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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 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

A method for calculating aerodynamic heating on sounding rocket tangent ogive noses.

A method is presented for calculating the aerodynamic heating and shear stresses at the wall for tangent ogive noses that are slender enough to maintain an attached nose shock through that portion of flight during which heat transfer from the boundary layer to the wall is significant. The lower entropy of the attached nose shock combined with the inclusion of the streamwise pressure gradient yields a reasonable estimate of the actual flow conditions. Both laminar and turbulent boundary layers are examined and an approximation of the effects of (up to) moderate angles-of-attack is included in the analysis. The analytical method has been programmed in FORTRAN IV for an IBM 360/91 computer.

Wing, L. D.↗
DOE OSTI2015

Current limitations and challenges in nanowaste detection, characterisation and monitoring

Highlights: • First review on detection of nanomaterials in complex waste samples. • Focus on nanoparticles in solid, liquid and gaseous waste samples. • Summary of current applicable methods for nanowaste detection and characterisation. • Limitations and challenges of characterisation of nanoparticles in waste. - Abstract: Engineered nanomaterials (ENMs) are already extensively used in diverse consumer products. Along the life cycle of a nano-enabled product, ENMs can be released and subsequently accumulate in the environment. Material flow models also indicate that a variety of ENMs may accumulate in waste streams. Therefore, a new type of waste, so-called nanowaste, is generated when end-of-life ENMs and nano-enabled products are disposed of. In terms of the precautionary principle, environmental monitoring of end-of-life ENMs is crucial to allow assessment of the potential impact of nanowaste on our ecosystem. Trace analysis and quantification of nanoparticulate species is very challenging because of the variety of ENM types that are used in products and low concentrations of nanowaste expected in complex environmental media. In the framework of this paper, challenges in nanowaste characterisation and appropriate analytical techniques which can be applied to nanowaste analysis are summarised. Recent case studies focussing on the characterisation of ENMs in waste streams are discussed. Most studies aim to investigate the fate of nanowaste during incineration, particularly considering aerosol measurements; whereas, detailed studies focusing on the potential release of nanowaste during waste recycling processes are currently not available. In terms of suitable analytical methods, separation techniques coupled to spectrometry-based methods are promising tools to detect nanowaste and determine particle size distribution in liquid waste samples. Standardised leaching protocols can be applied to generate soluble fractions stemming from solid wastes, while micro- and ultrafiltration can be used to enrich nanoparticulate species. Imaging techniques combined with X-ray-based methods are powerful tools for determining particle size, morphology and screening elemental composition. However, quantification of nanowaste is currently hampered due to the problem to differentiate engineered from naturally-occurring nanoparticles. A promising approach to face these challenges in nanowaste characterisation might be the application of nanotracers with unique optical properties, elemental or isotopic fingerprints. At present, there is also a need to develop and standardise analytical protocols regarding nanowaste sampling, separation and quantification. In general, more experimental studies are needed to examine the fate and transport of ENMs in waste streams and to deduce transfer coefficients, respectively to develop reliable material flow models.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

Unlocking the secret of lignin-enzyme interactions: Recent advances in developing state-of-the-art analytical techniques

Bioconversion of renewable lignocellulosics to produce liquid fuels and chemicals is one of the most effective ways to solve the problem of fossil resource shortage, energy security, and environmental challenges. Among the many biorefinery pathways, hydrolysis of lignocellulosics to fermentable monosaccharides by cellulase is arguably the most critical step of lignocellulose bioconversion. In the process of enzymatic hydrolysis, the direct physical contact between enzymes and cellulose is an essential prerequisite for the hydrolysis to occur. However, lignin is considered one of the most recalcitrant factors hindering the accessibility of cellulose by binding to cellulase unproductively, which reduces the saccharification rate and yield of sugars. This results in high costs for the saccharification of carbohydrates. The various interactions between enzymes and lignin have been explored from different perspectives in literature, and a basic lignin inhibition mechanism has been proposed. However, the exact interaction between lignin and enzyme as well as the recently reported promotion of some types of lignin on enzymatic hydrolysis is still unclear at the molecular level. Multiple analytical techniques have been developed, and fully unlocking the secret of lignin-enzyme interactions would require a continuous improvement of the currently available analytical techniques. This review summarizes the current commonly used advanced research analytical techniques for investigating the interaction between lignin and enzyme, including quartz crystal microbalance with dissipation (QCM-D), surface plasmon resonance (SPR), attenuated total reflectance-Fourier transform infrared (ATR-FTIR) spectroscopy, atomic force microscopy (AFM), nuclear magnetic resonance (NMR) spectroscopy, fluorescence spectroscopy (FLS), and molecular dynamics (MD) simulations. Interdisciplinary integration of these analytical methods is pursued to provide new insight into the interactions between lignin and enzymes. Finally, this review will serve as a resource for future research seeking to develop new methodologies for a better understanding of the basic mechanism of lignin-enzyme binding during the critical hydrolysis process.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Interactions between Polyelectrolyte Gel Surfaces

We see surfaces formed by charged polymeric species are highly abundant in both synthetic and biological systems, for which maintaining an optimum contact distance and a pressure balance is paramount. Here we investigate interactions between surfaces of two same-charged and highly swollen polyelectrolyte gels, using extensive molecular dynamic simulations and minimal analytical methods. The external-pressure responses of the gels and the polymer-free ionic solvent layer separating two surfaces are considered. Simulations confirmed that the surfaces are held apart by osmotic pressure resulting from excess charges diffusing out of the network. At a threshold pressure, the counterion-induced osmotic pressure in the gel interiors becomes nearly equal to that in solvent gap, and the gels begin to deform. At the threshold pressure, the distance between surfaces is equivalent to the electrostatic screening length imposed by excess charges. Both the solvent layer and pressure dependence are well described by an analytical model based on the Poisson–Boltzmann solution for low and moderate electrostatic strengths. Scaling descriptions for the threshold pressure and critical distance compare well with the simulations. The threshold pressure decreases with increasing polymerization degree of network chains, similar to sparsely grafted polyelectrolyte brushes. As the electrostatic coupling strength is increased, the deviations from the analytical model also increase due to condensed counterions. Our results are of great importance for systems where charged gels or gel-like structures interact in various solvents, including systems encapsulated by gels and microgels in confinement.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Analysis of N-16 concentration in primary cooling system of AP1000 power reactor

Nitrogen-16 (N-16) is one of the radiation safety parameter on the primary reactor system. The activation product, N-16, is the predominant contributor to the activity in the reactor coolant system during reactor operation. N-16 is activation product derived from activation of O-16 with fast neutron based on {sup 16}O(n,p){sup 16}N reaction. Thus study is needed and it performs to determine N-16 concentration in reactor coolant (primary coolant) in supporting radiation safety. One of the way is using analytical methode based on activation and redecay princip to obtain N-16 concentration. The analysis was performed on the configuration basis and operational of Westinghouse AP1000 power reactor in several monitoring points at coolant reactor system. The results of the calculation of N-16 concentration at the core outlet, reactor vessel outlet, pressurizer line, inlet and outlet of steam generators, primary pumps, reactor vessels inlet and core inlet are: 281, 257, 255, 250, 145, 142, 129 and 112 µCi/gram respectively. The results of analysis compared with AP1000 design control document as standard values. The verification showed very high accuracy comparation between analytical results and standard values.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1979

Testing of containers made of glass-fiber reinforced plastic with the aid of acoustic emission analysis

Acoustic emission analysis as a quasi-nondestructive test method makes it possible to differentiate clearly, in judging the total behavior of fiber-reinforced plastic composites, between critical failure modes (in the case of unidirectional composites fiber fractures) and non-critical failure modes (delamination processes or matrix fractures). A particular advantage is that, for varying pressure demands on the composites, the emitted acoustic pulses can be analyzed with regard to their amplitude distribution. In addition, definite indications as to how the damages occurred can be obtained from the time curves of the emitted acoustic pulses as well as from the particular frequency spectrum. Distinct analogies can be drawn between the various analytical methods with respect to whether the failure modes can be classified as critical or non-critical.

Wolitz, K.↗
DOE OSTI2017

Application of Synchrotron Radiation-based Methods for Environmental Biogeochemistry: Introduction to the Special Section

To understand the biogeochemistry of nutrients and contaminants in environmental media, their speciation and behavior under different conditions and at multiple scales must be determined. Synchrotron radiation-based X-ray techniques allow scientists to elucidate the underlying mechanisms responsible for nutrient and contaminant mobility, bioavailability, and behavior. The continuous improvement of synchrotron light sources and X-ray beamlines around the world has led to a profound transformation in the field of environmental biogeochemistry and, subsequently, to significant scientific breakthroughs. Following this introductory paper, this special collection includes 10 papers that either present targeted reviews of recent advancements in spectroscopic methods that are applicable to environmental biogeochemistry or describe original research studies conducted on complex environmental samples that have been significantly enhanced by incorporating synchrotron radiation-based X-ray technique(s). We believe that the current focus on improving the speciation of ultra-dilute elements in environmental media through the ongoing optimization of synchrotron technologies (e.g., brighter light sources, improved monochromators, more efficient detectors) will help to significantly push back the frontiers of environmental biogeochemistry research. As many of the relevant techniques produce extremely large datasets, we also identify ongoing improvements in data processing and analysis (e.g., software improvements and harmonization of analytical methods) as a significant requirement for environmental biogeochemists to maximize the information that can be gained using these powerful tools.

58 GEOSCIENCES↗
DOE OSTI2018

Materials science applications of Neutron Depth Profiling at the PGAA facility of Heinz Maier-Leibnitz Zentrum

Highlights: • Exploiting the range of NDP from thin films to electrodes for Li-ion batteries • Adopting an analytical method to probe undisturbed depth profiles from thick films • Revealing depth-dependent lithium immobilization in Li-ion battery electrodes Neutron depth profiling (NDP) is a non-destructive, isotope-sensitive profiling technique to monitor concentration profiles in almost any material matrix. Since NDP is sensitive to {sup 6}Li and lithium is widely used for different material science applications such as ceramics, optical waveguides or energy-storage systems, NDP offers answers to a broad spectrum of research questions. In the present work, the recently developed instrument N4DP at MLZ is used to address two research questions which are hardly accessible by conventional analytical techniques. First, the homogeneity of lithium formations within lithium niobate thin films for optical waveguide applications is investigated. Afterwards, the accumulation of inactive lithium in the solid-electrolyte-interphase (SEI) of silicon-graphite electrodes for lithium-ion batteries is studied ex situ. Since the material mass loading differs considerably between the two applications, a new analytical technique is introduced which mathematically separates the different particle signals and thus allows to investigate samples with high mass loadings.

36 MATERIALS SCIENCE↗
NASA NTRS2011

Broadband Via-Less Microwave Crossover Using Microstrip-CPW Transitions

The front-to-back interface between microstrip and CPW (coplanar waveguide) typically requires complex fabrication or has high radiation loss. The microwave crossover typically requires a complex fabrication step. The prior art in microstrip-CPW transition requires a physical vias connection between the microstrip and CPW line on a separate layer. The via-less version of this transition was designed empirically and does not have a close form solution. The prior art of the micro wave crossover requires either additional substrate or wire bond as an air bridge to isolate two microwave lines at the crossing junction. The disadvantages are high radiation loss, no analytical solution to the problem, lengthy simulation time, and complex fabrication procedures to generate air bridges or via. The disadvantage of the prior crossover is a complex fabrication procedure, which also affects the device reliability and yield. This microstrip-CPW transition is visualized as two microstrip-slotline transitions combined in a way that the radiation from two slotlines cancels each other out. The invention is designed based on analytical methods; thus, it significantly reduces the development time. The crossover requires no extra layer to cross two microwave signals and has low radiation loss. The invention is simple to fabricate and design. It produces low radiation loss and can be designed with low insertion loss, with some tradeoff with signal isolation. The microstrip-CPW transition is used as an interface to connect between the device and the circuit outside the package. The via-less microwave crossover is used to allow two signals to cross without using an extra layer or fabrication processing step to enable this function. This design allows the solution to be determined entirely though analytical techniques. In addition, a planar via-less microwave crossover using this technique was proposed. The experimental results show that the proposed crossover at 5 GHz has a minimum isolation of 32 dB. It also has low in-band insertion loss and return loss of 1.2 dB and 18 dB, respectively, over more than 44 percent of bandwidth at room temperature. This microstrip-CPW transition requires the microstrip line to be split into two sections. Each section is connected to a microstrip quarter-wavelength openended stub. A slotline is also placed perpendicular to the microstrip section. The slot is connected to a grounded-end quarter-wavelength slotline and generates a microstrip-slotline transition. When two of these sections are placed in parallel and with the microstrip section combined at transition, a microstrip- CPW transition is formed. The slotline radiation is suppressed as two slots are excited with the electric field in an opposite direction, which cancels the radiation in far field. The invention on the crossover consists of the invented microstrip-CPW transitions combined back-to-back and a microstrip low-pass filter. One signal is crossed through to the microstrip layer, while the other signal is crossed through the CPW line located on the ground plane of the microstrip line. The microstrip low-pass filter produces a narrow line at the crossing point to enhance the system isolation. It also produces broadband response in the operating frequency band. The microstrip-CPW transition allows a microwave signal to travel from microstrip line to CPW line with low radiation loss. The crossover allows two microwave signals to cross with minimal parasitic coupling.

Stevenson, Thomas↗
DOE OSTI2015

STEADY GENERAL RELATIVISTIC MAGNETOHYDRODYNAMIC INFLOW/OUTFLOW SOLUTION ALONG LARGE-SCALE MAGNETIC FIELDS THAT THREAD A ROTATING BLACK HOLE

General relativistic magnetohydrodynamic (GRMHD) flows along magnetic fields threading a black hole can be divided into inflow and outflow parts, according to the result of the competition between the black hole gravity and magneto-centrifugal forces along the field line. Here we present the first self-consistent, semi-analytical solution for a cold, Poynting flux–dominated (PFD) GRMHD flow, which passes all four critical (inner and outer, Alfvén, and fast magnetosonic) points along a parabolic streamline. By assuming that the dominating (electromagnetic) component of the energy flux per flux tube is conserved at the surface where the inflow and outflow are separated, the outflow part of the solution can be constrained by the inflow part. The semi-analytical method can provide fiducial and complementary solutions for GRMHD simulations around the rotating black hole, given that the black hole spin, global streamline, and magnetizaion (i.e., a mass loading at the inflow/outflow separation) are prescribed. For reference, we demonstrate a self-consistent result with the work by McKinney in a quantitative level.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Geometric Optimization of an Electrochemical Purification Cell to Prevent Corrosion in CSP Plants During Operation

When exposed to moisture or oxygen, molten chloride salts produce corrosive impurities which degrade containment alloys. This can significantly decrease the lifetime and increase costs of molten-salt-based systems. To overcome this barrier, we designed and modeled an electrochemical purification cell to remove the corrosive impurity MgOH+. Various reactor architectures, including continuous stirred tank reactors (CSTRs) and plug flow reactors (PFRs) were investigated. Steady-state thermoelectric properties were evaluated using analytical methods, allowing assessment of the effects of structure and design parameters such as flow rate, cell length, and cross-sectional area of molten salt. The results suggest that our design could most effectively increase reliability and decrease costs of molten-chloride-salt-based systems by protecting them during continuous operation using an annular plug flow reactor.

analytical modeling↗
DOE OSTI2015

Imaging spectroscopy algorithms for mapping canopy foliar chemical and morphological traits and their uncertainties

A major goal of remote sensing is the development of generalizable algorithms to repeatedly and accurately map ecosystem properties across space and time. Imaging spectroscopy has great potential to map vegetation traits that cannot be retrieved from broadband spectral data, but rarely have such methods been tested across broad regions. Here we illustrate a general approach for estimating key foliar chemical and morphological traits through space and time using NASA's Airborne Visible/Infrared Imaging Spectrometer (AVIRIS-Classic). We apply partial least squares regression (PLSR) to data from 237 field plots within 51 images acquired between 2008 and 2011. Using a series of 500 randomized 50/50 subsets of the original data, we generated spatially explicit maps of seven traits (leaf mass per area (M area ), percentage nitrogen, carbon, fiber, lignin, and cellulose, and isotopic nitrogen concentration, δ 15 N) as well as pixel-wise uncertainties in their estimates based on error propagation in the analytical methods. Both Marea and %N PLSR models had a R 2 > 0.85. Root mean square errors (RMSEs) for both variables were less than 9% of the range of data. Fiber and lignin were predicted with R 2 > 0.65 and carbon and cellulose with R 2 > 0.45. Although R 2 of %C and cellulose were lower than Marea and %N, the measured variability of these constituents (especially %C) was also lower, and their RMSE values were beneath 12% of the range in overall variability. Model performance for δ 15 N was the lowest (R 2 = 0.48, RMSE = 0.95‰), but within 15% of the observed range. The resulting maps of chemical and morphological traits, together with their overall uncertainties, represent a first-of-its-kind approach for examining the spatiotemporal patterns of forest functioning and nutrient cycling across a broad range of temperate and sub-boreal ecosystems. These results offer an alternative to categorical maps of functional or physiognomic types by providing non-discrete maps (i.e., on a continuum) of traits that define those functional types. A key contribution of this work is the ability to assign retrieval uncertainties by pixel, a requirement to enable assimilation of these data products into ecosystem modeling frameworks to constrain carbon and nutrient cycling projections.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1972

Atmospheric pressure, density, temperature and wind variations between 50 and 200 km

Data on atmospheric pressure, density, temperature and winds between 50 and 200 km were collected from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others. These data were analyzed by a daily difference method and results on the distribution statistics, magnitude, and spatial structure of the irregular atmospheric variations are presented. Time structures of the irregular variations were determined by the analysis of residuals from harmonic analysis of time series data. The observed height variations of irregular winds and densities are found to be in accord with a theoretical relation between these two quantities. The latitude variations (at 50 - 60 km height) show an increasing trend with latitude. A possible explanation of the unusually large irregular wind magnitudes of the White Sands MRN data is given in terms of mountain wave generation by the Sierra Nevada range about 1000 km west of White Sands. An analytical method is developed which, based on an analogy of the irregular motion field with axisymmetric turbulence, allows measured or model correlation or structure functions to be used to evaluate the effective frequency spectra of scalar and vector quantities of a spacecraft moving at any speed and at any trajectory elevation angle.

Justus, C. G.↗
NASA NTRS1992

Flow analysis and design optimization methods for nozzle-afterbody of a hypersonic vehicle

This report summarizes the methods developed for the aerodynamic analysis and the shape optimization of the nozzle-afterbody section of a hypersonic vehicle. Initially, exhaust gases were assumed to be air. Internal-external flows around a single scramjet module were analyzed by solving the 3D Navier-Stokes equations. Then, exhaust gases were simulated by a cold mixture of Freon and Ar. Two different models were used to compute these multispecies flows as they mixed with the hypersonic airflow. Surface and off-surface properties were successfully compared with the experimental data. The Aerodynamic Design Optimization with Sensitivity analysis was then developed. Pre- and postoptimization sensitivity coefficients were derived and used in this quasi-analytical method. These coefficients were also used to predict inexpensively the flow field around a changed shape when the flow field of an unchanged shape was given. Starting with totally arbitrary initial afterbody shapes, independent computations were converged to the same optimum shape, which rendered the maximum axial thrust.

Baysal, O.↗
DOE OSTI2017

Phase-field based Multiscale Modeling of Heterogeneous Solid Electrolytes: Applications to Nanoporous Li 3 PS 4

Modeling the effective ion conductivities of heterogeneous solid electrolytes typically involves the use of a computer-generated microstructure consisting of randomly or uniformly oriented fillers in a matrix. But, the structural features of the filler/matrix interface, which critically determine the interface ion conductivity and the microstructure morphology, have not been considered during the microstructure generation. In using nanoporous β-Li 3 PS 4 electrolyte as an example, we develop a phase-field model that enables generating nanoporous microstructures of different porosities and connectivity patterns based on the depth and the energy of the surface (pore/electrolyte interface), both of which are predicted through density functional theory (DFT) calculations. Room-temperature effective ion conductivities of the generated microstructures are then calculated numerically, using DFT-estimated surface Li-ion conductivity (3.14×10 -3 S/cm) and experimentally measured bulk Li-ion conductivity (8.93×10 -7 S/cm) of β-Li 3 PS 4 as the inputs. We also use the generated microstructures to inform effective medium theories to rapidly predict the effective ion conductivity via analytical calculations. Furthemore, when porosity approaches the percolation threshold, both the numerical and analytical methods predict a significantly enhanced Li-ion conductivity (1.74×10 -4 S/cm) that is in good agreement with experimental data (1.64×10 -4 S/cm). The present phase-field based multiscale model is generally applicable to predict both the microstructure patterns and the effective properties of heterogeneous solid electrolytes.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Prediction of hydrogen adsorption in nanoporous materials from the energy distribution of adsorption sites

We present a fast and accurate, semi-analytical method for predicting hydrogen adsorption in nanoporous materials. For any temperature and pressure, the adsorbed amount is calculated as an integral over the energy density of adsorption sites (guest-host interactions) plus an average guest-guest term. The guest-host interaction energy is calculated using a classical force field with hydrogen modelled as a single-site probe. The guest-guest interaction energy is approximated using an average coordination number, which is regressed using Gaussian Process Regression (GPR). Local adsorption at each site is then modelled using a Langmuir isotherm, which when weighted with its probability density gives an accurate description of hydrogen adsorption. The method is tested on 933 metal-organic frameworks (MOFs) from the Computation-Ready Experimental (CoRE) MOF database at 77 K from 10 –5 to 100 bar, and the results are compared against GCMC predictions. To demonstrate the utility of the method, we calculated hydrogen adsorption isotherms for 12,914 existing MOF structures, at two different temperatures at a speed about 100 times that of GCMC simulations and analyzed the results. Here, we found 13 MOFs with predicted deliverable capacities exceeding the DOE target of 50 g/L for adsorption at 100 bar, 77 K and desorption at 5 bar, 160 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

Computational predictive methods for fracture and fatigue

The damage-tolerant design philosophy as used by aircraft industries enables aircraft components and aircraft structures to operate safely with minor damage, small cracks, and flaws. Maintenance and inspection procedures insure that damages developed during service remain below design values. When damage is found, repairs or design modifications are implemented and flight is resumed. Design and redesign guidelines, such as military specifications MIL-A-83444, have successfully reduced the incidence of damage and cracks. However, fatigue cracks continue to appear in aircraft well before the design life has expired. The F16 airplane, for instance, developed small cracks in the engine mount, wing support, bulk heads, the fuselage upper skin, the fuel shelf joints, and along the upper wings. Some cracks were found after 600 hours of the 8000 hour design service life and design modifications were required. Tests on the F16 plane showed that the design loading conditions were close to the predicted loading conditions. Improvements to analytic methods for predicting fatigue crack growth adjacent to holes, when multiple damage sites are present, and in corrosive environments would result in more cost-effective designs, fewer repairs, and fewer redesigns. The overall objective of the research described in this paper is to develop, verify, and extend the computational efficiency of analysis procedures necessary for damage tolerant design. This paper describes an elastic/plastic fracture method and an associated fatigue analysis method for damage tolerant design. Both methods are unique in that material parameters such as fracture toughness, R-curve data, and fatigue constants are not required. The methods are implemented with a general-purpose finite element package. Several proof-of-concept examples are given. With further development, the methods could be extended for analysis of multi-site damage, creep-fatigue, and corrosion fatigue problems.

Cordes, J.↗
DOE OSTI2025

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING↗