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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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At least 91 records · Page 5

Thermal shock resistance of lightweight cements developed for geothermal conditions

Cements are a critical component in well construction, as they act to prevent well fluid and gas escape, prevent corrosion of the casing, and strengthen the wellbore to prevent deformation. Under the high temperature/pressure conditions common in geothermal systems, the injection of cold water for energy production is expected to induce cyclic damage to the borehole cement through the rapid temperature fluctuations. These “thermal shocks” are expected to cause casing shrinkage, annulus formation, and cement tensile stresses. To understand the effect of cold water injection on the wellbore environment, a set of rock-cement-steel samples were created to simulate the structure of a geothermal well. Lightweight thermally-insulating cement blends were tested under thermal shock conditions in this study. In each test, the samples were pressurized to an effective pressure of ~3.5 MPa and placed at high temperatures. Thermal shocks were performed by injecting cold water (~10-15 °C) through the samples at a constant rate while keeping the samples at high temperatures until the sample temperature stopped decreasing and deformation ceased. Eight thermal shock tests were conducted with each sample – two at 100 °C and six at 200 °C. Post-tests analysis was then conducted by cutting open each sample to examine the damage in each component of the simulated wellbore. Experimental results suggest that all samples experienced similar degrees of axial and lateral contraction during cold water injection, but for the most part this contraction is recoverable when injection halts. Post-test analysis revealed that fly ash cenosphere pre-treatment had the best effect on improving thermal shock resistance in the cement blends. Thermomechanical modeling of likely stress paths experienced by the cements during heating/cooling cycles shows that elasto-plastic cement constitutive behavior results in most plastic strain occurring during the initial heating steps, with mostly elastic strain occurring during the thermal shock cycles. In conclusion, this agrees with experimental evidence, suggesting that cement damage from shocking occurs via other mechanisms such as chemical alteration, corrosion, and fatigue.

36 MATERIALS SCIENCE↗

Varied enhancements in mechanical properties and sodium compatibility of Grade 92 by thermomechanical treatments

As a candidate material for advanced nuclear reactors, a ferritic-martensitic (FM) steel Grade 92 in the standard normalized and tempered (NT) condition was subjected to two types of thermomechanical treatments (TMTs) with one having a lower level of deformation (T5A) and the other having a higher level of deformation (T5B). The testing results of the three conditions indicated that the TMTs significantly improved yield strength, creep resistance, fracture toughness, and sodium corrosion resistance compared with the NT condition. T5A excelled at creep resistance while T5B at sodium corrosion resistance. Microstructural characterization of the three conditions supports the varied enhancements in the properties. This study suggests that an appropriate TMT can be developed and applied to FM steels to better meet specific application requirements.

36 MATERIALS SCIENCE↗

Multi-scale experimental study of creep-fatigue failure initiation in a 709 Stainless Steel alloy using high resolution digital image correlation. Final report

This report discusses the efforts made towards the multi-scale study of the creep-fatigue response of stainless steel 709. Multiple experimental techniques, including digital image correlation (DIC) and electron backscatter diffraction (EBSD), were used in assessing the evolution of damage accumulation during fatigue, creep-fatigue, and thermomechanical fatigue of alloy 709. The role of microstructural features, hold times, temperature, and loading profiles were quantified and the interchangeability of temperature and time was investigated. Finally, a thermomechanical fatigue model was shown to predict well the failure of samples with varying loading profiles. Results indicate that strain accumulation in 709 steel happens primarily near grain boundaries (GBs) with the strains around GBs being inversely proportional to their measured residual burgers vector. Furthermore, hot-spots for strain accumulation were shown to be the locations of eventual microcrack nucleation. The introduction of hold times to the periodic loading cycle increases the damage accumulation rate and thus shortens the fatigue life of samples–this was true for both room temperature and high temperature. Thermomechanical cycling was shown to have little effect on the end life of samples, with the damage accumulation rate for in-phase and out-of-phase cycling being similar to isothermal fatigue. The interchangeability of time and temperature was shown to be possible within the studied load, time, and temperature ranges, since deformation mechanisms driving strain accumulation did not change with temperature (up to 650°C). The Neu-Sehitoglu thermomechanical fatigue model, with constants obtained from the literature and in part from our experimental results, was applied to predict failure of isothermal creep-fatigue samples. The main objectives of this work were to:(a) Perform high-resolution digital image correlation measurements (HiDIC) for alloy 709; (b) Quantify and assess damage accumulation at the microstructure under fatigue, TMF, and creep-fatigue conditions of 709; (c) Study of the role of hold times, i.e., adding a creep component, to: Room temperature cycling, High temperature cycling, Failure; (d) Study the mechanisms of thermomechanical fatigue in this alloy; (e) Investigate the existence of a time-temperature interchangeability criterion to aid in accelerated creep-fatigue testing; (f) Establish the validity of a combined creep-fatigue model for life prediction for 709. This report is structured with each subsequent section detailing the efforts, results, and conclusions related to each of the objectives described, mostly in chronological order.

36 MATERIALS SCIENCE↗

High Temperature Thick Film Sensor Development Based on Refractory Oxide Semiconductors

Solid-state, high-temperature sensing devices are required for accurate temperature, strain/stress, and failure monitoring for a range of advanced manufacturing, transportation, and military applications. High temperature conditions limit sensing strategies, where typically traditional metal and semiconductor materials are unstable, and the sensing options are limited to optical spectroscopy methods. In addition, strategies to embed the sensors directly within active components and protective thermal refractory are of interest that permit near-environment sensing which is not possible with the traditional electronic materials and components. Rare-earth chromite semiconductors exhibit some properties of interest for high temperature sensing technologies, such as: high microstructure and chemical stability, relatively high electronic conductivity at high temperatures, and relative thermal expansion coefficient matching to refractory thermal protective insulation (such as high-zirconia and -alumina ceramics). In this work, n-type and p-type doped lanthanum chromites compositions were computationally modelled and prepared, and the electrical, thermoelectric, and thermomechanical properties were measured for the obtained material systems. A few compositions were then processed into thick film health and temperature sensors and tested at high temperatures. To establish relative stability under harsh environment conditions, post- mortem microstructure and chemical composition was characterized after extended and cycle testing at high temperatures.

20 FOSSIL-FUELED POWER PLANTS↗

Activation Energy for Solder Bond Degradation: Thermal Cycling of Field-aged Modules at Multiple Upper Temperatures

The reliability of solder joints in the solar cell metallization-interconnect system influences the lifetime of photovoltaic modules. Two field-aged modules-one with Sn 62 Pb 36 Ag 2 solder at the solder joints (Solarex MSX 60), and the other with the standard Sn 60 Pb 40 solder (Siemens M55)-were subjected to a modified thermal cycling (TC) test of IEC 61215. Three sections in each module were maintained at 85 degrees C, 95 degrees C, and 105 degrees C during the 15-minute high temperature dwell time. Current equivalent to the module short-circuit current was injected through the module when the chamber temperature was above 25 degrees C to simulate regular field operation. This novel approach aims to induce thermomechanical fatigue (TMF) at the solder joints and intermetallic compound (IMC) formation at the metal/solder interfaces. The activation energy (E a ) for solder bond degradation was calculated based on the series resistance (R s ) increase in TC testing rather than power drop to avoid the effect of confounding variables. Module-level R s increase in MSX 60 module after TC800 cycles and in M55 module after TC400 cycles was 1.22% and 183.7%, respectively. The E a determined for the module with 2wt% Ag is 0.24 eV and for that with the standard solder is 0.27 eV. The solder bond degradation seems to have been driven by TMF rather than IMC formation for both modules.

14 SOLAR ENERGY↗

Neutron Diffraction Residual Stress Study of a AA2219-T87 Self-Reacting Friction Stir Weld

2219-T87 is a precipitation hardenable aluminum-copper alloy which sees wide use in structural aerospace components. Thick panels of this alloy are joined via self-reacting friction welding (SRFSW); however, this thermomechanical process can result in significant loss of the alloy’s strengthening precipitates and large residual stresses which are detrimental to mechanical behavior and performance. High-resolution maps of the residual strain and stress states along the normal, transverse, and longitudinal directions of 2219-T87 SRFSW were obtained using neutron diffraction measurements. Residual stress had the highest tensile value in the heat-affected zone (HAZ) and the largest compressive stress in the base metal region of the normal and transverse directions. Line profile residual stress distributions displayed an “M”-shaped distribution in each direction with the longitudinal direction being the most pronounced while 2D residual stresses displayed an hourglass-shaped pattern. Further, average maximal longitudinal residual stress values ranged from 60.6 to 85.6% of yield. Microhardness testing across the transverse weld section produced a “V”-shaped curve with slight hardness recovery in the stir zone. Maximal and minimal microhardness values were observed in the base metal (154 HV) and thermomechanically affected zone (82 HV), respectively. Microstructural evolution was recorded using optical microscopy and showed decreasing grain size from the HAZ to the stir zone.

36 MATERIALS SCIENCE↗

Metallic Fuel Performance Code Requirements for the Versatile Test Reactor Project

Metallic nuclear fuels have been proposed for use in several emerging nuclear reactor designs, and a number of codes have been developed to model these fuels and assess their performance. Qualification of these metallic nuclear fuels will ultimately require monitored irradiation of lead test assemblies, but the use of fuel performance codes can reduce the uncertainty associated with these efforts by quantifying uncertainties and estimating margins to failure ahead of time. In this work, metallic fuel performance code requirements are defined for the Versatile Test Reactor (VTR) project using input from the Experimental Breeder Reactor II functional requirements, operational requirements, and design criteria. This work focuses on the thermomechanical responses and irradiation behaviors of metallic fuel elements that are representative of the proposed VTR driver fuel design concepts. As such, many of the code requirements and physics/modeling discussions in this work are expected to be broadly applicable to metallic fuel applications outside of the VTR project.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Creep Behavior of Compact γ′-γ″ Coprecipitation Strengthened IN718-Variant Superalloy

The development of high-temperature heavy-duty turbine disk materials is critical for improving the overall efficiency of combined cycle power plants. An alloy development strategy to this end involves superalloys strengthened by ‘compact’ γ′-γ″ coprecipitates. Compact morphology of coprecipitates consists of a cuboidal γ′ precipitate such that γ″ discs coat its six {001} faces. The present work is an attempt to investigate the microstructure and creep behavior of a fully aged alloy exhibiting compact coprecipitates. We conducted heat treatments, detailed microstructural characterization, and creep testing at 1200 °F (649 °C) on an IN718-variant alloy. Our results indicate that aged IN718-27 samples exhibit a relatively uniform distribution of compact coprecipitates, irrespective of the cooling rate. However, the alloy ruptured at low strains during creep tests at 1200 °F (649 °C). At 100 ksi (689 MPa) load, the alloy fails around 0.1% strain, and 75 ksi (517 MPa) loading causes rupture at 0.3% strain. We also report extensive intergranular failure in all the tested samples, which is attributed to cracking along grain boundary precipitates. The results suggest that while the compact coprecipitates are indeed thermally stable during thermomechanical processing, the microstructure of the alloy needs to be optimized for better creep strength and rupture life.

36 MATERIALS SCIENCE↗

Thermomechanical Properties of Neutron Irradiated Al 3 Hf-Al Thermal Neutron Absorber Materials

A thermal neutron absorber material composed of Al 3 Hf particles in an aluminum matrix is under development for the Advanced Test Reactor. This metal matrix composite was fabricated via hot pressing of high-purity aluminum and micrometer-size Al 3 Hf powders at volume fractions of 20.0, 28.4, and 36.5%. Room temperature tensile and hardness testing of unirradiated specimens revealed a linear relationship between volume fraction and strength, while the tensile data showed a strong decrease in elongation between the 20 and 36.5% volume fraction materials. Tensile tests conducted at 200 °C on unirradiated material revealed similar trends. Evaluations were then conducted on specimens irradiated at 66 to 75 °C to four dose levels ranging from approximately 1 to 4 dpa. Tensile properties exhibited the typical increase in strength and decrease in ductility with dose that are common for metallic materials irradiated at ≤0.4T m . Hardness also increased with neutron dose. The difference in strength between the three different volume fraction materials was roughly constant as the dose increased. Nanoindentation measurements of Al 3 Hf particles in the 28.4 vol% material showed the expected trend of increased hardness with irradiation dose. Transmission electron microscopy revealed oxygen at the interface between the Al 3 Hf particles and aluminum matrix in the irradiated material. Scanning electron microscopy of the exterior surface of tensile tested specimens revealed that deformation of the material occurs via plastic deformation of the Al matrix, cracking of the Al 3 Hf particles, and to a lesser extent, tearing of the matrix away from the particles. The fracture surface of an irradiated 28.4 vol% specimen showed failure by brittle fracture in the particles and ductile tearing of the aluminum matrix with no loss of cohesion between the particles and matrix. The coefficient of thermal expansion decreased upon irradiation, with a maximum change of –6.3% for the annealed irradiated 36.5 vol% specimen.

36 MATERIALS SCIENCE↗

Consensus DOE Advanced Fuels Campaign TREAT/SATS Test Plan [Slides]

This record is comprised of summary slides of the Combined TREAT-LOC & SATS Integral LOCA Experiment Plan. The experimental program has been developed to specifically address data gaps and opportunities identified through detailed review of the existing public knowledgebase on LOCA FFRD and specific experimental development for prototypic LOCA conditions for LWR systems. The test program relies on a unique combination of in-pile and out-of-pile experimental approaches to (1) provide clear tieback to the existing integral and semi-integral LOCA experiment database using state-of-the-art facilities. More importantly, this program will systematically investigate the impacts of: (2) prototypic HBu fuel and cladding thermomechanical behaviors under postulated LWR LOCA conditions never fully investigated before. These conditions correspond with prototypic decay-energy heat up (DEH) and stored-energy heat up (SEH) conditions. Unique TREAT capability will provide first evaluation of SEH conditions on HBu fuels. The test program includes an emphasis on developing improved mechanistic understanding of key phenomena through independent experimental systems, development of a database to support fuel performance modeling tools, world leading advanced materials characterization, and the most advanced approach to in-situ diagnostics ever deployed to evaluate FFRD. The results will represent a significant leap forward in the evaluation of prototypic conditions and novel data to support modeling development and validation, as well as to inform the technical basis of LOCA-induced FFRD.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Combined TREAT-LOC & SATS Integral LOCA Experiment Plan

The Transient Reactor Test Facility (TREAT) loss-of-coolant (LOC) and highburnup (HBu) experiment series, along with the Severe Accident Test Station (SATS) HBu experiment series, are integral LOC accident (LOCA) experiments planned under the Department of Energy (DOE) Advanced Fuels Campaign (AFC) program, which aims to support burnup extension needs by addressing identified R&D priorities in order to achieve an improved understanding of fuel fragmentation, relocation, and dispersal (FFRD) of HBu fuel during LOCA events. Priorities have been identified by the Electric Power Research Institute (EPRI)’s Collaborative Research on Advanced Fuel Technologies (CRAFT) Fuel Performance and Testing Technical Experts Group (FPTTEG). The data produced under this plan will be used to further validate and confirm existing models and inform future R&D and model development. The experimental program was specifically developed to address data gaps and opportunities identified via detailed review of the existing public knowledge base on LOCA FFRD, as well as reviewing specific experimental development activities regarding prototypic LOCA conditions for light-water reactor (LWR) systems. The test program relies on a unique combination of in- and out-of-pile experimental approaches to provide a clear tieback to the existing integral and semi-integral LOCA experiment database, using state-of-the-art facilities. More importantly, the program will systematically investigate the impacts of prototypic HBu fuel/cladding thermomechanical behaviors under postulated LWR LOCA conditions not yet fully investigated. These conditions correspond with prototypic decay-energy heatup (DEH) and stored-energy heatup (SEH) conditions. First, TREAT’s unique capability will enable the first evaluation of the impact of SEH conditions on HBu fuels. The test program will emphasize the development of an improved mechanistic understanding of key phenomena through independent experimental systems, development of a database to support fuel performance modeling tools, world-leading advanced materials characterization, and the most advanced approach to in situ diagnostics ever deployed to evaluate FFRD. The results will represent a significant leap forward in evaluating prototypic conditions and novel data to support modeling development and validation, as well as to inform the technical basis for LOCA-induced FFRD.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Combined TREAT-LOC and SATS LOCA Experiment Plan: Integral LOCA Experiments on High-Burnup Fuels

The Transient Reactor Test Facility (TREAT) loss-of-coolant (LOC) and high-burnup (HBu) experiment series, along with the Severe Accident Test Station (SATS) HBu experiment series, are integral LOC accident (LOCA) experiments planned under the DOE AFC program, which aim to support burnup extension needs by addressing identified R&D priorities in order to achieve an improved understanding of fuel fragmentation, relocation, and dispersal (FFRD) of HBu fuel during LOCA events. The data produced under this plan will be used to further validate and confirm existing models and inform future R&D and model development. The experimental program has been specifically designed to address knowledge gaps and opportunities identified through a detailed review of existing public knowledge on LOCA FFRD. The test program employs a unique combination of in- and out-of-pile experimental approaches and state-of-the-art facilities to provide a clear connection to the existing integral and semi-integral LOCA experiment database. The primary goal of the program is to investigate the impact of prototypic HBu fuel/cladding thermomechanical behaviors under postulated LWR LOCA conditions that have not yet been fully studied. These conditions correspond with prototypic decay-energy heatup (DEH) and stored-energy heatup (SEH) conditions. Importantly, TREAT’s unique capability will enable the first evaluation of the impact of SEH conditions on HBu fuels. The test program will emphasize the development of an improved mechanistic understanding of key experimental phenomena through independent experimental systems, development of a database to support fuel performance modeling tools and employing world-leading advanced materials characterization and in-situ diagnostics to evaluate FFRD. The results of the program will provide novel data to support modeling development and validation and will represent a significant advancement in evaluating prototypic conditions, as well as to inform the technical basis for LOCA-induced FFRD.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Multiscale investigation of thermomechanical and compositional developments in Ni alloy 718 under laser processing

Laser processing has been widely employed in various applications due to its exceptional spatial resolution. However, the rapid temperature gradients generated in localized areas present significant challenges for experimental characterization using conventional instruments. To characterize Ni alloy 718 during laser processing, we employed in-situ synchrotron X-ray diffraction with a high-speed detector, a method particularly well-suited for probing processes with high temporal and spatial resolution. Through a series of in-situ experiments, we investigated the local variations in the evolution of microstructures and thermomechanical behaviors within a keyhole mode melt pool. The in situ macroscopic thermomechanical behaviors were quantified using an empirical model derived from diffraction patterns, with experimental results showing reasonable agreement with finite element analysis. Various laser parameters were tested to assess their influences on the residual strains in the melt pools. The results revealed that the residual strain in the keyhole mode melt pool is relatively insensitive to variations in the parameters and is smaller than that in the melt pool created under conduction mode laser scanning. Additionally, we analyzed the shapes of individual diffraction spots, providing insights into the plastic behaviors and compositional developments in the resolidified alloy. The analysis confirmed that compositional variations in a dendritic microstructure manifest as asymmetric broadening of the diffraction spots.

Ni alloy 718↗

Chromium enhances the mechanical performance of 3d transition metal high entropy alloys

A comprehensive examination of the compositional effects on the deformation behavior of high entropy alloys (HEAs) was conducted through nanoindentation, indentation creep, and stress relaxation experiments at ambient temperature. The alloys investigated included NiCoFe, NiCoCr, NiCoCrFe, and NiCoCrFeMn, all of which underwent identical thermomechanical processing. From the experimental results, NiCoCr exhibited the highest maximum shear stress for dislocation nucleation (13 GPa) and nanoindentation hardness (3.8 GPa) among the alloys tested. It also showed the lowest stress sensitivity (0.02) and activation volume (3–4 b 3 ) under creep and stress relaxation conditions, indicative of its superior plastic flow properties. Density functional theory (DFT) calculations further revealed an uneven charge density and larger bonding-length variation in NiCoCr due to the presence of Cr, which increased lattice distortion, impeding dislocation movement. Furthermore, in this study, post-deformation microscopy using transmission electron microscopy (TEM) revealed a high density of stacking faults and twins in NiCoCr that effectively enhanced its creep strength. The results highlight the significance of specific elemental effects, particularly from Cr in this study, over configurational entropy effect (i.e., compositional complexity) in governing the deformation microstructure and mechanical properties of HEAs. Finally, these insights will be instrumental for the design and optimization of advanced alloys for load-bearing applications.

36 - MATERIALS SCIENCE↗

Designing metal halide perovskite solar modules for thermomechanical reliability

There is a significant deficiency in perovskite solar module (PSM) stability under thermomechanical stressors which is not well-understood. In this perspective, common issues seen with perovskite solar cell device fabrication related to thermomechanical reliability of PSM processing are discussed, with a focus on how the robustness of device layers and interlayer adhesion can be improved. Film stresses, adhesion of charge transport layers, and instability under light and heat are discussed with the purpose of providing insight on designing PSMs for durability. Processing conditions of encapsulation of PSMs and critical parameters to consider are also examined, and accelerated testing protocols for PSMs are discussed that probe mechanical degradation modes and ensure reliability of devices in the field.

14 SOLAR ENERGY↗

Composite binder, processing, and particle size effects on mechanical properties of non-hazardous high explosive surrogates

Plastic-bonded explosives (PBX) are polymer matrix composites that are highly loaded with micron-scale explosive crystals. The thermal and mechanical properties of these materials must be well-understood so that appropriate engineering models can be developed, but testing such properties under many scenarios can be hazardous and expensive. A non-hazardous PBX surrogate (“mock”) may be used in place of a PBX in many experiments if the thermomechanical properties are well-matched. Our previous research has shown that 5-iodo-2'-deoxyuridine (IDOX) is a promising crystalline filler material for the explosive cyclotetramethylene-tetranitramine (HMX). In this study, we investigate how the binder composition, variations in the IDOX particle size distribution, and pressing temperature affect the compressive strength and elastic modulus. We observe that while the binder system used in the composite dominates the mechanical response, the particle size distribution and pressing conditions do have a measurable effect on the material compliance and strength.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Characterization of Large Batch 14YWT Heat (NFA-2) for JOYO Irradiations (Rev.1)

The development and deployment of advanced cladding materials in advanced reactors requires the collection of relevant performance data for each cladding concept. Novel cladding concepts typically undergo significant innovation and iteration over the course of their development, and intention should be given to providing a snapshot of present performance. Thus, a modern heat of the nanostructured ferritic alloy (NFA) 14YWT is produced using state-of-the-art procedures for impurity minimization combined with thermomechanical processing methods designed to optimize fracture toughness, tensile strength, and ductility. This new heat of 14YWT, NFA-2, will provide the Advanced Fuels Campaign with adequate material for upcoming irradiation and mechanical testing campaigns. This report outlines procurement of new gas atomized 14YWT powder, production of four new bars of 14YWT, and subsequent mechanical and microstructural property characterization.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

RaDIATE Collaboration Thermal shock studies

As next-generation accelerator target facilities (High Energy Physics, Spallation Sources, ... ) become increasingly more powerful and intense, high power target systems face key technical challenges, such as radiation damage and thermal shock. Those ultimately degrade the performance and lifetime of targets and have been identified as the leading cross-cutting challenges of high-power target facilities. In order to operate reliable beam-intercepting devices in the framework of energy and intensity increase for next generation accelerators, the RaDIATE Collaboration (Radiation Damage In Accelerator Target Environment), established in 2012 and managed by Fermilab, brings together existing expertise in nuclear material and accelerator targets from 20 international institutions, including CERN, to execute a coordinated strategy for high power targetry R&D. In this context, several thermal shock studies were performed at CERN's HiRadMat (High-Radiation to Materials) facility, that took a key step towards improving our knowledge on target damage tolerance. The first experiment HRMT-24, supported by EURCARD2 and completed in 2015, successfully validated the Johnson-Cook strength model developed at SwRI on beryllium S200FH (used for beam window material), providing a better confidence in simulating the thermal shock response of current and future S200FH beryllium components. HRMT-43, supported by ARIES and completed in 2018, tested various materials (Be, C, SiC, Si, Ti and ceramic nanofiber). It was a first and unique test which included pre-irradiated specimens from high energy proton beam irradiation to identify thermal shock response differences between non-irradiated and previously irradiated materials. Real-time measurement of dynamic thermomechanical response of graphite helped to benchmark numerical simulations.

43 PARTICLE ACCELERATORS↗