Monte Carlo Collision Algorithm Research Articles

Collision Fluctuations of Lucky Droplets with Superdroplets

Abstract It was previously shown that the superdroplet algorithm for modeling the collision–coalescence process can faithfully represent mean droplet growth in turbulent clouds. An open question is how accurately the superdroplet algorithm accounts for fluctuations in the collisional aggregation process. Such fluctuations are particularly important in dilute suspensions. Even in the absence of turbulence, Poisson fluctuations of collision times in dilute suspensions may result in substantial variations in the growth process, resulting in a broad distribution of growth times to reach a certain droplet size. We quantify the accuracy of the superdroplet algorithm in describing the fluctuating growth history of a larger droplet that settles under the effect of gravity in a quiescent fluid and collides with a dilute suspension of smaller droplets that were initially randomly distributed in space (“lucky droplet model”). We assess the effect of fluctuations upon the growth history of the lucky droplet and compute the distribution of cumulative collision times. The latter is shown to be sensitive enough to detect the subtle increase of fluctuations associated with collisions between multiple lucky droplets. The superdroplet algorithm incorporates fluctuations in two distinct ways: through the random spatial distribution of superdroplets and through the Monte Carlo collision algorithm involved. Using specifically designed numerical experiments, we show that both on their own give an accurate representation of fluctuations. We conclude that the superdroplet algorithm can faithfully represent fluctuations in the coagulation of droplets driven by gravity.

Understanding the role of energetic particles during the growth of TiO2 thin films by reactive magnetron sputtering through multi-scale Monte Carlo simulations and experimental deposition

In this paper, a previously established 3D multi-scale simulation chain of plasma deposition process, based on a combination of a direct simulation Monte Carlo (gas phase) algorithm and a kinetic Monte Carlo (kMC) (film growth) code, is improved by the addition of a particle-in-cell Monte Carlo collision algorithm in order to take into account and clarify the role of charged particles. The kinetic Monte Carlo code is also extended with a binary collision approximation algorithm to handle charged particles. This modelling strategy is successfully applied to the growth of TiO2 thin films by means of reactive magnetron sputtering. In order to highlight the effects of negative oxygen ions, two substrate locations are selected: one in the median plane of the targets and another one off the median plane. The model efficiently predicts the densities and fluxes of both charged and neutral particles towards the substrate. Typical results such as particle densities, the discharge current density and ion flux onto the target, and the various substrate locations are calculated. The angular distribution and energy distribution of all involved particles are sampled at these very same substrate locations and the nanoscale modelling (NASCAM) code, implementing the kMC approach, uses these results to explain the morphology of the experimentally deposited coatings. The changes throughout the transition from metallic deposition to stoichiometric TiO2 of the columnar structure of the deposited films is explained by the suppression of the atom diffusion on the growing film due to Ti oxidation. Moreover, the high-energy negative atomic oxygen ions originating from the targets are identified as the origin of the abnormally low inclination of the columnar structure experimentally observed for the oxide mode coatings. Measurements of the normalized energy flux (energy per deposited atom) are experimentally investigated to support and highlight the important role of energetic particles during film growth.

Simulation study on electron extraction mechanism of an ECR neutralizer

To investigate electron extraction through the orifice of an electron cyclotron resonance (ECR) neutralizer, two-dimensional axisymmetric particle-in-cell simulations with a Monte Carlo collision algorithm (PIC-MCC) have been conducted. The diagnostic experiment of Langmuir probe verified that the plasma distribution in the ECR neutralizer with an L-shaped antenna was circumferentially uniform, which provided the experimental basis for two-dimensional axisymmetric simulations. The distribution of plasma parameters and extracted electron current of the neutralizer were obtained by tracking the motion of electrons and singly charged xenon ions, simulating the elasticity, excitation, ionization and Coulomb collisions. Moreover, computational results and analysis demonstrated that there were two kinds of electronic extraction channel in the ECR neutralizer. One was affected by the potential well between magnetic well and anode, another was affected by the valley potential of electronic double sheath. The property of these two electronic extraction channels determined the variation of extracted electron current and mode conversion voltage.

A Monte Carlo model of energy deposition, ionization, and sputtering due to thermal ion precipitation into Titan's upper atmosphere

A three-dimensional model of ion precipitation is developed to calculate incoming energy flux, number flux, charge exchange rates, energy deposition rates, and sputtering rates due to thermal (<10 keV) ion precipitation into Titan's upper atmosphere. We report results for a range of upstream conditions that represent Titan's environment in Saturn's plasma sheet. Our results show that Titan's induced magnetosphere is effective at shielding the atmosphere from thermal proton precipitation. However, the atmosphere is only partially shielded from thermal oxygen precipitation. The energy deposited by thermal magnetospheric oxygen (between about 100 to 400 MW) is smaller than solar EUV input but similar to the energy deposited by high energy neutral atoms and magnetospheric electrons. Oxygen deposits the most energy on the ram-side of Titan's atmosphere where we calculate an average energy deposition rate within 45° longitude of co-rotational ram-point between 17 and 85 eV cm−3 s−1. The number flux of oxygen atoms is ~1 × 105 cm−2 s−1, normalized to Titan's surface area. Maximum local charge exchange rates are around 0.5 cm−3 s−1, which is smaller than photoionization and impact ionization rates from magnetospheric electrons. We also test the model's sensitivity to various assumptions about cross-sections, collision parameters, and the characteristics of Titan's atmosphere. Our results imply that the energy deposition and charge exchange rates are variable due to fluctuations in Titan's atmospheric structure and its environment in Saturn's magnetosphere. The most significant source of uncertainty in the Monte Carlo collision algorithm is the collision scattering angle.

Simulation on the dynamic charge behavior of vacuum flashover developing across insulator involving outgassing

A 2D simulation based on particle-in-cell and Monte Carlo collision algorithm is implemented to investigate the accumulation and dissipation of surface charges on an insulator during flashover with outgassing in vacuum. A layer of positive charges is formed on the insulator after the secondary electrons emission (SEE) reaches saturation. With the build-up of local pressure resulting from gas desorption, the incident energy of electrons is affected by electron-neutral collisions and field distortion, remarkably decreasing the charge density on the insulator. Gas desorption ionization initiates near the anode, culminating, and then abates, followed by a steady and gradual augmentation as the negatively charged surface spreads towards the cathode and halts the SEE nearby. The initiation of flashover development is discussed in detail, and a subdivision of flashover development is proposed, including an anode-initiated desorption ionization avalanche, establishment of a plasma sheath, and plasma expansion. The transform from saturation to explosion of space charges and dissipation of the surface charge are revealed, which can be explained by the competition between multipactor electrons and ionized electrons.

Numerical simulation of full-aperture-pair ion optics in a miniature ion thruster

The 211-aperture-pair two-grid ion optics of a miniature ion thruster is numerically simulated. Since the plasma in the miniature ion thruster is too inhomogeneous to introduce mirror or translational boundary conditions between apertures, all the apertures of the grid system are considered. The simulation is self-consistent, the ion current profile in the discharge chamber plasma is given by the particle-in-cell with Monte Carlo collision algorithm calculations, and all the ion beams extracted from the full-aperture-pair array were tracked including charge-exchange ions. A scheme for the construction of the full-aperture-pair simulation domain is proposed based on the array of a six-fold hexagonal single-aperture-pair simulation domain, which can be extended to other numbers of aperture pairs. Numerical results on accel impingement current and ion-beam profile are compared to experimental data and shown to be in reasonable agreement. Furthermore, the full-aperture-pair ion-optics model is compared with the single-aperture-pair ion-optics models used in the majority of previous ion-optics simulations, which showed that the full-aperture-pair ion-optics model yielded the most accurate predictions. These results suggest that the ion thruster grid system using an inhomogeneous plasma source can be designed more accurately and effectively using full-aperture-pair ion-optics simulations.

Monte Carlo simulation of excitation and ionization collisions with complexity reduction

Kinetic simulation of plasmas with detailed excitation and ionization collisions presents a significant computational challenge due to the multiscale feature of the collisional rates. In the present work, we propose a complexity reduction method based on atomic level grouping for modeling excitation and ionization collisions. High order of accuracy of the reduction method is realized by allowing an internal distribution within each group. We apply the reduction method to the standard Monte Carlo collision algorithm to model an atomic Hydrogen plasma. Numerical results suggest that the stiffness of the collisional kinetics can be significantly reduced with minimal loss in accuracy.

Electron extraction mechanisms of a micro-ECR neutralizer

Three-dimensional particle simulations have been conducted to analyze the mechanisms of electron extraction through the orifices of a 4.2 GHz microwave discharge microneutralizer, using a xenon electron cyclotron resonance plasma. The dimensions of the neutralizer are 20 × 20 × 4 mm3, and a ring-shaped microwave antenna and permanent magnets are employed for its discharges. The numerical model is composed of a particle-in-cell simulation with a Monte Carlo collision algorithm for charged particle motions, a finite-difference time-domain method for microwaves, and a finite element analysis for magnetostatic fields. The simulation results have shown that the electrostatic field inside the plasma source has a dominant effect on electron extraction. The extracted electrons move along the magnetic field line to the orifice entrances and the E × B drift at the orifice edge induces electron extraction.

Three-dimensional particle-in-cell simulation of a miniature plasma source for a microwave discharge ion thruster

We have developed a three-dimensional particle model for a miniature microwave discharge ion thruster to elucidate the mechanism of ECR discharges confined in a small space. The model consists of a particle-in-cell simulation with a Monte Carlo collision algorithm (PIC-MCC) for the kinetics of charged particles, a finite-difference time-domain method for the electromagnetic fields of 4.2 GHz microwaves, and a finite element analysis for the magnetostatic fields of permanent magnets. The PIC-MCC results have shown that the electrons are well confined owing to the mirror magnetic fields and can be effectively heated in the ECR layer downstream of a ring-shaped antenna. The confinement results in the ring-shaped profiles of the plasma density along the antenna. The visual appearance of the plasma discharge of the thruster in operation was also ring-shaped. Moreover, the ions are expected to be accelerated effectively through the grid electrode without a large loss of ions toward side walls, that is, the plasma source developed here would be desirable in ion thrusters.

Effect of capacitive coupling in a miniature inductively coupled plasma source

Two-dimensional axisymmetric particle-in-cell simulations with a Monte Carlo collision algorithm (PIC-MCC) have been conducted to investigate the effect of capacitive coupling in a miniature inductively coupled plasma source (mICP) by using two models: an inductive model and a hybrid model. The mICP is 3 mm in radius and 6 mm in height with a three-turn planar coil, where argon plasma is sustained. In the inductive model, the coil is assumed to be electrostatically shielded, and thus the discharge is purely inductive coupling. In the hybrid model, we assume that the different turns of the coil act like electrodes in capacitive discharge to include the effect of capacitive coupling. The voltage applied to these electrodes decreases linearly from the powered end of the coil towards the grounded end. The numerical analysis has been performed for rf frequencies in the range of 100–1000 MHz, and the power absorbed by the plasma in the range of 5–50 mW at a fixed pressure of 500 mTorr. The PIC-MCC results show that potential oscillations at the plasma-dielectric interface are not negligible, and thus the major component of the absorbed power is caused by the axial motion of electrons in the hybrid model, although almost all of the power absorption is due to the azimuthal motion of electrons in the inductive model. The effect of capacitive coupling is more significant at lower rf frequencies and at higher absorbed powers under the calculation conditions examined. Moreover, much less coil currents are required in the hybrid model.

Perturbation of collisional plasma flow around a charged dust particle: Kinetic analysis

The ion density and electric potential distribution are found within the linear kinetic approach using the dielectrical permittivity of a flowing collisional plasma around a charged particle. The parameters of the disturbed plasma flow near the dust particle are also calculated numerically through a self-consistent solution of the ion kinetic equation and the Poisson equation with the particle-in-cell Monte Carlo collision algorithm. Scaling laws are formulated from an analysis of the linear kinetic equation. Comparison of the ion and potential distributions for sub- and supersonic ion flows in the collisional and collisionless regimes lends support to these scaling laws for flowing plasmas.

Different modes of a capacitively coupled radio-frequency discharge in methane.

The transition between different regimes of a capacitevely coupled radio-frequency gas discharge in methane is studied with a combined particle-in-cell Monte Carlo collision algorithm over a wide range of gas pressure P and discharge current j. The results of this study are compared with known experimental and numerical results and summarized on a P-j phase diagram, which constitutes the areas of existence of different discharge regimes.

Spatio-temporal variations in a three-dimensional DC glow discharge via particle-in-cell simulation

A particle-in-cell Monte Carlo collision algorithm has been developed to numerically investigate the three-dimensional structure of a parallel-plate direct current glow discharge. The discharge in argon under a low pressure of 42 mtorr has been simulated as taking place between two circular electrodes in a grounded rectangular chamber. The motion of ions and electrons was calculated in a self-consistent electric field, which was obtained from Poisson's equation by a fast Fourier transform algorithm at each electron time step. Spatial distributions and temporal behavior of the electric field and discharge macroparameters were analyzed. The oscillations and wavy structure of the discharge characteristics have been revealed.

A time-implicit monte carlo collision algorithm for particle-in-cell electron transport models

A time-implicit Monte Carlo collision algorithm has been developed to allow particle-in-cell electron transport models to be applied to arbitrarily collisional systems. The algorithm is formulated for electrons moving in response to electric and magnetic accelerations and subject to collisional drag and scattering due to a background plasma. The correct fluid or streaming transport results are obtained in the respective limits of strongly or weakly collisional systems, and reasonable behavior is produced even for time-steps greatly exceeding the magnetic-gyration and collisional-scattering times.