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At least 199 records · Page 11

Radiation Enhanced Anion Diffusion in Chromia

Cr 2 O 3 is a ubiquitous passivating film on alloys that is vital to their stability and performance in hostile environments. In this study, we directly observe and measure how anion transport through the oxide is affected by 400 keV Ar 2+ ion irradiation as a function of temperature (30–500 °C) and dose (0.33–2.00 dpa) in single-crystal Cr 2 O 3 films using embedded 18 O isotopic tracers and atom probe tomography. Diffusion coefficients are experimentally determined and compared to a chemical rate theory model. Experimental and theoretical results are broadly in agreement, showing anion diffusion increases by at least 4–5 orders of magnitude upon irradiation with a weak dependence on temperature and a stronger dose-driven sink-strength dependence. These results reveal that radiation could significantly reduce the protectiveness of Cr 2 O 3 films when passivity relies upon limited anion diffusivity, even at relatively modest levels of irradiation and low temperatures.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Ripening of Rh Nanoparticle Catalysts in Reverse Water–Gas Shift via a Data-Driven Model Combining Physics, Theory, and Experiment

Degradation via sintering is an ongoing challenge that impedes the broad commercial success of supported metallic nanoparticle catalysts. To mitigate degradation via informed catalyst design and process operations, here we aim to disambiguate the underlying mechanisms of sintering by combining theory and experiment in a quantitative framework. While mechanistic sintering models exist, they only model a single sintering pathway, even though multiple sintering mechanisms can occur simultaneously or dominate at different stages of the process. Data-driven machine learning models have emerged as a means to represent complex processes through data regression. However, machine learning models have very large data needs and lack mechanistic insights due to their black-box encoding. To develop an interpretive model of catalyst degradation via sintering, we constructed a hybrid model combining mechanistic “physics-based” models and data-driven methods to obtain both reliable predictions and mechanistic insights regarding experimentally observed sintering phenomena. Focusing on nanoparticle sintering in the Rh–TiO 2 catalyst for the reverse water–gas shift (RWGS) reaction, the hybrid model couples a mechanistic term for Ostwald ripening with energy values calculated via density functional theory (DFT) with a parametric, data-driven discrepancy function term for unmodeled mechanisms. The hybrid model is trained using Bayesian inference with data collected from small-angle X-ray scattering (SAXS) in situ experiments wherein average nanoparticle diameter versus time was measured at three relevant operating temperatures. The calibrated hybrid model results show that an Ostwald ripening-only model parameterized with fixed DFT energies does not fully capture the time and temperature dependence of the SAXS-observed sintering kinetics, and that an additional functional contribution, or DFT energy calibration, is required to reconcile simulation and experiment. Analysis of the hybrid-model error confirms that the hybrid model outperforms both the purely mechanistic and purely data-driven alternatives in terms of expected predictive accuracy for time-evolving average particle sizes. Furthermore, the results support the hypothesis that the Ostwald ripening mechanism is less important for explaining the sintering phenomena as operating temperature increases under an assumed fixed DFT parameterization. This could be explained in one of two ways: either latent, unmodeled sintering mechanisms dominate at higher temperatures, or the DFT uncertainty increases with temperature. The proposed modeling approach directly links theory to experiments and simulations via a statistical hybrid modeling framework and can be extended to other catalytic systems to improve predictive models and mechanistic understanding.

Bayesian hybrid modeling↗

Ensembles of Metastable States Govern Heterogeneous Catalysis on Dynamic Interfaces

Heterogeneous catalysis is at the heart of chemical industry. Being able to tune and design efficient catalysts for processes of interest is of an utmost importance, and for this, the molecular-level understanding of heterogeneous catalysts is the first step, and indeed a prime focus of the modern catalysis research. For a long time, a single most thermodynamically stable structure of the catalytic interface attained in reaction conditions had been envisioned as the reactive phase. However, some catalytic interfaces continue to undergo structural dynamics in the steady state, triggered by high temperatures, pressures, and binding and changing reagents. Among particularly dynamic interfaces are such widely-used catalysts as crystalline and amorphous surfaced supporting (sub-)nano metallic clusters. Recently, it became clear that this dynamic fluxionality causes the supported clusters to populate many distinct structural and stoichiometric states in catalytic conditions. Hence, the catalytic interface should be viewed as an evolving statistical ensemble of many (not one) structures. As such, every member in the ensemble contributes to the properties of the catalyst differently, and in proportion to its probability to be populated. This new notion flips the established paradigm and calls for new theory, modeling approaches, operando measurements, and updated design strategies. The statistical ensemble nature of surface-supported sub-nano cluster catalysts can be exemplified by oxide-supported and adsorbate-covered Pt, Pd, Cu, CuPd clusters, catalytic toward oxidative and non-oxidative dehydrogenation. They have access to a variety of 3D and quasi-2D shapes. The compositions of their thermal ensembles are dependent on the cluster size, leading to size-specific catalytic activities and the famous “every atom counts” phenomenon. The support and adsorbates affect catalyst structures, and state of the reacting species causes the ensemble to change in every reaction intermediate. The most stable member of the ensemble dominates the thermodynamic properties of the corresponding intermediate, whereas the kinetics can be determined by more active but less populated metastable catalyst states, and that suggests that many earlier studies might have overlooked the actual active sites. Both effects depend on the relative time-scales of catalyst restructuring and reaction dynamics. The catalyst may routinely operate off-equilibrium. Ensemble phenomena lead to surprising exceptions from established rules of catalysis, such as scaling relations, and Arrhenius behavior. Catalyst deactivation is also an ensemble property, and its extent of mitigation can be predicted through the new paradigm. These findings were enabled by advances in theory, such as global optimization and subsequent utilization of multiple local minima, and pathways sampling, as well as operando catalyst characterization. The fact that the per-site and per-species resolution is needed for the description and predicting of catalyst properties gives theory the central role in catalysis research, as most experiments provide ensemble-average information and cannot detect the crucial minority species that may be responsible for the catalytic activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CFD investigation of low-attrition air-reactor designs for the NETL chemical-looping combustion reactor

The flow dynamics and attrition characteristics of three air reactor designs are investigated using an Eulerian-Eulerian kinetic theory model. The hydrodynamics of these reactor designs are analyzed to identify the flow regimes in which the particles evolve. The investigated designs which differ in the configuration of the secondary flow ports, exhibit bubbling and turbulent fluidization regimes within similar spatial regions. The most substantial differences in the hydrodynamics was in the turbulent fluidized regions near the secondary inlets. The mechanical stressing environments undergone by the particles were analyzed using the collision energy spectra, reconstructed using the local flow field properties (i.e. granular temperature and particle number density). The spectra show that the increase in the specific collision power is associated with the regions near the secondary injector ports, which are in a turbulent fluidization regime. A simple analysis relying upon a partitioning of the energy spectrum, showed that attrition rate may be reduced by about 34% over the original design.

20 FOSSIL-FUELED POWER PLANTS↗

Atomically Revealing Bulk Point Defect Dynamics in Hydrogen‐Driven γ‐Fe 2 O 3 → Fe 3 O 4 → FeO Transformation

Understanding how point defects in the bulk govern redox transformations is essential for advancing hydrogen-based metal production and designing high-performance oxide materials. This study reveals the atomic-scale mechanisms driving hydrogen-induced reduction of γ-Fe 2 O 3 to Fe 3 O 4 , focusing on how bulk vacancy dynamics dictate structural evolution and reaction kinetics. A key finding is the pronounced contrast in defect behavior between the two oxides: in γ-Fe 2 O 3 , intrinsic Fe vacancies promote oxygen vacancy clustering, destabilizing the local lattice and driving nanopore formation. In contrast, Fe 3 O 4 exhibits a higher oxygen vacancy formation energy and lacks intrinsic Fe vacancies, suppressing vacancy aggregation and maintaining a dense, pore-free structure. This divergence governs distinct reduction pathways—γ-Fe 2 O 3 undergoes an interface-reaction-limited transformation confined to the γ-Fe 2 O 3 /Fe 3 O 4 boundary, while Fe 3 O 4 supports a uniform increase in oxygen vacancy concentration, enabling bulk-phase reduction to lower-oxide FeO. Integrated in situ electron microscopy and density functional theory modeling uncover a vacancy-mediated mechanism, where synergistic cation-anion vacancy dynamics steer microstructure evolution and phase progression. These insights highlight the critical role of vacancy dynamics in controlling oxide reactivity and offer a pathway toward vacancy engineering to enhance reduction kinetics in hydrogen metallurgy and to tailor porosity, reactivity, and structural resilience in oxide-based catalysts and energy materials.

36 MATERIALS SCIENCE↗

Vapor Phase Installation of CpCo(CO) 2 in MOF‐808

Metal-organic frameworks (MOFs), including MOF-808 present an opportunity for vapor phase installation of reactive centers that may serve as uniform sites for precision catalysis. The mechanism of cobalt installation in MOF-808 through atomic layer deposition (ALD) upon CpCo(CO )2 exposure is investigated through in situ FTIR spectroscopy complemented by density functional theory modeling. The role of subsequent H 2 O exposure in the hydrolysis of carbonyl and cyclopentadienyl ligands to complete the installation is also investigated. In situ FTIR study reveals that upon exposure of CpCo(CO) 2 to MOF-808 at 115 °C, a long-lived, stable intermediate is formed that presents carbonyl stretching vibrations similar to the undissociated precursor that are attributed to multiple chemisorbed carbonyl complexes. In MOF-808, cobalt species are initially absorbed near the BTC linker rather than directly on the nodes, revealing the importance of non-covalent interactions in the installation process. DFT suggests that H 2 O exposure promotes carbonyl elimination but leaves a cyclopentadienyl-capped cobalt that is more stable than the complete hydrolysis product. The simulations are consistent with cobalt installation in MOF-808 using CpCo(CO) 2 and H 2 O at 115 °C and further consistent with the lack of ALD thin film deposition of cobalt oxide thin films on planar supports.

36 MATERIALS SCIENCE↗

Search for nonresonant new physics signals in high-mass dilepton events produced in association with b-tagged jets in proton-proton collisions at $\sqrt{s}=13$ TeV

A search for nonresonant new physics phenomena in high-mass dilepton events produced in association with b-tagged jets is performed using proton-proton collision data collected in 2016–2018 by the CMS experiment at the CERN LHC, at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 138 fb −1 . The analysis considers two effective field theory models with dimension-six operators; involving four-fermion contact interactions between two leptons (ℓℓ, electrons or muons) and b or s quarks (bbℓℓ and bsℓℓ). Two lepton flavor combinations (ee and μμ) are required and events are classified as having 0, 1, or ≥2 b-tagged jets in the final state. No significant excess is observed over the standard model backgrounds. Upper limits are set on the production cross section of the new physics signals. These translate into lower limits on the energy scale Λ of 6.9 to 9.0 TeV in the bbℓℓ model, depending on model parameters, and on the ratio of energy scale and effective coupling, Λ/g*, of 2.0 to 2.6 TeV in the bsℓℓ model. Lepton flavor universality is also tested by comparing the dielectron (ee) and dimuon (μμ) mass spectra for different b-tagged jet multiplicities. No significant deviation from the standard model expectation of unity is observed.

Beyond Standard Model↗

Explaining word embeddings with perfect fidelity: a case study in predicting research impact

The best-performing approaches for scholarly document quality prediction are based on embedding models. In addition to their performance when used in classifiers, embedding models can also provide predictions even for words that were not contained in the labelled training data for the classification model, which is important in the context of the ever-evolving research terminology. Although model-agnostic explanation methods, such as Local interpretable model-agnostic explanations, can be applied to explain machine learning classifiers trained on embedding models, these produce results with questionable correspondence to the model. We introduce a new feature importance method, Self-Model Entities Rated (SMER), for logistic regression-based classification models trained on word embeddings. We show that SMER has theoretically perfect fidelity with the explained model, as the average of logits of SMER scores for individual words (SMER explanation) exactly corresponds to the logit of the prediction of the explained model. Quantitative and qualitative evaluation is performed through five diverse experiments conducted on 50,000 research articles (papers) from the CORD-19 corpus. In conclusion, through an AOPC curve analysis, we experimentally demonstrate that SMER produces better explanations than LIME, SHAP and global tree surrogates.

Coarse-grained models↗

Measurement and Simulation of Vacancy Formation in 2-MeV Self-irradiated Pure Fe

Positron annihilation spectroscopy is a powerful tool to quantify the amount of vacancies and vacancy clusters in materials. The technique has been utilized to study the induced defects in materials after ion beam and neutron irradiations. Here we make the case for how the technique can and should be utilized to quantify the defects created by irradiation in situ during irradiation to foster a more thorough understanding of the surviving defects after initial collision cascades. This paper outlines a future experimental approach and its meaning for the nuclear materials community, being able to benchmark commonly used rate theory models of damage evolution.

36 MATERIALS SCIENCE↗

Thermal diffusivity recovery and defect annealing kinetics of self-ion implanted tungsten probed by insitu transient grating spectroscopy

Tungsten is a promising candidate material for plasma-facing armour components in future fusion reactors. A key concern is irradiation-induced degradation of its normally excellent thermal transport properties. In this comprehensive study, thermal diffusivity degradation in ion-implanted tungsten and its evolution from room temperature (RT) to 1073 K is considered. Five samples were exposed to 20 MeV self-ions at RT to achieve damage levels ranging from 3.2 x 10 -4 to 3.2 displacements per atom (dpa). Transient grating spectroscopy with in-situ heating was then used to study thermal diffusivity evolution as a function of temperature. Using a kinetic theory model, an equivalent point defect density is estimated from the measured thermal diffusivity. The results showed a prominent recovery of thermal diffusivity between 450 K and 650 K, which coincides with the onset of mono-vacancy mobility. After 1073 K annealing samples with initial damage of 3.2 x 10 -3 dpa or less recover close to the pristine value of thermal diffusivity. For doses of 3.2 x 10 -2 dpa or higher, on the other hand, a residual reduction in thermal diffusivity remains even after 1073 K annealing. Transmission electron microscopy reveals that this is associated with extended, irradiation-induced dislocation structures that are retained after annealing. A sensitivity analysis shows that thermal diffusivity provides an efficient tool for the assessing total defect content in tungsten up to 1000 K.

36 MATERIALS SCIENCE↗

Cosmic antihelium-3 nuclei sensitivity of the GAPS experiment

The General Antiparticle Spectrometer (GAPS) is an Antarctic balloon experiment designed for low-energy (0.1-0.3 GeV/n) cosmic antinuclei as signatures of dark matter annihilation or decay. GAPS is optimized to detect low-energy antideuterons, as well as to provide unprecedented sensitivity to low-energy antiprotons and antihelium nuclei. The novel GAPS antiparticle detection technique, based on the formation, decay, and annihilation of exotic atoms, provides greater identification power for these low-energy antinuclei than previous magnetic spectrometer experiments. This work reports the sensitivity of GAPS to detect antihelium-3 nuclei, based on full instrument simulation, event reconstruction, and realistic atmospheric influence simulations. The report of antihelium nuclei candidate events by AMS-02 has generated considerable interest in antihelium nuclei as probes of dark matter and other beyond the Standard Model theories. GAPS is in a unique position to detect or set upper limits on the cosmic antihelium nuclei flux in an energy range that is essentially free of astrophysical background. In three 35-day long-duration balloon flights, GAPS will be sensitive to an antihelium flux on the level of $1.3^{+4.5}_{-1.2} $ ∙ 10 -6 m -2 sr -1 s -1 (GeV/n) -1 (95% confidence level) in the energy range of 0.11-0.3 GeV/n, opening a new window on rare cosmic physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Mechanisms and kinetics of citrate-promoted dissolution of a uranyl phosphate mineral

The formation of uranyl phosphate precipitates is a remediation strategy to limit the mobility of uranium in contaminated soils. However, exposure to organic ligands, like the plant exudate citrate, can remobilize the uranium. The purpose of this study is to provide a more thorough comprehension of citrate-promoted dissolution of a uranyl phosphate mineral, chernikovite [(H 3 O)(UO 2 )(PO 4 )·3H 2 O], by determining the extent of uranium release from chernikovite at a wide range of citrate concentrations. Here we have quantified the kinetics of dissolution and proposed potential mechanisms of chernikovite dissolution to gain a better understanding of the fate of uranyl phosphate precipitates in the environment. Batch dissolution and continuously stirred tank reactor (CSTR) experiments indicate that increasing citrate concentrations from 0.1 mM to 50 mM increases the concentration of dissolved uranium. However, at citrate concentrations of 10 mM and greater, the effectiveness of the ligand to enhance the dissolution decreases. Density functional theory modeling and Raman spectroscopy indicate a strong interaction between citrate and the uranyl ions at the surface of the uranyl phosphate. The interaction between citrate and uranyl suggests the formation of an alteration layer of uranyl-citrate surface complexes, which could impede uranium release at citrate concentrations of 10 mM or higher. Together, these results indicate that the citrate-promoted dissolution of chernikovite is a fast reaction that is hindered by a combination of surface saturation and a secondary-phase precipitation reaction at higher concentrations of citrate and reaction times greater than or equal to 72 min based on the hydraulic residence time of CSTR experiments. These findings improve our understanding of the stability of uranyl phosphate for use in sequestration of uranium groundwater plumes at contaminated sites.

58 GEOSCIENCES↗

Atom Probe Tomography Characterization of High-Dose Ion Irradiated MA957

This paper presents a comprehensive characterization study of the microstructural responses to ion irradiation of the oxide dispersion strengthened (ODS) ferritic alloy MA957 using atom probe tomography (APT). The MA957 specimens were irradiated by 1.8 MeV Cr3+ ions to doses and temperatures relevant to advanced fast reactors (100 and 500 dpa at 400-500 °C). The average sizes of the YTiO particles decreased slightly after irradiation at all temperatures, with the most pronounced change at 400 °C. The particle number densities for 400 and 500 °C were slightly below number densities for the unirradiated condition, while the values were slightly higher at 420 and 450 °C. This behavior is consistent with the Nelson-Hudson-Mazey rate theory model that considers the competing effects between recombination and dissolution. An increase in the Y/Ti ratio of the YTiO particles was observed at the two lower temperatures. The formation of Cr-rich precipitates (a') was observed in specimens irradiated at temperatures up to 450 °C. Irradiation-induced segregation on grain boundaries was also investigated. Grain boundary element concentration profiles and ion maps demonstrate differences among the irradiation temperatures, with most datasets differing from the unirradiated condition. A key focus of this ion irradiation study is the high-dose response, and this quantitative assessment revealed relatively small but distinct effects of irradiation on microstructure evolution. Overall, these results showing minor second phase evolution suggest that MA957 should retain mechanical performance generally well up to 500 dpa for the irradiation temperatures studied.

Wang, Jing↗

The u 3 si 2 -H system

U 3 Si 2 is of interest to the nuclear industry as a candidate fuel material due to its high uranium density and high thermal conductivity. However, it has been observed to react with hydrogen, resulting in material decrepitation. As a result, it is important to understand the thermodynamics of the U 3 Si 2 -H system. In this study, the thermodynamics of the hydrogen absorption reaction of USi were determined experimentally using Sievert’s gas absorption and related to crystallographic evolution with hydrogen content using X-ray diffraction. Experimentally-determined thermodynamic parameters were compared with results from density functional theory modeling. Results from this study were also compared with those determined in previous work. Sievert’s gas absorption results were used to develop the pressure-composition-temperature (PCT) curves of the U 3 Si 2 -H system. It was found that the hydride phase exhibited a maximum stoichiometry between U 3 Si 2 H 1.8 and U 3 Si 2 H 2 . The two-phase region for hydride formation from U 3 Si 2 exhibited a miscibility gap with a critical temperature between 623 and 673 K, as calculated from the PCT curves. Analysis of the PCT curves also showed that both the enthalpy and entropy of the hydrogen absorption reaction increased with hydrogen content but were lower than the values for uranium trihydride formation from uranium metal. The enthalpy of reaction for hydrogen absorption was calculated to range between -86.9 and -94.8 kJ mol -1 , while the entropy of reaction was calculated to range between 101.9 and 138.8 J mol -1 K -1 . Furthermore, DFT modeling of the thermoydnamic stability of the USi hydride phases yielded a decomposition temperature of U 3 Si 2 H 2 of approximately 600 K, which was consistent with the experimental results. Similarly, the DFT-calculated enthalpy and entropy of reaction to form USiH were determined to be -106.5kJ mol and 121.8J mol -1 K -1 , respectively, which were both in close agreement with the experimentally-determined values.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evolution of extended defects in UO 2 during high temperature annealing

The evolution of thermophysical characteristics of uranium oxide (UO 2 ) under irradiation is a critical aspect of nuclear fuel performance of light water reactors. This study examines the effect of high-temperature annealing at 1000 °C - 1600 °C on defect evolution in krypton irradiated UO 2 at room temperature. Transmission electron microscopy analysis reveals that the size of irradiation-induced bubbles and dislocation loops increases but their density decreases with annealing temperatures. Perfect dislocation loops with = <110> dominate, regardless of the annealing temperature. A rate theory model for extended defect evolution is applied to conclude that current understanding of dynamical loop and bubble evolution at high-temperature annealing is governed by defect coalescence.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Unlocking enhanced gas capture via core scrambling of porous-organic cages

The demand for low-cost, low-energy, and highly selective gas capture and separations is an ongoing driver of porous material development. Porous liquids have been identified as a promising gas separation material by creating permanent porosity in inorganic solvents through inclusion of nanoporous materials that sterically exclude solvent from their internal porosity. Among the nanoporous materials that can be used to form porous liquids, porous-organic cages (POCs) have been one of the most popular due to the inherent tunability of POCs. “Scrambled” POCs with varying functionalities on the POC vertices have been developed and incorporated into porous liquid compositions, increasing their gas adsorption capacity. An unexplored avenue to tailor the properties of porous liquids is through scrambling the functionality of the core of the POC. Here, therefore, we have synthesized a new POC, a CC3-OH derivative with scrambled hydroxides on the core and evaluated the impact on the CO 2 uptake capacity in silicon oil-based porous liquids. Core scrambling of the POC resulted in a twofold increase CO 2 adsorption capacity in the porous liquid, an emergent property that is a dramatic increase beyond a linear combination of the gas adsorption capacity of the neat solvent and the POC. Density functional theory modeling of the CC3 POC and its hydroxide-based derivatives identified that free rotation of the linker hydroxide allowed for forced interaction between the CO 2 molecule and the hydroxide in the pore window. Solvation of the POC may release scrambled core hydroxides from intramolecular bonding with a neighboring imine, allowing for increased gas uptake in the porous liquid over the neat POC. These results identify a key structural relationship of POCs that enables emergent properties in porous liquids and can guide future development of liquid phase gas capture and separation materials for environmental and industrial applications.

Gas capture↗

Design optimization of semiconductor piezoresistors with Schottky diode contacts

A modeling theory is developed to predict the performance of piezoresistors which incorporate Schottky diode electrical contacts. This new theory allows the design of high performance gauges which can be fabricated using NonLithographically-Based Microfabrication (NLBM) techniques. These semiconductor piezoresistors can be designed in customizable sizes and fabricated in parallel in order to integrate position sensing into MEMS flexural positioners. Customizable nanopositioning platforms will enable advances in a range of nano-scale fabrication and metrology applications. A semiconductor piezoresistor with Schottky diode contacts was fabricated and attached to a titanium flexure. This device is shown to match predicted electrical performance within about 8% and to show a gauge factor of 116, within 2% of the predicted value. Performance limits for Schottky diode semiconductor piezoresistors are identified to be about 127dB full noise dynamic range for a quarter bridge over a 10kHz sensor bandwidth on a 600µm width titanium flexure, making them ideal for sensing on meso-/micro-scale flexural positioners. Methods of reaching these performance bound are suggested and their impact on the sensor dynamic range are studied.

42 ENGINEERING↗

Electromagnetic turbulence in increased β plasmas in the Large Plasma Device

The variation of pressure-gradient-driven turbulence with plasma $\beta$ (up to $\beta \approx 15\,\%$ ) is investigated in linear, magnetized plasma. The magnitude of magnetic fluctuations is observed to increase substantially with increasing $\beta$ . More importantly, parallel magnetic fluctuations are observed to dominate at higher $\beta$ values, with $\delta B_\parallel / \delta B_\perp \approx 2$ and $\delta B / B_0 \approx 1\,\%$ . Parallel magnetic fluctuations are strongly correlated with density fluctuations and the two are observed to be out of phase. The relative magnitude of and cross-phase between density and parallel magnetic field fluctuations are consistent with the dynamic pressure balance ( $P+{B_{0}^2}/{2\mu _0} = \textrm {constant}$ ). A local slab model theory for electromagnetic, modified drift Alfvén waves, including parallel magnetic fluctuations, shows partial agreement with experimental observations.

Physics↗