Collision Parameters Research Articles

Kinetic study of head-on collisions of unequal-sized compound droplets

In this study, the head-on collision process of compound droplets of unequal sizes in a liquid environment is investigated using the volume of fluid method. The investigation reveals four main collision mechanisms: coalescence stabilization, coalescence release, rupture entrapment, and rupture coalescence. The transition between these collision mechanisms is analyzed in detail according to We. The effects of various initial collision parameters on the relative offset velocity CSrov, axial thicknesses l* and radial thicknesses h*, deformation coefficients, and core droplet release time Crt of compound droplet core shells were quantitatively analyzed. Additionally, this study examines the collision process of multi-layer compound droplets, revealing a more complex dynamic evolution of the interface, including the coalescence-release-entrapment phase and changes in the release direction. This study not only provides theoretical support for understanding the stability of compound droplets but also provides new insight into understanding multi-phase interactions in complex fluid systems.

Association Kinetics for Perfluorinated n-Alkyl Radicals.

Radical-radical reaction channels are important in the pyrolysis and oxidation chemistry of perfluoroalkyl substances (PFAS). In particular, unimolecular dissociation reactions within unbranched n-perfluoroalkyl chains, and their corresponding reverse barrierless association reactions, are expected to be significant contributors to the gas-phase thermal decomposition of families of species such as perfluorinated carboxylic acids and perfluorinated sulfonic acids. Unfortunately, experimental data for these reactions are scarce and uncertain. Furthermore, obtaining reliable theoretical predictions for such reactions is a laborious and computationally intensive task. In this work, the chemical kinetics of the various association/decomposition reactions producing/decomposing the C2-C4 series of unbranched n-perfluoroalkanes (C2F6, C3F8, and C4F10) are examined using state-of-the-art ab initio transition-state-theory-based master-equation calculations. The variable-reaction-coordinate transition-state theory (VRC-TST) formalism is employed in computing the microcanonical and canonical rates for the association reactions. Reaction thermochemistry is obtained via composite quantum chemistry calculations and the laddering of error-canceling reaction schemes via a connectivity-based hierarchy approach employing ANL1/ANL0-style reference energies. Lennard-Jones collision model parameters for the considered systems were estimated by a direct dynamics approach, and collisional energy transfer parameters were obtained from analogies to systems of similar size and heavy-atom connectivity. A one-dimensional master equation approach was used to convert the microcanonical rate coefficients from the VRC-TST analysis into temperature- and pressure-dependent rate constants for the association reactions and the reverse dissociation reactions. The data are reported in standardized formats for usage in comprehensive chemical kinetic models for PFAS thermal destruction.

Design and Validation of an Obstacle Contact Sensor for Aerial Robots.

Obstacle contact detection is not commonly employed in autonomous robots, which mainly depend on avoidance algorithms, limiting their effectiveness in cluttered environments. Current contact-detection techniques suffer from blind spots or discretized detection points, and rigid platforms further limit performance by merely detecting the presence of a collision without providing detailed feedback. To address these challenges, we propose an innovative contact sensor design that improves autonomous navigation through physical contact detection. The system features an elastic collision platform integrated with flex sensors to measure displacements during collisions. A neural network-based contact-detection algorithm converts the flex sensor data into actionable contact information. The collision system was validated with collisions through manual flights and autonomous contact-based missions, using sensor feedback for real-time collision recovery. The experimental results demonstrated the system's capability to accurately detect contact events and estimate collision parameters, even under dynamic conditions. The proposed solution offers a robust approach to improving autonomous navigation in complex environments and provides a solid foundation for future research on contact-based navigation systems.

Propagation dynamics of dust acoustic modes in collisional multicomponent plasmas

A comprehensive understanding of the physics underlying the dust-based processes and the ability to control the evolution of structures are essential in the field of plasma physics. This knowledge provides the foundation for numerous advanced scientific applications including the study of celestial objects and the synthesis of nanostructures. In this research, we consider the linear propagation of dust acoustic (DA) and dust ion acoustic (DIA) modes in a collisional plasma in the presence of an electron beam. The obtained dispersion relation demonstrates that the collision parameter and the electron beam density have significant contributions to the mode dynamics. The interactions of cold charged particles with neutrals result in a damping effect in the mode dynamics, which subsequently leads to a typical cutoff in the propagation of dust acoustic modes. Furthermore, the electron beam density can control the damping rate at different conditions. An increase in the electron beam density results in an acceleration of the DA mode damping, while the effect on the DIA mode is the opposite. The influence of the electron beam on the dynamics of the modes is more pronounced in the presence of strong collisions. Our analysis also shows that the propagation dynamics of each mode is strongly related to the wave vector. The damping rate is more pronounced in small wave vectors. Numerical analysis indicates that mode propagation can be controlled by the collision parameters and electron beam density. Furthermore, as a general trend, increasing the wave vector causes a shift in the cutoff toward higher collisions.

Realistic Outcomes of Moon–Moon Collisions in Lunar Formation Theory

The multiple impact hypothesis proposes that the Moon formed through a series of smaller collisions, rather than a single giant impact. This study advances our understanding of this hypothesis, as well as moon collisions in other contexts, by exploring the implications of these smaller impacts, employing a novel methodological approach that combines self-consistent initial conditions, hybrid hydrodynamic/N-body simulations, and the incorporation of material strength. Our findings challenge the conventional assumption of perfect mergers in previous models, revealing a spectrum of collision outcomes including partial accretion and mass loss. These outcomes are sensitive to collision parameters and the Earth’s tidal influence, underscoring the complex dynamics of lunar accretion. Importantly, we demonstrate that incorporating material strength is important for accurately simulating moonlet-sized impacts. This inclusion significantly affects fragmentation, tidal disruption, and the amount of material ejected or accreted onto the Earth, ultimately impacting the Moon’s growth trajectory. By accurately modeling diverse collision outcomes, our hybrid approach provides a powerful new framework for understanding the Moon’s formation. We show that most collisions (≈90%) do not significantly erode the largest moonlet, supporting the feasibility of lunar growth through accretion. Moreover, we revise previous estimates of satellite disruption, suggesting a higher survival rate and further bolstering the multiple-impact scenario.

Analysis of nonlinear vibration response to wear fault of big-end bearing shell of connecting rod in the ultra-high pressure five-cylinder plunger pump

The ultra-high-pressure five-cylinder plunger pump is core equipment in multi-field, with its important components, such as big-end bearing shell of connecting rod, being prone to wear under high-intensity operation. However, the vibration characteristics of this type of equipment are complex and are currently not adequately researched. In view of this, this paper takes a certain model of five-cylinder fracturing pump as the research object. A rigid–flex coupling model of fracturing pump considering the wear fault of the big-end bearing shell of connecting rod is established. And taking the pressure-flow variation at the hydraulic end as boundary condition, the influence of wear degree and position on its vibration response is revealed. The results show that the collision force, centroid displacement, and vibration acceleration of the big-end bearing shell of connecting rod are mainly affected by the clearance collision parameters. Among them, the vibration acceleration is also affected by the collision between the connecting rods. For connecting rod big-end bearing shell with abnormal clearances, the collision force average amplitude and the centroid displacement effective value of it, and the vibration acceleration effective value at the corresponding measurement point all increase with the degree of wear increases. The vibration acceleration effective value at remaining measuring point decreases, and the further away from the connecting rod of abnormal clearance, the decline tends to be gentle. The research results provide a theoretical basis for the optimization of structural performance and the development of fault diagnosis technology of the five-cylinder plunger pump.

Parameters of Collision and Adhesion Process Between a Rising Bubble and Quartz in Long-Chain Amine Solution and Their Correlation with Flotation

The successful adhesion of air bubbles to mineral particles is the crucial to flotation technology. This paper systematically investigates the parameters variation in the dynamic interaction process between a rising bubble and a quartz plate in long-chain amine solutions (dodecylamine, tedecylamine, and octadecylamine). The results show that the type and concentration of long-chain amine affected the collision and adhesion process between bubbles and quartz plates remarkably. The maximum rebound distance (rebound distance after the first collision) of bubbles and the stable-state liquid film thickness gradually decreases with the increase of reagent concentration. Additionally, the collision-rebound duration and induction time shorten accordingly, the surface tension of the solution decreases, the surface hydrophobicity of quartz increases, and the deformation degree and average movement velocity of bubbles decrease. With the increase in carbon chain length, the adsorption form of the amine collector and quartz surface becomes closer to vertical, and the density of water molecules decreases. The recovery of quartz particles is highest with octadecylamine systems, corresponding well with the changing trend in steady-state liquid film thickness. This research provides an effective method for in-depth analysis of the microscopic interaction mechanism between bubbles and mineral surfaces and the prediction of flotation results.

Theoretical Investigation of Rate Coefficients and Dynamical Mechanisms for N + N + N Three-Body Recombination Based on Full-Dimensional Potential Energy Surfaces

Three-body recombination reactions, in which two particles form a bound state while a third one bounces off after the collision, play significant roles in many fields, such as cold and ultracold chemistry, astrochemistry, atmospheric physics, and plasma physics. In this work, the dynamics of the recombination reaction for the N3 system over a wide temperature range (5000–20,000 K) are investigated in detail using the quasi-classical trajectory (QCT) method based on recently developed full-dimensional potential energy surfaces. The recombination products are N2(X) + N(4S) in the 14A″ state, N2(A) + N(4S) in the 24A″ state, and N2(X) + N(2D) in both the 12A″ and 22A″ states. A three-body collision recombination model involving two sets of relative translational energies and collision parameters and a time-delay parameter is adopted in the QCT calculations. The recombination process occurs after forming an intermediate with a certain lifetime, which has a great influence on the recombination probability. Recombination processes occurring through a one-step three-body collision mechanism and two distinct two-step binary collision mechanisms are found in each state. And the two-step exchange mechanism is more dominant than the two-step transfer mechanism at higher temperatures. N2(X) formed in all three related states is always the major recombination product in the temperature range from 5000 K to 20,000 K, with the relative abundance of N2(A) increasing as temperature decreases. After hyperthermal collisions, the formed N2(X/A) molecules are distributed in highly excited rotational and vibrational states, with internal energies mainly distributed near the dissociation threshold. Additionally, the rate coefficients for this three-body recombination reaction in each state are determined and exhibit a negative correlation with temperature. The dynamic insights presented in this work might be very useful to further simulate non-equilibrium dynamic processes in plasma physics involving N3 systems.

Study of nucleus orientation effect in the 238U+238U multinucleon transfer reaction

The improved quantum molecular dynamics model was employed to study the 238U+238U multinucleon transfer reaction at E c.m. = 833 MeV in this work. The influence of the orientation effect on the nuclear deformation at the contact moment, the composite system lifetime, the transfer rate and the fragment production mechanism are investigated. Statistical analysis reveals that at the contact moment, the orientation of the projectile and the target have less influence on each other and retain their respective initial characteristics to some extent. For collision parameters less than 6 fm, significant differences are observed in composite system lifetime and transfer rate under different orientation configurations; however, the orientation effect gradually diminishes with increasing collision parameters. Additionally, it is found that transfer reactions dominate when the collision parameter b ≤ 6 fm, while elastic and inelastic scattering events increase rapidly as the collision parameter exceeds 6 fm. Within the range of 10 ≤ b ≤ 13 fm, the transfer probability for side–side collisions is significantly higher compared to other cases.

Gravitational collapse at low to moderate Mach numbers: The relationship between star formation efficiency and the fraction of mass in the massive object

The formation of massive objects via gravitational collapse is relevant both for explaining the origin of the first supermassive black holes and in the context of massive star formation. Here, we analyze simulations of the formation of massive objects pursued by different groups and in various environments, concerning the formation of supermassive black holes, primordial stars, as well as present-day massive stars. We focus here particularly on the regime of small virial parameters, that is, low ratios of the initial kinetic to gravitational energy, low to moderate Mach numbers, and the phase before feedback is very efficient. We compare the outcomes of collapse under different conditions using dimensionless parameters, particularly the star formation efficiency є*, the fraction ƒ* of mass in the most massive object relative to the total stellar mass, and the fraction ƒtot of mass of the most massive object as a function of the total mass. We find that in all simulations analyzed here, ƒtot increases as a function of є*, although the steepness of the increase depends on the environment. The relation between ƒ* and є* is found to be more complex and also strongly depends on the number of protostars present at the beginning of the simulations. We show that a collision parameter, estimated as the ratio of the system size divided by the typical collision length, allows us to approximately characterize whether collisions are important. A high collision parameter implies a steeper increase in the relation between ƒtot and є*. We analyze the statistical correlation between the dimensionless quantities using the Spearman coefficient and further confirm via a machine learning analysis that good predictions of ƒ* can be obtained from є* together with a rough estimate of the collision parameter. This suggests that a good estimate of the mass of the most massive object can be obtained once the maximum efficiency for a given environment is known and an estimate for the collision parameter has been determined.

Numerical simulations of the interactions between counterflowing density currents

The collision and interactions between counterflowing density currents frequently occur in nature and engineering practices along the coastal regions. However, the mechanisms and implications of these interactions remain an active research area. In this study, we developed a high-resolution numerical model to simulate the hydrodynamic characteristics of symmetric and asymmetric colliding saline density currents. The aim was to understand the interaction mechanisms, quantify collision parameters, and provide baseline physical insights into the implications of such interactions. The direct numerical simulations reveal that when equal height counterflowing saline density currents collide, the dynamic characteristics of the resulting flow depend on the density difference between the colliding currents, collaborating experimental results. The interaction process initiated mixing and significant vertical motion in the resulting mixed fluid, which attained a maximum rise height of approximately twice that of the colliding currents, thereby enhancing the vertical motion of hypersaline fluid in the ambient column. While the extent of mixing at the collision boundary increases with increasing asymmetry between the colliding currents, a relationship is observed between the buoyancy ratio of the colliding currents and the maximum rise height of the vertically displaced fluid. Given that desalination operations require effective dispersion of brine into the marine environment to minimize local impacts, understanding the collision dynamics of counterflowing saline currents would facilitate improved engineering design and implementation of environmentally compliant coastal management strategies.

Temperature dependence of line shape parameters for N2- and O2-broadened methane lines by quantum cascade laser spectroscopy

This paper report nitrogen- and oxygen-broadening coefficients, their speed-dependencies, and the collisional narrowing parameters of lines in the ν4-band of methane. The parameters were determined from low (150 K) to high temperatures (600 K). The measurements were done with a high-resolution quantum cascade laser spectrometer coupled to specific absorption cells that allow to cool and heat the gas mixtures with a great stability. The spectroscopic parameters were determined at each temperature by fits of the experimental absorbances in a multispectrum fitting procedure using the Voigt, Speed-Dependent Voigt, Nelkin-Ghatak and Speed-dependent Nelkin-Ghatak theoretical line shape models. The temperature dependencies of the collisional half-widths, the speed-dependence of the broadening coefficients as well as the collisional narrowing parameters were studied with the empirical power law and the physics-based Gamache-Vispoel model (DPL) [Gamache and Vispoel, JQSRT, 217, 440–452, 2018]. The obtained line shape parameters and their temperature dependencies are compared, when possible, to existing data in literature. The DPL reproduces more accurately the evolution of the studied collisional parameters over the wide range of temperature considered in the study.

Exploring the effect of eccentricity on geometry nuclear collisions by Glauber Monte Carlo simulation

This paper will analyze different properties of a nuclear collision and their correlation with the geometry of collision using the Glauber Monte-Carlo based calculations. Among all properties, the eccentricity is the main focus of this research. In order to investigate its impact on collision parameters, three-dimensional histograms are created, using given collision parameters, under different categories of numbers of participant nucleons. Comparisons between the histograms allow the exploration of connections between this property and the geometries of lead nuclear collisions, namely, the ellipticity of the collision of the two lead nuclei as eccentricity increases from 0 to 1. Our result is intuitive. The ellipticity of the collision has a positive correlation with the eccentricity, as when the difference between the number of participant nucleons on the L1 and L2 axes increases with eccentricity. The number of nucleons participating in the collision also increases with eccentricity. These are all coherent with past studies conducted in this field.

Accurate reference spectra of HD in an H2–He bath for planetary applications

Context. The hydrogen deuteride (HD) molecule is an important deuterium tracer in astrophysical studies. The atmospheres of gas giants are dominated by molecular hydrogen, and the simultaneous observation of H2 and HD lines provides reliable information on the D/H ratios on these planets. The reference spectroscopic parameters play a crucial role in such studies. Under the thermodynamic conditions encountered in these atmospheres, spectroscopic studies of HD require not only the knowledge of line intensities and positions but also accurate reference data on pressure-induced line shapes and shifts. Aims. Our aim is to provide accurate collision-induced line-shape parameters for HD lines that cover any thermodynamic conditions relevant to the atmospheres of giant planets, namely any relevant temperature, pressure, and perturbing gas composition (the H2–He mixture). Methods. We performed quantum-scattering calculations on our new, highly accurate ab initio potential energy surface (PES), and we used scattering S matrices obtained in this way to determine the collision-induced line-shape parameters. We used cavity ring-down spectroscopy to validate our theoretical methodology. Results. We report accurate collision-induced line-shape parameters for the pure rotational R(0), R(1), and R(2) lines, the most relevant HD lines for investigations of the atmospheres of the giant planets. Besides the basic Voigt-profile collisional parameters (i.e., the broadening and shift parameters), we also report their speed dependences and the complex Dicke parameter, which can influence the effective width and height of the HD lines up to almost a factor of 2 for giant planet conditions. The sub-percent-level accuracy reached in this work is a considerable improvement over previously available data. All the reported parameters (and their temperature dependences) are consistent with the HITRAN database format, hence allowing for the use of the HITRAN Application Programming Interface (HAPI) for generating the beyond-Voigt spectra of HD.

An Evaluation and Improvement of Microphysical Parameterization for a Heavy Rainfall Process during the Meiyu Season

The present study assesses the simulated precipitation and cloud properties using three microphysics schemes (Morrison, Thompson and MY) implemented in the Weather Research and Forecasting model. The precipitation, differential reflectivity (ZDR), specific differential phase (KDP) and mass-weighted mean diameter of raindrops (Dm) are compared with measurements from a heavy rainfall event that occurred on 27 June 2020 during the Integrative Monsoon Frontal Rainfall Experiment (IMFRE). The results indicate that all three microphysics schemes generally capture the characteristics of rainfall, ZDR, KDP and Dm, but tend to overestimate their intensity. To enhance the model performance, adjustments are made based on the MY scheme, which exhibited the best performance. Specifically, the overall coalescence and collision parameter (Ec) is reduced, which effectively decreases Dm and makes it more consistent with observations. Generally, reducing Ec leads to an increase in the simulated content (Qr) and number concentration (Nr) of raindrops across most time steps and altitudes. With a smaller Ec, the impact of microphysical processes on Nr and Qr varies with time and altitude. Generally, the autoconversion of droplets to raindrops primarily contributes to Nr, while the accretion of cloud droplets by raindrops plays a more significant role in increasing Qr. In this study, it is emphasized that even if the precipitation characteristics could be adequately reproduced, accurately simulating microphysical characteristics remains challenging and it still needs adjustments in the most physically based parameterizations to achieve more accurate simulation.

The effect of collision parameters on the 3D Eulerian simulation of a thin rectangular bubbling fluidized bed

It is well known that the hydrodynamics of dense gas–particle flows depends heavily on inter-particle and particle–wall collisions; however, the subtleties of these interactions are not always fully recognized or appreciated. In this study, the two-fluid model is used to systematically examine the effects of collision parameters, i.e., particle–particle restitution coefficient, particle–wall restitution coefficient, and wall specularity coefficient, on simulations of the hydrodynamics of a pseudo two-dimensional bubbling fluidized bed.The utilization of high-resolution Eulerian simulations facilitates the representation of meso-scale structures without the use of a sub-grid scale model, while qualitatively reflecting the experimental data. To ensure statistically robust results and increase confidence in the simulations, a careful assessment of the time-averaging interval was first undertaken to smooth out the fluctuations that persist even after the bed reaches steady state.A quantitative analysis was then performed to analyze important facets of the flow, including bubble characteristics, particle velocity fields, and granular temperature. The underlying physical formulation was employed to elucidate how collision parameters impact the hydrodynamics of the flow.The notable findings of this study are threefold. First, the specific details of the collisions between particles are shown to significantly influence the bubble characteristics and overall flow pattern. However, the effect of the particle–particle restitution coefficient turns out to be minimal on the bed circulation time except in the limit of particle elastic collisions. It is also found that the elastic collision of particles highly affects the bubble count and unexpectedly changes the role of the wall from a source to a sink of granular temperature. Second, the effect of the particle–wall restitution coefficient is appreciable on the granular temperature while having a minimal effect on the flow hydrodynamics. Third, the effect of the wall specularity coefficient is felt across the bed such that an increase in this parameter increases the bed circulation time. The results of this systematic study enhance the understanding of how collision parameters impact flow characteristics while also providing insight into the selection of their values in simulations.

Risk assessment and prevention for typical railway bridge pier under rockfall impact

Railway bridges in mountainous regions are susceptible to damage and collapse due to rockfall impacts, posing a risk to train operations. This research specifically focuses on risk assessment of a typical railway bridge pier considering correlations between the collision parameters. Firstly, a comprehensive analysis of rockfall trajectories is conducted using the tool ROCFALL. Statistical features and correlation of impact parameters at the pier location are obtained and further characterized based on functional statistical models. Additionally, a high-fidelity finite element (FE) model of a two-span simply supported box girder with three piers is developed using LS-DYNA. Multiple structural dynamic responses including impact force, pier displacement, and internal energy of the directly impacted pier, are evaluated for both general rockfalls and potential boulders. The study examines the effects of individual impact parameters on the internal energy and displacement responses at the pier top, highlighting their significance in relation to load-bearing capacity and operational safety. Machine learning techniques are utilized to perform a comprehensive evaluation of risk states, wherein an Artificial Neural Network (ANN) model is employed for accurate prediction of risk indexes, and the K-means algorithm is applied to classify pier risk levels into minor, moderate, and severe. Furthermore, Monte Carlo (MC) simulations are employed to calculate the probabilities associated with different risk levels. A composite multilayer prevention measure is suggested to enhance the performance of a rockfall-prone bridge. It is proven that this measure can rapidly reduce associated vibrations and effectively mitigate structural damage resulting from the collision.

How Long-lived Grains Dominate the Shape of the Zodiacal Cloud

Grain–grain collisions shape the three-dimensional size and velocity distribution of the inner Zodiacal Cloud and the impact rates of dust on inner planets, yet they remain the least understood sink of zodiacal dust grains. For the first time, we combine the collisional grooming method combined with a dynamical meteoroid model of Jupiter-family comets (JFCs) that covers 4 orders of magnitude in particle diameter to investigate the consequences of grain–grain collisions in the inner Zodiacal Cloud. We compare this model to a suite of observational constraints from meteor radars, the Infrared Astronomical Satellite, mass fluxes at Earth, and inner solar probes, and use it to derive the population and collisional strength parameters for the JFC dust cloud. We derive a critical specific energy of QD*=5×105±4×105Rmet−0.24 J kg−1 for particles from JFC particles, making them 2–3 orders of magnitude more resistant to collisions than previously assumed. We find that the differential power-law size index −4.2 ± 0.1 for particles generated by JFCs provides a good match to observed data. Our model provides a good match to the mass-production rates derived from the Parker Solar Probe observations and their scaling with the heliocentric distance. The higher resistance to collisions of dust particles might have strong implications to models of collisions in solar and exosolar dust clouds. The migration via Poynting–Robertson drag might be more important for denser clouds, the mass-production rates of astrophysical debris disks might be overestimated, and the mass of the source populations might be underestimated. Our models and code are freely available online.

Hall physics during magnetic reconnection with collision effect

The Hall effect, decoupling between the ion and electron motions, is the core mechanism triggering fast reconnection. In plasmas with collision effects such as laboratory facilities, collision can suppress the Hall effect and influence the triggering of fast reconnection. Here, by conducting a series of kinetic simulations with varying collision parameters, we show that collisions can suppress the electron outflow, impairing the quadrupole Hall magnetic field. Besides, collision weakens the inflow of magnetic flux by reducing the charge separation and increasing the thermal pressure at the reconnection site, leading to a reduction of the Hall electric field. As the collisionality becomes larger, the Hall electric field diminishes more easily than the Hall magnetic field. We propose that the quadrupolar Hall magnetic field can be a significant indicator in reflecting Hall reconnection.

Analytical solutions for quantum radiation reaction in high-intensity lasers

While the Landau-Lifshitz equation, which describes classical radiation reaction, can be solved exactly and analytically for a charged particle accelerated by a plane electromagnetic wave, no such solutions are available for quantum radiation reaction (the recoil arising from the successive, incoherent emission of hard photons). Yet upcoming experiments with ultrarelativistic electron beams and high-intensity lasers will explore the regime where both radiation-reaction and quantum effects are important. Here we present analytical solutions for the mean and variance of the energy distribution of an electron beam that collides with a pulsed plane electromagnetic wave, which are obtained by means of a perturbative expansion in the quantum parameter χ0. These solutions capture both the quantum reduction in the radiated power and the stochastic broadening, and are shown to be accurate across the range of experimentally relevant collision parameters, i.e., GeV-class electron beams and laser amplitudes a0≲200. Published by the American Physical Society 2024