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DOE OSTI2025

Advanced Computational Modeling of High-Level Waste Vitrification at the Hanford Site

The U.S. Department of Energy (DOE) has selected vitrification for stabilizing legacy tank waste at the Hanford site, where radioactive waste from plutonium production was historically stored in underground tanks. This waste will be separated into low-activity waste (LAW) and high-level waste (HLW) fractions and processed at the Waste Treatment and Immobilization Plant (WTP). At WTP, glass melters are used for the vitrification of radioactive tank waste, transforming it into a stable borosilicate glass form for safe long-term storage. The melter vessel is constructed from highly durable and heat-resistant materials, where the vitrification process occurs. The main regions that are modeled are the melt pool, plenum, cold cap, riser/discharge chamber, and surrounding structure with insulation layers. Forced convection induced by air bubblers at the base of the melter ensure uniform temperature distribution and provide heat to the cold cap layer. The cold cap is a region of reacting batch feed that floats on top of the molten glass and is where the batch-to-glass reactions occur. Joule heating provided by electrodes mounted along the vertical walls of the melter and immersed directly in the glass, generates the necessary heat for the net endothermic conversion processes that occur in the cold cap. The high temperatures, radioactivity, and opaque nature of the glass prevent direct observation inside the melters. Therefore, computational models are essential for providing insight into factors that affect melter throughput. Thermocouples in the plenum provide operators with plenum temperature measurements. Operational adjustments include bubbling rate, voltage supplied to the electrodes, feed adjustments, and glass removal rate. Different computational fluid dynamics (CFD) models have been developed, each serving a specific purpose. There are CFD models of different scale melters, as well as models that capture the two-phase flow interfaces of rising bubbles in the molten glass or models with a simplified molten glass region so that the surrounding structure and plenum can be feasibly incorporated. Pilot-scale melter models have been developed to serve as validation of the methods employed in the simulation of the full-scale WTP melters. Models incorporating resolved bubbling are used to develop momentum source terms to implement into a single phase, multi-region, steady-state flow model that is being validated by measured process parameters such as glass production rate, voltage, input power, plenum temperatures, etc. The resolved bubbling model uses the multiphase volume of fluid approach to model the system with a high-resolution interface capturing scheme to maintain sharp interfaces between the molten glass and the air phase. The suite of CFD models is continually being improved to incorporate more realistic physics and achieve faster turnaround time. For example, an incremental controller is implemented to automatically adjust electrode voltage within the simulation to a molten glass set point temperature of 1150°C. Newer models feature improved meshes to ensure conformal meshes between regions and eliminate unnecessary mesh refinement in areas that are not of interest (such as boundary layers in offgas ports). Instead of explicitly modeling the structural, refractory, and insulation layers of the melter, a thermal resistance approach is used with published correlations used for boundary conditions. The development of robust and efficient CFD models will be instrumental in enabling the WTP to successfully fulfill its mission of safely stabilizing legacy nuclear waste.

12 - MGMT OF RADIOACTIVE AND NON-RADIOACTIVE WASTE↗

NASA NTRS2023

CFD Integrated Transition Modeling for High-Speed Flows via Coupled OVERFLOW-LASTRAC Analysis

This work details ongoing efforts at the NASA Langley Research Center to develop and validate a general-use CFD tool that includes built-in predictions of boundary-layer transition in high-speed flows. Existing tools for the coupling of the NASA OVERFLOW structured overset RANS solver and LASTRAC stability analysis code have been extended to capture boundary-layer transition in high-speed flows driven by either Mack’s first-mode or secondmode instabilities and/or crossflow instabilities. The efficacy of this coupled approach has been demonstrated by examining a variety of supersonic and hypersonic test cases for which experimental validation data is available. The intermittency prescription parameters inherited from prior low-speed applications are found to be suitable for some, but not all high-speed flow scenarios. The method is found to be robust for straight cone configurations and improvements necessary to accurately capture transition on geometries with spatially complex amplification factor envelopes with intermediate regions of slow N-factor variation are examined. The automated, coupled analysis is demonstrated for a 3d supersonic test case and found to perform well within the limits of the linear stability analysis on which it relies. Finally, a preliminary investigation of the method’s robustness to non-ideal CFD meshes is conducted.

High-speed flow↗

DOE OSTI2020

Enabling Highly Stable Li–O 2 Batteries with Full Discharge–Charge Capability: The Porous Binder- and Carbon-Free IrNi Nanosheet Cathode

Rechargeable aprotic Li-O 2 batteries have drawn much attention in light of their ultrahigh theoretical energy density. However, the sluggish kinetics of oxygen cathode reactions lead to huge energy loss, while the unfavorable side reactions associated with the widely used carbon and binder account for fast battery decay during cycles. In this work, hierarchically holey IrNi alloy nanosheets are facilely designed on Ni foam substrate as a freestanding, binder- and carbon-free cathode to address these challenges. The IrNi nanosheets consist of numerous interconnected nanoparticles, forming abundant nanoholes, benefiting active-site exposure. Moreover, the meso-/macropores pave channels for the transfer of oxygen and lithium ions and provide enough accommodation for the insoluble Li 2 O 2 product. The corresponding Li-O 2 batteries demonstrate low polarization and excellent cycle stability with full discharge/charge capability (up to 292 cycles at a current density of 0.2 mA cm -2 within a voltage range from 2.3 to 4.3 V). The long-term cycling performance is principally attributed to the exclusive catalytic stability of the holey IrNi nanosheets and its good compatibility with dimethyl sulfoxide-based electrolyte. Our research provides novel insights into the design of robust and freestanding porous cathodes for high energy density Li-O 2 batteries.

25 ENERGY STORAGE↗

DOE OSTI2020

Direct Demonstration of Topological Stability of Magnetic Skyrmions via Topology Manipulation

Topological protection precludes a continuous deformation between topologically inequivalent configurations in a continuum. Motivated by this concept, magnetic skyrmions, topologically nontrivial spin textures, are expected to exhibit topological stability, thereby offering a prospect as a nanometer-scale nonvolatile information carrier. In real materials, however, atomic spins are configured as not continuous but discrete distributions, which raises a fundamental question if the topological stability is indeed preserved for real magnetic skyrmions. Answering this question necessitates a direct comparison between topologically nontrivial and trivial spin textures, but the direct comparison in one sample under the same magnetic fields has been challenging. Here we report how to selectively achieve either a skyrmion state or a topologically trivial bubble state in a single specimen and thereby experimentally show how robust the skyrmion structure is in comparison with the bubbles. We demonstrate that topologically nontrivial magnetic skyrmions show longer lifetimes than trivial bubble structures, evidencing the topological stability in a real discrete system. Our work corroborates the physical importance of the topology in the magnetic materials, which has hitherto been suggested by mathematical arguments, providing an important step toward ever-dense and more-stable magnetic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Affinity propagation clustering of full-field, high-spatial-dimensional measurements for robust output-only modal identification: A proof-of-concept study

Determination of the model order is a challenging problem in system identification, especially in output-only or operational modal identification where some modes are weakly excited. While existing methods such as the stabilization diagram method (spectral information) are effective, they do not scale to high-dimensional data, which is usually needed for high-fidelity characterization of structural dynamics and has been made available in the emerging full-field measurement techniques using optical methods such as photogrammetry and laser vibrometers. In this proof-of-concept study we present a new non-parametric, data-driven approach for robust output-only identification of high-spatial-dimensional modal parameters of basic structures by efficiently processing and interactively exploiting the full-field measurement (i.e., very dense spatial measurement points). Specifically, we first over-estimate the system model once, producing a pool of candidate modes associated with their modal frequencies and full-field, high-spatial-dimensional mode shapes. This is accomplished by a data-driven method termed affinity propagation clustering (APC), where the active clusters, which are the active modes in our formulations, emerge from the "message-passing" procedure and does not require a pre-determination of the cluster number (mode or model order). Next, rather than using the spectral information to distinguish the physical and spurious modes in the stabilization diagram method, we exploit and visualize the spatial, full-field mode shape associated with each candidate mode to do so. We conduct extensive experiments on basic structural models with comparisons to a few existing methods. The results indicate that the new method is computationally efficient for identifying high-spatial-dimensional modal parameters, and robust to identify weak modes by exploiting the full-field measurement. We also discuss its applicability and limitations for structures with complex geometry (shapes).

42 ENGINEERING↗

DOE OSTI2020

Combining Chemistry, Material Science, Inspiration from nature, and Serendipity to Develop Stimuli-responsive Polymeric Materials

Neither of us can remember people talking about stimuli-responsive polymers when we were students. Even though this was still in the last century, it was almost 70 years after Staudinger's seminal paper "uber Polymerisation"![1] By the time we entered graduate school in the early 1990 s, the first papers on polymer light emitting diodes appeared, while research on electrically conducting, nonlinear optical, and other "functional" polymers was already in full swing. Looking back, there were some stimuli-responsive materials that were around at the time, but it took the better part of the last 30 years until the field had developed into what we think is one of the most vibrant areas of polymer science. Before the potential usefulness of this class of materials was recognized, researchers were focused on developing polymeric materials that would not respond to external influences, and in fact maintain (in particular) their mechanical properties in a wide range of environments. This has led to the development of many environmentally robust polymers, which have come to impact basically every aspect of our daily life. Ironically, this long-sought stability now comes back to haunt us in the form of plastic pollution, but this is another story. The concept of materials that adapt their properties in response to changing environmental conditions might appear like a complete reversal with respect to the original goals of creating stable materials. However, eventually a) it was recognized that materials that respond to a specific stimulus in a predictable and useful manner would significantly broaden the potential usefulness of polymers, and b) the field of polymer science had developed to the point where the rational design, preparation, and characterization of such materials became possible. The expression 'stimuli-responsive polymer' had been first used in the 1980's, however its use really only gained popularity a few decades later. In the early days, terms such as environmentally-sensitive or environmentally-responsive polymers, stimuli-reversible or stimuli-sensitive polymers, or polymers with phase transitions have also been used.

Rowan, Stuart J.↗

DOE OSTI2022

Engineering Nanostructured Interfaces of Hexagonal Boron Nitride-Based Materials for Enhanced Catalysis

Hexagonal boron nitrides (h-BNs) are attractive two-dimensional (2D) nanomaterials that consist of alternating B and N atoms and layered honeycomb-like structures similar to graphene. They have exhibited unique properties and promising application potentials in the field of energy storage and transformation. Recent advances in utilizing h-BN as a metal-free catalyst in the oxidative dehydrogenation of propane have triggered broad interests in exploring h-BN in catalysis. However, h-BN-based materials as robust nanocatalysts in heterogeneous catalysis are still underexplored because of the limited methodologies capable of affording h-BN with controllable crystallinity, abundant porosity, high purity, and defect engineering, which played important roles in tuning their catalytic performance. Here, in this account, our recent progress in addressing the above issues will be highlighted, including the synthesis of high-quality h-BN-based nanomaterials via both bottom-up and top-down pathways and their catalytic utilization as metal-free catalysts or as supports to tune the interfacial electronic properties on the metal nanoparticles (NPs). First, we will focus on the large-scale fabrication of h-BN nanosheets (h-BNNSs) with high crystallinity, improved surface area, satisfactory purity, and tunable defects. h-BN derived from the traditional approaches using boron trioxide and urea as the starting materials generally contains carbon/oxygen impurities and has low crystallinity. Several new strategies were developed to address the issues. Using bulk h-BN as the precursor via gas exfoliation in liquid nitrogen, single- or few-layered h-BNNS with abundant defects could be generated. Amorphous h-BN precursors could be converted to h-BN nanosheets with high crystallinity assisted by a magnesium metallic flux via a successive dissolution/precipitation/crystallization procedure. The as-fabricated h-BNNS featured high crystallinity and purity as well as abundant porosity. An ionothermal metathesis procedure was developed using inorganic molten salts (NaNH 2 and NaBH 4 ) as the precursors. The h-BN scaffolds could be produced on a large scale with high yield, and the as-afforded materials possessed high purity and crystallinity. Second, utilization of the as-prepared h-BN library as metal-free catalysts in dehydrogenation and hydrogenation reactions will be summarized, in which they exhibited enhanced catalytic activity over the counterparts from the previous synthesis method. Third, the interface modulation between metal NPs with the as-prepared defects’ abundant h-BN support will be highlighted. The h-BN-based strong metal–support interaction (SMSI) nanocatalysts were constructed without involving reducible metal oxides via the ionothermal procedure we developed by deploying specific inorganic metal salts, acting as robust nanocatalysts in CO oxidation. Under conditions simulated for practical exhaust systems, promising catalytic efficiency together with high thermal stability and sintering resistance was achieved. Across all of these examples, unique insights into structures, defects, and interfaces that emerge from in-depth characterization through microscopy, spectroscopy, and diffraction will be highlighted.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Tuning Thermal Stability through Dopant Size in Chemically Doped DPP–Thiophene Polymers

Molecular doping of conjugated polymers (CPs) is a key strategy for improving the performance of organic electronics devices, particularly thermoelectrics. Doped donor–acceptor (D–A) conjugated polymers, characterized by a tunable energy gap between the Fermi level and the transport band, show great promise in achieving high electrical conductivity (σ) while preserving a favorable Seebeck coefficient (S). Despite the promising performance enhancement of chemically doped D–A polymers, their thermal stability remains largely underexplored, a crucial consideration for the long-term operation of organic thermoelectric devices. In this study, we investigated the dopant size-dependent thermal stability of a diketopyrrolopyrrole-thiophene (DPP-T) D–A copolymer, utilizing two p-dopants: 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F 4 TCNQ) and Mo(tfd-CO 2 Me) 3 . Temperature-dependent UV–vis–NIR spectroscopy revealed that DPP-T/F 4 TCNQ is more prone to dedoping under a high temperature thermal stress than DPP-T/Mo(tfd-CO 2 Me) 3 . Although the F 4 TCNQ doped polymer shows higher initial in-plane conductivity than its Mo(tfd-CO 2 Me) 3 counterpart, it undergoes a conductivity loss of more than an order of magnitude after annealing at 120 °C for 30 min. In contrast, the in-plane conductivity of DPP-T/Mo(tfd-CO 2 Me) 3 remains stable under the same thermal conditions. Thermogravimetric analysis ruled out dopant sublimation as a primary contributor to dedoping, leading us to attribute the conductivity loss in F 4 TCNQ-doped DPP-T to dopant phase separation and migration. This observation was further confirmed by X-ray scattering studies and nanoscale infrared microscopy and spectroscopy studies. This work could provide further insights into the thermal stability of doped conjugated polymers and suggests that incorporating bulkier dopants is an effective strategy to enhance the thermal robustness of doped DPP-type systems.

Conjugated polymers↗

DOE OSTI2020

Order-disorder versus displacive transitions in Jahn-Teller active layered materials

Large anharmonic vibrations often play a crucial role in dynamically stabilizing crystalline phases whose structures are unstable at low temperature. Although the average structure of such phases can be measured through diffraction experiments, their local structure remains a challenge to characterize and understand. Dynamically stabilized phases are often classified as order/disorder or displacive based on the qualitative nature of their local structure. A robust understanding of how chemistry determines this distinction in behavior, however, is lacking. This article presents a parametric study of an anharmonic vibrational model that describes the transition from a cooperative to a noncooperative Jahn-Teller distortion in layered oxides—a class of materials widely used in Li-ion and Na-ion batteries. The results illustrate how the shape of the energy landscape determines the extent to which the high-temperature phase has order/disorder vs displacive character. In this work, we find that the nature of the high-temperature phase is determined by a competition between the strength of the elastic coupling between Jahn-Teller distortions at nearby sites and the energy scale driving the Jahn-Teller distortion. A comparison of the model to energy landscapes calculated with density-functional theory suggests that the high-temperature phases of the Jahn-Teller active layered compounds LiNiO 2 , NaNiO 2 , LiMnO 2 , and NaMnO 2 exhibit order/disorder character.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Implementation of Advanced Grid Support Functionalities by Smart Operation of Residential Loads with low Cost Converter Interface

This paper investigates a grid-supportive load concept for small-scale residential appliances, focusing on a residential refrigerator. Power consumption is adjusted based on grid conditions to achieve IEEE-1547 grid support functions. Two key aspects are presented: a low-cost refrigerator converter with Lyapunov energy function-based local controllers for speed control, and the impact on a standard microgrid system, demonstrating advanced grid support from the load side. This method enhances grid resilience and reliability and can be extended to other residential loads. The study contributes to efficient and robust grid-supportive load management systems, showing promising performance. This approach has the potential to improve overall grid stability and can be adapted for various types of residential appliances. The modeling and simulations in MATLAB/Simulink and PLECS confirm the feasibility and effectiveness of the proposed solution. Future work will explore real-world implementation and scalability of this concept for broader applications.

grid supportive loads (GSL)↗

DOE OSTI2024

Durable and High-Performance SOECs Based on Proton Conductors for Hydrogen Production

Proton-conducting solid oxide electrolysis cells (P-SOECs) are a promising technology for cost-effective and efficient production of green hydrogen. Breakthroughs in materials development, optimization of cell structure, and achievement of high performance and durability are essential to significantly increase the commercial competitiveness of these technologies. The main objective of this project is to gain scientific knowledge for the rational design, fabrication, and demonstration of a robust, highly efficient, and low-cost SOEC technology based on a proton-conducting electrolyte membrane for hydrogen production. We focused on better understanding the degradation mechanisms of proton-conducting electrolytes, air electrodes, and catalyst materials under electrolysis mode to develop an effective strategy for rationalizing new materials that are vital for enhancing cell performance and durability. The scope includes enhancing the performance and durability of the electrolyte and electrode materials under realistic operating conditions, developing highly active and robust catalysts to minimize electrode losses while improving tolerance to contaminant poisoning, revealing the mechanism of enhanced activity and stability of the catalyst, and understanding the underlying degradation mechanisms. In addition, various characterization techniques were employed to gain a fundamental understanding of the materials’ behavior and their impact on cell performance, providing vital information to guide materials discovery and cell design. After defect chemistry engineering, the optimized donor and acceptor co-doped electrolytes BaMo/W 0.03 Ce 0.71 Yb 0.26 O 3-δ (BM/W03) showed substantially improved chemical stability against high concentrations of CO 2 and H 2 O compared to the state-of-the-art electrolyte (BaZr 0.1 Ce 0.7 Y 0.1 Yb 0.1 O 3-δ , BZCYYb1711) while maintaining comparable ionic conductivity and ionic transference number. To bypass the inherent trade-off between conductivity and chemical stability, we fabricated a bi-layer electrolyte composed of BZCYYb1711 coated with a highly-stable thin layer of BaHf 0.83 Yb 0.17 O 3-δ (BHYb). This bi-layer electrolyte displayed excellent chemical stability against high concentration CO 2 ; there was no detectable formation of BaCO 3 after exposure to 97% CO 2 (with 3% H 2 O) at 500 °C for 1000 hours and the rate of degradation in resistance was about 0.4% per 1,000 hours (kh). In contrast, the same BZCYYb1711 electrolyte without a BHYb coating degraded significantly under the same testing conditions; the degradation rate was increased to 5.1%/kh. In addition, a triple conducting air electrode Ba 0.9 Pr 0.1 Hf 0.1 Y0.1Co 0.8 O 3-δ (BPHYC) was developed by heavily doping transition metal ions into a proton-conducting material. This air electrode material, composed of 3 distinct phases, exhibits superior electrocatalytic activity due to the synergistic effect from the three component phases. Moreover, an active and durable catalyst, La 2 Ni 0.5 Fe 0.5 O 4+δ (LNF), was developed, showing excellent catalytic activity and contaminant tolerance, with a degradation rate of only 0.49%/kh when exposed to high concentrations of steam and Cr. Finally, single cells were constructed from the best electrolytes, electrodes, and catalyst coatings developed in this project. These cells demonstrated superior high current density at a given cell voltage, high roundtrip efficiency, and remarkable durability (up to 1000 hours of operation).

08 HYDROGEN↗

NASA NTRS1981

An asymptotically stable damping enhancement controller for large space structures

A secondary controller which uses a number of Annular Momentum Control Devices (AMCD's) for enhancement of structural damping in large flexible space structures is investigated. The closed-loop secondary controller is shown to be equivalent to a certain closed-loop optimal linear regulator, and the necessary and sufficient conditions for asymptotic stability are obtained. Sufficient conditions for asymptotic stability are also obtained which are much less restrictive than those obtained in an earlier paper. Design of a robust stable primary controller is also discussed.

Joshi, S. M.↗

NASA NTRS1989

Periodic-disturbance accommodating control of the Space Station for asymptotic momentum management

Periodic-disturbance accommodating control is investigated for asymptotic momentum management of control moment gyros used as primary actuating devices for the Space Station. The proposed controller utilizes the concepts of quaternion feedback control and periodic-disturbance accommodation to achieve oscillations about the constant torque equilibrium attitude, while minimizing the control effort required. Three-axis coupled equations of motion, written in terms of quaternions, are derived for roll/yaw controller design and stability analysis. The quaternion feedback controller designed using the linear-quadratic regulator synthesis technique is shown to be robust for a wide range of pitch angles. It is also shown that the proposed controller tunes the open-loop unstable vehicle to a stable oscillatory motion which minimizes the control effort needed for steady-state operations.

Warren, Wayne↗

NASA NTRS1989

Periodic-disturbance accommodating control of the space station for asymptotic momentum management

Warren, Wayne↗

NASA NTRS1992

The 32nd CDC: System identification using interval dynamic models

Motivated by the recent explosive development of results in the area of parametric robust control, a new technique to identify a family of uncertain systems is identified. The new technique takes the frequency domain input and output data obtained from experimental test signals and produces an 'interval transfer function' that contains the complete frequency domain behavior with respect to the test signals. This interval transfer function is one of the key concepts in the parametric robust control approach and identification with such an interval model allows one to predict the worst case performance and stability margins using recent results on interval systems. The algorithm is illustrated by applying it to an 18 bay Mini-Mast truss structure.

Keel, L. H.↗

NASA NTRS2018

Progress and Plans for a US Laser System for the LISA Mission

NASA Goddard Space Flight Center is developing a master oscillator power amplifier (MOPA) laser transmitter for the ESA-led Laser Interferometer Space Antenna (LISA) mission. Taking advantage of our space laser experience and the emerging telecom laser technology, we are developing a full laser system for the LISA mission. Our research effort has included both master oscillator (MO) and power amplifier (PA) developments, and their environmental testing and reliability for space flight. Our current baseline for the MO is a low-mass, compact micro NPRO (m-NPRO) laser. The amplifier uses a robust mechanical design based on fiber components. We have performed laser system noise tests by amplitude- and frequency-stabilizing the PA output. We will describe our progress and plans to demonstrate a TRL 6 laser system, which is an essential step toward qualifying lasers for space applications, by 2021.

lasers↗

NASA NTRS2018

Progress and Plans for a US Laser System for the LISA Mission

NASA Goddard Space Flight Center is developing a master oscillator power amplifier (MOPA) laser transmitter for the ESA-led Laser Interferometer Space Antenna (LISA) mission. Taking advantage of our space laser experience and the emerging telecom laser technology, we are developing a full laser system for the LISA mission. Our research effort has included both master oscillator (MO) and power amplifier (PA) developments, and their environmental testing and reliability for space flight. Our current baseline for the MO is a low-mass, compact micro non-planar ring oscillator (m- NPRO) laser. The amplifier uses a robust mechanical design based on fiber components. We have performed laser system noise tests by amplitude- and frequency-stabilizing the PA output. We will describe our progress and plans to demonstrate a TRL 6 laser system, which is an essential step toward qualifying lasers for space applications, by 2021.

Numata, Kenji↗

NASA NTRS2017

Coronagraph Design Optimization for Segmented Aperture Telescopes

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-o between planet light throughput and di racted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) di racted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the "Auxiliary Field Optimization" (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, speci cally ctitious "auxiliary" electric elds which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a "dark hole" region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured o -axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.

Redding, Dave↗