Monte Carlo Collision Method Research Articles

Validation of Numerical Model of Penning Gas Discharge based on 2D/3V PIC-MCC Method

The data obtained in the experiments conducted in University of California, Berkley are used to validate numerical model of Penning gas discharge. Numerical model is based on 2D/3V axisymmetric electrostatic particle-in-cell method implemented on unstructured grids. Elementary processes in the gas discharge plasma are simulated using Monte-Carlo collision method. Electrodynamic structure of the Penning gas discharge is obtained using mentioned numerical model under conditions relevant to experimental and analyzed. Distributions of the potential, electric field, electrons and ions number densities, temperatures, distribution functions are presented in the study. Validation of numerical model is performed by comparison of the dependence of discharge current on applied magnetic field.

Numerical analysis of effects of ion-neutral collision processes on RF ICP discharge

The discharge process of a radiofrequency (RF) inductively coupled plasma (ICP) has been modeled by an ElectroMagnetic Particle-in-Cell Monte Carlo Collision method (EM PIC-MCC). Although the simulation had been performed by our previous model to investigate the discharge mode transition of the RF ICP from a kinetic point of view, the model neglected the collision processes of ions (H+ and H2+) with neutral particles. In this study, the RF ICP discharge process has been investigated by the latest version of the model which takes the ion-neutral collision processes into account. The basic characteristics of the discharge mode transition provided by the previous model have been verified by the comparison between the previous and present results. As for the H-mode discharge regime, on the other hand, the ion-neutral collisions play an important role in evaluating the growth of the plasma. Also, the effect of the ion-neutral collisions on the kinetic feature of the plasma has been investigated, which has highlighted the importance of kinetic perspective for modeling the RF ICP discharge.

Benchmark continuum and kinetic simulations of argon microplasmas in the direct current and microwave regimes

This study presents benchmark comparisons between continuum and kinetic simulations of argon microplasmas operating in the direct current and microwave regimes. Kinetic simulations using the particle-in-cell with Monte Carlo collisions (PIC-MCC) method and continuum simulations using the full-momentum equation for both ions and electrons are performed at various operating conditions in order to study the influence of product of pressure and gap size, pd (for a given gap size), influence of gap size (for a given value of pd) and operating frequency. It is shown that using the electron energy distribution function (EEDF) predicted by zero-dimensional Boltzmann solvers (such as BOLSIG+) in continuum simulations of direct current microplasmas leads to a significant under-prediction of plasma number densities with continuum simulations based on the Maxwellian EEDF performing better particularly for higher values of pd. The discrepancy between kinetic and continuum simulations is attributed to the presence of hot electrons created as a result of secondary emission and subsequent acceleration in the sheath. On the other hand, simulations performed for argon microwave microplasmas operating at 0.5 GHz, 0.8 GHz, 2 GHz and 4 GHz demonstrated that continuum simulations performed using the rate constants from BOLSIG+ showed excellent agreement with kinetic simulations for the plasma density profiles in spite of over-predicting the voltage/power required to achieve a given plasma density.

Characteristics of the Single-Gap Pseudospark Discharge Under Nanosecond Pulsed Voltages

In this paper, a single-gap pseudospark discharge chamber was built and tested with several electrode gap distances and pressures to explore the characteristics of the pseudospark under nanosecond pulsed voltages. Experimental results show that with the development of the discharge, anode plasma firstly forms near the anode, and then moves towards the cathode. The ionization initial voltage decreases with the increase of the electrode gap distance and pressure in our pseudospark discharge configuration. By analysing the emission spectra, it is concluded that the major emission spectra are composed of the second positive bands, and the electron energy of the plasma is in the level of several tens of electron volts. The mechanism of how the pressure and gap distance influence the characteristics has been discussed with the simulation of the collision ionization process using the Monte Carlo Collision method. Based on the simulation and experimental results, it is inferred that the breakdown voltages is decided by the ionization process of the electron with the neutral gas in the main gap, and a possible reason is put forward to explain the reason that U is a function of p2d.

Influence of the axial magnetic field on sheath development after current zero in a vacuum circuit breaker

After current zero, which is the moment when the vacuum circuit breaker interrupts a vacuum arc, sheath development is the first process in the dielectric recovery process. An axial magnetic field (AMF) is widely used in the vacuum circuit breaker when the high-current vacuum arc is interrupted. Therefore, it is very important to study the influence of different AMF amplitudes on the sheath development. The objective of this paper is to study the influence of different AMF amplitudes on the sheath development from a micro perspective. Thus, the particle in cell–Monte Carlo collisions (PIC–MCC) method was adopted to develop the sheath development model. We compared the simulation results with the experimental results and then validated the simulation. We also obtained the speed of the sheath development and the energy density of the ions under different AMF amplitudes. The results showed that the larger the AMF amplitudes are, the faster the sheath develops and the lower the ion energy density is, meaning the breakdown is correspondingly more difficult.

Ion velocity distribution functions in argon and helium discharges: detailed comparison of numerical simulation results and experimental data

Using the Monte Carlo collision method, we have performed simulations of ion velocity distribution functions (IVDF) taking into account both elastic collisions and charge exchange collisions of ions with atoms in uniform electric fields for argon and helium background gases. The simulation results are verified by comparison with the experiment data of the ion mobilities and the ion transverse diffusion coefficients in argon and helium. The recently published experimental data for the first seven coefficients of the Legendre polynomial expansion of the ion energy and angular distribution functions are used to validate simulation results for IVDF. Good agreement between measured and simulated IVDFs shows that the developed simulation model can be used for accurate calculations of IVDFs.

Simulations of ion velocity distribution functions taking into account both elastic and charge exchange collisions

Based on accurate representation of the He+–He angular differential scattering cross sections consisting of both elastic and charge exchange collisions, we performed detailed numerical simulations of the ion velocity distribution functions (IVDF) by Monte Carlo collision method (MCC). The results of simulations are validated by comparison with the experimental data of the ion mobility and the transverse diffusion. The IVDF simulation study shows that due to significant effect of scattering in elastic collisions IVDF cannot be separated into product of two independent IVDFs in the transverse and parallel to the electric field directions.

The Simulation of Surface Charge Accumulation on PMMA with Different Surface Roughness in Vacuum

The surface insulation properties of insulating material under DC voltage are closely related to the characteristics of surface charge accumulation, and the surface roughness of these materials has a direct impact on the surface charge distribution in vacuum. Therefore, it is significant to study their connection. In this paper, based on the secondary electron emission avalanche model, the surface charge accumulation on polymethyl methacrylate (PMMA) with different surface roughness was simulated by using particle in cell and Monte Carlo Collision method. The simulated environment was under the finger shaped electrode and in vacuum. The results showed that under the action of the electric field the electrons emitted from the cathode triple junction moved forward and collided with the insulating material, which may lead to the generation of secondary electrons or the accumulation of surface charge. The surface charge near the cathode was mostly negative since the effect of surface electron injection was greater than that of the collision ionization. Due to the change of electron energy and the influence of electric field distribution, the number of positive charge on the insulator gradually increased, reached the maximum, and then gradually reduced with the approaching of the anode. Moreover, when the surface roughness of the material increases or the secondary electron emission coefficient decreases, the amount of surface charge accumulated on the PMMA will reduce. This paper can provide some guidance for the practical application of insulating materials.

Appropriate use of the particle-in-cell method in low temperature plasmas: Application to the simulation of negative ion extraction

The Particle-In-Cell Monte Carlo Collision (PIC MCC) method has been used by different authors in the last ten years to describe negative ion extraction in the context of neutral beam injection for fusion. Questionable results on the intensity and profile of the extracted negative ion beamlets have been presented in several recently published papers. Using a standard explicit PIC MCC method, we show that these results are due to a non-compliance with the constraints of the numerical method (grid spacing, number of particles per cell) and to a non-physical generation of the simulated plasma. We discuss in detail the conditions of mesh convergence and plasma generation and show that the results can significantly deviate from the correct solution and lead to unphysical features when the constraints inherent to the method are not strictly fulfilled. This paper illustrates the importance of verification in any plasma simulation. Since the results presented in this paper have been obtained with careful verification of the method, we propose them as benchmarks for future comparisons between different simulation codes for negative ion extraction.

Particle-in-cell and Monte Carlo collision simulations of the cathode sheath in an atmospheric direct-current arc discharge

A sheath is the transition region from plasma to a solid surface, which also plays a critical role in determining the behaviors of many lab and industrial plasmas. However, the cathode sheath properties in arc discharges are not well understood yet due to its multi-scale and kinetic features. In this letter, we have adopted an implicit particle-in-cell Monte Carlo collision (PIC-MCC) method to study the cathode sheath in an atmospheric arc discharge plasma. The cathode sheath thickness, number densities and averaged energies of electrons and ions, the electric field distribution, as well as the spatially averaged electron energy probability function (EEPF), are predicted self-consistently by using this newly developed kinetic model. It is also shown that the thermionic emission at the hot cathode surface is the dominant electron emission process to sustain the arc discharges, while the effects from secondary and field electron emissions are negligible. The present results verify the previous conjectures and experimental observations.

The plasma sheath around planar probes: effects of ion collisions

The 2D numerical model of the ion current collection by a planar probe has been developed on the basis of a particle in cell with the Monte Carlo collision method for ion motion. This model is used to reveal the effects of ion collisions on the probe sheath area and spatial distribution of plasma density and to warn against current–voltage probe characteristic misinterpretation at plasma density measurements by commonly used Langmuir probe methods.

Structural changes of hydrogenated amorphous carbon films deposited on steel rods

In this study, hydrogenated amorphous carbon (a-C:H) films were deposited on steel rods of various radii by using bipolar-type plasma based ion implantation and deposition, and the film structure and mechanical properties have been investigated. Furthermore, the behavior of plasma surrounding the steel rods (i.e., flux and energy of incident ions and electrons) was investigated using the particle-in-cell Monte Carlo collision (PIC-MCC) method to examine the mechanism behind the structural changes of the a-C:H films. Three kinds of amorphous carbon films with different microstructures were prepared by changing the negative pulse voltages from −1kV to −5kV: one polymer-like carbon film and two diamond-like carbon films that possess the maximum FWHM(G) (full width at half maximum of Raman G-peak) and maximum hardness. The structure of the a-C:H films was evaluated through Raman spectroscopy, and the hardness of the films was measured using nanoindentation. It was found that the structures of a-C:H films deposited on the steel-rod surfaces are quite different from those on flat surfaces, and the film structures are directly affected by the curvature of the rod. It was also determined from the plasma simulation that the incident electron flux and ion flux become more intense as the curvature increases, resulting in the structural changes of the a-C:H films due to hydrogen evolution and thermal relaxation in the films.

Numerical Simulation Study on Barrel Erosion of Ion Thruster Accelerator Grid

The barrel erosion, one type of accelerator grid erosion in an ion thruster, is important and needs more detailed studies. In this paper, a three-dimensional numerical simulation code is developed using a hybrid immersed-finite-element particle-in-cell method and Monte Carlo collisions method; the dynamics of a neutral atom is modeled using a direct simulation Monte Carlo method; and a numerical simulation study is run to investigate the mechanism of aperture barrel erosion of an ion thruster accelerator grid. Simulation results indicate that the aperture barrel erosion of ion thruster accelerator grid is entirely caused by the charge-exchange ions under nominal operating condition, and the incident charge-exchange ions in four regions, namely the upstream region, the extraction (center) region, the extraction (edge) region, and downstream of the accelerator grid, are the causes of aperture barrel erosion. High-energy charge-exchange ions originated from upstream region are not well focused and play an important role in the erosion of the aperture barrel. Charge-exchange ions originated from the extraction (center) region, which play an important role in the whole incident charge-exchange ions, also cause significant erosion on the aperture barrel. It is therefore believed that these findings would facilitate the prediction of aperture barrel erosion of an ion thruster accelerator grid.

Simulation of beam gas coulomb scattering in HALS**Supported by Natural Science Foundation of China (11175182, 11175180)

In conventional research on beam gas coulomb scattering (BGCS), only the related beam lifetime using the analytical method is studied. In this paper, using the particle-in-cell Monte Carlo collisions (PIC-MCC) method, we not only simulated the beam lifetime but also explored the effect of BGCS on the beam distribution. In order to better estimate the effect on particle distribution, we study the ultra-low emittance electron beam. Here we choose the HeFei Advanced Light Source. By counting the lost particles in a certain time, the corresponding beam lifetime we simulated is 4.8482 h/13.8492 h in x/y, which is very close to the theoretic value (5.0555 h /13.7024 h in x/y). By counting the lost particles relative to the collided particles, the simulated value of the loss probability of collided particles is 1.3431e-04, which is also very close to the theoretical value (1.3824e-04). Besides, the simulation shows there is a tail in the transverse distribution due to the BGCS. The close match of the simulation with the theoretic value in beam lifetime and loss probability indicates our simulation is reliable.

Two-dimensional hybrid Monte Carlo–fluid modelling of dc glow discharges: Comparison with fluid models, reliability, and accuracy

Two-dimensional hybrid Monte Carlo–fluid numerical code is developed and applied to model the dc glow discharge. The model is based on the separation of electrons into two parts: the low energetic (slow) and high energetic (fast) electron groups. Ions and slow electrons are described within the fluid model using the drift-diffusion approximation for particle fluxes. Fast electrons, represented by suitable number of super particles emitted from the cathode, are responsible for ionization processes in the discharge volume, which are simulated by the Monte Carlo collision method. Electrostatic field is obtained from the solution of Poisson equation. The test calculations were carried out for an argon plasma. Main properties of the glow discharge are considered. Current-voltage curves, electric field reversal phenomenon, and the vortex current formation are developed and discussed. The results are compared to those obtained from the simple and extended fluid models. Contrary to reports in the literature, the analysis does not reveal significant advantages of existing hybrid methods over the extended fluid model.

Effect of electron Monte Carlo collisions on a hybrid simulation of a low-pressure capacitively coupled plasma

Fluid models have been widely used and conducted successfully in high pressure plasma simulations where the drift–diffusion and the local-field approximation are valid. However, fluid models are not able to demonstrate non-local effects related to large electron energy relaxation mean free path in low pressure plasmas. To overcome this weakness, a hybrid model coupling electron Monte Carlo collision (EMCC) method with the fluid model is introduced to obtain precise electron energy distribution functions using pseudo-particles. Steady state simulation results by a one-dimensional hybrid model which includes EMCC method for the collisional reactions but uses drift–diffusion approximation for electron transport in a fluid model are compared with those of a conventional particle-in-cell (PIC) and a fluid model for low pressure capacitively coupled plasmas. At a wide range of pressure, the hybrid model agrees well with the PIC simulation with a reduced calculation time while the fluid model shows discrepancy in the results of the plasma density and the electron temperature.

Breakdown Process of Pseudospark Discharge Using the Various Discharge Module

A argon Pseudospark discharge is studied and modelled with our developed simulation program. The structure of our code is flexible and transparent. The modular structure is divided into three main parts: electromagnetics module which forms the heart of the model, the neutral gas module, and the chemical reaction module. The above three parts with the plasma module are controlled by the user. The strong modularity makes the code easy to handle and easy to adjust or expand. This project will do in-depth numerical simulation for the study of the inception of breakdown characteristics via a electrostatic particle-in-cell plus Monte-Carlo collision method. The model tracks the trajectories of both electrons and ions, including ionizing collisions in the gas phase by electrons and ions, and secondary electron emission by ions on surfaces. The result indicated the pseudospark discharge breakdown process mainly induced by field emission.The peak discharge current is found to be dependent on gas pressure,electrode borehole diameter. The effect of these design parameters on the peak anode current has been analysed. Simulate the discharge breakdown physical processes for the Pseudospark in order to lay the theoretical foundation for the optimize and improve the pulse power electron beam.

DLC coating on a trench-shaped target by bipolar PBII

Bipolar-type plasma based ion implantation (bipolar PBII) and deposition is a promising coating technique, especially for the complex-shaped target surface. In this study, diamond-like carbon (DLC) films were prepared by a bipolar PBII technique to a trench-shaped target (20mm pitch and 10mm depth), and the uniformity, structural and mechanical properties of DLC films coated on the top, inside wall and bottom surfaces of the trench were evaluated by surface profilometer, Raman spectroscopy and nanoindentation hardness tests. Moreover, plasma simulation was conducted to reveal the DLC coating mechanism for finding the optimum coating conditions. Particle-In-Cell with Monte Carlo Collision (PIC–MCC) method and Direct Simulation Monte Carlo (DSMC) method were used for computing the plasma behavior. As a result, thickness uniformity of DLC films was improved with decreasing negative pulse voltage. On the other hand, the thickness of DLC films on the inside wall of the trench was much smaller than those of the top and bottom surfaces of the trench. This is because the conformal ion sheath cannot be formed around the inside wall, which in turn leads to the decrease of incidence ion flux to the inside wall, and the idea has been verified through the simulation of plasma behavior. From the Raman measurements of DLC coatings on the inside wall, it is observed that the Raman G-peak position shifts to a higher wave number and the Full Width at Half Maximum of G-peak (FWHM(G)) decreases to a smaller value compared to those of the films on the top and bottom surfaces. These indicate that the structure of DLC coatings on the inside wall surface has changed compared to those on top and bottom surfaces, i.e., graphitized, which results in the reduction of hardness.

DLC coating on a micro-trench by bipolar PBII&D and analysis of plasma behaviour

Bipolar plasma-based ion implantation and deposition (bipolar PBII&D) has been recognized as a promising technique for coating deposition on complex three-dimensional targets. As the target is fully immersed in the plasma throughout the process, the plasma sheath can be formed with quite high conformability around the target. In this study, diamond-like carbon (DLC) coating was deposited on a micro-trench pattern by using bipolar PBII&D, and the structure of the DLC film across the overall surface region of the trench was examined by making use of their corresponding Raman spectra. The two types of negative high voltage pulses were applied to the targets for comparison: −0.5 and −15 kV. The scale of the micro-trench used in the study is much smaller than that of the plasma sheath produced under these negative voltages (about 1 cm and 14 cm for −0.5 kV and −15 kV, respectively). The plasma behaviour (i.e., ion flux, impact angle and energy) in the surrounding of the micro-trench was calculated with the particle-in-cell Monte Carlo collision method (PIC-MCCM). As a result, DLC film was successfully coated on the overall surface of the trench. When the applied negative voltage was −0.5 kV, the structure of DLC film coated on the sidewall of the trench became a more polymer-like carbon (PLC) than those of the top and bottom surfaces. This, as indicated by the simulation results, is because the ions, which strike the sidewall, tend to have less incident energy. Whereas in the case of −15 kV, the DLC film on the sidewall was a more graphite-like carbon (GLC) film, despite its smaller incident ion energy in comparison to those of the top and bottom surfaces. This phenomenon is attributed to the sputtering effect from the bottom surface of the trench, as evidenced by the plasma simulation.

Multilevel Monte Carlo simulation of Coulomb collisions

We present a new, for plasma physics, highly efficient multilevel Monte Carlo numerical method for simulating Coulomb collisions. The method separates and optimally minimizes the finite-timestep and finite-sampling errors inherent in the Langevin representation of the Landau–Fokker–Planck equation. It does so by combining multiple solutions to the underlying equations with varying numbers of timesteps. For a desired level of accuracy ε, the computational cost of the method is O(ε−2) or O(ε−2(lnε)2), depending on the underlying discretization, Milstein or Euler–Maruyama respectively. This is to be contrasted with a cost of O(ε−3) for direct simulation Monte Carlo or binary collision methods. We successfully demonstrate the method with a classic beam diffusion test case in 2D, making use of the Lévy area approximation for the correlated Milstein cross terms, and generating a computational saving of a factor of 100 for ε=10−5. We discuss the importance of the method for problems in which collisions constitute the computational rate limiting step, and its limitations.