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DOE OSTI2021

Pentagonal prism spherical hohlraums for OMEGA

A new configuration is proposed for spherical hohlraums on OMEGA in which seven laser entrance holes (LEHs) are used—five around the equator and one at each pole [Farmer et al., Phys. Plasmas 26, 032701 (2019)]. This is known as the PEPR (pentagonal prism) hohlraum. A new view-factor code LORE is used to model the PEPR hohlraum and compare its performance with tetrahedral hohlraums shot on OMEGA. With optimization of beam pointings, the PEPR hohlraum produces a nonuniformity ranging from 1.1% (rms) at low albedos to 0.6% at high albedos. The tradeoffs between hohlraum-to-capsule ratio, uniformity, and background radiation temperature have been explored, and it has been shown that larger LEH radii on the poles can result in a modest improvement in uniformity. Here, the seven-hole PEPR hohlraum is well matched to the OMEGA symmetry and promises to provide insight into the performance of spherical hohlraums including octahedral (six-LEH) hohlraums.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Dephasingless two-color terahertz generation

A laser pulse composed of a fundamental and an appropriately phased second harmonic can drive a time-dependent current of photoionized electrons that generates broadband THz radiation. Over the propagation distances relevant to many experiments, dispersion causes the relative phase between the harmonics to evolve. This “dephasing” slows the accumulation of THz energy and results in a multi-cycle THz pulse with significant angular dispersion. Here, we introduce a novel optical configuration that compensates the relative phase evolution, allowing for the formation of a half-cycle THz pulse with almost no angular dispersion. The configuration uses the spherical aberration of an axilens to map a prescribed radial phase variation in the near field to a desired longitudinal phase variation in the far field. Simulations that combine this configuration with an ultrashort flying focus demonstrate the formation of a half-cycle THz pulse with a controlled emission angle and 1/4 the angular divergence of the multi-cycle pulse created by a conventional optical configuration.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules

Here, we present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma’s evolving temperature and drift velocity. The mesh motion is dealt with by transforming the underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: (1) an elastic moving wall boundary; (2) a time-dependent Maxwellian Dirichlet boundary; and (3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems — the first-ever reported using a Vlasov–Fokker–Planck model.

1D2V↗

DOE OSTI2024

Generalized kinetic equation for tokamak plasma equilibrium distribution function

A generalised kinetic equation for the equilibrium distribution function in a finite beta, arbitrary tokamak plasma is derived. The equation is correct to second order in ρ/L (ρ is the particle Larmor radius and L is the system size). Resolving finite Larmor radius length scales with no restriction on the ratio of poloidal to total equilibrium magnetic field, B $\vartheta$ /B, it generalises the drift kinetic theory of [Hazeltine Phys. Plasmas 15 (1973) 77] to the limit of B $\vartheta$ /B ~ 1 (e.g. to ensure validity for spherical tokamaks). Two cases are considered. The first provides the equilibrium distribution function, consistent with the generalised gyrokinetic formalism of [Dudkovskaia et al. Plasma Phys. Control. Fusion 65 (2023) 045010], derived specifically to capture neoclassical equilibrium currents in gyrokinetic stability analyses in strong gradient regions. The second assumes short length scales in the direction perpendicular to the magnetic field, which can occur as a result of small coherent magnetic structures in the plasma, such as neoclassical tearing mode magnetic islands close to threshold. This then extends the drift island equations of [Dudkovskaia et al. Nucl. Fusion 63 (2023) 016020] for the plasma response to magnetic islands to a spherical tokamak plasma configuration. In conclusion, resolving ρ ~ ρ $\vartheta$ (or B $\vartheta$ ~ B), where ρ $\vartheta$ is the particle poloidal Larmor radius, is also expected to influence calculations of the magnetic island propagation frequency and the associated contributions to the island onset conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Special Issue on the 22nd International Spherical Torus Workshop, 21–24 October 2024

This Special Issue contains papers resulting from research presented at the 22nd International Spherical Torus Workshop (ISTW), which was held during 21–24 October 2024, in Oxford, UK. The objectives of this workshop were to contribute to advancing the understanding of spherical tori (ST) configurations and to enhance their potential for fusion power applications. The scope of the meeting covers the full range of research activities on STs and aims to provide a forum for discussion and collaboration enhancement. The ISTW is organized by the International Energy Agency Technology Collaboration Programme on ST [1], and the 22nd was the latest in a series that started in 1994, but due to the global pandemic it had not been held in person for 5 years. With 15 thirty-minute overview presentations, 33 twenty-minute presentations, 32 posters and 93 total attendees, the 22nd ISTW was, to our knowledge, the largest to date. Representatives attended from at least 9 countries, representing at least 24 institutions, and presenting results from at least 18 existing or planned devices. Furthermore, this demonstrates the current broad interest in STs as fusion research devices and as candidates for future fusion pilot plants. Following on this momentum, the 23rd ISTW is planned to be held in Seville, Spain in late 2026.

Berkery, John W. [Princeton Plasma Physics Laborat↗

DOE OSTI2024

Quasinormal modes of naked singularities in presence of nonlinear scalar fields

We study linear perturbations against static spherically symmetric background configurations of general relativity with a real scalar field (SF), which is minimally coupled with gravity; it is nonlinear due to the presence of the self-action potential. The background solutions have a naked singularity at the center of the configuration. The focus is on the stability of the background and fundamental frequencies of the quasinormal modes (QNM) of the axial perturbations in the Regge-Wheeler gauge. The problem is reduced to one hyperbolic master equation with an effective potential 𝑊eff, which turns out to be positive for a general non-negative SF potential; this ensures the linear stability with respect to this kind of perturbations. For numerical simulations, the SF potential was chosen in the power-law form 𝑉⁡(𝜙) ∼ 𝜙 2⁢𝑛 with 2 < 𝑛 ≤40. We extracted the fundamental frequencies of QNM for different 𝑛 and various sets of the background configuration parameters. The results show that even for a small background SF, there is a significant difference between the fundamental frequencies and ones in case of the Schwarzschild background. Furthermore, the results are also compared with the case of the Fisher-Janis-Newman-Winicour background dealing with a massless linear scalar field.

General relativity↗

DOE OSTI2023

Droplet burning of n-butyl acetate/n-heptane mixtures in the standard atmosphere: experiments and numerical modeling

Blending petroleum fuels with oxygenates is a common approach to stem the depletion of crude oil while also mitigating the impact of their combustion on the environment. It has recently been considered that n-butyl acetate (BA, C6H12O2 , boiling point of 399K) could be a viable oxygenate additive to diesel fuel. In this application it is important to determine the influence of the fractional amount of BA on burning of the mixture. This presentation considers this problem from an experimental and computational approach using n-heptane (C7H14 , boiling point of 372K) as an essentially single component surrogate for diesel fuel. The burning configuration considered was ostensibly spherical symmetry as promoted by burning droplets under conditions where forced and natural convection effects were minimized. In this configuration the droplet and flame are concentric spheres and soot aggregates are trapped in a shell structure between the droplet and flame. Measurements were made of the droplet, flame and soot shell diameters through video imaging of the burning process. The experimental results were used to validate a detailed numerical model of the spherically symmetric droplet burning process that incorporated a consistent combustion kinetic mechanism for BA/heptane mixtures, comprised of 402 species and 16,872 reactions inclusive of soot chemistry. A model for soot formation was also included in the simulation to predict formation of the soot shell. The simulations agreed well with measured droplet and flame diameters. It was found both experimentally and computationally that adding BA to heptane had a minimal effect on the mixture burning rate, while the flame was positioned closer to the droplet surface and the simulated soot volume fraction decreased. The implications of these results are discussed for using BA as a potential additive to diesel fuel.

09 BIOMASS FUELS↗

DOE OSTI2022

Multi-harmonic electron cyclotron heating and current drive scenarios for non-inductive start-up and ramp-up in high field ST-40 spherical tokamak

We report non-inductive start-up and ramp-up is an important topic for spherical tokamak reactor design as the central solenoid implementation is highly restrictive particularly for the low-aspect-ratio tokamak configuration. In the high field spherical tokamak (ST), ST-40 with B T0 ≤ 3 T, a preparation is underway for high power ECH and ECCD current start-up/ramp-up experiments utilizing two MW-class 140/105 GHz gyrotrons. Here, we explored various ECH/ECCD scenarios for a low-field-side (LFS) launch-angle steerable waveguide launcher placed near the mid-plane region. Due to the large toroidal field variation of ST configuration, multiple cyclotron harmonic resonance layers could exist within the plasma. In this start-up and ramp-up regime, both fundamental and second harmonic ECH resonances must be considered. We find that even with the presence of X-II resonance layer in the plasma, an efficient X-I ECH and ECCD regime can be accessed for the low electron temperature T e0 as low as 200 eV which is a typical starting temperature of ECH heated plasmas in an open-field-line configuration. The presence of X-II resonance could become significant at higher T e0 as X-II absorption increases with T e0 which could reduce the current ramp-up efficiency as the power reaching X-I is reduced. Finally for the pure X-I regime where the 2Ω e resonance is moved outside the plasma with B T0 ~ 3.4 T, we find that it is possible to reach the full current of I p ~ 1 MA fully non-inductively with the ECH power of ~1 MW at n e0 ~ 1.0 × 10 19 m -3 using 105 GHz frequency gyrotron. By reducing the outer limiter position R L ~ 78 cm to 70 cm, the pure X-I regime is recovered at the rated ST-40 magnetic field of B T0 ~ 3.0 T. This X-I regime is accessible with a relatively broad range of launched n II or the launching angles. A survey of X-mode X-II ECH and ECCD at higher density regimes is also shown for completeness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Polymer Single‐Chain Nanoparticles: Shaping Solid Surfactants

Polymer single-chain nanoparticles (SCNPs) have found a wide range of applications spanning catalysts, sensors and nanomedicine. The generation of structured SCNPs from star-shaped polymers with diverse architectures and functionalities affords a new avenue to expand the emerging research area. The large-scale synthesis of structured SCNPs is described by the electrostatics-mediated intramolecular crosslinking of three types of 3-armed star-shaped polymers (T-P4VP, T-PS-b-P4VP, and T-P4VP-b-PS), whose configuration is tunable from spherical to cage-shaped to dumbbell-shaped and star-shaped. The structured SCNPs are amphiphilic and can be used as solid surfactants to stabilize different types of emulsions.

Li, Shuailong↗

DOE OSTI2024

Bottlebrush Block Copolymers at the Interface of Immiscible Liquids: Adsorption and Lateral Packing

Amphiphilic bottlebrush block copolymers (BBCPs), having a hydrophilic bottlebrush polymer (BP) linked covalently to a hydrophobic BP, were found to segregate to liquid-liquid interfaces to minimize the free energy of the system. The key parameter influencing the outcome of the experiments is the ratio between the degree of polymerization of the backbone (NBB) and that of the side-chain brushes (NSC). Specifically, a spherical, star-like configuration results when NBB < NSC, while a cylindrical, bottlebrush-like shape is preferred when NBB > NSC. Dynamic interfacial tension (γ) and fluorescence recovery after photobleaching (FRAP) measurements show that the BBCP configuration influences the areal density and in-plane diffusion at the fluid interface. The characteristic relaxation times associated with BBCP adsorption (τA) and reorganization (τR) were determined by fitting time-dependent interfacial tension measurements to a sum of two exponential relaxation functions. Both τA and τR initially increased with NBB up to 92 repeat units, due to the larger hydrodynamic radius in solution and slower in-plane diffusivity, attributed to a shorter cross-sectional diameter of the side-chains near the block junction. This trend reversed at NBB = 190, with shorter τA and τR attributed to increased segregation strength and exposure of the bare water/toluene interface due to tilting and/or wiggling of the backbone chains, respectively. The adsorption energy barrier decreased with higher NBB, due to a reduced BBCP packing density at the fluid interface. In conclusion, this study provides fundamental insights into macromolecular assembly at fluid interfaces, as it pertains to unique bottlebrush block architectures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Beam-ion Studies in NSTX and NSTX-U (Final Technical Report)

The confinement of high energy "fast ions" is crucial for the success of magnetic fusion as a practical energy source. The research performed by UC Irvine on NSTX and NSTX-U provided new information about this important topic in the configuration known as a "spherical tokamak." Injected neutral beams provided the fast ions (also known as "beam ions"). There were five overarching goals of the research. One objective was to measure the confinement of beam ions in order to ascertain if they were accomplishing their desired purpose of transferring their energy to the bulk plasma. A second goal was to better understand instabilities that are driven unstable by the fast ions. A related goal was to use the similarities and differences between NSTX and the DIII-D conventional tokamak to better understand the fast-ion driven instabilities. A fourth goal was to develop new instruments to measure fast ions and techniques that facilitate analysis of the data. The fifth objective was to measure and understand acceleration of beam ions by RF waves. Much was accomplished in all of these five areas. In the first, it was shown that the large magnetic moment of the beam ions did not harm confinement but instabilities known as the "sawtooth" and "long-lived mode" do. In the second area, much attention was devoted to the fast-ion instabilities known as "Alfvén eigenmodes." In particular, Alfvén eigenmode "avalanches" can cause ~ 30% of the fast ions to be lost in a single explosive burst. The comparative studies with DIII-D showed that an instability discovered on NSTX is also important in conventional tokamaks. In the fourth category, several instruments were developed, a number of effects that complicate interpretation of the data were understood, and progress toward a new method to infer the fast-ion distribution function from the data was made. In the fifth category, the measured profile of accelerated fast ions was initially much broader than theoretical predictions but subsequent improvements in the theoretical modeling achieved good agreement with the data.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Ultrahigh-pressure crystallographic passage towards metallic hydrogen

The structural evolution of molecular hydrogen H 2 under multi-megabar compression and its relation to atomic metallic hydrogen is a key unsolved problem in condensed-matter physics. Although dozens of crystal structures have been proposed by theory, only one, the simple hexagonal-close-packed (hcp) structure of only spherical disordered H 2 , has been previously confirmed in experiments. Through advancing nano-focused synchrotron X-ray probes, here we report the observation of the transition from hcp H 2 to a post-hcp structure with a six-fold larger supercell at pressures above 212 GPa, indicating the change of spherical H 2 to various ordered configurations. Theoretical calculations based on our XRD results found a time-averaged structure model in the space group $P\bar{6}2c$ with alternating layers of spherically disordered H 2 and new graphene-like layers consisting of H 2 trimers (H 6 ) formed by the association of three H 2 molecules. Here, this supercell has not been reported by any previous theoretical study for the post-hcp phase, but is close to a number of theoretical models with mixed-layer structures. The evidence of a structural transition beyond hcp establishes the trend of H 2 molecular association towards polymerization at extreme pressures, giving clues about the nature of the molecular-to-atomic transition of metallic hydrogen. Considering the spectroscopic behaviours that show strong vibrational and bending peaks of H 2 up to 400 GPa, it would be prudent to speculate the continuation of hydrogen molecular polymerization up to its metallization.

Ji, Cheng [Center for High Pressure Science and Te↗

DOE OSTI2022

Modifying Frank–Kasper Mesophases by Modulating Chain Configuration in PDMS- b -PTFEA Copolymers

The common spherical mesophases observed from chemically distinct compounds have promoted extensive studies of packing structures in soft-matter self-assemblies. In this report we present a new approach for controlling sphere-packing phases by modulating homologous copolymer chain configurations. To this end, three sets of sample pairs, compositionally asymmetric polydimethylsiloxane-b-poly(2,2,2-trifluoroethyl acrylate) (PDMS-b-PTFEA) diblock copolymers (diBCPs) and their homologues containing the corresponding triblock copolymer (triBCP), are synthesized via atom transfer radical polymerization and designed with the consistent volume fractions of the core-forming PTFEA block, f PTFEA = 0.20, 0.18, and 0.15. We identify the formation of C15 and hexagonally close-packed (HCP) phases in the triBCP-containing PDMS-b-PTFEAs, whereas the sigma and C14 phases are formed in their diBCP analogues, respectively. These phase shifts into C15 and HCP, due to molecular configuration differences, reveal a significant yet unrealized role of chain configurations and the associated chain size effects in determining the stable sphere-packing phases in BCP systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Coarse-grained methods for heterogeneous vesicles with phase-separated domains: Elastic mechanics of shape fluctuations, plate compression, and channel insertion

We develop coarse-grained particle approaches for studying the elastic mechanics of vesicles with heterogeneous membranes having phase-separated domains. We perform simulations both of passive shape fluctuations and of active systems where vesicles are subjected to compression between two plates or subjected to insertion into narrow channels. Analysis methods are developed for mapping particle configurations to continuum fields with spherical harmonics representations. Heterogeneous vesicles are found to exhibit rich behaviors where the heterogeneity can amplify surface two-point correlations, reduce resistance during compression, and augment vesicle transport times in channels. The developed methods provide general approaches for characterizing the mechanics of coarse-grained heterogeneous systems taking into account the roles of thermal fluctuations, geometry, and phase separation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Wide-angle effects for peculiar velocities

ABSTRACT The line-of-sight peculiar velocities of galaxies contribute to their observed redshifts, breaking the translational invariance of galaxy clustering down to a rotational invariance around the observer. This becomes important when the line-of-sight direction varies significantly across a survey, leading to what are known as ‘wide-angle’ effects in redshift-space distortions. Wide-angle effects will also be present in measurements of the momentum field, i.e. the galaxy density-weighted velocity field, in upcoming peculiar velocity surveys. In this work, we study how wide-angle effects modify the predicted correlation function and power spectrum for momentum statistics, both in autocorrelation and in cross-correlation with the density field. Using both linear theory and the Zel'dovich approximation, we find that deviations from the plane-parallel limit are large and could become important in data analysis for low-redshift surveys. We point out that even multipoles in the cross-correlation between density and momentum are non-zero regardless of the choice of line of sight, and therefore contain new cosmological information that could be exploited. We discuss configuration space, Fourier space, and spherical analyses; providing exact expressions in each case rather than relying on an expansion in small angles. We hope these expressions will be of use in the analysis of upcoming surveys for redshift-space distortions and peculiar velocities.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Improvement of SCALE-XSPROC Multigroup Cross Section Processing Based on the CENTRM Pointwise Slowing Down Calculation

The SCALE-XSProc multigroup (MG) cross section processing procedure based on the CENTRM pointwise slowing down calculation is the primary procedure to process problem-dependent self-shielded MG cross sections and scattering matrices for neutron transport calculations.This procedure supports various cell-based geometries including slab, 1-D cylindrical, 1-D spherical and 2-D rectangular configurations and doubly heterogeneous particulate fuels. Recently, this procedure has been significantly improved to be applied to any advanced reactor analysis covering thermal and fast reactor systems, and to be comparable to continuous energy (CE) Monte Carlo calculations. Some reactivity bias and reaction rate differences have been observed compared with CE Monte Carlo calculations, and several areas for improvement have been identified in the SCALE-XSProc MG cross section processing: (1) resonance self-shielding calculations within the unresolved resonance range, (2) 10 eV thermal cut-off energy for the free gas model, (3) on-the-fly adjustments to the thermal scattering matrix, (4) normalization of the pointwise neutron flux, and (5) fine MG energy structure. This procedure ensures very accurate MG cross section processing for high-fidelity deterministic reactor physics analysis for various advanced reactor systems.

Kim, Kang Seog↗

DOE OSTI2022

Formulation of the density eigenvalue problem in neutron transport for relevant engineering applications

A new formulation of the density eigenvalue problem for the neutron transport equation is presented. This new eigenvalue, named ζ eigenvalue can be introduced freely in the transport model, acting on a selected portion of the phase space. Despite its broader applications and its connection with the nature of the transport operator, the ζ eigenvalue has been presented here mainly as a design-oriented technique for the efficient evaluation of the critical concentration for a specific nuclide (or mixture of nuclides). This new eigenvalue is particularly adequate to study the definition of the material composition in the criticality design process of a multiplying system. The method is then applied for the study of classical problems such as the critical moderation ratio and the poison concentration to control the reactor. Some results are presented in one dimensional configuration using the multi- group spherical harmonics approach. This eigenvalue formulation proves to be a convenient and useful way to attain criticality, also for complex, realistic systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

Gravitational form factors of nuclei in the Skyrme model

Here, we compute the gravitational form factor D(t) of various nuclei in the generalized Skyrme model where nuclei are described as solitonic field configurations each with a definite baryon number B. We separately discuss the cases B = 1 (nucleons), B = 2 (deuteron), B = 3 (helium-3 and tritium), and extrapolate to larger B-values. Configurations with B > 1 are in general not spherically symmetric, and we demonstrate how group theory helps to extract the form factor. Numerical results are presented for the configurations with B = 1, 2, 3, 4, 5, 6, 7, 8, 32, 108. We find that the B-dependence is consistent with a power-law D(0) ∝ B β with β = 1.7–1.8. Other gravitational form factors can be calculated in the same framework, and we show the result for the J(t) form factor associated with the angular momentum for the B = 3 solution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗