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

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Achieving high rate performance in hybrid pristine-recycled cathodes using model-informed electrode designs

Direct recycling lithium-ion battery cathodes, a process that retains the engineered oxide structures from end-of-life materials, presents a cost-effective and energy-efficient alternative to other battery recycling methods. However, while direct-recycled cathodes have demonstrated performance comparable to that of pristine materials at low cycling rates, their high-rate performance remains uncertain. Morphology changes in cathode particles, a main mode of degradation, directly impact rate performance by limiting surface kinetics and solid-phase diffusion. If direct recycling processes do not sufficiently restore pristine-like morphologies, the recycled materials may retain structural defects that hinder high-rate performance. The present work uses a physics-based pseudo-2D model to simulate hybrid electrodes with pristine and artificially “aged/recycled” NMC materials to investigate potential impacts of incorporating performance-limited aged cathode materials into cells. The study highlights how differences in transport and kinetic properties can influence rate capabilities in mixed electrodes — particularly in high-loading cells in high-demand applications. However, model results also reveal a possible mitigation strategy via dual-layer electrode architectures with lower-performing materials positioned near the current collector. Simulations of 4.0 mAh cm −2 cells cycled at 4C using a dual-layer architecture provided approximately 5%–30% more capacity in constant-current protocols compared to homogeneously blended electrode architectures with the same loadings and mixed-material compositions. These findings highlight the importance of strategic electrode design in minimizing potential performance losses and facilitating the integration of recycled materials into high-performance batteries, advancing sustainable and cost-effective battery manufacturing.

25 ENERGY STORAGE↗
DOE OSTI2022

A three-dimensional pore-scale model for redox flow battery electrode design analysis

A three-dimensional (3-D) pore-scale model has been developed to construct multiscale fibrous electrodes for redox flow batteries (RFB). New designs, such as biporous electrodes modify electrode structures by creating secondary pores on single carbon fiber to reduce internal battery resistance. Existing pore-scale models only resolve electrodes to the single carbon fiber scale and cannot incorporate recent multiscale electrode designs into numerical models. Our new model aims to bridge this gap and provide a tool to rapidly screen new electrode configurations. Two multiscale electrodes, laser-perforated and biporous electrodes, were investigated at varying operation conditions with the proposed 3-D pore-scale models. The laser-perforated electrode exhibits a reduced pressure drop, but follows the same permeability correlation compared to the corresponding pristine electrode. For the biporous electrode, the added specific surface area and faster reaction kinetics from the secondary pores are the most influential factors leading to improved battery efficiency. However, operating the biporous electrode in limiting current density conditions should be avoided due to the decreased mass transfer efficiency and a more significant voltage loss. Finally, we believe that our 3-D pore-scale model can accelerate the flow battery electrode design process and provide new insights into electrode geometry optimizations.

25 ENERGY STORAGE↗
DOE OSTI2018

Microstructure Characterization and Modeling for Improved Electrode Design

As part of DOE's Computer-Aided Engineering of Batteries Program, the National Renewable Energy Laboratory is developing detailed models capturing the influence of lithium-ion battery electrode design, recipe and processing on the electrode's microstructure and relating that microstructure to device-level performance. Given the difficulty in obtaining 3D microstructural images of the electrode's inert components, team member Purdue University developed an algorithm to computationally generate the so-called carbon-binder domain (CBD) for any given recipe. Mesoscale models explore the device-level impact of the CBD phase on multiple idealized and actual electrode geometries. With the inclusion of this CBD phase, microstructure models are used to predict the tortuosity of 14 different graphite and NMC electrode designs. Tortuosity predictions are shown in good agreement with experimental direct measurement and electrochemical rate studies.

25 ENERGY STORAGE↗
DOE OSTI2017

Microstructure Characterization and Modeling for Improved Electrode Design

This presentation describes research work led by NREL with team members from Argonne National Laboratory and Texas A&M University in microstructure analysis, modeling and validation under DOE's Computer-Aided Engineering of Batteries (CAEBAT) program. The goal of the project is to close the gaps between CAEBAT models and materials research by creating predictive models that can be used for electrode design.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2019

Microstructure Characterization and Modeling for Improved Electrode Design

This presentation summarizes fiscal year 2018-2019 work under U.S. Department of Energy's Computer-Aided Engineering of Batteries (CAEBAT) program to develop computational tools for improved electrode design and to provide deeper fundamental understanding of the physics that limit the performance and cause degradation in lithium-ion batteries. Successes include (1) development of an electrode microstructure characterization tool box to be published open source later in 2019, (2) development of a large deformation electrochemical model capturing the volume expansion and performance limits of electrodes utilizing silicon and (3) development of a solid mechanics damage model describing the fracture of polycrystalline nickel-manganese-cobalt cathode materials with cycling.

30 DIRECT ENERGY CONVERSION↗
DOE OSTI2016

Computer Aided Battery Engineering Consortium

A multi-national lab collaborative team was assembled that includes experts from academia and industry to enhance recently developed Computer-Aided Battery Engineering for Electric Drive Vehicles (CAEBAT)-II battery crush modeling tools and to develop microstructure models for electrode design - both computationally efficient. Task 1. The new Multi-Scale Multi-Domain model framework (GH-MSMD) provides 100x to 1,000x computation speed-up in battery electrochemical/thermal simulation while retaining modularity of particles and electrode-, cell-, and pack-level domains. The increased speed enables direct use of the full model in parameter identification. Task 2. Mechanical-electrochemical-thermal (MECT) models for mechanical abuse simulation were simultaneously coupled, enabling simultaneous modeling of electrochemical reactions during the short circuit, when necessary. The interactions between mechanical failure and battery cell performance were studied, and the flexibility of the model for various batteries structures and loading conditions was improved. Model validation is ongoing to compare with test data from Sandia National Laboratories. The ABDT tool was established in ANSYS. Task 3. Microstructural modeling was conducted to enhance next-generation electrode designs. This 3- year project will validate models for a variety of electrodes, complementing Advanced Battery Research programs. Prototype tools have been developed for electrochemical simulation and geometric reconstruction.

25 ENERGY STORAGE↗
DOE OSTI2017

Optimizing Discharge Capacity of Li-O 2 Batteries by Design of Air-Electrode Porous Structure: Multifidelity Modeling and Optimization

We develop a new mathematical framework to study the optimal design of air electrode microstructures for lithium-oxygen (Li-O2) batteries. It can eectively reduce the number of expensive experiments for testing dierent air-electrodes, thereby minimizing the cost in the design of Li-O2 batteries. The design parameters to characterize an air-electrode microstructure include the porosity, surface-to-volume ratio, and parameters associated with the pore-size distribution. A surrogate model (also known as response surface) for discharge capacity is rst constructed as a function of these design parameters. The surrogate model is accurate and easy to evaluate such that an optimization can be performed based on it. In particular, a Gaussian process regression method, co-kriging, is employed due to its accuracy and eciency in predicting high-dimensional responses from a combination of multidelity data. Specically, a small amount of data from high-delity simulations are combined with a large number of data obtained from computationally ecient low-delity simulations. The high-delity simulation is based on a multiscale modeling approach that couples the microscale (pore-scale) and macroscale (device-scale) models. Whereas, the low-delity simulation is based on an empirical macroscale model. The constructed response surface provides quantitative understanding and prediction about how air electrode microstructures aect the discharge performance of Li-O2 batteries. The succeeding sensitivity analysis via Sobol indices and optimization via genetic algorithm ultimately oer a reliable guidance on the optimal design of air electrode microstructures. The proposed mathematical framework can be generalized to investigate other new energy storage techniques and materials.

25 ENERGY STORAGE↗
DOE OSTI2022

Thick Electrode Design for Facile Electron and Ion Transport: Architectures, Advanced Characterization, and Modeling

The demand for lithium ion batteries continues to expand for powering applications such as portable electronics, grid-scale energy storage, and electric vehicles. As the application requirements advance, the innovation of lithium ion batteries toward higher energy density and power output is required. Along with the investigation of new materials, an important strategy for increasing battery energy content is to design electrodes with high areal loading to minimize the fraction of nonactive materials such as current collectors, separators, and packaging components, resulting in significant gains in energy content and the reduction of the system-level cost. However, the adoption of thick high areal loading electrodes has been impeded by sluggish charge transport and mechanical instability. With conventional slurry cast electrodes, battery function significantly deteriorates with increases in electrode thickness due to high cell polarization and the incomplete utilization of active materials. Thus, a consideration of approaches that facilitate an understanding and eventual adoption of high-loading electrodes is warranted to enable the deliberate advancement of next-generation batteries. Herein, this Account considers three aspects critical to the science and technology of thick high-loading electrodes. The first discussion covers recent approaches to the design and fabrication of high-loading electrodes. Ensuring electrical contact throughout the electrode is accomplished through the manipulation of conductive additives or using a conductive scaffold within the electrode. Ion transport can be facilitated through electrode design and fabrication approaches that deliberately control the electrode porosity and tortuosity. Second, advanced characterization methodologies are presented as the ability to determine the origins of transport limitations provide the insight needed to deliberately approach future designs. Spectroscopic and diffraction methods have been used to characterize the 2D and 3D pore structure and composition of the electrodes. Furthermore, operando methods that yield spatially and temporally resolved information regarding the progression of the electrochemical reaction are highlighted. The third aspect considered is the utilization of modeling. Physically based continuum models linked with the results of experimental characterization have been demonstrated and then allow the rapid simulation of a variety of deliberate electrode designs and their impacts on functional electrochemistry. Variables relevant to the designs can be tested by the model under a series of use conditions to identify those of most promise for a specific application. Finally, an outlook on future opportunities for high-loading battery electrode research is provided to inform and entice practitioners in the field to pursue these important directions of inquiry.

25 ENERGY STORAGE↗
DOE OSTI2020

Design Principles to Govern Electrode Fabrication for the Lithium Trivanadate Cathode

A full depth of discharge mathematical model for the lithium trivanadate cathode, considering lithiation of the layered α-phase, phase change, and lithiation of the rock-salt like β-phase at lower potentials, is developed. The coupled electrode-scale and crystal-scale model is fit to electrochemical data, and additionally validated with operando EDXRD. There is good agreement between the simulated and measured spatial variation of the volume fraction of the β-phase. This mathematical model is used to guide electrode fabrication, accounting for both ionic and electronic transport effects. Values of three design parameters—electrode thickness, porosity, and volume fraction of conductor—are identified, and the sensitivity of the energy density to these design parameters is quantified. The model is also used to investigate electrode design to create electrodes that deliver the maximum achievable energy density under the constraint that the α to β-phase transition is avoided, since phase change has been demonstrated to reduce cycle life. The energy density sacrificed to avoid phase change decreases at higher discharge rates, but the target values for electrode fabrication remain the same as those when optimizing the electrode for the full depth of discharge.

25 ENERGY STORAGE↗
DOE OSTI2020

3D microstructure design of lithium-ion battery electrodes assisted by X-ray nano-computed tomography and modelling

Driving range and fast charge capability of electric vehicles are heavily dependent on the 3D microstructure of lithium-ion batteries (LiBs) and substantial fundamental research is required to optimise electrode design for specific operating conditions. Here we have developed a full microstructure-resolved 3D model using a novel X-ray nano-computed tomography (CT) dual-scan superimposition technique that captures features of the carbon-binder domain. This elucidates how LiB performance is markedly affected by microstructural heterogeneities, particularly under high rate conditions. The elongated shape and wide size distribution of the active particles not only affect the lithium-ion transport but also lead to a heterogeneous current distribution and non-uniform lithiation between particles and along the through-thickness direction. Building on these insights, we propose and compare potential graded-microstructure designs for next-generation battery electrodes. To guide manufacturing of electrode architectures, in-situ X-ray CT is shown to reliably reveal the porosity and tortuosity changes with incremental calendering steps.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Research three-dimensional hierarchical graphite architectures for anodes for fast charging

With current lithium ion batteries optimized for performance under relatively low charge rate conditions, implementation of XFC has been hindered by drawbacks including Li plating, kinetic polarization, and heat dissipation. This project will utilize model-informed design of 3-D hierarchical electrodes to tune key XFCrelated variables like 1) bulk porosity/tortuosity 2) vertical pore diameter, spacing, and lattice 3) crystallographic orientation of graphite particles relative to exposed surfaces 4) interfacial chemistry of the graphite surfaces through "artificial sEr' formation using ALD 5) current collector surface roughness (aspect ratio, roughness factor, etc.). A key aspect of implementing novel electrodes is characterizing them in relevant settings. For this project, ultimately led out of University of Michigan by Neil Dasgupta, that includes both coin cell and 2+ Ah pouch cell testing, as well as comparison testing against baselines. Sandia National Labs will be conducting detailed cell characterization on iterative versions/improvements of the model-based hierarchical electrodes, as well as COTS cells for baseline comparisons. Key metrics include performance under fast charge conditions, as well as the absence or degree of lithium plating. Sandia will use their unique high precision cycling and rapid EIS capabilities to accurately characterize performance and any lithium plating during 6C charging and beyond, coupling electrochemical observations with cell teardown. Sandia will also design custom fixturing to cool cells during rapid charge, to decouple any kinetic effects brought about by cell heating and allow comparisons between different cells and charge rates. Using these techniques, Sandia will assess HOH electrodes from the University of Michigan, as well as aiding in iterative model and electrode design.

25 ENERGY STORAGE↗
DOE OSTI2018

Research three-dimensional hierarchical graphite architectures for anodes for fast charging

With current lithium ion batteries optimized for performance under relatively low charge rate conditions, implementation of XFC has been hindered by drawbacks including Li plating, kinetic polarization, and heat dissipation. This project will utilize model-informed design of 3-D hierarchical electrodes to tune key XFC related variables like 1) bulk porosity/tortuosity 2) vertical pore diameter, spacing, and lattice 3) crystallographic orientation of graphite particles relative to exposed surfaces 4) interfacial chemistry of the graphite surfaces through "artificial sEr formation using ALD 5) current collector surface roughness (aspect ratio, roughness factor, etc.). A key aspect of implementing novel electrodes is characterizing them in relevant settings. For this project, ultimately led out of University of Michigan by Neil Dasgupta, that includes both coin cell and 2+ Ah pouch cell testing, as well as comparison testing against baselines. Sandia National Labs will be conducting detailed cell characterization on iterative versions/improvements of the model-based hierarchical electrodes, as well as COTS cells for baseline comparisons. Key metrics include performance under fast charge conditions, as well as the absence or degree of lithium plating. Sandia will use their unique high precision cycling and rapid EIS capabilities to accurately characterize performance and any lithium plating during 6C charging and beyond, coupling electrochemical observations with cell teardown. Sandia will also design custom fixturing to cool cells during rapid charge, to decouple any kinetic effects brought about by cell heating and allow comparisons between different cells and charge rates. Using these techniques, Sandia will assess HOH electrodes from the University of Michigan, as well as aiding in iterative model and electrode design.

25 ENERGY STORAGE↗
DOE OSTI2024

Topology optimization for the full-cell design of porous electrodes in electrochemical energy storage devices

In this paper, we introduce a density-based topology optimization framework to design porous electrodes for maximum energy storage. We simulate the full cell with a model that incorporates electronic potential, ionic potential, and electrolyte concentration. The system consists of three materials, namely pure liquid electrolyte and the porous solids of the anode and cathode, for which we determine the optimal placement. We use separate electronic potentials to model each electrode, which allows interdigitated designs. As a result, a penalization is required to ensure that the anode and cathode do not touch, i.e., causing a short circuit. We compare multiple 2D designs generated for different fixed conditions, e.g. material properties. A 3D design with complex channel and interlocked structure is also created. All optimized designs are far superior to the traditional monolithic electrode design with respect to energy storage metrics. We observe up to a 750% increase in energy storage for cases with slow effective ionic diffusion within the porous electrode.

25 ENERGY STORAGE↗
DOE OSTI2021

Guiding the Design of Heterogeneous Electrode Microstructures for Li-Ion Batteries: Microscopic Imaging, Predictive Modeling, and Machine Learning

Electrochemical and mechanical properties of lithium-ion battery materials are heavily dependent on their 3D microstructure characteristics. A quantitative understanding of the role played by stochastic microstructures is critical for the prediction of material properties and for guiding synthesis processes. Furthermore, tailoring microstructure morphology is also a viable way of achieving optimal electrochemical and mechanical performances of lithium-ion cells. To facilitate the establishment of microstructure-resolved modeling and design methods, a review covering spatially and temporally resolved imaging of microstructure and electrochemical phenomena, microstructure statistical characterization and stochastic reconstruction, microstructure-resolved modeling for property prediction, and machine learning for microstructure design is presented here. The perspectives on the unresolved challenges and opportunities in applying experimental data, modeling, and machine learning to improve the understanding of materials and identify paths toward enhanced performance of lithium-ion cells are presented.

25 ENERGY STORAGE↗
DOE OSTI2025

Development of a Robust Reference Electrode in Aggressive Chemical and Radiation Environments in the Hanford Waste Tanks

The Hanford site stores more than 200 million liters of radioactive and chemically hazardous wastes from the production of weapons materials. The wastes are stored in 177 underground carbon-steel storage tanks, separated between 149 single shell tanks (SSTs) and 28 double shell tanks (DSTs). The DSTs provide critical retrieval and interim storage before the waste is vitrified in the Waste Treatment and Isolation Plant (WTP). The tanks will need to remain in-service far beyond the initial 40-year design life, and effective corrosion control practices must remain in force to extend the tanks’ lifespans. This effort includes direct measurements of corrosion rate (e.g., ultrasonic measurements and corrosion coupons) and electrochemical processes (e.g., linear polarization measurements and open circuit potential measurements). The Hanford site began monitoring the corrosion potential in select DSTs in 2008. Of the 45 reference electrodes that have been installed, 29 have failed and 6 others provided unreliable results. DOE-EM is supporting a 3-year program to develop a chemical and radiation resistant reference electrode for application in the Hanford tanks. The first year of the program focused on understanding the failure mechanism for the reference electrodes and identification of candidate construction materials that would mitigate degradation of the electrodes in the waste environment. During the second year of the program, the objectives were to: 1) test candidate materials under simulated waste conditions, 2) design components that will extend the service life of the electrode, 3) fabricate materials for prototype reference electrodes, and 4) assemble prototype reference electrodes for accelerated testing. The reference electrode is constructed of four principal parts: 1) junction, 2) casing, 3) inner chamber backfill materials, and 4) the sensing wire. Principally, improvements of the junction, casing, and inner chamber backfill materials are being pursued. The junction material at the interface between the waste and the inner chamber of the reference electrode was identified as a critical component in the failure of the reference electrodes. Nine candidate replacement junction materials were tested under simulated waste conditions to evaluate permeation rate. These materials included a variety of polymeric and ceramic materials, some of which were 3-D printed. Thus far, porous polyvinylidene fluoride materials have performed satisfactorily and are being considered for prototype development. The commercial electrode casing materials in general have performed well. Additionally, 3-D printing of chemically and mechanically stable materials is being investigated as a means for further improvement in fabrication consistency. SRNL has also investigated altering the reference electrode design to extend the service life. The new design of the interior of the reference electrode casing creates a longer, more tortuous path between the junction material and the electrode sensing wire. A finite element model was used to optimize the design without adversely impacting the circuit resistance of the electrode during the measurements, thus preserving the measurement accuracy while enhancing the service life. The inner chamber back fill materials are also critical to the performance of the reference electrode. Materials that are resistant to intruding tank waste and provide a conductive path to the sensing wire were investigated. Gel and powder materials that are interspersed with a conductive chloride bearing material were tested for their influence on diffusion and electrode resistance. All the investigated materials and components will be assembled, with collaboration from commercial vendors, to fabricate the initial prototypes. Accelerated testing of the prototypes will be initiated in Year 2 of the program and will be completed in Year 3. A recommendation on the materials of construction and the design of the new robust reference electrode will be presented to the Hanford tank farm facility.

Sykes, Kiana [Savannah River National Laboratory (↗
DOE OSTI2024

Electromagnetic Energy-Assisted Thermal Conversion of Fossil-Based Hydrocarbons to Low-Cost Hydrogen

The goal of this project was to develop and optimize catalysts for methane decomposition, particularly focusing on regeneration via an electromagnetic energy-assisted mechanism, to produce hydrogen more cost-effectively compared to electrolysis routes. To achieve this goal, the project pursued several key objectives. The project began with the preparation and testing of various catalysts. A nickel-silica based catalyst was identified as the most promising material for the pyrolysis of methane into carbon and hydrogen. Kinetic parameters for methane decomposition were determined, aiding in computational modeling efforts. Structured catalysts were investigated, highlighting the need for frequent cleaning or regeneration to maintain performance, with methane conversion rates exceeding 70% in tube furnace tests. Computational fluid dynamics modeling was employed to optimize reactor designs and electrode angles, leading the project team to propose a multi-compartment thermal conversion system for larger setups. This modeling work was important in understanding reaction characteristics, carbon deposition rates, and temperature profiles under various conditions. A bench-scale reactor system was assembled to evaluate catalyst regeneration using electromagnetic energy-assisted mechanisms. Experiments demonstrated the potential for carbon removal, though further optimization is needed. The carbon produced from the methane conversion process was evaluated for potential use in lithium-ion battery electrodes. The carbon exhibited properties similar to commercially available high-purity multi-walled carbon nanotubes and nanofibers, with a carbon content greater than 95%. Coin cell batteries assembled with this carbon showed that lower replacement levels (10% to 33%) outperformed the control group, improving specific capacity density and stability. However, higher replacement levels (100%) demonstrated poorer performance, suggesting that excessive carbon substitution negatively impacts battery performance. These findings indicate the potential marketability of the produced carbon as a component in lithium-ion batteries, though further testing is necessary to confirm long-term advantages and disadvantages associated with the use of the carbon product. These results however justified further technoeconomic assessments to determine if the process can provide low-cost hydrogen. The economic feasibility and technical performance of methane decomposition for hydrogen production were assessed, focusing on three plant configurations: 100E (electrically heated), 100C (combustion heated using produced hydrogen), and PE-Hybrid (a combination of pyrolysis (indicating decomposition) and electrolysis). The Levelized Cost of Hydrogen (LCOH) for the pyrolysis configurations was found to be approximately 25% lower than that of electrolysis. The 100E configuration had the lowest LCOH at $\$$3.12/kg. Including carbon product sales significantly improved the economics, with the 100C configuration achieving a negative LCOH of -$\$$0.35/kg. The PE-Hybrid configuration was not economically advantageous compared to pure pyrolysis plants due to its complexity and additional equipment requirements. Ultimately, methane pyrolysis presents a viable method for near carbon dioxide-free hydrogen production, with significant economic advantages over electrolysis, especially when considering the sale of carbon byproducts. The 100E and 100C configurations showed the most promise, with the choice between them ultimately depending on the prices of power and natural gas. In conclusion, this technology has the potential to lower hydrogen production costs by leveraging the methane decomposition process with the sale of valuable carbon byproducts. By optimizing catalyst performance and integrating electromagnetic energy-assisted regeneration, the process can achieve higher efficiency and economic viability, making it a competitive alternative to traditional hydrogen production methods.

08 HYDROGEN↗
DOE OSTI2023

A hybrid 3D/2D field response calculation for liquid argon detectors with PCB based anode plane

Liquid Argon Time Projection Chamber (LArTPC) technology is commonly utilized in neutrino detector designs. It enables detailed reconstruction of neutrino events with high spatial precision and low energy threshold. Its field response (FR) model describes the time-dependent electric currents induced in the anode-plane electrodes when ionization electrons drift nearby. An accurate and precise FR is a crucial input to LArTPC detector simulations and charge reconstruction. Established LArTPC designs have been based on parallel wire planes. It allows accurate and computationally economic two-dimensional (2D) FR models utilizing the translational symmetry along the direction of the wires. Recently, novel LArTPC designs utilize electrodes formed on printed circuit board (PCB) in the shape of strips with through holes. The translational symmetry is no longer a good approximation near the electrodes and a new FR calculation that employs regions with three dimensions (3D) has been developed. Extending the 2D models to 3D would be computationally expensive. Fortuitously, the nature of strips with through holes allows for a computationally economic approach based on the finite-difference method (FDM). In this paper, we present a new software package pochoir that calculates LArTPC field response for these new strip-based anode designs. This package combines 3D calculations in the volume near the electrodes with 2D far-field solutions to achieve fast and precise field response computation. We apply the resulting FR to simulate and reconstruct samples of cosmic-ray muons and 39 Ar decays from a Vertical Drift (VD) detector prototype operated at CERN. We find the difference between real and simulated data within 5%. Current state-of-the-art LArTPC software requires a 2D FR which we provide by averaging over one dimension and estimate that variations lost in this average are smaller than 7%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗