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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Longitudinal Single‐Cell Imaging of Engineered Strains with Stimulated Raman Scattering to Characterize Heterogeneity in Fatty Acid Production

Abstract Understanding metabolic heterogeneity is critical for optimizing microbial production of valuable chemicals, but requires tools that can quantify metabolites at the single‐cell level over time. Here, longitudinal hyperspectral stimulated Raman scattering (SRS) chemical imaging is developed to directly visualize free fatty acids in engineered Escherichia coli over many cell cycles. Compositional analysis is also developed to estimate the chain length and unsaturation of the fatty acids in living cells. This method reveals substantial heterogeneity in fatty acid production among and within colonies that emerges over the course of many generations. Interestingly, the strains display distinct types of production heterogeneity in an enzyme‐dependent manner. By pairing time‐lapse and SRS imaging, the relationship between growth and production at the single‐cell level are examined. The results demonstrate that cell‐to‐cell production heterogeneity is pervasive and provides a means to link single‐cell and population‐level production.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Scalable Manufacturing of Efficient Perovskite/Silicon Tandem Modules

Crystalline-Si (c-Si) technology produces excellent solar cells with conversion efficiencies of up to 26.7%—nearly their practical limit of 27%—and has been commercialized extensively to produce panels below $\$0.40$/W. Techno-economic analysis shows that module efficiency will continue to be a primary cost driver because of high balance-ofsystems costs, and there is no path to higher efficiencies with single-junction silicon cells. In this project, three research teams from University of North Carolina, Arizona State University and National Renewable National Laboratory worked together to develop perovskite-silicon tandem cells with a high throughput process which can handle 5000 wafers per hour, enabled by very low added CAPEX of ~$20k for a doctor-blade coater. This can potentially increase the module efficiency to 30% (with grid) with small increase of cost, which will drive down the cost of silicon modules to be at least 16% cheaper than present silicon PERC modules. We also explored the alternative narrow bandgap perovskites as silicon replacement for all perovskite tandem cells. This project has substantially advanced the progress of solution-process perovskitessilicon tandem solar cells and perovskite-perovskite tandem solar cells with many inventions and discoveries, evidenced by 18 publications and 6 invention disclosures. Several notable examples include 1) we developed the new idea of small pyramid in combination with solution grown perovskites and demonstrated record-efficiency of 28.5% for 1 cm2 on textured silicon bottom cells and 25.2% for 24 cm2 on chemically etched silicon bottom cells for perovskite-silicon tandem cells. 2) We developed perovskite ink that can coat perovskites onto texture silicon without voids;, and new device structure to enhance the yield of fabrication by reducing shunting 3) We identified the origin of open circuit voltage on mixed halide wide bandgap perovskites, and came with a solution for this problem, reducing the voltage loss to a record small value, which can potentially push the perovskite-silicon tandem cell efficiency to over 31%; 4) We have developed efficient alternative low bandgap semiconductors, i.e. gradient-doped Sn based perovskites by Ba ions, new oxide hole transport layers which increase the efficiency of perovskite/perovskite tandem cells reached record efficiency of 26.3%; 5) We developed bifacial perovskite/perovskite tandem cells by overcoming contacts issues and regaining light absorption, further boosting the equivalent efficiency to 29.3% under 1 sun illumination with 30% albedo light; 6) We developed the first all perovskite tandem module fabricated in air by discovery a combination of oxidization and reduction couples, yield an aperture efficiency of 21.6% for all perovskite mininodules, exceeding that of single junction perovskite minimodules. These discoveries not only accelerate the commercialization of perovskite-silicon tandem solar cells, but also provide guidance in designing other type of perovskite solar cell technologies.

14 SOLAR ENERGY↗
DOE OSTI2025

Quantitative multiplexed analysis of gene and protein expression patterns in Yarrowia lipolytica

In this report, we present coordinated observations of protein and mRNA transcript counts at the single-cell level in the oleaginous yeast model Yarrowia lipolytica. The transcription factor Xbp1p regulates entry into a quiescent state, representing a shift of resources to sequestration of nutrients rather than cell division. We observed the responses of wild-type and Δxbp1 cells to protein (by fluorescence) and transcript quantification and localization at both single-cell and population-averaged levels. Data were collected via single-molecule fluorescence in situ hybridization (smFISH) and qPCR under nitrogen depletion, a condition that drives lipid accumulation. These techniques reveal a complex and heterogeneous population of Xbp1p dynamics and downstream regulation. Our findings highlight the need for single-cell resolution analyses to describe cellular dynamics and regulatory processes.

Yarrowia lipolytica↗
DOE OSTI2024

Transport Analysis & Optimization in a MW-Scale CO2 Electrolyzer (Final Report)

As Twelve continues to scale up their CO2 electrolyzers, both in the size of a single cell and in the number of cells used in a stack, thermal management becomes a growing concern, since excess heat can affect reaction yield and accelerate degradation. In this project, we aim to computationally explore how the anode flow fields used in Twelve’s CO2 electrolyzers function as heat exchangers. In particular, using a homogenized model of a CO2 electrolyzer, we first estimate the amount of heat generated in a cell. Then, we develop a computational fluid dynamics (CFD) model of the so-called “flow field”, i.e. a flow manifold, based on Twelve’s CAD drawings, to evaluate how these flow fields perform as a heat exchanger for the generated heat. We explore both a single cell and a 3-cell stack operating in parallel, where heat generated in one cell can now be transferred to another cell. We evaluate how performance is affected when environmental heat losses are taken into account. Finally, we leverage topology optimization to explore the types of design features a computational optimization algorithm would suggest to supplement our intuition. Overall, our work aims to provide design recommendations for CO2 electrolyzer flow fields and provides a foundation for future studies of flow field optimization.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Diversification of multipotential postmitotic mouse retinal ganglion cell precursors into discrete types

The genesis of broad neuronal classes from multipotential neural progenitor cells has been extensively studied, but less is known about the diversification of a single neuronal class into multiple types. We used single-cell RNA-seq to study how newly born (postmitotic) mouse retinal ganglion cell (RGC) precursors diversify into ~45 discrete types. Computational analysis provides evidence that RGC transcriptomic type identity is not specified at mitotic exit, but acquired by gradual, asynchronous restriction of postmitotic multipotential precursors. Some types are not identifiable until a week after they are generated. Immature RGCs may be specified to project ipsilaterally or contralaterally to the rest of the brain before their type identity emerges. Optimal transport inference identifies groups of RGC precursors with largely nonoverlapping fates, distinguished by selectively expressed transcription factors that could act as fate determinants. Our study provides a framework for investigating the molecular diversification of discrete types within a neuronal class.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Single-cell quantification of ribosome occupancy in early mouse development

Translation regulation is critical for early mammalian embryonic development. However, previous studies had been restricted to bulk measurements, precluding precise determination of translation regulation including allele-specific analyses. Here, to address this challenge, we developed a novel microfluidic isotachophoresis (ITP) approach, named RIBOsome profiling via ITP (Ribo-ITP), and characterized translation in single oocytes and embryos during early mouse development. We identified differential translation efficiency as a key mechanism regulating genes involved in centrosome organization and N 6 -methyladenosine modification of RNAs. Our high-coverage measurements enabled, to our knowledge, the first analysis of allele-specific ribosome engagement in early development. These led to the discovery of stage-specific differential engagement of zygotic RNAs with ribosomes and reduced translation efficiency of transcripts exhibiting allele-biased expression. By integrating our measurements with proteomics data, we discovered that ribosome occupancy in germinal vesicle-stage oocytes is the predominant determinant of protein abundance in the zygote. The Ribo-ITP approach will enable numerous applications by providing high-coverage and high-resolution ribosome occupancy measurements from ultra-low input samples including single cells.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Imaging the kinetics of anisotropic dissolution of bimetallic core–shell nanocubes using graphene liquid cells

Chemical design of multicomponent nanocrystals requires atomic-level understanding of reaction kinetics. Here, we apply single-particle imaging coupled with atomistic simulation to study reaction pathways and rates of Pd@Au and Cu@Au core-shell nanocubes undergoing oxidative dissolution. Quantitative analysis of etching kinetics using in situ transmission electron microscopy (TEM) imaging reveals that the dissolution mechanism changes from predominantly edge-selective to layer-by-layer removal of Au atoms as the reaction progresses. Dissolution of the Au shell slows down when both metals are exposed, which we attribute to galvanic corrosion protection. Morphological transformations are determined by intrinsic anisotropy due to coordination-number-dependent atom removal rates and extrinsic anisotropy induced by the graphene window. Our work demonstrates that bimetallic coreshell nanocrystals are excellent probes for the local physicochemical conditions inside TEM liquid cells. Furthermore, single-particle TEM imaging and atomistic simulation of reaction trajectories can inform future design strategies for compositionally and architecturally sophisticated nanocrystals.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

Single-Cell Genomics of Novel Actinobacteria With the Wood–Ljungdahl Pathway Discovered in a Serpentinizing System

Serpentinite-hosted systems represent modern-day analogs of early Earth environments. In these systems, water-rock interactions generate highly alkaline and reducing fluids that can contain hydrogen, methane, and low-molecular-weight hydrocarbons-potent reductants capable of fueling microbial metabolism. In this study, we investigated the microbiota of Hakuba Happo hot springs (~50°C; pH~10.5–11), located in Nagano (Japan), which are impacted by the serpentinization process. Analysis of the 16S rRNA gene amplicon sequences revealed that the bacterial community comprises Nitrospirae (47%), “Parcubacteria” (19%), Deinococcus-Thermus (16%), and Actinobacteria (9%), among others. Notably, only 57 amplicon sequence variants (ASV) were detected, and fifteen of these accounted for 90% of the amplicons. Among the abundant ASVs, an early-branching, uncultivated actinobacterial clade identified as RBG-16-55-12 in the SILVA database was detected. Ten single-cell genomes (average pairwise nucleotide identity: 0.98–1.00; estimated completeness: 33–93%; estimated genome size: ~2.3 Mb) that affiliated with this clade were obtained. Taxonomic classification using single copy genes indicates that the genomes belong to the actinobacterial class-level clade UBA1414 in the Genome Taxonomy Database. Based on metabolic pathway predictions, these actinobacteria are anaerobes, capable of glycolysis, dissimilatory nitrate reduction and CO 2 fixation via the Wood–Ljungdahl (WL) pathway. Several other genomes within UBA1414 and two related class-level clades also encode the WL pathway, which has not yet been reported for the Actinobacteria phylum. For the Hakuba actinobacterium, the energy metabolism related to the WL pathway is likely supported by a combination of the Rnf complex, group 3b and 3d [NiFe]-hydrogenases, [FeFe]-hydrogenases, and V-type (H + /Na + pump) ATPase. The genomes also harbor a form IV ribulose 1,5-bisphosphate carboxylase/oxygenase (RubisCO) complex, also known as a RubisCO-like protein, and contain signatures of interactions with viruses, including clustered regularly interspaced short palindromic repeat (CRISPR) regions and several phage integrases. This is the first report and detailed genome analysis of a bacterium within the Actinobacteria phylum capable of utilizing the WL pathway. The Hakuba actinobacterium is a member of the clade UBA1414/RBG-16-55-12, formerly within the group “OPB41.” We propose to name this bacterium ‘Candidatus Hakubanella thermoalkaliphilus.'

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Thermal Analysis of High Entropy Rare Earth Oxides

Phase transformations in multicomponent rare earth sesquioxides were studied by splat quenching from the melt, high temperature differential thermal analysis and synchrotron X-ray diffraction on laser-heated samples. Three compositions were prepared by the solution combustion method: (La,Sm,Dy,Er,RE) 2 O 3 , where all oxides are in equimolar ratios and RE is Nd or Gd or Y. After annealing at 800 °C, all powders contained mainly a phase of C-type bixbyite structure. After laser melting, all samples were quenched in a single-phase monoclinic B-type structure. Thermal analysis indicated three reversible phase transitions in the range 1900–2400 °C, assigned as transformations into A, H, and X rare earth sesquioxides structure types. Unit cell volumes and volume changes on C-B, B-A, and H-X transformations were measured by X-ray diffraction and consistent with the trend in pure rare earth sesquioxides. The formation of single-phase solid solutions was predicted by Calphad calculations. The melting point was determined for the (La,Sm,Dy,Er,Nd) 2 O 3 sample as 2456 ± 12 °C, which is higher than for any of constituent oxides. An increase in melting temperature is probably related to nonideal mixing in the solid and/or the melt and prompts future investigation of the liquidus surface in Sm 2 O 3 -Dy 2 O 3 , Sm 2 O 3 -Er 2 O 3 , and Dy 2 O 3 -Er 2 O 3 systems.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Stochastic journeys of cell progenies through compartments and the role of self-renewal, symmetric and asymmetric division

Abstract Division and differentiation events by which cell populations with specific functions are generated often take place as part of a developmental programme, which can be represented by a sequence of compartments. A compartment is the set of cells with common characteristics; sharing, for instance, a spatial location or a phenotype. Differentiation events are transitions from one compartment to the next. Cells may also die or divide. We consider three different types of division events: (i) where both daughter cells inherit the mother’s phenotype (self-renewal), (ii) where only one of the daughters changes phenotype (asymmetric division), and (iii) where both daughters change phenotype (symmetric division). The self-renewal probability in each compartment determines whether the progeny of a single cell, moving through the sequence of compartments, is finite or grows without bound. We analyse the progeny stochastic dynamics with probability generating functions. In the case of self-renewal, by following one of the daughters after any division event, we may construct lifelines containing only one cell at any time. We analyse the number of divisions along such lines, and the compartment where lines terminate with a death event. Analysis and numerical simulations are applied to a five-compartment model of the gradual differentiation of hematopoietic stem cells and to a model of thymocyte development: from pre-double positive to single positive (SP) cells with a bifurcation to either SP4 or SP8 in the last compartment of the sequence.

Science & Technology - Other Topics↗
DOE OSTI2025

Enhanced MPM framework with multipatch isogeometric analysis for geotechnical applications

Achieving stable stress solutions at large strains using the Material Point Method (MPM) is challenging due to the accumulation of errors associated with geometry discretization, cell-crossing noise, and volumetric locking. Several simplified attempts exist in the literature to mitigate these errors, including higher-order frameworks. However, the stability of the MPM solution in such frameworks has been limited to simple geometries and the single-phase formulation (i.e., neglecting pore fluid). Although never explored, multipatch isogeometric analysis offers desirable qualities to simulate complex geometries while mitigating errors in the MPM. The degree of required high-order spatial integration has also never been investigated to infer a minimum limit for the stability of the stress solution in MPM. This paper presents a general-purpose numerical framework for simulating stable stresses in porous media, capturing both near incompressibility and multiphase interactions. First, the numerical framework is presented considering Non-Uniform Rational B-splines (NURBS) to perform isogeometric analysis (IGA) in MPM. Additionally, a volumetric strain smoothing algorithm is used to alleviate errors associated with volumetric locking. Second, the manifestation of cell-crossing errors is assessed via a series of problems with orders ranging from linear to cubic interpolation functions. Third, the use of NURBS is investigated and verified for problems with circular geometries. Finally, multipatch analysis is deployed to simulate plane strain and 3D penetration in soils, considering nearly incompressible elastoplastic (total stress) analysis and fully-coupled hydro-mechanical (effective stress) analysis. The stability of the solution is also analyzed for different constitutive models. From the results, it can be concluded that the framework using cubic interpolation functions with strain smoothing is the most convenient, presenting stable stress solutions for a broad range of multiphase geotechnical applications.

58 GEOSCIENCES↗
DOE OSTI2025

Structural and Spectroscopic Characterization of Plutonium and Other Tetravalent Metals Complexed to a Keggin Ion

Here, we report the isolation of the first plutonium(IV) complex with a Keggin ion chelator: Cs 20 [Pu(PW 11 O 39 ) 2 ] 2 ·13H 2 O. Single crystal XRD and solid-state UV–vis absorbance analysis demonstrate the stabilization of Pu 4+ by the Keggin ligand. The unit cell contains two [Pu(PW 11 O 39 ) 2 ] 10– complexes (Pu(PW 11 ) 2 ) bridged by Cs + . Raman and 31 P NMR spectra of Pu(PW 11 ) 2 are consistent with the analogous Zr 4+ , Hf 4+ , Ce 4+ , and Th 4+ complexes. The Pu–O bond distances at the two Pu sites are 2.35(3) and 2.34(3) Å, matching the value extrapolated from the bonding trend built with the other 8-coordinated tetravalent cations. However, the long-range arrangement of the Pu(PW 11 ) 2 complexes within the lattice is unique in the series of M IV (PW 11 ) 2 compounds: pairs of Pu(PW 11 ) 2 are organized perpendicular to each other. Based on solution-state UV–visible absorbance, small-angle X-ray scattering (SAXS), and 31 P NMR, the tetravalent cations quantitatively form the 1:2 species in solution ([Pu(PW 11 O 39 ) 2 ] 10– (aq) ) and no 1:1 species ([Pu(PW 11 O 39 )(H 2 O) x ] 3– (aq) ). Finally, a linear correlation exists between the metal–oxygen distances in the M IV (PW 11 ) 2 compounds and the corresponding metal dioxides, allowing for extrapolation for Pa 4+ , Am 4+ , and Bk 4+ . The results indicate that our microscale POM approach represents a viable pathway to probe properties of rare actinide ions in discrete molecules, beyond the traditional oxide extended solids.

and nuclear chemistry↗
DOE OSTI2023

Proposed minimal standards for description of methanogenic archaea

Methanogenic archaea are a diverse, polyphyletic group of strictly anaerobic prokaryotes capable of producing methane as their primary metabolic product. It has been over three decades since minimal standards for their taxonomic description have been proposed. In light of advancements in technology and amendments in systematic microbiology, revision of the older criteria for taxonomic description is essential. Most of the previously recommended minimum standards regarding phenotypic characterization of pure cultures are maintained. Electron microscopy and chemotaxonomic methods like whole-cell protein and lipid analysis are desirable but not required. Because of advancements in DNA sequencing technologies, obtaining a complete or draft whole genome sequence for type strains and its deposition in a public database are now mandatory. Genomic data should be used for rigorous comparison to close relatives using overall genome related indices such as average nucleotide identity and digital DNA–DNA hybridization. Phylogenetic analysis of the 16S rRNA gene is also required and can be supplemented by phylogenies of the mcrA gene and phylogenomic analysis using multiple conserved, single-copy marker genes. Additionally, it is now established that culture purity is not essential for studying prokaryotes, and description of Candidatus methanogenic taxa using single-cell or metagenomics along with other appropriate criteria is a viable alternative. The revisions to the minimal criteria proposed here by the members of the Subcommittee on the Taxonomy of Methanogenic Archaea of the International Committee on Systematics of Prokaryotes should allow for rigorous yet practical taxonomic description of these important and diverse microbes.

Microbiology↗
DOE OSTI2023

Identifying strengths and weaknesses of methods for computational network inference from single-cell RNA-seq data

Single-cell RNA-sequencing (scRNA-seq) offers unparalleled insight into the transcriptional programs of different cellular states by measuring the transcriptome of thousands of individual cells. An emerging problem in the analysis of scRNA-seq is the inference of transcriptional gene regulatory networks and a number of methods with different learning frameworks have been developed to address this problem. Here, we present an expanded benchmarking study of eleven recent network inference methods on seven published scRNA-seq datasets in human, mouse, and yeast considering different types of gold standard networks and evaluation metrics. We evaluate methods based on their computing requirements as well as on their ability to recover the network structure. We find that, while most methods have a modest recovery of experimentally derived interactions based on global metrics such as Area Under the Precision Recall curve, methods are able to capture targets of regulators that are relevant to the system under study. Among the top performing methods that use only expression were SCENIC, PIDC, MERLIN or Correlation. Addition of prior biological knowledge and the estimation of transcription factor activities resulted in the best overall performance with the Inferelator and MERLIN methods that use prior knowledge outperforming methods that use expression alone. We found that imputation for network inference did not improve network inference accuracy and could be detrimental. Comparisons of inferred networks for comparable bulk conditions showed that the networks inferred from scRNA-seq datasets are often better or at par with the networks inferred from bulk datasets. Our analysis should be beneficial in selecting methods for network inference. At the same time, this highlights the need for improved methods and better gold standards for regulatory network inference from scRNAseq datasets.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

In Vivo Molecular Insights into Syntrophic Geobacter Aggregates

Direct interspecies electron transfer (DIET) has been considered as a novel and highly efficient strategy in both natural anaerobic environments and artificial microbial fuel cells. A syntrophic model consisting of Geobacter metallireducens and Geobacter sulfurreducens was studied in this work. We conducted in vivo molecular mapping of the outer surface of the syntrophic community as the interface of nutrients and energy exchange. System for Analysis at the Liquid Vacuum Interface combined with time-of-flight secondary ion mass spectrometry was employed to capture the molecular distribution of syntrophic Geobacter communities in the living and hydrated state. Principal component analysis with selected peaks revealed that syntrophic Geobacter aggregates were well differentiated from other control samples, including syntrophic planktonic cells, pure cultured planktonic cells, and single population biofilms. Our in vivo imaging indicated that a unique molecular surface was formed. Specifically, aromatic amino acids, phosphatidylethanolamine components, and large water clusters were identified as key components that favored the DIET of syntrophic Geobacter aggregates. Moreover, the molecular changes in depths of the Geobacter aggregates were captured using dynamic depth profiling. Our findings shed new light on the interface components supporting electron transfer in syntrophic communities based on in vivo molecular imaging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Ligand-conjugated quantum dots for fast sub-diffraction protein tracking in acute brain slices

Semiconductor quantum dots (QDs) have demonstrated utility in long-term single particle tracking of membrane proteins in live cells in culture. To extend the superior optical properties of QDs to more physiologically relevant cell platforms, such as acute brain slices, we examine the photophysics of compact ligand-conjugated CdSe/CdS QDs using both ensemble and single particle analysis in brain tissue media. We find that symmetric core passivation is critical for both photostability in oxygenated media and for prolonged single particle imaging in brain slices. We then demonstrate the utility of these QDs by imaging single dopamine transporters in acute brain slices, achieving 20 nm localization precision at 10 Hz frame rates. Finally, these findings detail design requirements needed for new QD probes in complex living environments, and open the door to physiologically relevant studies that capture the utility of QD probes in acute brain slices.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Voltage-Matched Strings using 3-Terminal Tandems: Fundamentals and End Losses

Strings constructed from 3-terminal tandem (3TT) cells can provide some of the performance benefits of voltage-matching with less cell complexity than strings based on 4-terminal tandem cells. However, the circuitry for a 3TT string can become more complex, making circuit analysis more challenging. Here we illustrate the essential features of single-polarity voltage-matched (VM) 3TT strings using representative examples. End losses are intrinsic to this type of string, but can be reduced by minimizing m and n in the Vtop/Vbot VM ratio m/n, and further mitigated by increasing the string length. This analysis agrees with preliminary experimental results.

3TT↗
DOE OSTI2023

Multimode theory of electron hole transverse instability

We present Vlasov–Poisson three-dimensional linear stability analysis of an initially planar electron hole structure, solving for the distribution function by integration along unperturbed orbits. The non-sinusoidal potential perturbation shape (parallel to $B$ ) is expanded in eigenfunctions of the adiabatic Poisson operator, generalizing the prior assumption of a rigid shift of the equilibrium. We show that the shiftmode is then modified by a second discrete mode plus an integral over a continuum of wave-like modes. A rigorous treatment shows that the continuum can be approximated effectively by a single mode that satisfies the external wave dispersion relation, thus making the perturbation a weighted sum of three modes. We find numerically the solution for the complex instability frequency, and the corresponding three mode amplitudes determining the perturbation eigenmode. This multimode analysis refines the accuracy of the prior single-mode results, giving slightly higher growth rates at most parameters, as expected from the extra mode shape freedom. Oscillating modes near stability boundaries have larger mode distortions which help explain particle-in-cell simulations that observe instability up to ${\sim }20$ % beyond the prior shiftmode thresholds, and narrowing of the perturbation. At high magnetic field, the multimode analysis predicts a reduction of the already small growth rate.

Physics↗