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DOE OSTI2025

Fabrication of the HFVMTF Double-Bath Cryostat

The High Field Vertical Magnet Test Facility (HFVMTF) at Fermilab is designed to test superconducting magnets up to 20 tons and 1.3 meters in diameter. Central to the facility is a double-bath superfluid helium cryostat reaching 1.8 K at 1.2 bar. Integrated with a 15 T superconducting dipole from LBNL, HFVMTF supports HTS cable testing for fusion applications. This paper presents the design and fabrication of the cryostat, with a focus on two complex components: the 2 K heat exchanger and the lambda plate. The heat exchanger thermally links sub-atmospheric and pressurized helium baths. The 1.4-meter lambda plate provides thermal isolation and structural support for over 20 tons under 1.3 bar pressure differential. Finite Element Analysis validated the vessel’s integrity under maximum load conditions.

Bruce, Romain [Fermilab] (ORCID:0000000234200612)↗

DOE OSTI2023

Bison Verification and Validation Activities for TRISO

Numerical modeling and simulation (M&S) tools play a key role in the research, development, and overall safety assessments of next-generation nuclear energy systems. One such tool, Bison, is a nuclear fuel performance code that is applicable to many fuel forms (e.g., light-water reactor fuel, oxide and metallic fuel for fast reactors, tri-structural isotropic (TRISO) fuel, and plate fuel), and it uses the finite element method to model the thermo- mechanical response of nuclear fuels. One fuel form widely utilized in Generation-IV high-temperature gas-cooled and fluoride- salt-cooled nuclear reactor concepts is TRISO fuel. Recently, Bison’s capabilities were significantly expanded to enable it to model the performance of TRISO particles and compacts. It is important that Bison’s computational results be reliable and predictive, since this code is used to inform high-consequence decisions. The various processes developed to address this issue generally entail two fundamental steps: verification and validation (V&V). Verification ensures that the code functions correctly and is reliable. Code/solution verification, code benchmark, and software quality assurance exercises are examples of verification activities. On the other hand, validation is the process of assessing a code’s capability to accurately model physical problems. Comparisons between code results and experiments quantify the validation level. Application of V&V procedures is crucial to the development of computational tools that are free of coding mistakes and can accurately represent reality. The current study presents an overview of Bison V&V activities relevant to the TRISO fuel concept, which include code/solution verification exercises, CRP-6 Benchmark—a Coordinated Research Program through the International Atomic Energy Agency (IAEA)—exercises, and validation exercises with the Advanced Gas Reactor (AGR)- 1/2/3/4 experiment series.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Fabrication of the HFVMTF Double-Bath Cryostat

Bruce, R. [Fermilab] (ORCID:0000000234200612)↗

DOE OSTI2025

Initial Engineering Framework for Species Tracking in MSRs Involving Fuel Salt and Structures

This report implements a high-fidelity multiphysics modeling framework using the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program tools to track leaching and plating of materials between the fuel salt and structures in Molten Salt Reactors (MSRs). Specifically, this framework is demonstrated in modeling various processes within MSRs including hot and cold leg corrosion, redox potential driven corrosion, colloid precipitation and deposition, and noble metal plating and decay heat modeling. The model integrates neutronics, thermal-hydraulics, depletion, and thermochemistry to simulate the evolving chemical behavior of the fuel salt in interactions with structural materials. Initial findings suggest that hot-cold leg corrosion in MSR systems may become significant if the redox potential of the fuel salt is not sufficiently controlled. Additionally, the impact of noble metal decay heat deposition in large power reactors is explored. The resulting engineering framework for species tracking will be applied in the future toward specific validation work with ongoing experimental efforts focusing on both chloride and fluoride salt loop experiments with in-situ corrosion and redox control instrumentation.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Effects of charging rates on LiNi 0.6 Mn 0.2 Co 0.2 O 2 (NMC622)/graphite Li-ion cells

Enabling fast charging capability of lithium-ion battery is of great importance to widespread adoption of electric vehicles. Increasing the charging rates from state-of-the-art 2C (30 min) to 6C (10 min) requires deep understanding on the cell aging mechanism. Here, 400 mAh pouch cells are cycled at 1C, 4C and 6C charging rates with 1C discharging rate. Capacity fading, cathode structural changes, Li inventory loss, electrolyte composition changes and Li plating on graphite electrodes are thoroughly studied by various characterization techniques. The rapid capacity fading in cells at 6C charging rate is mainly due to Li inventory loss from cathode structure and metallic Li plating on graphite electrode at higher charging rate. Post-mortem analysis also revealed changes in electrolyte such as increased salt molarity and transesterification during fast charging.

25 ENERGY STORAGE↗

DOE OSTI2026

Proximity Ferroelectricity in Compositionally Graded Structures

Proximity ferroelectricity is a novel paradigm for inducing ferroelectricity in a non-ferroelectric polar material, such as AlN or ZnO that are typically unswitchable with an external field below their dielectric breakdown field. When placed in direct contact with a thin switchable ferroelectric layer (such as Al 1-x Sc x N or Zn 1-x Mg x O), they become a practically switchable ferroelectric. Using the thermodynamic Landau-Ginzburg-Devonshire theory, in this work, we perform the finite element modeling of the polarization switching in the compositionally graded AlN-Al 1-x Sc x N, ZnO-Zn 1-x Mg x O, and MgO-Zn 1-x Mg x O structures sandwiched in both a parallel-plate capacitor geometry as well as in a sharp probe-planar electrode geometry. We reveal that the compositionally graded structure allows the simultaneous switching of spontaneous polarization in the whole system by a coercive field significantly lower than the electric breakdown field of unswitchable polar materials. The physical mechanism is the depolarization electric field determined by the gradient of chemical composition “x”. The field lowers the steepness of the switching barrier in the otherwise unswitchable parts of the compositionally graded AlN-Al 1-x Sc x N and ZnO-Zn 1-x Mg x O structures. In the MgO-like regions of the compositionally graded MgO-Zn 1-x Mg x O structure, a shallow double-well free energy potential emerges. Proximity ferroelectric switching of the compositionally graded structures placed in the probe-electrode geometry occurs due to nanodomain formation under the tip. We predict that a gradient of chemical composition “x” significantly lowers effective coercive fields of the compositionally graded AlN-Al 1-x Sc x N and ZnO-Zn 1-x Mg x O structures compared to the coercive fields of the corresponding multilayers with a uniform chemical composition in each layer. A tip-induced switching further lowers the coercive field, enabling control of ferroelectric domains in otherwise unswitchable compositionally graded structures, which can provide nanoscale domain control for memory, actuation, sensing, and optical applications.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Complementary Measurements of Residual Stresses Before and After Base Plate Removal in an Intricate Additively-Manufactured Stainless-Steel Valve Housing

Residual stress measurements using neutron diffraction and the contour method were performed on a valve housing made from 316 L stainless steel powder with intricate three-dimensional internal features using laser powder-bed fusion additive manufacturing. The measurements captured the evolution of the residual stress fields from a state where the valve housing was attached to the base plate to a state where the housing was cut free from the base plate. Making use of this cut, thus making it a non-destructive measurement in this application, the contour method mapped the residual stress component normal to the cut plane (this stress field is completely relieved by cutting) over the whole cut plane, as well as the change in all stresses in the entire housing due to the cut. The non-destructive nature of the neutron diffraction measurements enabled measurements of residual stress at various points in the build prior to cutting and again after cutting. Good agreement was observed between the two measurement techniques, which showed large, tensile build-direction residual stresses in the outer regions of the housing. The contour results showed large changes in multiple stress components upon removal of the build from the base plate in two distinct regions: near the plane where the build was cut free from the base plate and near the internal features that act as stress concentrators. These observations should be useful in understanding the driving mechanisms for builds cracking near the base plate and to identify regions of concern for structural integrity. Neutron diffraction measurements were also used to show the shear stresses near the base plate were significantly lower than normal stresses, an important assumption for the contour method because of the asymmetric cut.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Study of detached plasma profile in the divertor simulation experimental module of tandem mirror GAMMA 10/PDX

A divertor simulation experimental module (D-module) in the tandem mirror GAMMA 10/PDX was used for the study of plasma detachment. In previous studies, it was difficult to measure far-upstream plasma parameters in the D-module, and only electrostatic probes on the target plate were used to perform electron temperature and density measurements. Furthermore, to study the detached plasma structure, a Thomson scattering (TS) system and a microwave interferometer system have been installed to measure the inside plasma parameters of the D-module, and a movable electrostatic probe has been placed at the inlet of the D-module to measure the inlet plasma density and temperature. The TS system in the central cell observed the electron temperature and density of the core plasma simultaneously. These measurements revealed the entire density and temperature structure from the core plasma to the divertor plate. The line average electron density measured by the microwave interferometer showed a rollover behavior during detachment. The results indicated that the ionization region was located around the center of the D-module, and it appears to move upstream along the axis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Operating High-Energy Lithium-Metal Pouch Cells with Reduced Stack Pressure Through a Rational Lithium-Host Design

Transitioning from a liquid electrolyte to an inorganic solid electrolyte offers a potential pathway to enable highly reversible lithium-metal anodes. However, the solid-electrolyte-protected lithium-metal anode suffers from poor interfacial ionic contacts and requires an impractically high stack pressure (>1.0 MPa) to maintain the interfacial contacts. It is demonstrated here that combining a hollow silver/carbon fiber scaffold and an inorganic/organic composite electrolyte enables a highly reversible lithium-metal anode. Since the high surface area of the electrode provides intimate contact and the hollow structure of the electrode relieves the lithium plating-induced stress, the electrode/electrolyte interface remains stable during cycling even under mild stack pressure. This unconventional structural design is validated in practical pouch cells assembled with the 3D lithium host containing a onefold excess of lithium and a high-nickel cathode. At a mild stack pressure of 320 kPa, the pouch cell displays 83% capacity retention for 200 cycles. This work illustrates that combining a hollow electrode architecture and a robust solid electrolyte offers a practical pathway toward rechargeable lithium-metal anodes.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Influence of processing on secondary phase formation and microstructural evolution at U-10Mo alloy and Zr interlayer interfaces

Thermo-mechanical processing of uranium-10 wt. % molybdenum (U-10Mo) fuel plates leads to microstructure changes at the U-10Mo/Zr interfaces. Secondary phases formed at this interface are particularly important to interfacial bond strength, process optimization, and maintaining structural integrity of the U-10Mo fuel plates during irradiation. In this work, we determined the phases and phase transformation products occurring at the interface of the U-10Mo fuel and Zr interlayer when the fuel plate is subjected to short and long hot isostatic pressure times. Interfacial morphology, structure and composition of phases formed, and relative hardness across the U-10Mo/Zr interfaces were studied using a multi-length scale, multi-modal characterization approach involving electron microscopy, atom probe tomography, and atomic force microscopy. Here, results highlight that the extent of phase transformations, secondary phase formation, and hardness variability across interfaces can be controlled by modifying processing parameters. Phase diagram construction and thermodynamic calculations were performed using the Thermocalc software to identify expected phases formed at interfaces during the maximum hold temperature of 560 °C experienced during HIP.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Dendrite-free Al recycling via electrodeposition using ionic liquid electrolytes: The effects of deposition temperature and cathode surface roughness

In this report, the electrodeposition of Al from aluminum scrap alloys (A2020) on copper cathode substrates with varied surface roughness under different deposition temperatures was studied using low-temperature AlCl 3 -1-butyl-3-methyl-imidazolium chloride (BMIC) ionic liquid electrolytes. The bulk electrodeposition of Al was carried out under a voltage of 1.5 V at a stirring rate of 120 rpm using a fixed ionic liquid electrolyte concentration (molar ratio AlCl 3 : BMIC = 2:1). The effects of deposition temperature (range from 80 °C to 140 °C) and surface roughness of Cu cathode substrates (polished by 320, 600, 800, 1200 grits SiC sandpapers and mirror polishing process) on the morphology of deposited Al, current density, current efficiency and energy consumption, were investigated. The Al deposits were characterized using scanning electron microscopy (SEM) with energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), profilometer, and electrochemical measurements for current density, current efficiency, and energy consumption. It is demonstrated that the deposition temperature and surface roughness of Cu electrodes play a critical role in the nucleation and growth of Al deposits. Higher deposition temperature promotes the diffusion and/or migration of Al 2 Cl 7 - ions and then enhances the current density and efficiency during the electrodeposition of Al. Smoother surface of Cu electrodes is preferred for the formation of dendrite-free Al deposits. Typically, on the mirror polished Cu electrode, no Al dendrite structure was observed, and only plate-like Al deposits were formed at the deposition temperature of 100 °C. Pure metallic Al was successfully deposited on Cu electrodes in AlCl 3 + BMIC ionic liquid electrolytes for all experiments with a current efficiency range from 72% to 99% and energy consumption of 4.6–6.3 kW h/kg Al.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Highly Ordered Hierarchical Anodes for Extreme Fast Charging Batteries (Final Report)

The goal of this project is to enable extreme fast charging (XFC) of Li-ion batteries, which was accomplished through a combination of 1) rational design and manufacturing of hierarchically structured anode architectures; 2) blending graphite/hard carbon into a bulk hybrid anode; 3) engineering artificial solid-electrolyte interphase (SEI) coatings with reduced interphase impedance; 4) computational modeling of coupled transport, kinetic, and electrochemical phenomena; and 5) improved fundamental understanding of lithium plating through operando analysis. This work integrated structural, compositional, and surface modification of graphite anodes, multi-physics modeling of ion transport, electrochemical activity, and heat transfer, advanced strategies to detect Li plating, and semi-automated roll-to-roll cell assembly. The unique facilities at the University of Michigan (UM) and Sandia National Laboratories (SNL) were leveraged to manufacture, prototype, and characterize commercially relevant >2Ah and >180 Wh/kg cells with a target of <20% capacity fade over 500 XFC cycles.

25 ENERGY STORAGE↗

DOE OSTI2024

Impacts of Irradiation Structural Behavior on Thermal Hydraulics Safety Analysis to Support MURR LEU Conversion

The University of Missouri Research Reactor (MURR) located in Columbia, Missouri is one of six U.S. High Performance Research Reactors (USHPRR), including one critical facility, that is actively collaborating with U. S. Department of Energy (DOE) National Nuclear Security Administration (NNSA) Material Management and Minimization (M3) Office of Reactor Conversion and Uranium Supply to convert from the use of highly enriched uranium (HEU; ≥20 wt% U-235) to low-enriched uranium (LEU; <20 wt% U-235) fuel. A new type of very high-density LEU fuel based on an alloy of uranium and 10 wt% molybdenum (U-10Mo) is expected to allow the conversion to LEU of MURR, as well as four other USHPRR. MURR has been working with the Reactor Conversion Pillar at Argonne to perform fuel element design and fuel cycle performance analyses, steady-state thermal hydraulics safety analysis, and accident safety analyses in preparation for the conversion of MURR and to support a preliminary safety analysis report for conversion to LEU fuels. Subsequent analyses have also been performed, including transition cycles where all-fresh LEU fuel elements are introduced upon conversion and progressing through reactor operations the core is brought to equilibrium. Thermal hydraulics safety analyses performed as part of the above have employed an assumption on channel gap reduction due to burnup-related phenomena including fuel swelling, irradiation creep, and oxide layer buildup. Recently, a series of structural analyses have been performed on the MURR LEU fuel plates and an element due to significant differences between the plate and element designs of the MURR HEU and LEU fuels. In addition, NUREG-1537 indicates that structural phenomena are to be evaluated. Two separate types of structural analyses were performed for the MURR LEU fuel element: fluid-structure interaction (FSI) and irradiation thermo-mechanical. The FSI analysis evaluated the effects of hydraulic forces on the MURR LEU fuel element to quantify the flow-induced plate deflection, and a minimal impact to the channel gap thickness was predicted under prototypic and bounding conditions. The irradiation thermo-mechanical analysis evaluated the effects of fuel swelling, irradiation creep, and thermal expansion for the MURR LEU plates and the element for prototypic thermal and irradiation conditions based on a high-fidelity approach multiphysics approach. Overall, this thermo-mechanical analysis predicts smaller gap thickness changes in previously limiting regions. Larger changes are predicted in the middle of channels, and for end channels where power density is not typically a maximum. An additional thermo-mechanical analysis was performed for the outermost HEU fuel plate, which showed a similar magnitude of deflection as the outermost LEU plate. Due to substantial differences between the channel gap reductions assumed for the previous safety analyses and those predicted by the irradiation thermo-mechanical analysis, a need to evaluate their impact on the thermal hydraulics safety analyses arose. This report presents the results from the steady-state safety analyses for normal operation as well as the accident analyses for the two most limiting accident scenarios.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Terahertz Chiral Metamaterials Enabling Broadband Polarization Conversion Using Polarization Guiding Effect

Polarization control plays a vital role in terahertz (THz) photonics, enabling a wide range of applications from imaging and spectroscopy to sensing and wireless communication. However, conventional polarization control methods at THz frequencies are limited by narrow operational bandwidths and excessive absorption losses. In this work, we present a broadband THz polarization control based on the polarization guiding effect. We design and fabricate a THz polarization rotator capable of rotating incident linear polarization by 90°. The device consists of 24 twistingly stacked silicon–air metagrating layers that introduce a large degree of form birefringence, with each metagrating layer being 280 µm thick and sequentially twisted by 3.75°. Numerical simulations using the Berreman 4 × 4 method predict broadband operation of the device. Experimental validation using THz time-domain spectroscopy confirms efficient and broadband 90° polarization rotation from 0.2 to 1.25 THz. Based on this concept, we further propose THz Q-plates for the generation of broadband structured vector beams with radial and azimuthal polarization states. This work offers a scalable, material-agnostic platform for advanced THz polarization manipulation and vector beam engineering, opening new pathways for next-generation THz photonic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Micro-tensile testing of neutron-irradiated Al/Zr and Zr/U-Mo diffusion bonds

This study focuses on micro-tensile testing of neutron-irradiated Al/Zr and Zr/U-Mo diffusion bonds, which are integral to the structure and performance of nuclear fuel plates used in the fuel being developed for U.S. high-power research reactors. During fabrication, two distinct diffusion bonds occur—one at the Zr/U-10Mo interface via roll bonding, and the Zr/Al interface via hot isostatic pressing at 833 K. This work utilizes micro-tensile testing specimens approximately 7 × 7 × 18 μm 3 , which are sufficiently large to encompass the identified diffusion zones to evaluate the failure strength and identify the failure location. For the Zr/Al interface, all failures occurred in the bulk aluminum. The average yield strength, ultimate strength, and strain at failure for the two parent samples were: 125 ± 10 MPa, 139 ± 24 MPa, 156 ± 21 MPa, 185 ± 14 MPa, 37.9 ± 5.6 %, and 29.7 ± 3.4 %, respectively. For specimens across the Zr/U-Mo interface, failures occurred either in the bulk Zr or U-Mo, with no failures observed in the diffusion region. For specimens that failed in the bulk Zr the failure strength and strain for the two parent samples were 570 MPa, 710 ± 131 MPa, and 43.3 %, 27.3 ± 6.6 % respectively. The specimens that failed in the bulk U-Mo had failure strengths and strains of 596 ± 32 MPa, 548 ± 124 MPa, and 2.2 ± 1.3 %, 1.5 ± 0.6 % respectively. In conclusion, these findings support the development of accurate thermo-mechanical models for irradiated fuel performance by identifying the mechanical limits and failure locations within the bonded regions.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Toward a Realistic Representation of Sucrose Transport in the Phloem of Plants

The significance of phloem hydrodynamics to plant mortality and survival, which impacts ecosystem-scale carbon and water cycling, is not in dispute. The phloem provides the conduits for products of photosynthesis to be transported to different parts of the plant for consumption or storage. The M$\ddot{u}$nch pressure flow hypothesis (PFH) is the leading framework to mathematically represent this transport. It assumes that osmosis provides the necessary pressure differences to drive water and sucrose within the phloem. Mathematical models utilizing the PFH approximate the phloem by a relatively rigid slender semi-permeable tube. However, the phloem consists of living cells that contract and expand in response to pressure fluctuations. The effect of membrane elasticity on osmotically driven sucrose front speed has rarely been considered and frames the scope here. Laboratory experiments were conducted to elucidate the elastic-to-plastic pressure-deformation relation in membranes and their effect on sucrose front speeds. It is demonstrated that membrane elasticity acts to retard the sucrose front speed. The retardation emerges because of two effects: (a) part of the osmotic pressure is diverted to perform mechanical work to expand the membrane instead of pressurizing water, and (b) expansion of the membrane reduces the sucrose concentration driving osmotic potential due to volume increases and concomitant dilution effects. Finally, these results offer a novel perspective about the much discussed presence of sieve plates throughout the phloem acting as structural expansion dampers.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Mechano-Electrochemical Interaction in Solid-State Lithium Batteries

A solid-state lithium (Li) battery primarily consists of Li metal anode, solid electrolyte separator, and cathode. The asymmetric volume changes, originating from ion transport and interfacial Li growth during plating, lead to significant stresses in the layered architecture. In this study, we develop a coupled mechanics-electrochemistry formalism for polymer electrolyte based solid-state batteries, in particular, focusing on the stress effect on electrochemical performance. By means of a coupling coefficient, it is found that stress-assisted ion transport in the electrolyte results in a delayed Sand’s time and increased critical current density of unstable electrodeposition, and consequently, alleviates the propensity of dendrite formation. Stress at the Li metal-electrolyte interface affects the electrochemical reaction kinetics, and the influences from the deviatoric stress and hydrostatic pressure vary with Li plating time. In addition, a low restraint stiffness to the layered structure could elastically buffer the volumetric changes and thus reduce the stress during Li plating. This fundamental study provides guidance for the design of solid-state batteries, aimed at stable electrodeposition and mechanical integrity.

25 ENERGY STORAGE↗

DOE OSTI2022

Magnetic cores with high reluctance differences in flux paths

Embodiment of the present invention includes a magnetic structure and a magnetic structure used in a direct current (DC) to DC energy converter. The magnetic structure has an E-core and a plate, with the plate positioned in contact or in near contact with the post surfaces of the E-core. The E-core has a base, a no-winding leg, a transformer leg, and an inductor leg. The no-winding leg, the transformer leg, and the inductor leg are perpendicular and magnetically in contact with the base. The plate is a flat slab with lateral dimensions generally larger than its thickness. The plate has a plate nose that overlaps a top no-winding leg surface of the no-winding leg with a no-winding gap area to form a no-winding gap with a no-winding gap reluctance. The plate also has a plate end that overlaps a top inductor leg surface of the inductor leg with an inductor gap area to form an inductor gap with an inductor gap reluctance. In some embodiments, e.g., where the duty cycle is less than 50 percent, the inductor gap reluctance will be designed to be less than the no-winding gap reluctance. In these cases, the majority of the magnetic flux that passes through the transformer leg will return through the inductor leg, instead of through the no-winding leg. The inductor and no-winding gap reluctances can he adjusted, so that the electromotive force applied to a charge passing through the inductor will partially cancel the electromotive force applied by the transformer secondary. The gap reluctance ratio can be defined, so that the difference in secondary and inductor electromotive forces is equal to the output voltage defined by an optimal no-ripple duty cycle. In this way no changing current is required through the inductor to create a dI/dt inductive voltage drop across the output inductor. Zero output current ripple is achieved.Various embodiments of the plate, plate shape, and no-winding leg are disclosed. These embodiments allow achieving a high ratio of no-winding gap reluctance to inductor gap reluctance, for practical, affordable magnetic material structures and aspect ratios. A high gap reluctance ratio enables zero output current ripple for the high transformer turns ratios that are needed to achieve high input to output voltage ratios. The embodiments therefore allow achieving low output current ripple for 48 V or higher input voltages, 1 V or lower output voltages, and high output currents.

Yao, Yuan↗