator fusion reactor

Tokamaks are affected by two serious problems. The first problem is the radiation damage to the internal reactor structures by energetic neutrons carrying 80% of the total fusion energy that are generated by the deuterium–tritium fusion cycle that tokamaks are planning to use. The second problem is a loss of plasma control because of the onset of instabilities, causing the sudden shutdown of the tokamak itself. Certainly, no electric utility knowing about these disruptive events would dare to use a tokamak reactor for powering the turbines of its power plant! This paper describes a new fusion reactor based on the Model-C Stellarator that would not be affected by these fatal phenomena.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Development of five-moment two-fluid modeling for Z-pinch physics

The Z-pinch m = 0 instability as well as its stabilization by radially sheared axial flow is studied using the nonlinear ideal five-moment twofluid (5M2F) model with an extension of that model to include Braginskii heat and momentum transport. Using the ideal 5M2F model, linear growth rate results are compared with prior work using MHD and Hall MHD. At small normalized wavenumber, 1 < k a < 4 , where a is the effective pinch radius, 5M2F results agree with Hall MHD within 20% in scenarios without radially sheared axial flow. With the sheared flow and focusing on ka = 10/3, agreement with Hall MHD is excellent. In the limit of small ion inertial length, results also match with MHD. A comparison with PIC modeling of shear-free m = 0 stability focuses on a plasma scenario based on recent experimental results. In a scan of mode wavenumber, ideal 5M2F results are qualitatively similar to PIC: the growth rate rises to a peak at a moderate wavenumber and declines at a large wavenumber in contrast to MHD results, which show the saturation of the growth rate with the increasing wavenumber rather than a decline. The peak normalized 5M2F growth rate is γ τ A = 1.5 , where sA is the Alfven transit time across the pinch. The peak occurs at normalized wavenumber ka = 10. For comparison, PIC results have a peak growth of γ τ A = 0.77 at ka = 5. Including Braginskiibased closure of the 5M2F model does not qualitatively change the ideal results in this particular case. Nonlinear saturation is studied using the 5M2F model with the dissipative Braginskii-based closure in cases with pinch-edge sheared-flow speed equal to half the Alfven speed. Nonlinear mixing due to the sheared flow yields a quasi-steady state after modest losses of pinch ion inventory and pinch thermal energy, approximately 30% and 10%, respectively. 5M2F modeling captures the essential physics of m = 0 instability and offers a computationally tractable route to high-fidelity modeling of 3D Z-pinch behavior, including m = 1 instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Modeling cross-beam energy transfer with sector ray tracing

Ray-based cross-beam energy transfer (CBET) models are an essential feature of the radiation-hydrodynamic codes used to simulate inertial confinement fusion implosions, but full 3D ray-based CBET calculations can have a prohibitively high computational cost. Sector ray tracing can be used to reduce the cost by orders of magnitude in cases where the coronal plasma and laser drive can be approximated as spherically symmetric. An extension of sector ray tracing (section ray tracing) can be used to relax the assumption of a spherically symmetric drive while still retaining most of the computational savings of a sector ray trace. We discuss the foundations of sector and section ray tracing and compare them to full ray tracing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Many-body Nuclear Dynamics

The principal goal of this work was to better understand the fusion of neutron-rich nuclei a topic relevant to the fields of both nuclear physics and nuclear astrophysics. The work provides insight into the structure and reactions of neutron-rich nuclei namely the extent of their neutron density distribution and its polarizability. By comparing the fusion excitation functions for a chain of isotopes with a common target nucleus changes in the attractive nuclear potential are assessed. This change in the attractive potential is related to changes in the neutron density distribution with increasing number of neutrons or changes in fusion dynamics with increasing neutron number. The impact of the pairing of valence neutrons and protons on the fusion cross-section is also examined. Measurement of an isotopic chain is a powerful tool to address this topic. The experimental program made use of several different accelerator facilities. The core of the experimental work involved experiments at the ReA3 accelerator and the Facility for Rare Isotope Beams (FRIB) situated at Michigan State University, at GANIL, the French national nuclear physics laboratory, and the University of Notre Dame. At ReA3 the degree to which α-clusters associated with fusion of 28,30,32 Si + 28 Si result from the collision dynamics or reflect an initial α-cluster structure was explored. Alpha clusters observed in fusion reactions exceed the predictions of the standard statistical model. This experiment provides a measure of how clusterization is impacted by the increasing neutron-richess of the system. In the experiment at GANIL we investigated fusion in 19 O + 12 C and 20 O + 12 C. This experiment utilized the recently developed active-target detector MuSIC@Indiana. Using this proven, highly efficient, active-target detector we measured the fusion excitation function for these neutron-rich systems. Grounded by these experimental measurements, theoretical models were used to examine the role of unpaired valence neutrons on the fusion cross-section at energies just above the fusion barrier.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Extension of the energetic particle transport kick model in TRANSP to multiple fast ion species

Abstract Alfvénic instabilities (AEs) are well known to cause enhanced transport of energetic particles (EPs) in fusion devices. Most studies until now have focused on characterizing and understanding AE stability in single-species plasmas heated by neutral beams (NB), where deuterium is typically used as both main plasma species and NB fuel. As the fusion community moves toward fusion reactors that target burning plasma conditions, such as ITER, the single-species picture breaks down. Burning plasmas, which will use a mix of deuterium and tritium (DT) as main fuel, also feature the presence of several supra-thermal fusion products such as alpha particles, protons, helium isotopes and high-energy tritium ions. This work presents the extension of the EP transport kick model implemented in the TRANSP time-dependent tokamak transport code to study the combined effect of multiple EP species on AE stability and, in turn, the response of different EP species to plasma instabilities in terms of their redistribution and losses. Further validation of the enhanced model is planned based on experimental results expected from the JET DT campaign scheduled for 2021, in preparation for ITER plasmas and beyond.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Final Report for Tech-X Corporations’s contribution to Enhancing Understanding of High Energy Density Plasmas from Wire Array and Solid Liner Implosions Using Fluid Modeling with Kinetic Closures

Recent results from experiments and simulation of magnetically driven pulsed power liners have explored the role of the early-time electrothermal instability in the evolution of the magneto-Rayleigh-Taylor instability. Our focus will be on understanding the development of such instabilities and the potential stabilization mechanisms via electron thermal conduction, viscosity, and large magnetic fields which we expect could play a significant role in supporting the success of the MagLIF program. Experiments have shown that studies of high-energy density plasmas from wire-array implosions require physics modeling that goes well beyond simple models such as ideal magnetohydrodynamics. The goal of this work is to provide increased understanding of these experiments by employing simulations with a multi-fluid extended-MHD model which uses kinetic closures for thermal conduction, resistivity and viscosity. We will use codes easily available to the wider research community, including university students, with a secondary goal of providing the community with well-benchmarked tools capable of advanced modeling of high-energy-density plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2018

Preliminary Analysis of the Gradient Field Imploding Liner Fusion Propulsion Concept

The advancement of human deep space exploration requires the continued development of energetic in-space propulsion systems, advancing from current chemical engines to nuclear thermal rockets to future high energy concepts such as nuclear fusion. This paper presents the initial results of a NASA Innovative Advanced Concepts (NIAC) Phase I study funded to investigate the feasibility of a new pulsed fusion propulsion concept based on the rapid implosion of a fuel target injected at high velocity into a strong stationary magnetic field. The proposed concept takes advantage of the significant advances in terrestrial magneto-inertial fusion designs while attempting to mitigate the most common engineering impediments to in-space propulsion applications. A semi-analytic numerical model used to estimate target compression physics and energy release is presented, leading to estimates for engine performance. A preliminary vehicle design concept is outlined, and representative trajectory analyses for rapid Mars and Saturn missions are provided. The paper concludes with an overview of proposed next steps for theoretical and experimental validation of the concept.

Propulsion↗

DOE OSTI2025

Approximating the particle distribution in rotating and tandem mirror traps

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form ana- lytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady- state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

Li, G.X.↗

DOE OSTI2025

Approximating the particle distribution in rotating and tandem mirror traps

Steady-state distribution functions can be used to calculate stability conditions for modes, radiation energy losses and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true distributions such as the relative speeds of different transport processes while possessing computational advantages over their numerical counterparts. In this paper, we motivate and present a closed-form analytic model for a distribution of particles in a centrifugal or tandem mirror. We find that our model outperforms other known models in approximating numerical steady-state simulations outside of a narrow range of low confining potentials. We demonstrate the model’s suitability in the high confining potential regime for applications such as loss-cone stability thresholds, fusion yields and available energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Theory of ignition and burn propagation in inertial fusion implosions

A detailed analytic model is presented here to investigate the physics of burn propagation in inertially confined plasmas. The onset of ignition and burn propagation occurs when alpha heating of the hot spot causes rapid ablation of shell mass into the hot spot. This allows large energy gains to be achieved since most of the fuel mass is located in the shell. Here, we first present a comprehensive review of previous analytic models that have been used to describe the physics of hot-spot evolution and ignition; we then show that a proper description of a propagating burn wave requires a comprehensive model of hot spot and shell evolution that includes proper mass conservation in the shell, fusion reactivity, and fuel depletion. The analytic theory is in good agreement with detailed radiation-hydrodynamic simulations that predict the onset of burn propagation as occurring when the yield enhancement caused by alpha heating is between 15- and 25-fold, $f_α$ ~ 1.4, where $f_α$ = alpha energy deposited/hot-spot energy at bang time, and the hot-spot burnup fraction is approximately 2%. We show that the definition of ignition is not sensitive to the alpha-particle stopping power nor asymmetries provided that the absorbed fraction of alpha particles $θ_α$ is correctly accounted for. Finally, we use the results of 2-D simulations to show that even when $θ_α$ is small and unknown (as is true in hot spots with mid modes that have significant leakage of alpha particles into the surrounding cold bubbles), one can still relate the experimentally measureable parameter $\chi^{53}_α$ to the yield amplification and the burning-plasma parameter $Q^{\text{hs}}_α$ = alpha energy deposited/total input work delivered to the hot spot

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Numerical Analysis of Liquid Metal MHD Flow and Heat Transfer for Open-Surface Li Divertor in FNSF

Within the ongoing U.S.-based program on the development of liquid metal plasma-facing components, numerical simulations and analyses are performed to address the feasibility of the open-surface Li divertor. In the previous scoping studies (Smolentsev, 2021), heat-removal capabilities of the divertor were assessed using a simplified flow model for a slug-type velocity profile and constant flow thickness. Here, new analyses take into account forces acting on the flowing Li layer. Three reduced-order mathematical models are applied under the conditions of the U.S. Fusion Nuclear Science Facility (FNSF) to access magnetohydrodynamic (MHD) flow development effects, velocity distribution, and surface waves: 1) fully developed MHD flow; 2) quasi-2-D developing MHD flow; and 3) multiphase MHD flow. The obtained results for MHD flows and the surface heat flux computed with the plasma code scrape-off layer plasma simulation for ITER (SOLPS-ITER) are then used as input data to compute the temperature distribution in the divertor by solving the convection–diffusion energy equation.

Smolentsev, Sergey↗

DOE OSTI2024

Divertor-safe nonlinear burn control based on a SOLPS parameterized core-edge model for ITER

Abstract For ITER operations, the range of desirable burning-plasma regimes with high fusion power output will be restricted by various operational constraints. These constraints include the saturation of ITER’s various heating and fueling actuators such as the neutral beam injectors, the ion and electron cyclotron heating systems, the gas puffing system, and the deuterium–tritium pellet injectors. In addition to these actuator constraints, the H-mode power threshold, divertor detachment, and the heat load on the divertor targets may apply limitations to ITER’s operational space. In this work, Plasma Operation Contour (POPCON) plots that map the aforementioned constraints to the temperature-density space are used to investigate which constraints are most limiting towards accessing regimes with high fusion power output. The presented POPCON plots are based on a control-oriented core-edge model that couples the nonlinear density and energy response models for the core-plasma region with SOLPS4.3 parameterizations for conditions in the edge-plasma regions (scrape-off-layer and divertor). Using this control-oriented core-edge model, a nonlinear burn controller, which aims to regulate the plasma temperature and density in the core-plasma region, is constructed in this work. This controller is augmented with an online optimization scheme that governs the control references such that the plasma can be guided towards regimes with high fusion powers while protecting the divertor targets from dangerously high heat loads. A closed-loop simulation study illustrates the capability of this burn control scheme.

Physics↗

DOE OSTI2021

The advanced tokamak path to a compact net electric fusion pilot plant

Abstract Physics-based simulations project a compact net electric fusion pilot plant with a nuclear testing mission is possible at modest scale based on the advanced tokamak concept, and identify key parameters for its optimization. These utilize a new integrated 1.5D core-edge approach for whole device modeling to predict performance by self-consistently applying transport, pedestal and current drive models to converge fully non-inductive stationary solutions, predicting profiles and energy confinement for a given density. This physics-based approach leads to new insights and understanding of reactor optimization. In particular, the levering role of high plasma density is identified, which raises fusion performance and self-driven ‘bootstrap currents’, to reduce current drive demands and enable high pressure with net electricity at a compact scale. Solutions at 6–7 T, ∼4 m radius and 200 MW net electricity are identified with margins and trade-offs possible between parameters. Current drive comes from neutral beam and ultra-high harmonic (helicon) fast wave, though other advanced approaches are not ruled out. The resulting low recirculating power in a double null configuration leads to a divertor heat flux challenge that is comparable to ITER, though reactor solutions may require more dissipation. Strong H-mode access (x2 margin over L–H transition scalings) and ITER-like heat fluxes are maintained with ∼20%–60% core radiation, though effects on confinement need further analysis. Neutron wall loadings appear tolerable. The approach would benefit from high temperature superconductors, as higher fields would increase performance margins while potential for demountability may facilitate nuclear testing. However, solutions are possible with conventional superconductors. An advanced load sharing and reactive bucking approach in the device centerpost region provides improved mechanical stress handling. The prospect of an affordable test device which could close the loop on net-electric production and conduct essential nuclear materials and breeding research is compelling, motivating research to validate the techniques and models employed here.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Using distributions to understand neutron and x-ray production in ICF ignition capsules and other high energy density plasmas

Here this paper describes how x-ray and neutron distribution functions can be useful tools to visualize the conditions measured in many types of plasma physics experiments. In particular, we model a standard inertial confinement fusion ignition capsule that consists of a Si doped plastic ablator surrounding a layer of deuterium–tritium (DT) ice as the yield varies from 18 kJ to 16.7 MJ and use the distribution functions to show that neutrons and high energy x rays (15 keV) are produced under similar conditions when the yield is low. However, as the capsule starts to support a propagating burn due to alpha heating, the x rays and neutrons are produced under somewhat different conditions in different parts of the plasma. In particular, the x-ray production takes place mainly in the hot plastic ablator for the full yield ignition capsule under quite different plasma conditions from the DT region producing the 14 MeV neutrons, which results in x-ray images with larger radii than the corresponding neutron images. These same distribution functions can be applied to many other plasma physics experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Development of multi-scale computational frameworks to solve fusion materials science challenges

Over the past two decades, the US-DOE has funded multiple projects that rely on high-performance computing and exascale computing platforms to accelerate scientific discoveries and address grand scientific challenges, such as harnessing fusion energy. In this article, we review in detail one of these efforts aimed at enhancing our capability to model plasma-facing materials subject to plasma and high-energy ion/neutron irradiation. The plasma surface interactions project has built a multi-scale modeling framework where many of the plasma- and high-energy ion/neutron irradiation-induced effects occurring in tungsten are explored. Here, this knowledge is used to develop atomistically-informed, high-fidelity continuum and meso-scale models that can be validated against experiments. We review the developments within this project, with attention to experimental validation efforts, and specifically highlight activities associated with: helium bubble bursting and equation of state, and hydrogen-helium interactions in tungsten; atomistically-informed model development for beryllium-tungsten material mixing; coupling of scrape-of-layer plasma, sheath and material models; and coupling of stochastic cluster-dynamics and crystal plasticity models to address radiation effects in tungsten under stress. Finally, we present how the project is preparing for future computational architectures, for instance through efforts to adapt atomistic methods to exascale computing.

36 MATERIALS SCIENCE↗

NASA NTRS2024

Extreme Temperature Additively Manufactured GRX-810 Alloy Development and Hot-fire Testing for Liquid Rocket Engines

Additive manufacturing (AM) has revolutionized component design for liquid rocket engines by offering rapid manufacturing capabilities. This has led to significant opportunities for development and flight programs in the propulsion industry, resulting in cost and schedule savings, as well as performance improvements through new designs and alloy development. A noteworthy example is the GRX-810 oxide dispersion strengthened (ODS) alloy, which was specifically developed for extreme temperatures. This Ni-Co-Cr based alloy was created using integrated computational materials engineering (ICME) techniques to focus on a new class of materials with exceptional temperature and oxidation-resistant properties. The GRX-810 alloy utilizes AM processes to incorporate nano-scale yttria particles throughout its microstructure, resulting in remarkable enhancements. Compared to traditional Nickel-based superalloys, the GRX-810 alloy offers a two-fold increase in tensile strength, 1,000-fold better creep properties, and two-fold improvement in oxidation resistance. NASA successfully demonstrated the development and manufacturing of components using the GRX-810 alloy through laser powder bed fusion (L-PBF) and laser powder directed energy deposition (LP-DED) processes. Extensive efforts were made to model, evaluate metallurgical properties, develop heat treatment processes, characterize the microstructure, and determine mechanical properties. The GRX-810 alloy was specifically designed for aerospace applications, including liquid rocket engine injectors, preburners, turbines, and hot-section components, capable of withstanding temperatures up to 1,100 °C. The objective of this alloy development is to bridge the temperature gap between traditional Nickel-based superalloys and refractory alloys. This paper provides a comprehensive comparison of the GRX-810 alloy with other aerospace alloys, discussing its microstructure, mechanical properties, processing advancements, component development, and hot-fire testing results. The ultimate goal of this development was to elevate the Technology Readiness Level (TRL) of the GRX-810 alloy, enabling its integration into NASA and commercial aerospace applications.

GRX-810↗

NASA NTRS2024

Extreme Temperature Additively Manufactured GRX-810 Alloy Development and Hot-fire Testing for Liquid Rocket Engines

GRX-810↗

DOE OSTI2024

Validation of implosion modeling through direct-drive shock timing experiments at the National Ignition Facility

Precise modeling of shocks in inertial confinement fusion implosions is critical for obtaining the desired compression in experiments. Shock velocities and post-shock conditions are determined by laser-energy deposition, heat conduction, and equations of state. This paper describes experiments at the National Ignition Facility (NIF) where multiple shocks are launched into a cone-in-shell target made of polystyrene, using laser pulse shapes with two or three pickets and varying on-target intensities. Shocks are diagnosed using the Velocity Interferometric System for Any Reflector diagnostic. Simulated and inferred shock velocities agree well for the range of intensities studied in this work. These results are the first shock-velocity measurements using direct drive on the NIF and provide a good measure of early-time, directly driven laser-energy coupling. Furthermore, the validated models add to the credibility of direct-drive-ignition designs at the megajoule scale.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗