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DOE OSTI2022

Thermodynamic assessment of lithium halide reciprocal salt systems for energy applications

Lithium halides are of interest because of their unique applications as fuel or coolants in molten salt reactors (MSRs) and electrolytes in thermally activated batteries. Because iodine is an important fission product for MSRs, the Molten Salt Thermal Properties Database-Thermochemical (MSTDB-TC) is being expanded to include relevant iodide reciprocal salt systems. In this work, we assess the thermochemical properties of lithium halide pseudobinary systems based on reported experimental phase diagrams, eutectic temperatures, and enthalpies of mixing. Within the framework of the modified quasi-chemical model in the quadruplet approximation (MQMQA), extrapolations to the related pseudoternary and pseudoquaternary systems have been performed. The pseudoquaternary representations of phase equilibria, enthalpy, entropy, and heat capacity are represented in the resultant models. Of interest for generating source terms for accident analysis is the ability to compute the vapor pressures of the dominant iodide species for the systems at any composition. Here, an example of such calculations is provided for the LiF-LiI system at x LiI = 0.01 and x LiI = 0.70, in this case indicating that the LiI vapor species are predominant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Thermodynamic description of molten salt systems: KCl-LiCl-NaCl and KCl-LiCl-NdCl 3

The mixture of KCl and LiCl has been used as electrolyte in the electrorefining process to recover uranium from used nuclear fuels due to the low melting point. However, lanthanides and sodium in the reactor waste continuously dissolve into it and thus alter its thermodynamic properties. To understand the thermodynamic behavior evolution of the electrolyte with the accumulation of impurities, thermodynamic modeling for KCl-LiCl-NaCl and KCl-LiCl-NdCl 3 and four constituent binary systems in the entire composition space was performed using the CALPHAD (CALculation of PHAse Diagrams) approach. The ionic liquid was described by the two-sublattice model, where neutral species were introduced to consider short-range ordering (SRO) within the melt, whereas the solid solution was modeled based on the Compound Energy Formalism. Literature data on phase equilibria and thermochemical properties were critically evaluated and used during the optimization of thermodynamic parameters for KCl-LiCl-NaCl and KCl-LiCl-NdCl 3 and their subsystems. The calculated phase diagrams and mixing enthalpies are in good agreement with the experimental data. The thermodynamic modeling for the KCl-LiCl-NdCl 3 system was carried out for the first time. To fill the gap in experimental measurement, enthalpy of mixing for the KCl-LiCl-NdCl 3 melt was estimated using the surrounded-ion model. These data then served as critical inputs for thermodynamic optimization. Furthermore, the present study can provide insights into thermodynamic property evolution of the electrolyte and solubility limit of various impurities during the electrorefining process.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Modeling aqueous association constants and mineral solubilities at subcritical and supercritical temperatures

The need for sustainable power generation has increased interest in the use of hydrothermal fluids for industrial applications. New high-enthalpy geothermal systems and biowaste-to-fuel processes are two relevant examples that employ supercritical fluids which require an in-depth understanding of complex chemical reactions occurring near the supercritical temperature of water (374 °C). As these processes operate in thermodynamic regimes that are not currently covered by a standard molar Gibbs energy of formation model, only empirical fits for single reaction systems are available which limit the use of multi-component phase equilibria calculations that are standard practice for less extreme environments. Here, in this paper, we advance a standard molar Gibbs energy of formation model able to operate in these otherwise inaccessible thermodynamic states to include species needed for key mineral solubility systems and ion association reactions. This work extends a model based on molecular statistical thermodynamics (MST) into four new systems (Na 3 PO 4 -H 2 O, LiOH-H 2 O, KOH-H 2 O, and BaSO 4 -H 2 O) by extending the model to cover 10 new species. For each of these systems, model predictions were consistently within the experimental uncertainties for the new systems covered. A breakdown of MST contributions to the model revealed that electrostatic and hard sphere contributions were key to reproducing density dependencies of standard molar Gibbs energy of formation values around the critical point of water.

42 ENGINEERING↗

DOE OSTI2024

Computational thermodynamics-guided alloy design and phase stability in CoCrFeMnNi-based medium-and high-entropy alloys: An experimental-theoretical study

A computational thermodynamics approach has been employed to design CoCrFeMnNi-based medium- and high-entropy alloys (M/HEAs) with systematically varied compositions (Co(( 80-X )/ 2 )Cr(( 80-X )/ 2 )Fe X Mn 10 Ni 10 with x = 30, 40, and 50 at.%) and phase stability. Since the formation of sigma phase, usually brittle and undesirable, is a common concern, when this class of alloys is subjected to elevated temperatures (600–1000 °C), predicting its formation becomes essential. Thus, its formation and the phase equilibria were studied using the CALPHAD method, and two empirical methods, namely, valence electron concentration (VEC) and paired sigma-forming element (PSFE). Isothermal aging treatments at 900–1100 °C for 20 h were performed, since CALPHAD and VEC/PSFE predictions diverged. Both prediction methods were compared with experimental characterization by a combination of scanning electron microscopy and high-energy synchrotron X-ray diffraction. In conclusion, the predictions from the VEC/PSFE and CALPHAD calculations (depending on the database used) were shown to be quite accurate.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Phase diagram to demarcate supercritical, transcritical, and continuous phase regimes for binary fluid equilibrium mixing relevant to combustion applications

Here, a robust methodology to develop phase diagrams of binary fluid mixtures at fixed thermo dynamic conditions (pressure, temperature, and mole fraction) as well as of two initially separated fluids undergoing mixing near critical conditions are presented for fluids and con ditions relevant to rockets, gas turbines, and diesel engine applications. Phase equilibria of mixtures is first examined to provide insight into the continuous-phase mixing behavior (including but not limited to supercritical behavior), and to develop a broadly applicable phase-diagram for binary fluid mixtures at fixed conditions. Next, adiabatic mixing theory and reduced Helmholtz equations of state are used to predict the thermodynamic conditions required to attain continuous-phase binary fluid mixing near critical conditions. Then, a 3D surface diagram (P,T fuel ,T amb ) separating single and two-phase regions is constructed by varying the ambient pressure and the initial temperatures of the two fluids. Polynomial fits of the 3D surfaces for 10 different binary mixtures are tabulated for nitrogen-alkane and methane-oxygen blends relevant to air-breathing and propellant based engines, respectively.

42 ENGINEERING↗

DOE OSTI2020

Charged particle dynamics near an X-point of a non-symmetric magnetic field with closed field lines

Understanding particle drifts in a non-symmetric magnetic field is of primary interest in designing optimized stellarators in order to minimize the neoclassical radial loss of particles. Quasisymmetry and omnigeneity, two distinct properties proposed to ensure radial localization of collisionless trapped particles in stellarators, have been explored almost exclusively for magnetic fields with nested flux surfaces. In this work, we examine radial particle confinement when all field lines are closed. We then study charged particle dynamics in the special case of a non-symmetric vacuum magnetic field with closed field lines obtained recently by Weitzner & Sengupta ( Phys. Plasmas , vol. 27, 2020, 022509). These magnetic fields can be used to construct magnetohydrodynamic equilibria for low pressure. Expanding in the amplitude of the non-symmetric fields, we explicitly evaluate the omnigeneity and quasisymmetry constraints. We show that the magnetic field is omnigeneous in the sense that the drift surfaces coincide with the pressure surfaces. However, it is not quasisymmetric according to the standard definitions.

Physics↗

DOE OSTI2021

Vacuum magnetic fields with exact quasisymmetry near a flux surface. Part 1. Solutions near an axisymmetric surface

While several results have pointed to the existence of exactly quasisymmetric fields on a surface (Garren & Boozer, Phys. Fluids B, vol. 3, 1991, pp. 2805–2821; 2822–2834; Plunk & Helander, J. Plasma Phys. , vol. 84, 2018, 905840205), we have obtained the first such solutions using a vacuum surface expansion formalism. We obtain a single nonlinear parabolic partial differential equation for a function $\eta$ such the field strength satisfies $B = B(\eta )$ . Closed-form solutions are obtained in cylindrical, slab and isodynamic geometries. Numerical solutions of the full nonlinear equations in general axisymmetric toroidal geometry are obtained, resulting in a class of quasihelical local vacuum equilibria near an axisymmetric surface. The analytic models provide additional insight into general features of the nonlinear solutions, such as localization of the surface perturbations on the inboard side. The local solutions thus obtained can be continued globally only for special initial surfaces.

Physics↗

DOE OSTI2021

Combined plasma–coil optimization algorithms

Combined plasma–coil optimization approaches for designing stellarators are discussed and a new method for calculating free-boundary equilibria for multiregion relaxed magnetohydrodynmics (MRxMHD) is proposed. Four distinct categories of stellarator optimization, two of which are novel approaches, are the fixed-boundary optimization, the generalized fixed-boundary optimization, the quasi-free-boundary optimization, and the free-boundary (coil) optimization. These are described using the MRxMHD energy functional, the Biot–Savart integral, the coil-penalty functional and the virtual casing integral and their derivatives. The proposed free-boundary equilibrium calculation differs from existing methods in how the boundary-value problem is posed, and for the new approach it seems that there is not an associated energy minimization principle because a non-symmetric functional arises. We propose to solve the weak formulation of this problem using a spectral-Galerkin method, and this will reduce the free-boundary equilibrium calculation to something comparable to a fixed-boundary calculation. In our discussion of combined plasma–coil optimization algorithms, we emphasize the importance of the stability matrix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Hamiltonian kinetic-Hall magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes

We present two generalized hybrid kinetic-Hall magnetohydrodynamics (MHD) models describing the interaction of a two-fluid bulk plasma, which consists of thermal ions and electrons, with energetic, suprathermal ion populations described by Vlasov dynamics. The dynamics of the thermal components are governed by standard fluid equations in the Hall MHD limit with the electron momentum equation providing an Ohm's law with Hall and electron pressure terms involving a gyrotropic electron pressure tensor. The coupling of the bulk, low-energy plasma with the energetic particle dynamics is accomplished through the current density (current coupling scheme; CCS) and the ion pressure tensor appearing in the momentum equation (pressure coupling scheme; PCS) in the first and the second model, respectively. The CCS is a generalization of two well-known models, because in the limit of vanishing energetic and thermal ion densities, we recover the standard Hall MHD and the hybrid kinetic-ions/fluid-electron model, respectively. This provides us with the capability to study in a continuous manner, the global impact of the energetic particles in a regime extending from vanishing to dominant energetic particle densities. The noncanonical Hamiltonian structures of the CCS and PCS, which can be exploited to study equilibrium and stability properties through the energy-Casimir variational principle, are identified. As a first application here, we derive a generalized Hall MHD Grad–Shafranov–Bernoulli system for translationally symmetric equilibria with anisotropic electron pressure and kinetic effects owing to the presence of energetic particles using the PCS.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Heat conduction in an irregular magnetic field. Part 2. Heat transport as a measure of the effective non-integrable volume

Given the large anisotropy of transport processes in magnetized plasmas, the magnetic field structure can strongly impact heat diffusion: magnetic surfaces and cantori form barriers to transport while chaotic layers and island structures can degrade confinement. When a small but non-zero amount of perpendicular diffusion is included, the structure of the magnetic field becomes less important, allowing pressure gradients to be supported across chaotic regions and island chains. We introduce a metric for the effective volume over which the local parallel diffusion dominates based on the solution to the anisotropic heat diffusion equation. To validate this metric, we consider model fields with a single island chain and a strongly chaotic layer for which analytic predictions of the relative parallel and perpendicular transport can be made. We also analyse critically chaotic fields produced from different sets of perturbations, highlighting the impact of the mode number spectrum on the heat transport. Our results indicate that this metric coincides with the effective volume of non-integrability in the limit $\kappa _{\perp } \rightarrow 0$ , where $\kappa_{\perp}$ is the perpendicular diffusion coefficient. We propose that this metric be used to assess the impact of non-integrability on the heat transport in stellarator equilibria.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Thermal equilibrium of collisional non-neutral plasma in a magnetic dipole trap

This paper discusses thermal equilibrium states of single-species plasmas, such as pure electron plasmas and pure positron plasmas, that are confined in a dipole trap. Thermal equilibrium states for such plasmas are routinely realized in the homogeneous magnetic field of Penning–Malmberg traps. We generalize the theory of these states to include inhomogeneous magnetic dipole fields. The approach to thermal equilibrium takes place in two stages with well separated time scales. On the collision time scale, thermal equilibrium is established along each magnetic field line. On the much longer transport time scale, heat conduction and viscosity bring the plasmas on different flux contours into thermal equilibrium, we call this a state of global thermal equilibrium. We present numerical results for local and global thermal equilibria. These results agree with the analytic predictions for charge collections that are large compared with the Debye length. There is, in principle, no limit to the confinement time of a single-species plasma in a global thermal equilibrium state. Experiments with hot electron–ion plasmas performed in the LDX and RT1 devices give us confidence that, in contrast to a Penning–Malmberg trap, a magnetic dipole field can also confine cold quasi-neutral electron–positron pair plasmas on the time scale of the phenomena of interest. Such pair plasmas are assumed to form in the magnetosphere of neutron stars but have so far not been realized in a laboratory. The creation of an electron–positron pair plasma is the main goal of the APEX collaboration.

Steinbrunner, P. (ORCID:0000000317693686)↗

DOE OSTI2024

Optimization of nonlinear turbulence in stellarators

We present new stellarator equilibria that have been optimized for reduced turbulent transport using nonlinear gyrokinetic simulations within the optimization loop. The optimization routine involves coupling the pseudo-spectral GPU-native gyrokinetic code GX with the stellarator equilibrium and optimization code DESC . Since using GX allows for fast nonlinear simulations, we directly optimize for reduced nonlinear heat fluxes. To handle the noisy heat flux traces returned by these simulations, we employ the simultaneous perturbation stochastic approximation (SPSA) method that only uses two objective function evaluations for a simple estimate of the gradient. We show several examples that optimize for both reduced heat fluxes and good quasi-symmetry as a proxy for low neoclassical transport. Finally, we run full transport simulations using the T3D stellarator transport code to evaluate the changes in the macroscopic profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

A quasi-linear model of electromagnetic turbulent transport and its application to flux-driven transport predictions for STEP

A quasi-linear reduced transport model is developed from a database of high-β electromagnetic nonlinear gyrokinetic simulations performed with spherical tokamak for energy production (STEP) relevant parameters. The quasi-linear model is fully electromagnetic and accounts for the effect of equilibrium flow shear using a novel approach. Its flux predictions are shown to agree quantitatively with predictions from local nonlinear gyrokinetic simulations across a broad range of STEP-relevant local equilibria. This reduced transport model is implemented in the T3D transport solver that is used to perform the first flux-driven simulations for STEP to account for transport from hybrid kinetic ballooning mode turbulence, which dominates over a wide region of the core plasma. Nonlinear gyrokinetic simulations of the final transport steady state from T3D return turbulent fluxes that are consistent with the reduced model, indicating that the quasi-linear model may also be appropriate for describing the transport steady state. Within the assumption considered here, our simulations support the existence of a transport steady state in STEP with a fusion power comparable to that in the burning flat top of the conceptual design, but do not demonstrate how this state can be accessed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Constructing nested coordinates inside strongly shaped toroids using an action principle

A new approach for constructing polar-like boundary-conforming coordinates inside a toroid with strongly shaped cross-sections is presented. A coordinate mapping is obtained through a variational approach, which involves identifying extremal points of a proposed action in the mapping space from [0,2π] 2 ×[0,1] to a toroidal domain in $\mathbb{R}$ 3 . This approach employs an action built on the squared Jacobian and radial length. Extensive testing is conducted on general toroidal boundaries using a global Fourier–Zernike basis via action minimisation. The results demonstrate successful coordinate construction capable of accurately describing strongly shaped toroidal domains. The coordinate construction is successfully applied to the computation of three-dimensional magnetohydrodynamic equilibria in the GVEC code where the use of traditional coordinate construction by interpolation from the boundary failed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

How does ion temperature gradient turbulence depend on magnetic geometry? Insights from data and machine learning

Magnetic geometry has a significant effect on the level of turbulent transport in fusion plasmas. Here, we model and analyse this dependence using multiple machine learning methods and a dataset of >200 000 nonlinear gyrokinetic simulations of ion-temperature-gradient turbulence in diverse non-axisymmetric geometries. The dataset is generated using a large collection of both optimised and randomly generated stellarator equilibria. At fixed gradients and other input parameters, the turbulent heat flux varies between geometries by several orders of magnitude. Trends are apparent among the configurations with particularly high or particularly low heat flux. Regression and classification techniques from machine learning are then applied to extract patterns in the dataset. Due to a symmetry of the gyrokinetic equation, the heat flux and regressions thereof should be invariant to translations of the raw features in the parallel coordinate, similar to translation invariance in computer vision applications. Multiple regression models including convolutional neural networks (CNNs) and decision trees can achieve reasonable predictive power for the heat flux in held-out test configurations, with highest accuracy for the CNNs. Using Spearman correlation, sequential feature selection and Shapley values to measure feature importance, it is consistently found that the most important geometric lever on the heat flux is the flux surface compression in regions of bad curvature. The second most important geometric feature relates to the magnitude of geodesic curvature. These two features align remarkably with surrogates that have been proposed based on theory, while the methods here allow a natural extension to more features for increased accuracy. The dataset, released with this publication, may also be used to test other proposed surrogates, and we find that many previously published proxies do correlate well with both the heat flux and stability boundary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Bootstrap current modeling in M3D-C1

Bootstrap current plays a crucial role in the equilibrium of magnetically confined plasmas, particularly in quasi-symmetric stellarators and in tokamaks, where it can represent bulk of the electric current density. Accurate modeling of this current is essential for understanding the magnetohydrodynamic (MHD) equilibrium and stability of these configurations. This study expands the modeling capabilities of M3D-C1, an extended-MHD code, by implementing self-consistent physics models for bootstrap current. It employs two analytical frameworks: a generalized Sauter model (Sauter et al. 1999 Phys. Plasmas vol. 6, no. 7, pp. 2834–2839), and a revised Sauter-like model (Redl et al. 2021 Phys. Plasmas vol. 28, no. 2, pp. 022502). The isomorphism described by Landreman et al. (2022 Phys. Rev. Lett. vol. 128, pp. 035001) is employed to apply these models to quasi-symmetric stellarators. The implementation in M3D-C1 is benchmarked against neoclassical codes, including NEO, XGCa and SFINCS, showing excellent agreement. These improvements allow M3D-C1 to self-consistently calculate the neoclassical contributions to plasma current in axisymmetric and quasi-symmetric configurations, providing a more accurate representation of the plasma behavior in these configurations. A workflow for evaluating the neoclassical transport using SFINCS with arbitrary toroidal equilibria calculated using M3D-C1 is also presented. This workflow enables a quantitative evaluation of the error in the Sauter-like model in cases that deviate from axi- or quasi-symmetry (e.g. through the development of an MHD instability).

fusion plasma↗

DOE OSTI2026

Omnigenous umbilic stellarators

To better understand the dependence of the magnetic field structure in the plasma edge on the plasma boundary shape, in the context of X-point and island divertor designs, we define and develop a class of stellarators called umbilic stellarators. These equilibria are characterised by a single continuous high-curvature edge on the plasma boundary that goes around multiple times toroidally before meeting itself. We develop a technique that allows us to simultaneously optimise the plasma boundary along with a curve lying on the boundary on which we impose a high curvature while imposing omnigenity – a property of the magnetic field that ensures trapped particle confinement throughout the plasma volume. We find that umbilic stellarators naturally tend to favour piecewise omnigenity instead of omnigenity with a specific helicity. After generating omnigenous umbilic stellarators, we design coil sets for some of them and explore the fieldline structure in the edge and its sensitivity to small fluctuations in the plasma. Finally, using single-stage optimisation, we simultaneously modify the plasma and coil shape and propose an experiment to modify an existing tokamak to a finite-𝛽 stellarator using this technique and explore a potentially simpler way to convert a limited tokamak into a diverted stellarator.

fusion plasma↗

DOE OSTI2022

Hydrated Anions: From Clusters to Bulk Solution with Quasi-Chemical Theory

The interactions of hydrated ions with molecular and macromolecular solution and interface partners are strong on a chemical energy scale. Here we recount the foremost ab initio theory for the evaluation of the hydration free energies of ions, namely, quasi-chemical theory (QCT). We focus on anions, particularly halides but also the hydroxide anion, because they have been outstanding challenges for all theories. For example, this work supports understanding the high selectivity for F – over Cl – in fluoride-selective ion channels despite the identical charge and the size similarity of these ions. QCT is built by the identification of inner-shell clusters, separate treatment of those clusters, and then the integration of those results into the broader-scale solution environment. Recent work has focused on a close comparison with mass-spectrometric measurements of ion-hydration equilibria. We delineate how ab initio molecular dynamics (AIMD) calculations on ion-hydration clusters, elementary statistical thermodynamics, and electronic structure calculations on cluster structures sampled from the AIMD calculations obtain just the free energies extracted from the cluster experiments. That theory–experiment comparison has not been attempted before the work discussed here, but the agreement is excellent with moderate computational effort. This agreement reinforces both theory and experiment and provides a numerically accurate inner-shell contribution to QCT. The inner-shell complexes involving heavier halides display strikingly asymmetric hydration clusters. Asymmetric hydration structures can be problematic for the evaluation of the QCT outer-shell contribution with the polarizable continuum model (PCM). Nevertheless, QCT provides a favorable setting for the exploitation of PCM when the inner-shell material shields the ion from the outer solution environment. For the more asymmetrically hydrated, and thus less effectively shielded, heavier halide ions clustered with waters, the PCM is less satisfactory. We therefore investigate an inverse procedure in which the inner-shell structures are sampled from readily available AIMD calculations on the bulk solutions. This inverse procedure is a remarkable improvement; our final results are in close agreement with a standard tabulation of hydration free energies, and the final composite results are independent of the coordination number on the chemical energy scale of relevance, as they should be. Finally, a comparison of anion hydration structure in clusters and bulk solutions from AIMD simulations emphasize some differences: the asymmetries of bulk solution inner-shell structures are moderated compared with clusters but are still present, and inner hydration shells fill to slightly higher average coordination numbers in bulk solution than in clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗