Binary Collision Research Articles

Regularizable collinear periodic solutions in the n-body problem with arbitrary masses

For n-body problem with arbitrary positive masses, we prove there are regularizable collinear periodic solutions for any ordering of the masses, going from a simultaneous binary collision to another in half of a period with half of the masses moving monotonically to the right and the other half monotonically to the left. When the masses satisfy certain equality condition, the solutions have extra symmetry. This also gives a new proof of the existence of Schubart orbit, when n=3.

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.

Flattenicity as centrality estimator in p-Pb collisions simulated with PYTHIA/Angantyr

Abstract In this paper, a centrality estimator based on flattenicity is studied using PYTHIA~8.312 Angantyr, whose existing implementation is enough to study the particle production in p--Pb collisions in the absence of medium effects. The number of binary nucleon-nucleon collisions for different centrality estimators are compared. The studies include forward multiplicity, forward flattenicity and midrapidity multiplicity. The results using flattenicity show the smallest deviations ($<8$\%) with respect to the results which use impact parameter for centrality classes. On the other hand, the multiplicity-based estimators exhibit huge deviations (up to a factor 2) with respect to the results using impact parameter. The particle ratios (proton-to-pion and kaon-to-pion ratios) and nuclear modification factors as a function of $p_{\rm T}$ are also studied for the different centrality estimators. The studies presented here are relevant to help in the investigation of the plethora of effects, which have been reported by experiments at the LHC.

Asymptotic solutions of the quantum scattering problem for binary collisions in a system of three charged particles. The inclusion of the dipole interaction

Asymptotic solutions of the quantum scattering problem for binary collisions in a system of three charged particles. The inclusion of the dipole interaction

What does it take to stabilize a naphthalene anion?

We investigate attachment of slow electrons (0-10eV) to naphthalene (Np) clusters in a crossed beam experiment. Supersonic expansions under different conditions using different buffer gases generate the clusters: in He, Ne, and low pressure Ar, neat (Np)N clusters are formed, while we also observe mixed clusters of naphthalene with rare-gas atoms in co-expansion with Ar above 0.5bar and with Kr. Negatively charged (Np)n- and Rgm(Np)n- (Rg = Ar, Kr) clusters are analyzed by mass spectrometry, and electron energy dependent ion yields are measured. We show that the smallest stable naphthalene complex with an excess electron, the dimer (Np)2- anion, cannot be formed in a binary collision of a free electron with (Np)2 dimer, nor with (Np)3 trimer. Evaporation of a weakly bound Ar atom(s) from a mixed ArM(Np)2 cluster following electron attachment leads to the dimer (Np)2- anion. Larger (Np)n-, n > 3, transient cluster anions decay via evaporation of an Np unit on a timescale of tens of microseconds. The self-scavenging process opens around 6eV, where a naphthalene unit is electronically excited by the incoming electron, which is slowed down and trapped. However, the transient negative ion is efficiently stabilized only in the mixed clusters, from which Ar atom(s) can be evaporated.

Ideal Collision Rate of Symmetric Hexapods in a Simple Shear Flow.

An ideal collision rate (ICR) is defined as the average rate of contact between two particles that translate and rotate with the imposed fluid flow in the absence of interparticle interactions. ICR in a simple shear flow provides an estimate of the collision rate in a flowing dilute particle suspension, and its value is known only for traditional convex shapes such as spheres and cylinders. In this work, we compute the ICR for a family of symmetric hexapods (shown in Figure 1) that are particles composed of three orthogonal cylinders with coinciding centers (forming six arms) with at least two cylinders having the same length. We employed the finite-element method to obtain the rotational dynamics of hexapods and Monte Carlo simulations to calculate their ICR. Our results indicate that the ICR for hexapods is not directly proportional to the volume of the particle, in contrast to what is observed for convex shapes such as spheres and cylinders. For hexapods of the same size, the ICR could be similar for particles with order-of-magnitude differences in their volumes and it could also vary by an order of magnitude for particles with similar volumes. Specifically for hexapods termed branched fibers, which have one longer cylinder, the ICR changes by an order of magnitude even when the shorter cylinders are significantly smaller than the longer cylinder. This change is attributed to the increase in the tumbling frequency of the particle due to hydrodynamic forces acting on the shorter arms, in addition to the increased probability of collision afforded by them. Using asymptotic theory for high-aspect ratio cylinders, we showed that the tumbling period of hexapods was proportional to an algebraic power of the ratio of its arm lengths and has a weaker logarithm relationship with the aspect ratio of its arms. The collision cross-section provided the relative cross-streamline particle separations for the most likely binary collisions in the suspensions, and its value was sensitive to the arm lengths, as well. The collision rate of hexapods also could not be estimated within an order of magnitude from existing geometric models, such as the ICR of a circumscribing convex shape, ICR for one of the individual cylinders of the hexapod, or using the particle volume times the shear rate. Our work indicates that collision rate for non-convex particles in shear flows critically depends on the shape of the particle due to nontrivial changes in the particle's orientational dynamics, and the ICR calculation serves as a more reliable method for estimating their true collision rates in the suspension.

On the Use of a Chloride or Fluoride Salt Fuel System in Advanced Molten Salt Reactors, Part 3; Radiation Damage

Structural materials in fast reactors with harsh radiation environments due to high energy neutrons—compared to thermal reactors—potentially suffer from a higher degree of radiation damage. This radiation damage can change the thermophysical and mechanical properties of materials and, as a result, alter their performance and effective lifetime, in some cases leading to their disintegration. These phenomena can jeopardize the safety of fast reactors and thus need to be investigated. In this study, the effect of radiation damage on the vessels of molten salt fast reactors (MSFR) was evaluated based on two fundamental radiation damage parameters: displacement per atom (dpa) and primary knock-on atom (pka). Following the previous part of this article (Parts 1 and 2), an iMAGINE reactor core design (University of Liverpool, UK—chloride-based salt fuel system) and an EVOL reactor core design (CNRS, Grenoble, France, fluoride-based salt fuel system) with stainless steel and nickel-based alloy material vessels, respectively, were considered as case studies. The SPECTER and SPECTRA-PKA codes and a PTRAC card of MCNPX, integrated with a module which has been developed in MATLAB, named PTRIM and SRIM-2013 (using binary collision approximation), were employed individually to calculate and compare dpa and PKA (this master module containing all three tools has been appended to the iMAGINE-3BIC package for future use during reactor operations). Additionally, SRIM-2013 was applied in a 3D simulation of a radiation damage map on a small sample of vessels based on the calculated PKA. Our results showed a higher degree of radiation damage in the iMAGINE vessel compared to the EVOL one, which could be expected due to the harder neutron flux spectrum of the iMAGINE core compared to EVOL. In addition, the nickel alloy vessel showed better radiation damage resistance against high energy neutrons compared to the stainless steel one, although more investigations are required on thermal neutrons and alloy corrosion mechanisms to determine the best material for use in MSFR vessels.

Note on the low deposition rate during reactive magnetron sputtering

Previously published data on the metal partial sputter yield from a poisoned target during reactive magnetron sputtering is confronted with the metal partial sputter yield from the corresponding compound calculated based on an existing semi-empirical model validated with experimental ion beam data. Both yields are linearly correlated but the magnetron based sputter yields are approximately 8 times lower. The lower yield is explained from the formation of an oxygen rich top layer. This hypothesis is verified by binary collision approximation Monte Carlo simulations.

Radiation induced athermal diffusivity in uranium mononitride

Uranium mononitride (UN) is one of the ceramic nuclear fuel alternatives to oxide fuel considered for light water reactors and advanced reactor designs. Properties like self- and fission gas diffusivity need to be better understood, given that they influence key fuel performance phenomena such as fission gas swelling and release. In particular, the radiation induced athermal (D3) diffusivity remains challenging to accurately predict and has only been sparsely characterized in UN, despite its importance as it likely governs diffusion at the low temperatures this high-thermal-conductivity fuel form may operate. Molecular Dynamics simulations are used to estimate the mean square displacement induced by a primary knock-on atom (PKA) with a given kinetic energy. These results are combined with the PKA energy distributions obtained from binary collision approximation calculations to obtain the displacement due to a particular fission fragment. Finally, this is combined with experimental fission fragment yields to determine the displacement due to an average fission event and, thus, express the athermal diffusivity as a function of the fission rate density. These results are in excellent agreement with available experimental data. A particular importance is given to the understanding and the quantification of the variability of these results.

Exploration of microscopic physical processes of Z-pinch by a modified electrostatic direct implicit particle-in-cell algorithm

Abstract For investigating efficiently the stagnation kinetic-process of Z-pinch, we develop a novel modified electrostatic implicit particle-in-cell algorithm in radial one-dimension for Z-pinch simulation in which a small-angle cumulative binary collision algorithm is used. In our algorithm, the electric field in z-direction is solved by a parallel electrode-plate model, the azimuthal magnetic field is obtained by Ampere’s law, and the term for charged particle gyromotion is approximated by the cross product of the averaged velocity and magnetic field. In simulation results of 2 MA deuterium plasma shell Z-pinch, the mass-center implosion trajectory agrees generally with that obtained by one-dimensional MHD simulation, and the plasma current also closely aligns with the external current. The phase space diagrams and radial-velocity probability distributions of ions and electrons are obtained. The main kinetic characteristic of electron motion is thermal equilibrium and oscillation, which should be oscillated around the ions, while that of ion motion is implosion inwards. In the region of stagnation radius, the radial-velocity probability distribution of ions transits from the non-equilibrium to equilibrium state with the current increasing, while of electrons is basically the equilibrium state. When the initial ion density and current peak are not high enough, the ions may not reach their thermal equilibrium state through collisions even in its stagnation phase.

Effect of coal suspension concentration and gas-air medium temperature on liquid droplets collisions

Relevance. Understanding the mechanisms of liquid droplets interaction with each other is important for many industrial and technical applications related to solving a range of problems like slag removal in a high-temperature environment, obtaining components of the desired fraction in the food industry, etc. Aim. Establishment of the main patterns of suspension droplets interaction in a gas-air environment with temperature variation. Methods. Using shadow high-speed video recording, the main patterns of the binary collision of suspensions droplets were determined. The paper introduces the results of experimental studies of the characteristics of collisions of droplets of coal-water suspensions in a gas-air environment with a temperature of 90–120°C. Parameters of the generated droplets: radius 1.0–2.2 mm, velocity 0.5–2.0 m/s. Results and conclusions. The authors have determined the modes of collision of droplets of suspensions (coagulation and separation) and the main characteristics of secondary fragments and constructed the maps of the modes of interaction of drops of suspensions with each other when varying the concentration of solid particles in the suspension, the temperature of the gas-air environment and the time the target drop spent in a gas-air environment with an elevated temperature. The conditions were established for the coagulation of droplets, as well as their intensive secondary grinding to intensify their drying, ignition and combustion in boiler furnaces. It was established that an increase in the temperature of the gas-air environment leads to a significant change in the size and properties of droplets, as well as to the occurrence of oscillatory phenomena in the system. It is substantiated that collision of droplets of suspensions in a gas-air environment with elevated temperature is complex and multi-parametric. Its characteristics depend on a combination of factors (surface tension and liquid viscosity, size and shape of droplets, speed of their movement, density and viscosity of gas-air environment). The authors obtained mathematical expressions to describe the boundaries of the modes of the studied processes and schemes for using the results obtained in order to increase the efficiency of the corresponding technological processes.

Numerical investigation of non-Newtonian droplet collisions: Comparison of volume of fluid and the local front reconstruction method with experimental data

Droplet-droplet collisions of non-Newtonian fluids are often encountered in industrial applications such as spray drying, fluid catalytic cracking, coating and granulation. However, there has been limited focus on a comprehensive analysis of the dynamics of these non-Newtonian binary droplet collisions. In this work, the non-Newtonian binary droplet collisions of 500 ppm xanthan gum solutions are simulated using the Volume of Fluid method and the Local Front Reconstruction Method to determine the applicability of these methods for the simulations of binary non-Newtonian droplet collisions. After verification, the simulations are compared to experimental data from literature. The outcomes for off-center collisions in the simulations resemble the experimental observations, including the oscillation of the ligament. For head-on collisions, the initial interactions and collision dynamics can be predicted with both methods at low Weber numbers, while LFRM shows improved performance at higher Weber numbers. Further, the use of an effective viscosity for the simplified representation of the droplet collision has been proven unsuccessful due to the absence of a universal effective viscosity for all situations.

Simulations of classical three-body thermalization in one dimension.

One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of pointlike particles, typically the dominant process for reaching thermal equilibrium in higher-dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential V_{ij}∝1/|x_{i}-x_{j}|^{n} or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equationto evolve a perturbed thermal state with temperature T toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low-density limit. For the inverse power-law potential, the rate of thermalization is proportional to ρ^{2}T^{1/2-1/n}, where ρ is the number density. The corresponding proportionality constant decreases with increasing n.

Electron correlation effects in electron promotion processes during binary atomic collisions at solid surfaces

We report energy distributions of electrons emitted by Aluminum and Magnesium surfaces under the impact of singly charged neon ions with energies in the range 100–5000 eV, focusing on the Auger decay of electronic excitations produced during binary atomic collisions. The autoionization spectra of the projectiles show several peaks that are identified and assigned to specific collisional excitation processes. The data provide evidence for electron correlation effect that occur while the colliding atoms are still coupled in the quasi-molecular system and results in two-electron transitions.

On the question whether surface roughness can explain the absence of a prominent single-collision peak in keV heavy-ion scattering off a polycrystalline Ru surface

In a joint experimental and modeling effort, we have studied 15 keV Ar2+, Kr2+, and Xe2+ projectiles scattering off a polycrystalline Ru surface to assess the possible role of surface roughness in the apparent near-absence of the single-collision (SC) peak for Xe, the heaviest of the ions. The surface roughness of the Ru sample was determined by atomic force microscopy (AFM). The AFM image is used as input to simulations by means of the ray tracing code SPRAY. The observed spectra display a significant SC peak in the energy distributions of reflected Ar and Kr ions, which is not the case for Xe. The energy spectrum produced by the reflection of Xe and recoiled Ru ions closely corresponds to the results obtained from our SPRAY simulations. It is evident that surface roughness plays a crucial role in the visibility of the SC peak. From simulations for different target roughnesses, it is clear that a concentrated distribution of inclination angles centered around 2° effectively reduces the intensity of the single-collision peak for Xe ion scattering. The presence of a distinct SC peak for Ar and Kr ions, unlike Xe ions, supports the notion that the absence of a prominent SC peak in Xe ion scattering is not primarily due to geometric blocking of trajectories by surface roughness. This suggests that for slow, heavy ions like Xe, scattering effects arising from the nearest neighbors to the binary collision partner are significant and should be carefully examined.

To plasma electrons motion theory in high-frequency fields

The article is dedicated to the kinetic theory of plasma, where the problem of interaction of high-frequency electric fields with weakly non-uniform plasma is investigated using kinetic equations with binary collision integrals for plasma particles. A new methodology for determining the expression of the averaged highfrequency pressure force is proposed based on solving the kinetic equation and using the method of successive approximations (separation of slow motions and fast oscillations) under the limiting conditions. An expression for the averaged quasi-potential force is derived based on the kinetic equation for the electron distribution function in weakly inhomogeneous magnetoactive plasma, taking into account electrons collisions with fixed ions and the presence of a longitudinally inhomogeneous high-frequency electric field using wellknown methods of theoretical and mathematical physics, such as successive approximations, averaging over the effective field oscillation period, and integration over trajectories. The amplitude of the field is a slowly varying function in both time and space coordinates. The obtained expression allows us to estimate the influence of collisions of plasma particles on the Miller force, and under limiting conditions it coincides with the known expressions for the high-frequency pressure force derived from the equation of plasma electrons motion in high-frequency fields. In all calculations, the contribution of the magnetic component of the electromagnetic field is neglected, which is quite justified for the longitudinal electric field.

Developing of a Monte Carlo calculations-based on simulation code for binary collision approximation in amorphous materials

In this work, we present a computer code developed and named MCIS (Monte Carlo Collisions In Solids) in his first version allowing the study and determination of the structure properties (arrangement, vacancies, energy losses...) during ion implantation in an amorphous solid matrix. This code is based on both the binary collisions approximation (BCA) theory and statistical Monte Carlo method within C++ Builder environment. The properties of this code can be summarized as: simulate 92 chemical elements of periodic table, the energy of projectile tuned from 1eV to few MeV, variable angle of incidence projectile, it can simulated 4 layers with a maximum of 4 elements per layer, it can use of the electronic losses of energies by choose of Firsov or Robinson approximation, various interactions potentials such as the ZBL, Moliers and C-Kr. Possibility of choose of scattering phenomenon among the Magic Formula and the Rutherford scattering. The results generated by our code are very promising when compared to those given by SRIM (Stopping and Range of Ions in Matter) code along with the advantage that our code takes into account the effect of the interaction potential which is neglected in SRIM.

Hypergolic Ignition by Off-Center Binary Collision of Monoethanolamine-NaBH4 and Hydrogen Peroxide Droplets

Hypergolic ignition of H2O2 and MEA-NaBH4 by off-center collision of their droplets was experimentally studied, focusing on the characteristics and mechanism of droplet mixing, droplet heating and evaporation, and gas-phase ignition. The whole collision ignition process was divided into five stages, which were compared, respectively, with that of head-on collision. Under the condition of a slightly off-center collision (for cases where B < 0.35), H2O2 droplets penetrate MEA-NaBH4 droplets after the collision and coalesce with it, but the internal H2O2 drop inside the MEA-NaBH4 droplet does not form a stable sphere. Instead, it rotates and expands inside the mixed droplet. With B increasing to 0.59, the droplets no longer coalesce after collision but separate away, forming satellite droplets. In such cases, multi-ignition mode is observed. When B increases to a certain extent, specifically, 0.85, a grazing collision is observed such that no mass transfer exists during the interaction of droplets, which leads to ignition failure. A theoretical model quantifying droplet swelling rate was established to calculate the volume change of the droplet. It was found that the swelling can be attributed to the flash boiling of superheated internal H2O2 fluid. Meanwhile, the ignition delay time was found to linearly decrease with B at various Wes until the extent where the chemical reaction takes over control, leading to an almost constant time delay defined as RDT. Additionally, the regime of ignition modes corresponding to different droplet mixing features is summarized in the We-B parametric space.

Toward Building a Virtual Laboratory to Investigate Rainfall Microphysics at Process Scales

Abstract A 3D numerical model was built to serve as a virtual microphysics laboratory (VML) to investigate rainfall microphysical processes. One key goal for the VML is to elucidate the physical basis of warm precipitation processes toward improving existing parameterizations beyond the constraints of past physical experiments. This manuscript presents results from VML simulations of classical tower experiments of raindrop collisional collection and breakup. The simulations capture large raindrop oscillations in shape and velocity in both horizontal and vertical planes and reveal that drop instability increases with diameter due to the weakening of the surface tension compared with the body force. A detailed evaluation against reference experimental datasets of binary collisions over a wide range of drop sizes shows that the VML reproduces collision outcomes well including coalescence, and disk, sheet, and filament breakups. Furthermore, the VML simulations captured spontaneous breakup, and secondary coalescence and breakup. The breakup type, fragment number, and size distribution are analyzed in the context of collision kinetic energy, diameter ratio, and relative position, with a view to capture the dynamic evolution of the vertical microstructure of rainfall in models and to interpret remote sensing measurements. Significance Statement Presently, uncertainty in precipitation estimation and prediction remains one of the grand challenges in water cycle studies. This work presents a detailed 3D simulator to characterize the evolution of drop size distributions (DSDs), without the space and functional constraints of laboratory experiments. The virtual microphysics laboratory (VML) is applied to replicate classical tower experiments from which parameterizations of precipitation processes used presently in weather and climate models and remote sensing algorithms were derived. The results presented demonstrate that the VML is a robust tool to capture DSD dynamics at the scale of individual raindrops (precipitation microphysics). VML will be used to characterize DSD dynamics across scales for environmental conditions and weather regimes for which no measurements are available.

Elastic scattering cross sections and transport of tin ions in extreme ultraviolet lithography sources

Energetic tin ions are created by laser produced plasmas in extreme-ultraviolet lithography sources where hydrogen must be used as a buffer gas to protect critical optical components. In this study, the quantum chemistry code NWChem is used to calculate the interatomic potential between singly ionized tin and molecular hydrogen. The interatomic potential was fit by an inverse-power potential, a modified universal ZBL potential, and a two-piece-Lennard-Jones potential which were in turn used to calculate the classical distance of closest approach, scattering angle, total elastic scattering cross sections. Furthermore, the universal Ziegler-Biersack-Littmark (ZBL) potential was used in the open-source binary collision approximation codes RustBCA as well as Stopping Range in Matter and Transport of Ion in Matter (SRIM/TRIM) to calculate ion ranges, straggling, and stopping cross sections in a hydrogen gas target.