to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The MARBLE project is a novel inertial confinement fusion platform for studying the development of atomic mixing and temperature equilibration in inertial confinement fusion implosions and their impact on thermonuclear burn. Experiments involve the laser-driven implosion of capsules filled with deuterated engineered foams whose pores are filled with a gaseous mixture of hydrogen and tritium. By varying the size of the foam pores, we can study the timescale of the development of atomic mix relative to the development of thermal equilibrium between species. In contrast, previous separated reactant experiments have only provided information on the total amount of mix mass. We report on the series of MARBLE experiments [first reported in Haines et al., Nat. Commun. 11, 544 (2020)] performed on the University of Rochester's OMEGA laser facility and detailed and highly resolved three-dimensional radiation-hydrodynamic simulations of the implosions. In both the experimental and simulation results, we observe that the reactants do not achieve thermal equilibrium during the course of the implosion except in atomically mixed regions—i.e., that atomic mixing develops faster than thermal equilibration between species. The results suggest that ion temperature variations in the mixture are at least as important as reactant concentration variations for determining the fusion reaction rates.

The rate of development of atomic mixing and temperature equilibration in inertial confinement fusion implosions

https://escholarship.org/content/qt1z6480mj/qt1z6480mj.pdf?t=ovg3xy

Neutronics and activation analysis of lithium-based ternary alloys in IFE blankets

Author(s): Jolodosky, Alejandra | Advisor(s): Fratoni, Massimiliano | Abstract: The goal of this dissertation is to examine the neutronic properties of a novel type of fusion reactor blanket material in the form of lithium-based ternary alloys. Pure liquid lithium, first proposed as a blanket for fusion reactors, is utilized as both a tritium breeder and a coolant. It has many attractive features such as high heat transfer and low corrosion properties, but most importantly, it has a very high tritium solubility and results in very low levels of tritium permeation throughout the facility infrastructure. However, lithium metal vigorously reacts with air and water and presents plant safety concerns including degradation of the concrete containment structure. The work of this thesis began as a collaboration with Lawrence Livermore National Laboratory in an effort to develop a lithium-based ternary alloy that can maintain the beneficial properties of lithium while reducing the reactivity concerns. The first studies down-selected alloys based on the analysis and performance of both neutronic and activation characteristics. First, 3-D Monte Carlo calculations were performed to evaluate two main neutronics performance parameters for the blanket: tritium breeding ratio (TBR), and energy multiplication factor (EMF). It was found that the elements that exhibit low absorption cross sections and higher Q-values, such as Pb, Sn, and Sr, perform well with those that have high neutron multiplication such as Pb and Bi. These elements meet TBR constraints ranging from 1.02 to 1.1. However, most alloys do not reach EMFs greater than 1.15. Alloys with adequate results based on TBR and EMF calculations were considered for activation analysis. Activation simulations were executed with 50 years of irradiation and 300 years of cooling. It was discovered that bismuth is a poor choice due to achieving the highest decay heat, contact dose rates, and accident doses. In addition, it does not meet the waste disposal ratings (WDR). The straightforward approach to obtain Monte Carlo TBR and EMF results required 231 simulations per alloy and became computationally expensive, time consuming, and inefficient. Consequently, alternate methods were pursued. A collision history-based methodology recently developed for the Monte Carlo code Serpent, calculates perturbation effects on practically any quantity of interest. This allows multiple responses to be calculated by perturbing the input parameter without having to directly perform separate calculations. The approach is strictly created for critical systems, but was utilized as the basis of a new methodology implemented for fixed source problems, known as Exact Perturbation Theory (EPT). EPT can calculate the tritium breeding ratio response, caused by a perturbation in the composition of the ternary alloy. The downfall of EPT methodology is that it cannot account for the collision history at large perturbations and thus, produces results with high uncertainties. Preliminary analysis for EPT with Serpent for a LiPbBa alloy demonstrated that 25 simulations per ternary must be completed so that most uncertainties calculated at large perturbations do not exceed 0.05. To reduce the uncertainties of the results, generalized least squares (GSL) method was implemented, to replace imprecise TBR results with more accurate ones. It was demonstrated that a combination of EPT Serpent calculations with the application of GLS for results with high uncertainties is the most effective and produces values with the highest fidelity. This approach was used to create an optimization scheme. The scheme finds an alloy composition that has a TBR within a range of interest, while imposing constraint on the EMF, and a requirement to minimize lithium concentration. It involved a three-level iteration process with each level zooming in closer on the area of interest to fine tune the correct composition. Both alloys studied, LiPbBa and LiSnZn, had optimized compositions close to the leftmost edge of the ternary, increasing the complexity of optimization due to the highly uncertain results found in these regions. Additional GPT methodologies were considered for optimization studies, specifically with the use of deterministic codes. Currently, an optimization deterministic code, SMORES, is available in the SCALE code package, but only for critical systems. Subsequently, it was desired to change this code to solve problems for fusion reactors similarly to what was done in SWAN. So far, the fixed and adjoint source declaration and definition was added to the input file. As a result, alterations were made to the source code so that it can read in and utilize the new input information. Due to time constraints, only a detailed outline has been created that includes the steps one has to take to make the transition of SMORES from critical systems to fixed source problems. Additional time constraints limited the goal to perform chemical reactivity experiments on candidate alloys. Nevertheless, a review of past experiments was done and it was determined that large-scale experiments seem more appropriate for the purpose of this work, as they would better depict how the alloys would behave in the actual reactor environment. Both air and water reactions should be considered when examining the potential chemical reactions of the lithium alloy.

Composition Optimization of Lithium-Based Ternary Alloy Blankets for Fusion Reactors

Conceptual design of a ceramic breeding blanket for laser fusion power plants with online tunable tritium breeding ratio based on a variable neutron reflector: Remarkable no need of isotopic enrichment

The CD Mix campaign has given a detailed explination of the mix mechanics in the current ignition capsule designs by investigating the relationship between material mixing, shell-fuel interfaces, and the change in thermonuclear yield given a deuterated layer in the capsule. Alternative ignition scenarios include the use of double shell designs that incorporate high-Z material in the capsule. Simulations are conducted on a proposed capsule platform using the ARES code on a scaled capsule design using a partially reduced glass capsule design. This allows for the inclusion of deuterium on the inner surface of the pusher layer similar to the CD mix experiments. The presence of silicon dioxide allows for the investigation of the influence of higher Z material on the mixing characteristics.

http://iopscience.iop.org/article/10.1088/1742-6596/717/1/012076/pdf

Proposed pushered single shell capsule design for the investigation of mid/high Z mix on the NIF

A parameter study of a proposed inertial fusion energy chamber is performed. A baseline case of a 6-m-radius chamber filled with 6 μg/cm3 of xenon is studied in detail. The maximum first-wall tempe...

Parameter Study of an Inertial Fusion Energy Chamber Response Using the 1-D BUCKY Radiation Hydrodynamics Code

Integrated inertial fusion energy chamber dynamics and response

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Proposed pushered single shell capsule design for the investigation of mid/high Z mix on the NIF

Parameter Study of an Inertial Fusion Energy Chamber Response Using the 1-D BUCKY Radiation Hydrodynamics Code

Integrated inertial fusion energy chamber dynamics and response