Collision Model Research Articles

A machine-learning augmented mixed method for simulating α particle transport in inertial confinement fusion

The plasma heating by the α particle transport is a main self-heating source in inertial confinement fusion (ICF) that determines the capsule implosion performance. Due to the high energy of α particle and the high temperature in the ICF capsule hot spot, significant non-equilibrium effect exists and the continuum mechanics breaks down. For the numerical simulation of implosion and charged particle transport, the Boltzmann equation needs to be solved to capture the kinetic effects. However, the 7-dimensional Boltzmann equation, the highly frequent Coulomb collision, and the multi-folded integral stopping power formulation greatly limits the computational efficiency and challenges the computational power. To overcome the high computational cost of high-frequent Coulomb collisions, we propose a mixed collision model according to which the collisions are categorized into low-frequent large-angle collisions and high frequent small-angle grazing collisions. The large-angle collision process is precisely solved based on the Coulomb cross-section. For the highly frequent small-angle grazing, a statistic model is constructed with second-order accuracy in time. The mixed collision model reduces the computational cost of scattering calculation by two orders of magnitude. For the multi-folded integral stopping power formulation, a neural network is used to improve computational efficiency. Based on the proposed algorithm, we develop one-dimensional to three-dimensional module code to directly solve the α particle transport Boltzmann equation. The α transport module code is integrated into the multi-physics LARED-S program. The MC version ICF software is verified by a simulation study of the N210207 and N191110 experiment.

Extension of ion-neutral reactive collision model DNT+ to polar molecules based on average dipole orientation theory

The ion-neutral reactive collision model DNT+, which generates comprehensive ion-neutral collision cross section (CS) data sets for atoms and nonpolar molecules, has been extended to polar molecules. The extension is based on the average dipole orientation (ADO) theory, which adds the dipole moment to Langevin–Hassé CS. Furthermore, the ADO CS for short-range reactive collisions is covered with a rigid core to incorporate long-range elastic and charge-exchange collisions. The modified version of DNT+, i.e., DNT+DM, is applied to gas-phase H2O+–H2O and low-energy CF3+–CO collisions for its validation. The cross sections (CSs) for those collisions using DNT+DM show good agreement with literature data, proving that DNT+DM is valid to some extent. Help with ion swarm analyses and measurements is needed to make the predicted CSs more accurate.

A phenomenological study of the evolution of shock-induced O i emission lines in the spectrum of nova V2891 Cygni

ABSTRACT The eruption of Nova V2891 Cygni in 2019 offers a rare opportunity to explore the shock-induced processes in novae ejecta. The spectral evolution shows noticeable differences in the evolution of various oxygen emission lines such as O i 7773 Å, O i 8446 Å, O i 1.1286 μm, O i 1.3164 μm, etc. Here, we use spectral synthesis code cloudy to study the temporal evolution of these oxygen emission lines. Our photoionization model requires the introduction of a component with a very high density ($n \sim 10^{11}$ cm$^{-3}$) and an enhanced oxygen abundance (O/H $\sim$ 28) to produce the O i 7773 Å emission line, suggesting a stratification of material with high oxygen abundance within the ejecta. An important outcome is the behaviour of the O i 1.3164 μm line, which could only be generated by invoking the collisional ionization models in cloudy. Our phenomenological analysis suggests that O i 1.3164 μm emission originates from a thin, dense shell characterized by a high density of about $10^{12.5}\!-\!10^{12.8}$ cm$^{-3}$, which is most likely formed due to the strong internal collisions. If such is the case, the O i 1.3164 μm emission presents itself as a tracer of shock-induced dust formation in V2891 Cyg. The collisional ionization models have also been successful in creating the high-temperature conditions ($\sim 7.07\!-\!7.49 \times 10^5$ K) required to reproduce the observed high ionization potential coronal lines, which coincide with the epoch of dust formation and evolution of the O i 1.3164 μm emission line.

Coalescence model of rock-paper-scissors particles

The rock–paper–scissors game, commonly played in East Asia, gives a simple model to understand physical, biological, psychological, and other problems. The interacting rock–paper–scissors particle system connects two models: the collision model (Maxwell and Boltzmann’s kinetic theory of gas) and the coalescence model (Smoluchowski’s coagulation theory). A 2s+1 type rock–paper–scissors collision model naturally introduces a nonlinear integrable Lotka–Volterra system. The time evolution of the coalescence model is obtained from the logarithmic time change of the collision model. We also discuss the behavior of a discrete rock–paper–scissors coalescence model.

Discrete Boltzmann model with split collision for nonequilibrium reactive flows* *This work is supported by the National Natural Science Foundation of China (under Grant Nos. U2242214, 51806116 and 91441120), the Guangdong Basic and Applied Basic Research Foundation (under Grant Nos. 2022A1515012116 and 2024A1515010927), the Natural Science Foundation of Fujian Province (under Grant Nos. 2021J01652, 2021J01655), and the China Scholarship Council

A multi-relaxation-time discrete Boltzmann model (DBM) with split collision is proposed for both subsonic and supersonic compressible reacting flows, where chemical reactions take place among various components. The physical model is based on a unified set of discrete Boltzmann equations that describes the evolution of each chemical species with adjustable acceleration, specific heat ratio, and Prandtl number. On the right-hand side of discrete Boltzmann equations, the collision, force, and reaction terms denote the change rates of distribution functions due to self- and cross-collisions, external forces, and chemical reactions, respectively. The source terms can be calculated in three ways, among which the matrix inversion method possesses the highest physical accuracy and computational efficiency. Through Chapman–Enskog analysis, it is proved that the DBM is consistent with the reactive Navier–Stokes equations, Fick's law and the Stefan–Maxwell diffusion equation in the hydrodynamic limit. Compared with the one-step-relaxation model, the split collision model offers a detailed and precise description of hydrodynamic, thermodynamic, and chemical nonequilibrium effects. Finally, the model is validated by six benchmarks, including multicomponent diffusion, mixture in the force field, Kelvin–Helmholtz instability, flame at constant pressure, opposing chemical reaction, and steady detonation.

Quantifying the effects of inlet gas and collision models in direct metal deposition using a CFD-DEM approach

Simulations of the powder jet in direct metal deposition (DMD) are often made with significant simplifications such as being incompressible, steady-state, or single-component, and do not provide explanation for the choice of parameters in the collision model. This work presents a coupled Computational Fluid Dynamics–Discrete Element Method model for the powder jet in DMD that considers all of the following features: compressibility effects, particle–wall and particle–particle collisions, turbulence, gas mixing, and melt pool boundaries. The goal of the simulation is to optimize the operating conditions and to predict the outcomes of experiments. After effective validation against experimental results, the effects of inlet gas, collision models and different boundary conditions in DMD have been comprehensively studied. It is demonstrated that gases with higher diffusivities, such as helium, are less effective shielding gases than those with lower diffusivities, such as argon. The increased wall temperature arising from the melt pool and track has little influence on the particle distribution.

A Rare, Strong Shock Front in the Merging Cluster SPT-CLJ 2031-4037

We present our findings from the new deep Chandra observations (256 ks) of the merging galaxy cluster SPT-CLJ 2031-4037 at z = 0.34. Our observations reveal intricate structures seen in a major merger akin to the Bullet Cluster. The X-ray data confirm the existence of two shock fronts, one to the northwest and one to the southeast, by directly measuring the temperature jump of gas across the surface brightness edges. The stronger shock front in the northwest has a density jump of 3.16 ± 0.34 across the sharp surface brightness edge and Mach number M=3.36−0.48+0.87 , which makes this cluster one of the rare merging systems with a Mach number M > 2. We use the northwestern shock to compare two models for shock heating—the instant heating model and the Coulomb collisional heating model—and we determine that the temperatures across the shock front agree with the Coulomb collisional model of heating. For the shock front in the southeastern region, we find a density jump of 1.53 ± 0.14 and a Mach number of M=1.36−0.08+0.09 .

Ion temperature and rotation velocity measurements of carbon and boron ions using VUV spectroscopy on EAST.

A space-resolved vacuum ultraviolet spectroscopy is employed to measure impurity emission profiles (500-3200Å) on EAST. This study successfully captures C IV (1548.20 and 1550.77Å) lines emitted from carbon ions and derives ion temperatures using Doppler broadening and a collision model based on their intensity ratios. Both the emission intensity and ion temperature profiles are determined. However, the calculated results reveal a lower temperature of around 10-20eV with the collision model, suggesting a potential need for further correction in subsequent calculations. Furthermore, this study explores relative rotation velocities from the Doppler shift, indicating an increase in toroidal rotation velocity with applied neutral beam injection. The measured results exhibit concordance with the charge exchange recombination spectrometer data. Furthermore, during boron powder dropping discharges on EAST, B II (1623.60, 1623.79, 1623.95, 1624.02, 1624.17, and 1624.38Å) emission lines exhibiting a similar time behavior trend with boron powder injection are identified. Ion temperatures are measured using B II (1362.46Å) through the Doppler broadening method. These techniques hold significant promise for future impurity analysis at the edge of EAST, providing valuable insights into the behavior of carbon and boron ions.

Hysteresis between gas breakdown and plasma discharge

In direct-current (DC) discharge, it is well known that hysteresis is observed between the Townsend (gas breakdown) and glow regimes. Forward and backward voltage sweep is performed using a one-dimensional particle-in-cell Monte Carlo collision (PIC-MCC) model considering a ballast resistor. When increasing the applied voltage after reaching the breakdown voltage (Vb), transition from Townsend to glow discharges is observed. When decreasing the applied voltage from the glow regime, the discharge voltage (Vd) between the anode–cathode gap can be smaller than the breakdown voltage, resulting in a hysteresis, which is consistent with experimental observations. Next, the PIC-MCC model is used to investigate the self-sustaining voltage (Vs) in the presence of finite initial plasma densities between the anode and cathode gap. It is observed that the self-sustaining voltage coincides with the discharge voltage obtained from the backward voltage sweep. In addition, the self-sustaining voltage decreases with increased initial plasma density and saturates above a certain initial plasma density, which indicates a change in plasma resistivity. The decrease in self-sustaining voltage is associated with the electron heat loss at the anode for the low pd (rarefied) regime. In the high pd (collisional) regime, the ion energy loss toward the cathode due to the cathode fall and the inelastic collision loss of electrons in the bulk discharge balance out. Finally, it is demonstrated that the self-sustaining voltage collapses to a singular value, despite the presence of a initial plasma, for microgaps when field emission is dominant, which is also consistent with experimental observations.

Decision support for traffic safety: case of rear-end collision modelling

ABSTRACT This paper presents the decision problem of selecting a collision-warning activation algorithm for Rear-End Collision Alert Signal (RECAS) systems installed in motorcycles and other powered two-wheelers. Using Agent-Based Modelling, Discrete Event Simulation and System Dynamics, we have developed a hybrid simulation model of three scenarios of rear-end collisions to measure the performance of several algorithms found in the literature. The best-performing algorithm, by Hirst & Graham, has reduced the probability of collisions on average by 31.21% in comparison with the baseline scenario of using a standard brake light. Using this algorithm also resulted in up to 11.20% reduction in the estimated severity of injuries when a rear-end collision was not averted. As the Hirst & Graham algorithm was the most effective in all the tested emergency braking scenarios and across all the tested speed limits, we recommend this algorithm to be used in RECAS systems in powered two-wheelers.

Investigation on the Enhancement of the Flotation Performance in Fine Molybdenum Particles Based on the Probability of Collision Model

Investigation on the Enhancement of the Flotation Performance in Fine Molybdenum Particles Based on the Probability of Collision Model

Study on the Influence of Some Ventilation Parameters on Dust Dispersion in Heading Face Coal Mine Using CFD Numerical Model

Coal dust is one of the environmental factors that seriously affect the health of workers as well as the mining equipment in underground coal mines. At present, coal dust is commonly generated during drilling, blasting, excavation, and transportation processes in mining operations. During mining blasting processes, coal dust is generated with varying particle sizes and high concentration levels. High concentrations of dust will affect mining operations and increase the ventilation time required for mining faces. In addition, coal dust exists in suspended form in the roadway and is harmful to human health, especially fine dust particles that have a negative impact on work efficiency. To improve ventilation efficiency and eliminate coal dust, this article presents a CFD-DPM numerical modeling method that integrates a DEM collision model based on the finite element method to analyze the motion characteristics of airflow and dust particles in the mine tunnel, while considering collisions between particles and between particles and walls. The article analyzes the distribution of wind speed, the dispersion of dust in the space around the roadway, and dust concentrations at distances of 1 m, 3 m, and 6 m from the working personnel and at a position 1.5 m above the roadway floor, corresponding to the breathing zone of the workers, with varying parameters such as velocity and duct position. The results indicate that with a wind velocity of V = 18 m/s and an air duct height h = 3.0 m, the best dust reduction results are achieved, and they provide theoretical guidance for selecting and optimizing ventilation parameters in dust control.

Particle-in-cell simulations of EUV-induced hydrogen plasma in the vicinity of a reflective mirror

Particle-In-Cell (PIC) simulations were performed in this work to study the dynamics of the EUV-induced hydrogen plasma. The Monte-Carlo Collision (MCC) model was employed to deal with the collisions between charged particles and background gas molecules. The dynamic evolution of the plasma sheath, as well as the flux and energy distribution of ions impacting on the mirror surface, was discussed. It was found that the emission of secondary electrons under the EUV irradiation on the ruthenium mirror coating creates a positively charged wall and then prevents the ions from impacting on the mirror and therefore changes the flux and energy distribution of ions reaching the mirror. Furthermore, gas pressure has a notable effect on the plasma sheath and the characteristics of the ions impinging on the mirrors. With greater gas pressure, the sheath potential decreases more rapidly. The flux of ions received by the mirror grows approximately linearly and at the same time the energy corresponding to the peak flux decreases slightly. However, the EUV source intensity barely changes the sheath potential, and its influence on the ion impact is mainly limited to the approximate linear increase in ion flux.

Reducing the computational complexity of implicit schemes in the modeling of kinetic inelastic collisions in a partially ionized plasma

AbstractModeling the time evolution of atomic number densities and the kinetic (non‐Maxwellian) electron energy distribution function under the action of electron impact collisions by classical approaches requires an implicit time‐stepping scheme to maintain numerical stability. The resulting linear system that must be iteratively solved at each time step incorporates a dense (nonsparse) matrix. For variables being propagated, the computational cost is . We present an alternative approach with a computational cost of , which is the same order as the computational cost of an explicit method for propagating a system of this type. The approach relies on a combination of classical iterative derivative evaluations, combinatorial approximations, and some ideas from deep machine learning.

A machine learning-based simplified collision model for granular flows

This study aims to create an efficient, rapid, and reliable particle collision model utilizing machine learning techniques for granular flow simulations. A simplified surrogate collision model developed in the framework of a Hybrid Euler–Lagrange (HEL) technique was successfully applied to model particle interactions for flows with a low fraction of the granular phase. The precision of the simplified collision model was evaluated using experimental data obtained from the in-house, two-stream particle collision test rig, focusing on solid phase velocity profiles. The implemented model demonstrates strong concordance with the experimental results. The simulations carried out highlight the relation between the simulation time step and the collision rate, which affects the cost of the numerical simulation. The execution time for both the conventional Discrete Element Method (DEM) on a CPU and the streamlined collision HEL model saw a reduction exceeding 70%.

Assessment of runaway electron beam termination and impact in ITER

The vertical motion and shrinking of the cold plasma column after a tokamak disruption leads to a natural decrease in the edge safety factor when most of the current is carried by runaway electrons (REs). Reaching a low edge safety factor can potentially cause a strong plasma instability. We present magnetohydrodynamic simulations of the termination of a post-disruption plateau-phase RE beam in ITER when the edge safety factor falls close to two. Growth of instabilities is observed to result in stochastization of the magnetic field and a prompt loss of REs. As RE impact must be mitigated in ITER, the effect of parameters that influence the final termination have been assessed. Higher background plasma resistivity is seen to cause larger mode magnitudes and stronger stochastization, leading to less remnant REs after the termination event. Lower ion-densities also project a qualitatively similar behavior although weaker in effect. Using computations from a wall collision model, the ensuing load distribution on the first-wall is also presented.

Effects of cross flow on the launching process of submarine-launched vehicle considering the 6-DOF motion at barrel-exit stage

Submarine-launched vehicle (SLV) is a research hotspot due to its strong strike capability, among which underwater launching technology is a key issue hindering its development. In this paper, a numerical model is proposed to simulate the launching problem of SLV. The high nonlinearity induced by the coupling of multi-degree-of-freedom motions and the interaction between fluid and structure is solved. Specifically, the 6-DOF motion model of structure considering its strong added-mass effect, cavitation model and collision model are adopted. This numerical model is firstly validated by simulating the launching of SLV in still water. And then, the applicability of this model is discussed, as well as the effect of cross flow and initial launching velocity on the launching process. The results indicate that proposed numerical model could be used under both low-speed and high-speed cross flow situations. Cross flow changes the attitude and locomotion state of SLV. When flow velocity exceeds 1.25 m/s, the collision occurs between SLV (with the initial launching velocity of 40 m/s) and its barrel. This obtained locomotion of SLV after leaving its barrel causes the launching failure. Besides, a method of increasing launching velocity is introduced to promote the success rate of launching in high-speed cross flow situation.

Numerical modeling of the heat and mass transfer of rarefied gas flows in a double-sided oscillatory lid-driven cavity

In micro/nano research and engineering applications, internal flows of rarefied gas in confined geometries with moving parts are of great interest. The rarefied gaseous flows in an oscillating lid-driven cavity are investigated numerically in this work, taking into account both the parallel and antiparallel motion of the driving walls. The discrete unified gas kinetic scheme (DUGKS) is applied to the evolution of the flow and temperature fields. The Shakhov collision model is incorporated into DUGKS to account for flows of non-unit Prandtl numbers. The validity of the Shakhov-DUGKS is confirmed in both single-sided oscillating and steady lid-driven cavity flows. The effects of gas compressibility, rarefaction, and lid oscillation frequency on the mass and heat transport are then thoroughly examined. The corresponding parameter spaces of the Mach, Knudsen and Stokes numbers are 0.16 ≤ Ma ≤ 1.2, 0.075 ≤ Kn ≤ 10 and 0.5 ≤ St ≤ 5, respectively. The shear force and Nusselt number Nu on the cavity walls, as well as the velocity, temperature, and heat flux lines in the cavity, are measured and analyzed. The results suggest that the anti-Fourier heat transfer phenomenon might also occur in the rarefied double-sided oscillating cavity flow. Nu is prone to non-simple harmonic oscillation in its evolution. Furthermore, in the parallel motion as opposed to the anti-parallel motion, the left wall experiences a greater intensity of heat transmission. Compressibility, expansion cooling, and viscous heating compete to provide the complicated flow and heat transfer characteristics found in cavities.

Numerical Analysis and Quantification of Transfer Efficiency Coupled with Capillary and Quadrupole Ion Guide in an API-MS System.

Ion trajectory simulation is a significant and useful tool for understanding ion transfer mechanisms within the first vacuum region of the atmospheric pressure ionization mass spectrometer (API-MS). However, the complex dynamic gas field and wide pressure range lead to inaccurate simulation and huge computational costs. In this work, a novel electrohydrodynamic simulation called the statistical diffusion-hard-sphere (SDHS) mixed collision model was developed for characterizing the ion trajectories. For the first time, the influence of the dynamic pressure on the ion trajectory is considered for simulation, which helps to avoid an intolerable computational cost. Comparing with the conventional Monte Carlo collision model, the SDHS method helps to improve the calculation accuracy of ion trajectories under the first vacuum region and reduce the computational cost for at least 12-folds. Simulation results showed that the maximum ion loss came from the gap of the electrodes. The distance of the capillary-quadrupole ion guide was also a non-negligible factor. The trend of quantitative experimental results matches the SDHS simulation results. The maximum ion transfer efficiencies of quantitative experiment and simulation were 55% and 52%, respectively. Moreover, three ions, caffeine, reserpine, and Ultramark 1621, were measured for evaluating the applicability of SDHS in real API-MS. The trend of experimental results showed good agreement with that of computation. And the results of caffeine further illustrated the reason that the small mass ion transfer efficiency decreased with increasing radio frequency voltage. SDHS method is expected to be useful in the design of ion guides for further improvement of the sensitivity of API-MS.

IDSimF: An Open-Source Framework for the Simulation of Molecular Ion Dynamics in Mass Spectrometry and Ion Mobility Spectrometry.

The development of mass spectrometric and ion mobility devices heavily depends on a comprehensive understanding of the behavior of ions within such systems. Therefore, numerical modeling of ion paths helps to optimize and verify existing devices, and contributes to the development of innovative ion optical systems and multipole geometries. This Article introduces IDSimF (Ion Dynamics Simulation Framework), an open-source simulation tool tailored to the nonrelativistic dynamics of molecular ions in mass and ion mobility spectrometry applications. Addressing limitations in existing software packages, as for example SIMION, OpenFOAM, and COMSOL, IDSimF offers a specialized platform for simulating ion trajectories in electric fields. IDSimF efficiently accounts for space charge effects and considers various ion-neutral collision models while handling chemical kinetics. The framework is highly modular with reduced user input configuration complexity and aims to support simulation efforts in development and optimization of in mass spectrometers.