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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Measuring dynamics of differentially rotating, unmagnetized, free-boundary plasma produced by soft x-ray irradiation

We present results from a new experiment, fielded on the MAGPIE pulsed power generator, producing a rotating, boundary-free plasma with no pre-imposed magnetic field. Angular momentum is introduced to the rotating system by the oblique collision of multiple plasma flows, which are driven by x-ray ablation of solid targets using the soft x-rays emitted from the implosion of wire array z-pinches. This produces a hydrodynamically stable plasma which undergoes ~2-3 rotations over the duration of the experiment, significantly more than previous pulsed-power platforms. Estimating the angular frequency from the electron density profile in the inner part of the rotating plasma shows that it has a quasi-Keplerian rotation profile. The system also allows for the addition of a controllable magnetic field. This, combined with the sufficiently large Reynolds (~10 5 ) and magnetic Reynolds (~10) numbers, will enable investigation of the effect of magnetic field on the structure and stability of the rotating plasma.

Physics - Plasma physics↗
DOE OSTI2020

Deep learning of free boundary and Stefan problems

Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/DeepStefan.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. Here the algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An Adaptive Newton-Based Free-Boundary Grad–Shafranov Solver

Equilibria in magnetic confinement devices result from force balancing between the Lorentz force and the plasma pressure gradient. In an axisymmetric configuration like a tokamak, such an equilibrium is described by an elliptic equation for the poloidal magnetic flux, commonly known as the Grad–Shafranov equation. It is challenging to develop a scalable and accurate free-boundary Grad–Shafranov solver, since it is a fully nonlinear optimization problem that simultaneously solves for the magnetic field coil current outside the plasma to control the plasma shape. In this work, we develop a Newton-based free-boundary Grad–Shafranov solver using adaptive finite elements and preconditioning strategies. The free-boundary interaction leads to the evaluation of a domain-dependent nonlinear form of which its contribution to the Jacobian matrix is achieved through shape calculus. The optimization problem aims to minimize the distance between the plasma boundary and specified control points while satisfying two nontrivial constraints, which correspond to the nonlinear finite element discretization of the Grad–Shafranov equation and a constraint on the total plasma current involving a nonlocal coupling term. The linear system is solved by a block factorization, and AMG is called for subblock elliptic operators. The unique contributions of this work include the treatment of a global constraint, preconditioning strategies, nonlocal reformulation, and the implementation of adaptive finite elements. Furthermore, it is found that the resulting Newton solver is robust, successfully reducing the nonlinear residual to 1e-6 and lower in a small handful of iterations while addressing the challenging case to find a Taylor state equilibrium where conventional Picard-based solvers fail to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Free-boundary MRxMHD equilibrium calculations using the stepped-pressure equilibrium code

Here the stepped-pressure equilibrium code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 , 112 502) is extended to enable free-boundary multi-region relaxed magnetohydrodynamic (MRxMHD) equilibrium calculations. The vacuum field surrounding the plasma inside an arbitrary 'computational boundary', , is computed, and the virtual-casing principle is used iteratively to compute the normal field on so that the equilibrium is consistent with an externally produced magnetic field. Recent modifications to SPEC are described, such as the use of Chebyshev polynomials to describe the radial dependence of the magnetic vector potential, and a variety of free-boundary verification calculations are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Alluvial fan morphology: A self-similar free boundary problem description

In this work, we examine approximate geometrically self-similar solutions to a parabolic free boundary value problem applied to alluvial fan surface morphology and growth. Alluvial fans are fan- or cone-shaped sedimentary deposits caused by the rapid deposition of sediment from a canyon discharging onto a flatter plain. Longitudinal, topographic profiles of fans can be readily described by a seemingly time independent dimensionless profile (DeChant et al., 1999). However, because an alluvial fan can be expected to grow over time, it is clear that this “steady” profile is certainly time dependent and can be described using a space-time self-similar solution. In an experimental and theory-based study, Guerit et al. (2014) developed a self-similar (or as they describe it a self-affine) linear solution based upon an approximate first order small parameter expansion solution for a 1-d homogeneous nonlinear diffusion equation. Direct substitution of this result into a linear diffusion equation suggests that this first order expression may not fully satisfy the associated governing equation. In contrast, we develop a more complete solution based upon a modeled approximation for the axi-symmetric formulation such that the associated temporal behavior is consistent with a 1/3 time power-law as described by Reitz and Jerolmack (2014). The resulting expression is an exact solution to a linear heat equation. Furthermore, we emphasize that a small parameter is not inherent to the resulting profile result and is not included in our model development. Though developed using rather different approaches, the formal solution developed here is in good agreement with the simple polynomial described by DeChant et al. (1999) suggesting that this self-similar solution is a suitable time dependent representation of alluvial fan longitudinal profile form and improves on earlier work.

58 GEOSCIENCES↗
DOE OSTI2024

Multilevel Monte Carlo methods for the Grad-Shafranov free boundary problem

The equilibrium configuration of a plasma in an axially symmetric reactor is described mathematically by a free boundary problem associated with the celebrated Grad-Shafranov equation. The presence of uncertainty in the model parameters introduces the need to quantify the variability in the predictions. This is often done by computing a large number of model solutions on a computational grid for an ensemble of parameter values and then obtaining estimates for the statistical properties of solutions. In this study, we explore the savings that can be obtained using multilevel Monte Carlo methods, which reduce costs by performing the bulk of the computations on a sequence of spatial grids that are coarser than the one that would typically be used for a simple Monte Carlo simulation. We examine this approach using both a set of uniformly refined grids and a set of adaptively refined grids guided by a discrete error estimator. Numerical experiments show that multilevel methods dramatically reduce the cost of simulation, with cost reductions typically on the order of 60 or more and possibly as large as 200. Furthermore, adaptive griding results in more accurate computation of geometric quantities such as x-points associated with the model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Surrogate approximation of the Grad–Shafranov free boundary problem via stochastic collocation on sparse grids

In magnetic confinement fusion devices, the equilibrium configuration of a plasma is determined by the balance between the hydrostatic pressure in the fluid and the magnetic forces generated by an array of external coils and the plasma itself. The location of the plasma is not known a priori and must be obtained as the solution to a free boundary problem. The partial differential equation that determines the behavior of the combined magnetic field depends on a set of physical parameters (location of the coils, intensity of the electric currents going through them, magnetic permeability, etc.) that are subject to uncertainty and variability. The confinement region is in turn a function of these stochastic parameters as well. In this work, we consider variations on the current intensities running through the external coils as the dominant source of uncertainty. This leads to a parameter space of dimension equal to the number of coils in the reactor. With the aid of a surrogate function built on a sparse grid in parameter space, a Monte Carlo strategy is used to explore the effect that stochasticity in the parameters has on important features of the plasma boundary such as the location of the x-point, the strike points, and shaping attributes such as triangularity and elongation. Furthermore, the use of the surrogate function reduces the time required for the Monte Carlo simulations by factors that range between 7 and over 30.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Verification of the Shafranov shift in free-boundary VMEC, DESC, and SPEC calculations with elliptical geometry

Here, given a set of current-carrying filaments that create a magnetic field with rotating elliptical flux surfaces, we present verification calculations using the VMEC, DESC, and SPEC free-boundary magnetohydrostatic equilibrium codes for both the “vacuum” equilibrium, for which there is no plasma pressure and no plasma currents, and for a non-zero pressure, zero toroidal current equilibrium. For the vacuum case, these codes are quantitatively compared to the magnetic field produced by the coils. For the non-zero pressure case, they are compared to each other. As the stepped pressure profile used in SPEC approaches the continuous profile used in VMEC and DESC, the SPEC magnetic axis approaches the VMEC and DESC axes. To within an error given by the difference between the pressure profiles, the VMEC, DESC, and SPEC calculations give the same pressure-induced geometric shift of the magnetic axis, known as the Shafranov shift.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Aircraft Observations of Turbulence in Cloudy and Cloud-Free Boundary Layers Over the Western North Atlantic Ocean From ACTIVATE and Implications for the Earth System Model Evaluation and Development

This study examines boundary layer turbulence derived from high temporal resolution meteorological measurements from 40 research flights over the western North Atlantic Ocean during the 2020 deployments of ACTIVATE. Frequency distributions of various turbulent quantities reveal stronger turbulence during the winter deployment than in summer and for cloud‐topped than in cloud‐free boundary layers during the summer deployment. Maximum turbulence kinetic energy (TKE) is most often within cloud from observations in winter and summer, whereas it is mostly below cloud in both seasons by a global model turbulence parameterization. Further, bivariate frequency distributions are consistent with the bivariate Gaussian probability distribution functions assumed for the closure of higher‐order turbulence/shallow convection parameterizations used by some global models. Turbulence simulated by the Community Atmosphere Model version 6 and the Energy Exascale Earth System Model Atmosphere Model version 2 using such parameterizations is not as strong as observed, with more TKE going into vertical wind perturbations rather than into zonal wind perturbations as observed, suggesting that the treatment of turbulence in Earth system models still needs to be further improved.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Controlled Growth of Single‐Crystal Graphene Wafers on Twin‐Boundary‐Free Cu(111) Substrates

Single-crystal graphene (SCG) wafers are needed to enable mass-electronics and optoelectronics owing to their excellent properties and compatibility with silicon-based technology. Controlled synthesis of high-quality SCG wafers can be done exploiting single-crystal Cu(111) substrates as epitaxial growth substrates recently. However, current Cu(111) films prepared by magnetron sputtering on single-crystal sapphire wafers still suffer from in-plane twin boundaries, which degrade the SCG chemical vapor deposition. Here, in this study, it is shown how to eliminate twin boundaries on Cu and achieve 4 in. Cu(111) wafers with ≈95% crystallinity. The introduction of a temperature gradient on Cu films with designed texture during annealing drives abnormal grain growth across the whole Cu wafer. In-plane twin boundaries are eliminated via migration of out-of-plane grain boundaries. SCG wafers grown on the resulting single-crystal Cu(111) substrates exhibit improved crystallinity with >97% aligned graphene domains. As-synthesized SCG wafers exhibit an average carrier mobility up to 7284 cm 2 V −1 s −1 at room temperature from 103 devices and a uniform sheet resistance with only 5% deviation in 4 in. region.

36 MATERIALS SCIENCE↗
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 OSTI2022

Closed-form existence conditions for bandgap resonances in a finite periodic chain under general boundary conditions

Bragg scattering in periodic media generates bandgaps, frequency bands where waves attenuate rather than propagate. Yet, a finite periodic structure may exhibit resonance frequencies within these bandgaps. This is caused by boundary effects introduced by the truncation of the nominal infinite medium. Previous studies of discrete systems determined existence conditions for bandgap resonances, although the focus has been limited to mainly periodic chains with free–free boundaries. In this paper, we present closed-form existence conditions for bandgap resonances in discrete diatomic chains with general boundary conditions (free–free, free–fixed, fixed–free, or fixed–fixed), odd or even chain parity (contrasting or identical masses at the ends), and the possibility of attaching a unique component (mass and/or spring) at one or both ends. The derived conditions are consistent with those theoretically presented or experimentally observed in prior studies of structures that can be modeled as linear discrete diatomic chains with free–free boundary conditions. An intriguing case is a free–free chain with even parity and an arbitrary additional mass at one end of the chain. Introducing such an arbitrary mass underscores a transition among a set of distinct existence conditions, depending on the type of chain boundaries and parity. The proposed analysis is applicable to linear periodic chains in the form of lumped-parameter models, examined across the frequency spectrum, as well as continuous granular media models, or similar configurations, examined in the low-frequency regime.

Bastawrous, Mary V.↗
DOE OSTI2020

Helical spin structure in iron chains with hybridized boundaries

In this paper, we have compared the magnetic properties of well-controlled ultra-short (≤50 nm) atomic iron (Fe) chains embedded in Fe-phthalocyanine films with those in Fe–hydrogen (H2) phthalocyanine superlattices. Surprisingly, we found that the coercivity of the atomic chains with free boundary conditions is independent of the chain length, whereas the one subject to hybridization of the chain ends exhibits an unexpected length dependence. These findings suggest that ferromagnetism in the free-boundary condition system is caused by an intrinsic indirect exchange. On the other hand, controlled boundary conditions produce a helical spin structure due to an extrinsic indirect exchange, which arises from the interaction between iron atoms at the ends of the chain and the hydrogen in the H 2 phthalocyanine spacer. As a consequence, during magnetic reversal, ultra-short iron chains subject to boundary clamping develop a helical spin structure, leading to increased coercivity. These findings suggest unique insights and ideas for the design of atomic-scale ultra-dense magnetic storage nanodevices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Mutual Diffusion Coefficients of Na 2 SO 4 at C = 0.02989 mol·dm -3 and 298.15 K by Using Rayleigh Interferometry with Free Diffusion Boundary Conditions: Experimental Test of the Effect of the C 3/2 Concentration Dependence of Refractive Index at Low Concentration

Rayleigh interferometry is one of the most precise and accurate methods for the experimental determination of the mutual diffusion coefficients of both electrolytes and non-electrolytes in liquid solutions. For binary solutions at moderate and high concentrations where the concentration dependences of both diffusion coefficient and refractive index can be assumed to be linear or almost linear and the concentration difference ΔC between a pair of solutions undergoing free diffusion is not large compared to their average concentration, and by using proper combinations of the interference fringe positions as they vary with time, under these conditions diffusion coefficients are obtained that are independent of the size of ΔC. However, this situation becomes more complicated at low concentrations for electrolyte solutions where the concentration dependences of both the diffusion coefficient and refractive index are non-linear, with C 1/2 dependence for the diffusion coefficient and C 3/2 dependence for the refractive index. As a test of these effects on calculated mutual diffusion of electrolyte solutions at low concentrations as measured by Rayleigh interferometry, apparent mutual diffusion coefficients D v,a (volume-fixed reference frame) were measured for fixed average concentrations C=(0.02989 ± 0.00001) mol·dm –3 of Na 2 SO 4 (aq) at 298.15 K while varying ΔC/C from 0.66673 to 2, a threefold variation. The dependence of the diffusion coefficient on ΔC/C was found to be linear, yielding D v = 1.041 6 × 10 –9 m 2 ·s –1 for an infinitely small concentration difference between the diffusing solutions.

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

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. ( Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗