Search NASA⌕ Search

SEARCH · Search NASA

Results for “Time Constant”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Consequences of the failure of equipartition for the p – V behavior of liquid water and the hydration free energy components of a small protein

Earlier we showed that in the molecular dynamics simulation of a rigid model of water it is necessary to use an integration time-step δ t ≤ 0.5 fs to ensure equipartition between translational and rotational modes. Here we extend that study in the NVT ensemble to NpT conditions and to an aqueous protein. We study neat liquid water with the rigid, SPC/E model and the protein BBA (PDB ID: 1FME) solvated in the rigid, TIP3P model. We examine integration time-steps ranging from 0.5 fs to 4.0 fs for various thermostat plus barostat combinations. We find that a small δ t is necessary to ensure consistent prediction of the simulation volume. Hydrogen mass repartitioning alleviates the problem somewhat, but is ineffective for the typical time-step used with this approach. The compressibility, a measure of volume fluctuations, and the dielectric constant, a measure of dipole moment fluctuations, are also seen to be sensitive to δ t . Using the mean volume estimated from the NpT simulation, we examine the electrostatic and van der Waals contribution to the hydration free energy of the protein in the NVT ensemble. These contributions are also sensitive to δ t . In going from δ t = 2 fs to δ t = 0.5 fs, the change in the net electrostatic plus van der Waals contribution to the hydration of BBA is already in excess of the folding free energy reported for this protein.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Stoichiometrically-informed symbolic regression for extracting chemical reaction mechanisms from data

A data-driven computational method is introduced to extract chemical reaction mechanisms from time series chemical concentration data. It is realized through the use of dynamic symbolic regression in which a sparse analytical form for a dynamical system is discoverable from the underlying data. We specifically develop the stoichiometrically-informed symbolic regression (SISR) method to address a standing challenge in complex chemical reaction networks: given a time-series dataset of concentrations of several components, what is the mechanism and the associated rate constants? SISR finds the optimal mechanism, kinetic equations and rate constants by combining differential optimization with a genetic optimization approach that searches a symbolic space of possible reaction mechanisms. Use of SISR in several paradigmatic examples spanning linear and nonlinear reaction schemes results in excellent agreement between true and predicted mechanisms, including when the method is applied to noisy data. The advantages of a stoichiometrically-informed approach such as SISR to address reaction discovery is illustrated through comparison with the use of generic state-of-the-art data-driven approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Mechanistic and Mitigation-Strategy Insights into NaCl and CaCl 2 Contamination of Proton-Exchange-Membrane Water Electrolysis Using Continuum Modeling

Cationic contaminants are detrimental to proton-exchange-membrane water electrolyzers (PEMWEs). To obtain insight, a 1-D, nonisothermal, multiphase continuum cell model including cationic contamination is developed. Simulations of steady-state cell performance predict decreased performance due to an increase in kinetic overpotential associated with the hydrogen-evolution reaction, which was attributed to decreased protonic-activity within the cathode catalyst layer from proton supplantation with contaminant cations. The accumulation and extent of cation exchange in the cathode catalyst layer depends on the operating current density due to migration. Simulations of cell recovery of potential suggest that a contaminated cell can recover approximately 78% (450 mV) with 24 h of constant current density operation at 2 A cm –2 , with higher current densities accelerating reduced recovery times. Parametric studies show that anode-side acidification at lower current densities inhibit cation contaminant adsorption, and cathode-side acidification at larger current densities facilitate the expulsion of adsorbed cations; for a cathode-side pH of 6 and 5, the cell can recover an additional 10% and 100% performance, respectively. Overall, the model serves as a framework for modeling other aspects of PEMWE systems to address durability and performance aspects, which can assist in improving the viability of the technology.

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

Continuous surface-to-distributed acoustic sensor snapshots explain reactivation of individual natural fractures during an unconventional reservoir stimulation

ABSTRACT Fiber-optic sensing technologies allow petroleum engineering teams to detect hydraulic fracture interaction with boreholes during unconventional reservoir stimulation. In combination with high-repeatability seismic sources, the same distributed acoustic sensors (DASs) enable vertical seismic profiling (VSP) of the fracture evolution away from the boreholes. We discovered clear signatures of seismic scattering on activated fractures during nine days of continuous seismic monitoring of the fracturing stages at the Austin Chalk/Eagle Ford Field Laboratory. The present study applies a novel approach for quantitative analysis of the scattering events in terms of the evolution of the geometry and elastic stiffness of individual fractures. Our characterization strategy sequentially refines the fracture models: from a stack of 1D soft layers to 3D rectangular inclusions. First, we estimate the number of fracture locations and reflectivity using a modified sparse-spike deconvolution of the stacked VSP traces. The fracture set consists of five fractures spaced by 15–30 m with a reflectivity of approximately 1%. Then, we develop a scattering integral method to refine these estimates along with an inversion of the fracture top and bottom for each monitoring vintage. We find that, initially, some of the fractures are located above the monitoring fiber with the height of approximately 100 m. Then we integrate the seismic interpretation with the low-frequency DAS and pressure and microseismic monitoring to reconstruct the activation process of the fractures. Most likely, some of the natural fractures slowly grew downward to the monitoring fiber as a result of fluid injections in the stimulated well. This led to bright strain anomalies but did not trigger seismicity. The top of the fractures remained almost constant and were limited by a lithologic boundary/stress barrier. To our knowledge, this is the first time VSP data enabled tracking of the fracture evolution with such high spatial and temporal resolution, which was previously only available for crosswell surveys and at a much smaller scale.

Glubokovskikh, Stanislav↗
DOE OSTI2026

Enabling Grid-Forming Control with Fault Ride-Through in Unbalanced Distribution Networks

Distribution networks are often unbalanced, causing oscillatory responses in inverter control designed for balanced conditions. Here, to address this problem, this paper proposes a novel time-domain transformation appropriate for inverter control and enables the decomposition of three-phase unbalanced signals into constant positive and negative components. Relations useful for calculating unbalanced active and reactive power are derived from first principle, providing insight into vector products of unbalanced three-phase signals. Furthermore, a grid-forming control effective under unbalanced conditions is developed, which delivers superior performance while meeting UNIFI1 specifications for grid-forming control under unbalanced conditions. specifications applicable to category 4 inverter-based resource, like setting and regulating frequency/voltage, providing voltage support, sharing active power, injecting negative sequence current, and riding through faults. A current limiter is proposed for safe fault ride-through and integrates with the grid-forming control featuring frequency/voltage droop controllers and current and voltage control loops. The transformation of interconnected inverters is formulated and stability of the proposed control analyzed to support robust parameter selections. The effectiveness of the proposed transformation and grid-forming control is demonstrated through analytical results and real-time simulation of a IEEE 123 distribution network on the Real-Time Digital Simulator. Comparison with existing methods shows that the proposed strategy satisfies the UNIFI specifications with a much better performance.

24 - POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Predicting critical heat flux using localized sensing at invisible vapor-liquid interfaces

Predicting critical heat flux (CHF) in two-phase electronics cooling systems remains a significant challenge due to the sudden onset of boiling crisis and the difficulty in directly visualizing vapor-liquid interfaces. Existing sensing methods rely on lagging temperature measurements, optically accessible systems, or spatially averaged signals that cannot pinpoint CHF initiation at localized high-heat-flux regions. Here, we report a planar capacitive sensing approach that enables real-time, localized detection of vapor-liquid interface dynamics for CHF prediction in boiling heat transfer. The capacitive sensor exploits the dielectric constant difference between liquid and vapor phases to capture bubble nucleation, growth, and departure dynamics with a temporal resolution down to 2 ms. The capacitive sensing reveals distinct signals across boiling regimes: from high-frequency fluctuations during strong nucleate boiling to low-frequency fluctuations with increased amplitudes when approaching CHF. The multi-sensor array experiments demonstrate real-time localized sensing, where each sensor responds exclusively to boiling in its immediate vicinity without crosstalk from neighboring regions. This non-intrusive sensing approach provides predictive rather than lagging sensing signals of CHF occurrence, offering predictive diagnosis of two-phase liquid cooling for the thermal management of high-power-density electronics.

CHF↗
DOE OSTI2025

Attosecond Transient Grating Spectroscopy with Near-Infrared Grating Pulses and an Extreme Ultraviolet Diffracted Probe

Transient grating spectroscopy has become a mainstay among metal and semiconductor characterization techniques. Here, we extend the technique toward the shortest achievable time scales by using tabletop high-harmonic generation of attosecond extreme ultraviolet (XUV) pulses that diffract from transient gratings generated with sub-5 fs near-infrared (NIR) pulses. We demonstrate the power of attosecond transient grating spectroscopy (ATGS) by investigating the ultrafast photoexcited dynamics in an Sb semimetal thin film. ATGS provides an element-specific, background-free signal unfettered by spectral congestion, in contrast to transient absorption spectroscopy. With ATGS measurements in Sb polycrystalline thin films, we observe the generation of coherent phonons and investigate the lattice and carrier dynamics. Among the latter processes, we extract carrier thermalization, hot carrier cooling, and electron-hole recombination, which are on the order of 20 fs, 50 fs, and 2 ps time scales, respectively. Furthermore, the simultaneous collection of transient absorption and transient grating data allows us to extract the total complex dielectric constant in the sample dynamics with a single measurement, including the real-valued refractive index, from which we are also able to investigate carrier-phonon interactions and longer-lived phonon dynamics. The outlined experimental technique expands the capabilities of transient grating spectroscopy and attosecond spectroscopies by providing a wealth of information concerning carrier and lattice dynamics with an element-selective technique at the shortest achievable time scales.

Quintero-Bermudez, Rafael↗
DOE OSTI2026

Quantum Time-Space Tradeoffs for Matrix Problems

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems—including matrix-vector product, matrix inversion, matrix multiplication and powering—existing classical time-space tradeoffs, several of which are tight for every space bound, also apply to quantum algorithms with at most a constant factor loss. For example, for almost all fixed matrices 𝐴, including the discrete Fourier transform matrix, we prove that quantum circuits with at most 𝑇 input queries and 𝑆 qubits of memory require 𝑇 = Ω⁢(𝑛 2 /𝑆) to compute matrix-vector product 𝐴⁢𝑥 for 𝑥 ∈{0,1 𝑛 . We similarly prove that matrix multiplication for 𝑛 ×𝑛 binary matrices requires 𝑇 = Ω⁢(𝑛 3 /$\sqrt{𝑆}$). Because many of our lower bounds are matched by deterministic algorithms with the same time and space complexity, our results show that quantum computers cannot provide any asymptotic advantage for these problems with any space bound. We obtain matching lower bounds for the stronger notion of quantum cumulative memory complexity—the sum of the space per layer of a circuit. We also consider Boolean (i.e., AND-OR) matrix multiplication and matrix-vector products, improving the previous quantum time-space tradeoff lower bounds for 𝑛 × 𝑛 Boolean matrix multiplication to 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/4 ) from 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/2 ). Our improved lower bound for Boolean matrix multiplication is based on a new coloring argument that extracts more from the strong direct product theorem that was the basis for prior work. To obtain our tight lower bounds for linear algebra problems, we require much stronger bounds than strong direct product theorems. We obtain these bounds by adding a new bucketing method to the quantum recording-query technique of Zhandry that lets us apply classical arguments to upper bound the success probability of quantum circuits.

lower bounds↗
DOE OSTI2025

ATR-SEIRAS Reveals Potential Inversion and Associated Electron Transfer Kinetics in the Reduction of Surface-Confined Anthraquinone

The detection of stable semiquinone radicals on an anthraquinone (AQ) layer chemically grafted to an electrode surface in aqueous electrolytes has been elucidated by using attenuated total reflection surface enhanced infrared absorption spectroscopy (ATR-SEIRAS). In very alkaline conditions (pH 13), the reduction of the AQ involves no proton transfer, but surface sensitive infrared spectroscopy reveals that the anthraquinone dianion forms a strong hydrogen bonding network with coadsorbed water, leading to irreversible features in the voltammetry. The potential dependence of the IR band assigned to the AQ radical is consistent with the enhanced hydrogen bonding network causing increased stabilization of the quinone radical and supports the predicted response of a system under mild potential inversion, whereby the formal potential for the reduction of the anthraquinone radical is positive of the reduction potential of the neutral AQ molecule. Time-resolved ATR-SEIRAS is used to measure the transient formation of the AQ •– radical, from which rate constant information can be extracted using the Butler–Volmer model involving two one-electron transfers without a direct disproportionation reaction. The potential dependence of the rate constants is consistent with the potential inversion and can be used to qualitatively simulate the measured cyclic voltammograms. In conclusion, the thermodynamic and kinetic analyses re-emphasize long established deficiencies associated with using one-electron reaction formalisms to characterize multi-electron systems.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗
DOE OSTI2025

Process intensification approach to enhancing heat and mass transfer during drying: Ultrasonic (US) assisted drying of paper and board

Drying of paper and board is conventionally achieved through alternating conduction (steam-heated cylinders) and pocket convection (heated air over the paper web surface). These conventional drying systems rely heavily on steam from fossil fuels, resulting in inefficiencies, high energy usage, and thermal losses due to surface-driven mechanisms. Here, to address these challenges, an experimental system, with in-situ drying characteristics measurements, was developed to investigate process intensification using ultrasonic-based dewatering—a volumetric, pressure-driven acoustic energy system—integrated with conventional drying. The objectives of this study are to assess the impact of ultrasonics (US) on dewatering; compare performances to conventional drying systems; identify improvements in drying rate and energy use as a function of moisture content; and gain potential insights on heat and mass transfer mechanisms during US-assisted drying. US performance was evaluated across frequencies, power levels, pulp types, and basis weights. Results show that improvements to ultrasonic applications in conjunction with convection were 30-43% in drying rate and 20-35% in drying time over continuous and intermittent applications. When combined with conduction and convection, ultrasonics yielded up to 20% improvement in both rate and time and up to 20% reduction in energy consumption. Observations support a hypothesis of extension of the constant rate period due to improved capillary flow at higher moisture content and enhancing vapor diffusion and boundary layer disruption at lower moisture contents during falling rate period. These findings will inform future modeling, simulation, design and optimization of advanced drying systems.

42 ENGINEERING↗
DOE OSTI2024

Quantum real-time evolution of entanglement and hadronization in jet production: Lessons from the massive Schwinger model

The possible link between entanglement and thermalization, and the dynamics of hadronization are addressed by studying the real-time response of the massive Schwinger model coupled to external sources. This setup mimics the production and fragmentation of quark jets, as the Schwinger model and quantum chromodynamics (QCD) share the properties of confinement and chiral symmetry breaking. By using simulations of quantum dynamics on classical hardware, we study the entanglement between the produced jets, and observe the growth of the corresponding entanglement entropy in time. This growth arises from the increased number of contributing eigenstates of the reduced density matrix with sufficiently large and close eigenvalues. We also investigate the physical nature of these eigenstates, and find that at early times they correspond to fermionic Fock states. We then observe the transition from these fermionic Fock states to mesonlike bound states as a function of time. In other words, we observe how hadronization develops in real time. At late times, the local observables at midrapidity (such as the fermion density and the electric field) approach approximately constant values, suggesting the onset of equilibrium and approach to thermalization. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Hydrogen Production Cost from Proton-Conducting Solid Oxide Electrolysis

Rigorous stakeholder-vetted techno-economic analysis (TEA) was conducted to estimate the cost of hydrogen (H 2 ) production using Proton-Conducting Solid Oxide (PSO) electrolysis. The analysis evaluates Current (2025) and Future (2035) technology cases at centralized plant scales of 50 and 500 metric tonnes per day (MTD), assuming electricity, water, and air as the only system inputs. Untaxed, unsubsidized levelized cost of hydrogen (LCOH) is projected to range from 2020 $\$$1.81 to $\$$2.47/kg H 2 at an electricity price of $\$$0.03/kWh and 97% capacity factor under Nth-of-a-kind (NOAK) deployment assumptions. Total installed capital cost was developed using bottom-up Design for Manufacture and Assembly (DFMA) stack cost modeling and detailed balance-of-plant estimates, including mechanical and electrical subsystems, installation, site preparation, engineering, and contingency. Stack performance assumptions include thermoneutral operation, degradation over time, and periodic replacement. LCOH was calculated using the Hydrogen Analysis (H2A) discounted cash flow model in constant 2020 dollars. Results indicate PSO electrolysis has potential for competitive hydrogen production costs under low-cost electricity and mature manufacturing conditions.

08 HYDROGEN↗
DOE OSTI2026

Constraints on Dynamical Dark Energy from Multiple Probes in the Full Dark Energy Survey

We present results on dark energy evolution, assuming a time-dependent equation of state $w(a)=w_0+w_a(1-a)$, from growth and geometric probes using the full six-year Dark Energy Survey dataset: type Ia supernovae, baryon acoustic oscillations, and weak gravitational lensing and galaxy clustering (3$\times$2pt). The combination yields $w_0=-0.84^{+0.10}_{-0.10}$ and $w_a=-0.44^{+0.60}_{-0.55}$, the tightest constraints ever obtained from a single survey, with $2.2σ$ deviation from a cosmological constant. Adding the DESI DR2 BAO data yields $w_0=-0.84^{+0.06}_{-0.07}$ and $w_a=-0.53^{+0.33}_{-0.28}$, representing the most stringent low-redshift-only test of dynamical dark energy to date, with a $2.3σ$ deviation. In this combination, adding 3$\times$2pt doubles the constraining power. Finally, when combined with primary CMB information, we obtain $w_0=-0.82^{+0.05}_{-0.05}$, $w_a=-0.63^{+0.21}_{-0.18}$, with a $3.0σ$ deviation. We find that including 3$\times$2pt in the previously studied SN + DESI BAO + CMB combination leaves the significance essentially unchanged ($3.2 σ$ to $3.0σ$) while improving the figure of merit by $\sim$10%. We systematically investigate the impact of leaving out each one of the probes and find that the significance of the deviation from a cosmological constant ranges from 2.3 to 3.2$σ$, with best-fit parameters consistently in the region $w_0 >-1$ and $w_a <0$. Excluding SN from the all data combination yields a $2.6σ$ departure from $Λ$CDM, providing a cross-check independent of supernova photometric calibration. These results support the weak preference for evolving dark energy reported by several recent cosmological analyses. By combining growth and geometric probes from a single survey, this work realizes the multi-probe dark energy program envisioned at the inception of DES.

Abbott, T. M.C. [Cerro-Tololo InterAmerican Obs.] ↗
DOE OSTI2026

Quantum utility in simulating the real-time dynamics of the Fermi–Hubbard model using superconducting quantum computers

The Fermi–Hubbard model is a fundamental model in condensed matter physics that describes strongly correlated electrons. On the other hand, quantum computers are emerging as powerful tools for exploring the complex dynamics of these quantum many-body systems. In this work, we demonstrate the quantum simulation of the one-dimensional Fermi–Hubbard model using IBM's superconducting quantum computers, employing over 100 qubits. We introduce a first-order Trotterization scheme and extend it to an optimized second-order Trotterization for the time evolution in the Fermi–Hubbard model, specifically tailored for the limited qubit connectivity of quantum architectures, such as IBM's platforms. Notably, both Trotterization approaches are scalable and maintain a constant circuit depth at each Trotter step, regardless of the qubit count, enabling us to precisely investigate the relaxation dynamics in the Fermi–Hubbard model by measuring the expectation value of the Néel observable (staggered magnetization) for time-evolved quantum states. Lastly, our successful measurement of expectation values in such large-scale quantum many-body systems, especially at longer time scales with larger entanglement, highlights the quantum utility of superconducting quantum platforms over conventional classical approximation methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Stochastic Adaptive Droop Control in Frequency Regulation of Power Systems With Intermittent Generators

Modern power systems (MPSs), including microgrids (MGs), are increasingly incorporating multiple renewable energy sources (RESs) such as wind and solar power, as well as battery storage and controllable loads. While environmentally beneficial, these sources pose challenges for control and management due to their intermittent and stochastic nature, especially in maintaining frequency stability with multiple interconnected generators of varying capacities. Traditional droop control methods are effective in systems with generators that are dispatchable and have fixed generation capacities, but they fall short when applied to systems with RESs, where generation capacities are dynamic and affected by unpredictable environmental conditions. To address these challenges, this paper introduces a novel stochastic adaptive droop control (SADC) method for load frequency control (LFC). The proposed method adapts droop coefficients in real time, based on the measured stochastic data of power generation capacities, enabling more effective frequency regulation in systems with variable and intermittent power generation. Unlike traditional adaptive control methods, which assume constant or slowly-varying system parameters, this approach accounts for stochastic processes by modeling them as Markov chains, enabling robust performance under highly dynamic and unpredictable conditions. The key contributions of this work include the development of real-time droop coefficient adaptation algorithms, derivation of their stability and convergence properties, and the demonstration of the advantages of the method through simulations. Case studies highlight the improved performance of frequency regulation, particularly in addressing the impact of stochastic weather conditions and the benefits of reducing dependence on battery reserves in dealing with intermittency of RESs. Finally, this paper provides a comprehensive analysis of the theoretical foundations of the method, as well as practical implementation insights for future power systems with high penetration of RESs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Fuel Property Effects on Stochastic Preignition Events During Engine Load Transitions

Stochastic preignition (SPI) is an abnormal combustion phenomenon that can cause catastrophic engine damage. There have been several proposed mechanisms of SPI, where a uniform source is still not certain, however, SPI tendencies have been shown to be influenced by engine operating conditions, oil composition, engine age, and fuel chemical and physical properties. Laboratory research and testing for SPI propensity is challenging given the stochastic nature of events, as well as the potential for significant degradation of the engine platform and measuring equipment over time. Thus, SPI specific experiments are generally conducted under either sustained or cyclic patterning of steady-state operating conditions to avoid the influence of transient engine boundary conditions on test parameters of interest (e.g. oil additive package, fuel properties, engine speed/load, etc.). In this work a cyclically varying SPI test sequence involves a 5 min engine warmup period at a low engine load of around 4 bar gross indicated mean effective pressure (IMEPg), followed by a transition to high load (~20 bar IMEPg) at a constant 2000 rev/min engine speed for a total of 25 min. This individual test sequence load schedule is then sequentially repeated 10 times to generate significant statistical data for analysis. This work examines the influence of fuel chemical and physical properties on SPI tendency during the unsteady portion of the 10-cycle sequence (the first 5 min of the high load operation in each sequence of the loading cycle) which has been discarded from previous analyses due to the uncertainty in engine operating and thermal boundary conditions. Results from this analysis suggest an increasing trend in the ratio of SPI events during the unsteady test period relative to the steady test period with increasing fuel Reid Vapor Pressure (RVP), implying differences in uncontrolled ignition source terms, possibly from, fuel wall interactions and retention during the load transition phase of the test.

Splitter, Derek [ORNL] (ORCID:0000000174044047)↗
DOE OSTI2024

Generation and Life Cycle of Solar Spicules

The physical mechanism for the creation of solar spicules is proposed with three stages of their life cycle. It is assumed that at stage I the density hump is formed locally in the x-y plane in the lower chromosphere in the presence of temperature gradients of electrons and ions along the z-axis (the vertical direction). In this region, the density structure of quasi-neutral (n i ≃ n e = n) plasma after taking birth is accelerated in the vertical direction owing to the thermal force F th ∝ ∇n(x, y, t) × (∇T e + ∇T i ). The exact time-dependent analytical solution of two-fluid plasma equations is presented assuming that density is maximum at the center of the density structure and decays away from it gradually. The 2D density structure is created as a step function H(t) in time at the bottom of the chromosphere, and consequently, the vertical plasma velocity turns out to be the ramp function of time R(t) = tH(t), whereas the source term S(x, y, t) for the density follows the delta function δ(t) form. The upward acceleration a = a(x, y) $\hat{z}$ produced in this density structure is greater than the downward constant solar acceleration −g ⊙ in the chromosphere. In the transition region, the temperature gradients are steeper; therefore, the upward acceleration increases in magnitude g ⊙ ≪ a and the density hump spends less time there. This is stage II of its life cycle. In stage III, the density structure enters into the corona, where the gradients of temperatures vanish and the structure decelerates to zero velocity under the action of the solar gravitational force.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Bounce-averaged theory in arbitrary multi-well plasmas: solution domains and the graph structure of their connections

Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic time scale and reduces the dimensionality of the modelled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields – particularly in the presence of local maxima of the electric potential and magnetic field – the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Previously, these domains have been imposed by hand, or by recognising local maxima in the fields, limiting the flexibility of bounce-averaged simulations. Here, we present a general set of conditions for identifying consistent domains and the boundary condition connections between the domains, allowing the application of bounce-averaged theories in arbitrarily complicated and dynamically evolving electromagnetic field geometries. We also show how the connections between the domains can be represented by a directed graph, which can help to succinctly represent the trajectory bifurcation structure.

fusion plasma↗