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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Experimental Validation of Exact Burst Pressure Solutions for Thick-Walled Cylindrical Pressure Vessels

Burst pressure is one of the critical strength parameters used in the design and operation of pressure vessels because it represents the maximum pressure that a vessel can withstand before failing. Historically, the Barlow formula was used as a design base for estimating burst pressure. However, it does not consider the plastic flow response for ductile steels and is applicable only to thin-walled cylinders (i.e., the diameter to thickness ratio D/t ≥ 20). A new multiaxial plastic yield theory was developed to consider the plastic flow response, and the associated theoretical (i.e., Zhu–Leis) solution of burst pressure was obtained and has gained extensive applications in the pipeline industry because it was validated by different full-scale burst test datasets for large-diameter, thin-walled pipelines in a variety of steel grades from Grade B to X120. The Zhu–Leis flow theory of plasticity was recently extended to thick-walled pressure vessels, and the associated exact flow solution of burst pressure was obtained and is applicable to both thin and thick-walled cylindrical shells. Many full-scale burst tests are available for thin-walled line pipes in the pipeline industry, but limited pressure burst tests exist for thick-walled vessels. To validate the newly developed exact solutions of burst pressure for thick-walled cylinders, this paper conducts a series of burst pressure tests on small-diameter, thick-walled pipes. In particular, six burst tests are carried out for three thick-walled pipes in Grade B carbon steel. These pipes have a nominal diameter of 2.375 inches (60.33 mm) and three nominal wall thicknesses of 0.154, 0.218, and 0.344 inches (3.91, 5.54, and 8.74 mm), leading to D/t = 15.4, 10.9, and 6.9, respectively. With the burst test data, comparisons show that the Zhu–Leis flow solution of burst pressure matches well the burst test data for thick-walled pipes. Thus, these burst tests validate the accuracy of the Zhu–Leis flow solution of burst pressure for thick-walled cylindrical vessels.

42 ENGINEERING↗
DOE OSTI2026

Charge Density Mismatch is a Key Characteristic of Highly Concentrated Electrolyte Solutions and Highly Water‐Soluble Salts

Only very soluble electrolytes can form concentrated solutions. Some salts are so soluble that there are less than four water molecules per ion in saturated solution. Ions usually form clusters or networks with more than one counterion in their coordination sphere in these concentrated solutions. Do these ultraconcentrated solutions form because the counterions have high affinity for each other in liquid, or because they have a poor affinity for each other in solids? Here, in this study, this question is addressed using the valence matching principle of the bond valence model by comparing the charge density mismatch between counterions to their solubility for a series of alkali fluorides, carboxylates, and oxyanions. The solubilities are plotted against the characteristic average bond valence of the alkali, and the lowest solubilities are those where alkali and anion had matching bond valences. Conversely, the highest solubilities are those with poorly matching bond valences. Available ion-pairing constants indicate that the weakest ion-pairs are those with the largest bond valence mismatch, indicating that the large water solubilities occur despite weak ion-pairing rather than because of strong ion-pairing. Therefore, a key characteristic of highly water-soluble salts is that the counterions have mismatched charge densities.

concentrated solutions↗
DOE OSTI2024

Vacancy-mediated transport and segregation tendencies of solutes in fcc nickel under diffusional creep: A density functional theory study

The Nabarro-Herring (NH) diffusional creep theory postulates the vacancy-mediated transport of atoms under a stress gradient as the creep mechanism under low-stress and high-temperature conditions. In multicomponent alloys, we premise that this stress-assisted flow of vacancies to and from grain boundaries will produce elemental segregation. An observation of such segregation, validated with theoretical predictions, can provide the necessary experimental evidence for the occurrence of NH creep. Theoretical calculations of the segregation tendencies via analyzing the dominant solute diffusion mechanisms and the difference in diffusivities of the elements are therefore essential. To this end, this study applies density functional theory calculations of migration barriers and solute-vacancy binding energies as input to the self-consistent mean-field theory to assess the vacancy-mediated diffusion mechanisms, transport coefficients, and segregation tendencies of Co, Cr, Mo, Re, Ta, and W solutes in face-centered-cubic Ni. We find Co, Re, and W to be slow diffusers at high temperatures and Cr, Mo, and Ta to be fast diffusers. Further analysis shows that the slow diffusers tend to always enrich at vacancy sinks over a wide range of temperatures. In contrast, the fast diffusers show a transition from depletion to enrichment as the temperature lowers. Furthermore, our analysis of the segregation tendencies under tensile hydrostatic strains shows that slow diffusers are largely unaffected by the strain and favor enrichment. On the other hand, the fast diffusers exhibit high sensitivity to strain and their segregation tendency can transition from depletion to enrichment at a given temperature. Finally, the transport coefficients calculated in this work are expected to serve as input to mesoscale microstructure models to provide a more rigorous assessment of solute segregation under NH creep conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Persistence and potential of soil organic carbon in nature‐based climate solutions: A review of managed disturbances

Societal Impact Statement Implementing nature-based climate solutions is important for mitigating climate change, which is a global issue, but requires local adjustments in management practices. Using the association between soil carbon and minerals as a proxy for carbon persistence, we evaluated the effect of different management regimes on soil carbon sequestration and loss. We identified areas where management practices that increase carbon inputs should be prioritized and areas where management should focus on avoiding severe disturbances. Using this storage-potential-and-persistence framework to identify how to increase or maintain soil organic carbon storage locally will increase the effectiveness of nature-based climate solutions globally. Summary Increasing soil organic carbon storage could reduce the pace of climate change, but the longevity of this nature-based climate solution depends on the persistence of carbon in soils, not just the input rates into soils. We apply a framework for considering how soil carbon persistence—namely, via the association with minerals—sheds light on soil carbon sequestration. We review how management of disturbances, such as prescribed burning, forestry, and grazing, can change soil carbon storage, persistence, and potential. Past work demonstrated that management of disturbances can sequester soil carbon, but it remains unclear how the potential stabilization of that accrual and vulnerability to loss varies across disturbance types and geographies. We found that there is substantial geographical heterogeneity in the overlap among estimates of carbon accrual, disturbance occurrence, and potential stabilization: Fire-prone grasslands and intensively grazed rangelands occur in areas estimated to have high potential to store mineral-associated organic carbon, and studies also find that adjusted fire and grazing can promote mineral-associated organic carbon. Plantation forestry and burned area span large regions where particulate organic matter is the dominant form, and studies find that particulate organic carbon is disproportionately lost following intense wildfires and forest harvests. Thus, areas with high mineral-associated organic carbon deficits should be prioritized for practices that increase carbon inputs; whereas areas with high proportions of particulate organic carbon should be prioritized for practices that help to avoid severe disturbances. Taken together, the distribution of and changes in persistence mechanisms shed light on the durability of nature-based climate solutions.

fire↗
DOE OSTI2024

Concurrent measurement of strain and chemical reaction rates in a calcite grain pack undergoing pressure solution: Evidence for surface-reaction controlled dissolution

Pressure solution is inferred to be a significant contributor to sediment compaction and lithification, especially in carbonate sediments. For a sediment deforming primarily by pressure solution, the compaction rate should be directly related to the rate of calcite dissolution, transport along grain contacts, and calcite reprecipitation. Previous experimental work has shown that there is evidence that deformation in wet calcite grain packs is consistent with control by pressure solution, but considerable ambiguity remains regarding the rate limiting mechanism. We present the results of laboratory compaction experiments designed to directly measure calcite dissolution and precipitation rates (recrystallization rates) concurrently with strain rate to test whether measured rates are consistent with predicted rates both in absolute magnitude and time evolution. Recrystallization rates are measured using trace element chemistry (Sr/Ca, Mg/Ca) and isotopes (87Sr/86Sr) of fluids flowing slowly through a compacting grain pack as it is being triaxially compressed. Imaging techniques are used to characterize the grain contacts and strain effects in the post-experiment grain pack. Our data show that calcite recrystallization rates calculated from all three geochemical parameters are in approximate agreement and that the rates closely track strain rate. The geochemically inferred rates are close to predicted rates in absolute magnitude. Uncertainty in grain contact dimensions makes distinguishing between surface reaction control and diffusion control difficult. Measured reaction rates decrease faster than predicted from standard pressure solution creep flow laws. This inconsistency may indicate that calcite dissolution rates at grain contacts are more complex, and more time-dependent, than suggested by geometric models designed to predict grain contact stresses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Analytic soliton solutions of nonlinear extensions of the Schrödinger equation

A method is presented to construct analytic solitary wave solutions in nonlinear extensions of the Schrödinger equation starting from analytic solutions of the ordinary Schrödinger equation. We provide several examples illustrating the method. We rederive three well-known soliton solutions including the N-dimensional non-relativistic Gausson as well as the one-dimensional 1 / cosh-soliton and a theory with a power-like nonlinearity proportional to |ψ| 2λ with λ > 0. We also find several new solutions in different nonlinear theories in various space dimensions which, to the best of our knowledge, have not yet been discussed in literature. Our method can be used to construct further nonlinear theories and generalized to relativistic soliton theories, and may have many applications.

Analytical soliton solutions↗
DOE OSTI2026

Chemical complexity suppresses interstitial solute segregation to screw dislocation cores in the bcc NbTaTiHfZr high-entropy alloy

Recent reports suggest that interstitial solute additions to body-centered cubic (bcc) high-entropy alloys (HEAs) may enhance their mechanical properties. However, details of interactions between interstitial atoms and dislocations in these HEAs remain incompletely understood. Using first-principles calculations, we examine the energetics of C, N, and O interstitial solutes in elemental bcc metals and NbTaTiHfZr, focusing on their segregation in screw dislocation cores. We examine two types of core sites and show that the low-energy configuration and associated segregation energy depend on the transition metal group. In NbTaTiHfZr, we find that chemical complexity substantially suppresses interstitial segregation in dislocation cores, as fluctuations in bulk solute energies induce energetically favorable sites that disfavor segregation to core sites. Local chemical order further enhances this effect by promoting solute clustering away from dislocation cores. These findings reveal fundamental differences between the behavior of interstitial atoms in elemental metals and HEAs, with implications for high-temperature plasticity and dynamic strain aging.

Body-centered cubic transition metals↗
DOE OSTI2024

Predicting RNA structure and dynamics with deep learning and solution scattering

Advanced deep learning and statistical methods can predict structural models for RNA molecules. However, RNAs are flexible, and it remains difficult to describe their macromolecular conformations in solutions where varying conditions can induce conformational changes. Small-angle x-ray scattering (SAXS) in solution is an efficient technique to validate structural predictions by comparing the experimental SAXS profile with those calculated from predicted structures. There are two main challenges in comparing SAXS profiles to RNA structures: the absence of cations essential for stability and charge neutralization in predicted structures and the inadequacy of a single structure to represent RNA’s conformational plasticity. We introduce a solution conformation predictor for RNA (SCOPER) to address these challenges. This pipeline integrates kinematics-based conformational sampling with the innovative deep learning model, IonNet, designed for predicting Mg 2+ ion binding sites. Validated through benchmarking against 14 experimental data sets, SCOPER significantly improved the quality of SAXS profile fits by including Mg 2+ ions and sampling of conformational plasticity. We observe that an increased content of monovalent and bivalent ions leads to decreased RNA plasticity. Therefore, carefully adjusting the plasticity and ion density is crucial to avoid overfitting experimental SAXS data. SCOPER is an efficient tool for accurately validating the solution state of RNAs given an initial, sufficiently accurate structure and provides the corrected atomistic model, including ions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

The physical origin of heterogeneous solute clustering and nanoprecipitation at grain boundaries in ultrafine-grained immiscible alloys

Here, grain-boundary segregation effects on heterogeneous solute clustering and nanoprecipitation at low solute concentrations were investigated in sputter-deposited ultrafine-grained Ag-Cu alloy films. X-ray diffraction and scanning transmission electron microscopy revealed extended solubility of Cu in Ag matrix, accompanied by the formation of Cu-rich nanoprecipitates and solute clusters at grain boundaries and their junctions. Atomistic simulations further demonstrated that Cu solutes heterogeneously segregate to Ag GBs and form small clusters that grow into nuclei for Cu nanoprecipitates. These findings provide critical insights into the role of heterogeneous grain-boundary segregation in governing the phase separation pathways of immiscible nanocrystalline and ultrafine-grained alloys.

Heterogeneous segregation↗
DOE OSTI2024

Smaller Is Better: The Case for Lower-Order Iodoplumbate Species Dominating MAPbI 3 /Dimethylformamide Solutions

Here, using complementary experimental measurements and computational predictions of spectroscopic measurements (EXAFS, XANES, and UV–vis), we have determined the identity of the most stable iodoplumbate species in dilute lead halide perovskite precursor solutions. We have determined which species are most likely to be thermodynamically stable compared to others that are unstable or metastable. Condensed phase ab initio models were constructed, and the resulting ensembles were used to directly compare the computed signals to the experimental results of the EXAFS, XANES, and UV–vis spectra of PbI 2 :MAI in DMF. The results of this study suggest that only Pb 2+ , PbI + , and PbI 2 are dominant in the dilute lead perovskite precursor solutions as thermodynamically stable entities. Our interpretation of the relative stability of iodoplumbate species in solution, based on an analysis of EXAFS and XANES spectra, provides critically important new insight into the species most likely to be responsible for crystal nucleation and growth in these materials. This insight will have a significant consequence on the broad scientific community and will necessitate the reinterpretation of peaks in the UV–vis spectra of lead halide perovskite precursor solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Stoichiometric Lanthanide Compounds with Diglycolamides: A Synthetic Approach toward Understanding Rare-Earth Speciation in Solution

A fundamental understanding of coordination chemistry across the lanthanide series is essential for explaining the chemical behavior of rare-earth metals in complex liquid–liquid extraction processes. Probing the exact bonding between the extractant and the metal is sometimes done through the synthesis of solid-state compounds that can serve as models for metal speciation in solution. In the case of diglycolamide (DGA), a commonly used neutral diamide extractant, extensive studies identify the stepwise formation of 1:1 [Ln(DGA)(H 2 O) 6 ] 3+ , 1:2 [Ln(DGA) 2 (H 2 O) 3 ] 3+ , and 1:3 [Ln(DGA) 3 ] 3+ complexes in solution. The crystallographic reports, however, exclusively show a 1:3 [Ln(DGA) 3 ] 3+ moiety in the solid state, while the structures of 1:1 and 1:2 complexes are yet to be isolated and comprehensively studied. In this work, we report the synthesis and characterization of three new families of stoichiometric N,N,N′,N’ -tetramethyldiglycolamide (TMDGA) compounds: [Ln(TMDGA)(H 2 O) 5 Cl]Cl 2 ·2H 2 O, [Ln(TMDGA) 2 (H 2 O) 3 ]Cl 3 ·3H 2 O, and [Ln(TMDGA) 3 ]Cl 3 ·7H 2 O, where Ln = Nd, Eu, Gd, with Ln:TMDGA ratios of 1:1, 1:2, and 1:3, respectively. Further, the compounds have been analyzed using vibrational spectroscopy (both Raman and FT-IR), as well as variable temperature fluorescence spectroscopy. A spectrophotometric titration of Eu(III) was performed to confirm the presence of the [Eu(TMDGA) n ] 3+ ( n = 1, 2, and 3) species in solution and to compare the individual solid-state emission spectra to their respective analogues in solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Ion Clusters in Multicomponent Solutions Determined from X-ray PDF and SAXS Analysis: The NaNO 2 –NaOH–H 2 O System

Here, this study explores ion cluster formation in the NaNO 2 –NaOH–H 2 O system to understand how ion cluster formation is influenced by the composition in multicomponent mixtures. X-ray pair distribution function (PDF) and small-angle X-ray scattering (SAXS) identified complex ion clusters in concentrated NaNO 2 and NaOH solutions as well as their mixtures. PDF analysis showed that the Na–O distance depended primarily on total Na + concentrations rather than anion composition, whereas the nitrite-water oxygen distance stayed the same regardless of concentration or composition. This result indicates that the nitrite ion hydration was relatively independent of composition. SAXS confirms local fluctuations and coherent clusters with notable size differences between NaOH and NaNO 2 solutions. SAXS analysis of mixed solutions shows that their clusters are an average of the individual solutions, indicating mixed clusters.

Reynolds, Jacob G. [Central Plateau Cleanup Compan↗
DOE OSTI2024

Development of an Attenuated Total Reflectance–Ultraviolet–Visible Probe for the Online Monitoring of Dark Solutions

Optical spectroscopy is a valuable tool for on-line monitoring of a variety of processes. Ultraviolet-visible (UV-vis) spectroscopy in particular, can monitor the concentration of analytes as well as identify speciation and oxidation state. However, it can be difficult to impossible to employ UV-vis based sensors on chemical systems that are very dark (i.e., high optical density) as exceedingly short pathlengths are required (for transmission approaches) or effective means of backscattering are needed (for reflectance approaches). Examples of processes that would benefit significantly from the use of optical sensors and encounter these challenges include used nuclear fuel recycling and molten salts with high concentrations of dissolved uranium. Utilizing an attenuated total reflectance (ATR) UV-vis approach can overcome these challenges and allow for the measurement of solutions orders of magnitude more concentrated than transmission UV-vis. However, determining ideal sensor specifications for varied processes can be time consuming and expensive. Here, in this study, we evaluate the ability for a novel ATR-UV-vis probe to measure very concentrated solutions of Co(II) and Ni(II) nitrate as well as organic dyes (methylene blue, acid red 1, and crystal violet). This sensor design provides a modular method for exploring possible “pathlengths” by altering the exposed ATR fiber length. Also studied were approaches to loading and measuring the sensor cell. These results are compared to a traditional 1 cm cuvette measured by transmission UV-vis. It was found that the ATR-UV-vis probe was capable of measuring solutions 600 times more concentrated than the 1 cm cuvette. Advanced data analysis in the form of multivariate curve resolution (MCR) was used to analyze the speciation of methylene blue over a large concentration range. The application of this novel ATR-UV-vis probe to the interrogation of dark solutions is a promising avenue for use in on-line monitoring of nuclear processes.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Direct Observations of Solute Dispersion in Rocks With Distinct Degree of Sub‐Micron Porosity

Abstract The transport of chemical species in rocks is affected by their structural heterogeneity to yield a wide spectrum of local solute concentrations. To quantify such imperfect mixing, advanced methodologies are needed that augment the traditional breakthrough curve analysis by probing solute concentration within the fluids locally. Here, we demonstrate the application of asynchronous, multimodality imaging by X‐ray computed tomography (XCT) and positron emission tomography (PET) to the study of passive tracer experiments in laboratory rock cores. The four‐dimensional concentration maps measured by PET reveal specific signatures of the transport process, which we have quantified using fundamental measures of mixing and spreading. We observe that the extent of solute spreading correlate strongly with the strength of subcore‐scale porosity heterogeneity measured by XCT, while dilution is enhanced in rocks containing substantial sub‐micron porosity. We observe that the analysis of different metrics is necessary, as they can differ in their sensitivity to the strength and forms of heterogeneity. The multimodality imaging approach is uniquely suited to probe the fundamental difference between spreading and mixing in heterogeneous media. We propose that when multi‐dimensional data is available, mixing and spreading can be independently quantified using the same metric. We also demonstrate that one‐dimensional transport models have limited predictive ability toward the internal evolution of the solute concentration, when the model is solely calibrated against the effluent breakthrough curves. The data set generated in this study can be used to build realistic digital rock models and to benchmark transport simulations that account deterministically for rock property heterogeneity.

Kurotori, Takeshi [Department of Chemical Engineer↗
DOE OSTI2026

Nanoengineering of non-aqueous liquid electrolyte solutions for future lithium metal batteries

Research and development of non-aqueous electrolyte solutions are essential for practical advancement towards the production of high-energy lithium metal batteries (LMBs). An ideal LMB electrolyte solution should enable highly efficient, uniform and prolonged lithium metal plating and stripping, preserve the electrodes’ electro(chemo)mechanical properties and ensure compatibility with all cell components. However, despite extensive research efforts, scientists have yet to achieve an electrolyte design that meets these requirements simultaneously. Here, by examining the nanoengineering aspects of various non-aqueous electrolyte solution designs, we elucidate the understanding of the nanoscale physicochemical and electrochemical processes taking place in LMBs, which are mainly governed by the thermodynamic and kinetic properties of the electrolyte system. We also explore emerging research directions and propose an accelerated, iterative framework that integrates nanoengineering principles with machine learning, high-throughput computation and experimentation to facilitate the development of next-generation non-aqueous electrolyte solutions for practical LMBs.

Weintz, Dominik↗
DOE OSTI2024

Performance enhancement of aqueous ionic liquids with lower critical solution temperature (LCST) behavior through ternary mixtures

Thermally responsive ionic liquids (ILs) exhibit liquid–liquid phase separation when mixed with water and heated above a lower critical solution temperature (LCST), resulting in a water-rich (WR) and an IL-rich (ILR) phase. These binary IL–water mixtures can be employed in a variety of thermodynamic processes such as forward osmosis (FO) desalination, for which two solution properties are desirable: low phase separation temperature and high osmotic strength (osmolality). However, these two properties are interlinked, with ILs that exhibit higher osmotic strengths typically requiring higher phase separation temperatures. This behavior tends to arise from the hydrophilicity of the IL cations, which enhances osmotic strength while also elevating the phase separation temperature. In this work, we highlight a pathway to overcome this tradeoff by developing ternary IL mixtures (two ILs with varying cation hydrophilicity mixed with water), which lowers the phase separation temperature while maintaining and even enhancing the osmotic strength of the solution. We characterize the mixing behavior (osmolality, phase separation temperature, WR phase purity, and WR to ILR phase mass ratio) of four ILs as a function of their concentration in solution. We find that an enhancement of up to 81.6% in the osmolality with a concomitant reduction of up to 15.4% in the phase separation temperature can be achieved using this approach. The ternary mixture is also shown to improve the phase separation kinetics by nearly 95% compared to the binary mixture. Overall, this work highlights a new pathway to improve the performance of LCST ILs for water and energy applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Structure and ultrafast dynamics of tri-nuclear Ag-/Tl–Pt 2 POP 4 complexes in solution

The energetics and dynamics of ion assembly in solution has broad influence in nanomaterials and inorganic synthesis. To investigate the fundamental processes involved, we present a time-resolved x-ray solution scattering (TR-XSS) study of the trinuclear silver and thallium complexes of the diplatinum ion PtPOP [Pt 2 (H 2 P 2 O 5 )$_4^{4−}$] in aqueous solution. These complexes, their structural properties, and their electronic structure are not well understood and afford a unique opportunity to study the metal–metal bond formation that influences molecular and material assembly in solution. We present model-independent analysis of the observed dynamics as well as an analysis incorporating time-resolved structural refinements of key bond lengths with $<$100 fs time resolution. We find that upon photoexcitation, the Pt atoms contract ∼0.25 Å toward the center of both the Ag- and the Tl-PtPOP complexes, as previously observed for the PtPOP anion. For the AgPtPOP system, an ultrafast Ag-Pt bond expansion of ∼0.2 Å is observed, whereas in contrast, the TlPtPOP system exhibits a Tl-Pt bond contraction of ∼0.3 Å upon photoexcitation. For both complexes, the change in electronic state leads to coherent (“wave-packet”) oscillations along the metal–Pt coordinates. Based on these structural dynamics, we propose an electronic structure model that describes the metal–metal bonding behavior in both the ground and excited state for both complexes.

Lenzen, Philipp [Technical Univ. of Denmark, Lyngb↗
DOE OSTI2024

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗