Particle-in-cell With Monte Carlo Collision Research Articles

Simulating vacuum arc initiation by coupling emission, heating and plasma processes

Vacuum arcing poses significant challenges for high-field vacuum devices, underscoring the importance of understanding it for their efficient design. A detailed description of the physical mechanisms involved in vacuum arcing is yet to be achieved, despite extensive research. In this work, we further develop the modeling of the physical processes involved in the initiation of vacuum arcing, starting from field emission and leading to plasma onset. Our model concurrently combines particle-in-cell with Monte Carlo collisions (PIC-MCC) simulations of plasma processes with finite element-based calculations of electron emission and the associated thermal effects. Including the processes of evaporation, impact ionization and direct field ionization allowed us to observe the dynamics of plasma buildup from an initially cold cathode surface. We simulated a static nanotip at various local fields to study the thresholds for thermal runaway and plasma initiation, identifying the significance of various interactions. We found that direct field ionization of neutrals has a significant effect at high fields on the order of 10 GV/m. Furthermore, we find that cathode surface interactions such as evaporation, sputtering and bombardment heating play a major role in the initiation of vacuum arcs. Consequently, the inclusion of these interactions in vacuum arc simulations is imperative.

Simulation of the First Two Microseconds of an Ar CCP Cold Plasma Discharge by the PIC-MCC Method

Most simulations of capacitively coupled radiofrequency cold-plasma discharges (RF-CCP) are focused on the steady state, but the initial discharge time is important for understanding the ignition process and the behavior of pulsed discharges. In this work, the time evolution of an RF-CCP Ar discharge was simulated, considering a pressure of 66.6 Pa, a distance between the electrodes of 20 mm, and RF (13.56 MHz) bias amplitudes in range 100–400 V, and the discharge evolution was observed for the first 2 μs. A 1d3v (1 dimension for particle positions and 3 dimensions for particle velocities) electrostatic particle in cell with montecarlo collisions (PIC-MCC) model was used, with separated particle weights for electrons and ions that varied with the particle density. During the simulations, the time evolution of the electron density, mean electron energy, Debye length, Debye number, and plasma frequency were observed. The spatial distribution of electric potential and the electron energy distribution function were also monitored. A transition between two regimes was observed; the first was characterized by strong oscillation of the mean electron energy and an exponential increase of the mean plasma density with time, while in the second the mean electron energy was lower, and the plasma density increased linearly. The time required for the transition between the two regimes increased as the RF amplitude was raised from 100 to 250 V, then decreased with a further increase of the RF amplitude to 300 and 350 V.

Numerical simulation of electron extraction from micro electron cyclotron resonance neutralizer under different magnetic circuits

The electron cyclotron resonance (ECR) neutralizer is an important part of the micro ECR ion thruster. The electrons extracted from the neutralizer are used to neutralize the ions extracted from the ECR ion source, thereby avoiding the surface charges accumulating on the spacecraft, and the behaviour of electron extraction affects the overall performance of the thruster. In order to investigate the electron extraction through the orifices of the micro ECR neutralizer, a two-dimensional particle-in-cell with Monte Carlo collision (PIC/MCC) model is established in this work. The effects of different magnetic circuits on the electron extraction of the neutralizer and the influence of different cavity lengths on the wall current loss are studied through numerical simulation. The effects of different magnetic circuit structures on the electron extraction and wall current loss of the neutralizer are studied. The calculation results show that the position of the ECR layer and the magnetic flux lines near the extraction orifices are very important for the electron extraction performance of the neutralizer. When the ECR layer is located upstream of the antenna, electrons are easily lost in migration and diffusion motion, and the energy required for the electrons to cross the potential well before the extraction hole is higher. If more magnetic flux lines pass parallelly through the extraction orifices, the neutralizer requires a small voltage to extract the same electron current. When the ECR layer is cut by the antenna or is located downstream of antenna, more electrons may migrate along the magnetic flux lines to the vicinity of the extraction orifices, thereby reducing the voltage of collector plate. The effects of different cavity lengths on the extraction of electrons under the same magnetic circuit structure are studied. It is found that increasing the length of the cavity allows more parallel-axis magnetic flux lines to pass through the extraction holes to avoid electron loss on the surface of the extraction plate, and thus increasing the extraction electron current. The research results conduce to designing a reasonable neutralizer magnetic circuit and cavity size.

Characterization of plasma discharge channel in EDM using photography and spectroscopy

The plasma discharge channel of electrical discharge machining (EDM) brings a temperature of several thousands of degrees Celsius into the gap between the anode and cathode, resulting in the material removal by means of melting and evaporating. To investigate the characteristics of the plasma discharge channel, high-speed imaging technology is adopted to observe the dimension of the plasma. A spectrometer is used to calibrate the temperature of the plasma as well. Then the particle-in-cell with Monte Carlo collision (PIC-MCC) simulation is conducted to analyze the variation and distribution of the plasma and heat flux. The experimental results demonstrate that the discharge channels’ morphology obtained is stable after a few microseconds of expansion after breakdown, and the diameter of discharge channel and the current density increases with the increase of discharge current. Besides, the emission intensity of plasma increases with the increase of electrical parameters. However, the temperature of plasma decreases after high current, which means debris particles make machining condition deteriorated. Finally, the simulation results demonstrate that despite the current density increases, the maximum heat flux at the center of electrode reduces rapidly with the expansion of the discharge channel. The distribution of heat flux upon electrode evolves towards "wider and flatter", leading to larger debris particles than exceptional size.

Numerical simulation of influence of magnetic field on plasma characteristics and surface current of ion source of 2-cm electron cyclotron resonance ion thruster

The cathode-less miniature electron cyclotron resonance ion thruster (ECRIT) has the advantages of long-life and simple-structure. In the ECRIT ion source, the plasma distribution will affect the beam extraction, and the relative position of the ECR layer determined by the magnetic field structure and the flat-ring antenna together affect the plasma distribution. Due to the sheath, the ions or electrons in the plasma will be accelerated to sputter the surface of wall and induce plasma loss. It is important to investigate the wall currents and plasma characteristics. Therefore, particle-in-cell with Monte Carlo collision (PIC/MCC) model is established in this article to study the influence of the magnetic field structure on the plasma and wall current characteristics of 2-cm ECRIT ion source. The calculation results show that the electrons are confined near the ECR layer of antenna by the magnetic mirror, which leads the plasma to be distributed near the ECR layer. When the ECR layer is located on the upstream side of the flat-ring antenna, the plasma is concentrated between the antenna and magnet rings, and the ion density in front of the grid is lowest, which results in a lower ion beam current extracted from ion source and a lower current on the surface of magnetic ring and antenna. When the ECR layer is located on the downstream side of the flat-ring antenna, the plasma density near the upstream side of the antenna and grid is high, which results in higher ion beam current extracted from the ion source and higher current on the surface of antenna and magnetic ring. The plasma distribution and the total wall current of the ion source are affected weakly by the magnetic field structure. In this magnetic field structure, the ion sputtering on the flat-ring antenna is serious. Although such a magnetic field design can increase the extracted ion beam current, it will shorten the working life of the ion source. In the future, when designing a new thruster, it is necessary to weigh the ion current of extraction and lifetime to select the appropriate magnetic field structure.

Expansion of alternatively extracted ion–ion beam in a low pressure collisional medium

The aim of this paper is to investigate, through particle-in-cell with Monte Carlo collisions (PIC-MCC) simulations, the effects of collisions on the expansion of an ion–ion beam formed by the alternate extraction of oppositely charged ions. This beam is extracted from an ion–ion plasma, formed in the downstream of a radiofrequency magnetically filtered iodine electronegative plasma, by the mean of two extraction grids. In this grid system, the screen grid is biased with a square voltage waveform, in the low MHz range, while the acceleration grid is grounded. The collisionless interaction between the extracted ion packets involves and enhances electrostatic waves propagating at beam velocity. Our results show that in addition to these electrostatic waves, the presence of significant fraction of low energy ions, produced by charge exchange, beside extracted fast ions gives rise to two-stream instability. Furthermore, space and time dependent electric field might accelerate the slow ions, produced by charge exchange collision. This acceleration, involving Landau damping and its inverse mechanism, is mainly due to the interaction between ions and potential patterns inherent to two-stream instability.

Computational characterization of plasma transport across magnetic filter in ROBIN using PIC-MCC simulation

The RF based negative ion source experimental facility ROBIN has been setup to understand and investigate the different issues related to production, transport and extraction of negative hydrogen ions in negative ion sources for fusion applications. The source consists of a driver, an expansion chamber, a magnetic filter and extraction system consisting of different grids. The first phase of the ROBIN experiments have been conducted for hydrogen plasma generation and measurement of different plasma parameters without negative ion generation/ extraction. We require accurate characterization of plasma to completely understand the experimental results, the complex physics, and plasma dynamics. As a first step in this direction, we have developed an in-house parallel 2D-3v Particle-In-Cell with Monte Carlo Collision (PIC-MCC) code to understand the transport across magnetic filter under conditions similar to real ROBIN operational parameters (magnetic field, pressure, power, density etc.). Simulation results from our 2D-3v PIC-MCC code reproduces the qualitative as well as quantitative behaviors observed during the first phase of the ROBIN experiments such as decrement in electron temperature and similar plasma density profile across the magnetic filter. Our exhaustive PIC simulations helps us in quantifying the plasma transport across magnetic filter as well as the actual input power that is coupled to the plasma. Electron energy distribution function (EEDF) obtained from our simulations shows a Maxwellian distribution and is in agreement with similar experimental calculations reported in the literature. Several case studies have been performed to understand the role of the magnetic filter profile on plasma transport, which will help in planning future experiments by using the magnetic filter as a switching mechanism to achieve the required density and electron temperature profiles for efficient operation of ROBIN.

Breakdown phenomena across micrometer scale surface gap under negative voltage application

With the miniaturization of electrical devices, the insulation width and the separation between electrodes have been accordingly reduced. Consequently, electrical breakdown across micrometer-scale gaps is of great practical interest for insulation design. In this paper, electrical breakdown across micrometer scale surface gap in atmospheric air was investigated under inhomogeneous field. The breakdown was measured under negative impulse voltage and the generation and movement of neutral and charged particles were simulated based on PIC-MCC (particle-in-cell with Monte Carlo collision). The result shows that the breakdown phenomena across micrometer scale gaps is mainly determined by field emission current from the cathode surface, similar to the discharge process in vacuum. The positive ions generated by collision of electrons to neutral particles enhance the electric field near the cathode, resulting in the increase of the field emission current from the cathode.

A kinetic study of electron heating and plasma dynamics in microwave microplasmas

Microwave microplasmas ignited in argon are studied using a one-dimensional particle-in-cell with Monte Carlo collision (PIC-MCC) approach. One-dimensional PIC-MCC simulations are performed at specified input power densities to determine the influence of the applied frequency (ranging from 1 to 320 GHz), pressure, and total deposited power on the plasma dynamics. The frequency response study performed at a fixed input power density shows the presence of off-axis peaks in the electron number density profile at intermediate frequencies. These peaks are attributed to the interplay between the production of hot electrons by the oscillating sheath and their inability to diffuse sufficiently at higher operating pressures, thereby resulting in enhanced ionization at off-axis locations. This is confirmed by the pressure dependence study which shows that the electron number density peaks at the mid-point when the microplasma is ignited at lower pressures. As the excitation frequency is increased further, the sheath oscillation heating decreases and eventually vanishes, thereby requiring the bulk plasma to couple power to the electrons which in turn leads to an increase in electron temperature in the plasma bulk and the electron number density peak appearing at the mid-point. When the power coupled to the microplasma is decreased, the sheath oscillation at a given frequency decreases, thereby leading to higher contribution from heating in the bulk plasma which leads to the disappearance of off-axis peaks even at intermediate frequencies. The microplasma dynamics at all conditions considered in this work demonstrate the interplay between the electron momentum transfer collision frequency, the angular excitation frequency, and the plasma frequency.

Effects of Electrode Structure and Electron Energy on Abatement of NO in Dielectric Barrier Discharge Reactor

Electrode structure and electron energy effects on NO abatement were studied in two different structure DBD reactors. Final product analysis of NO abatement in coaxial cylinder dielectric barrier discharge (CC-DBD) and tubular multilayer dielectric barrier discharge (TM-DBD) reactors indicated that the electrode structure of TM-DBD was better under low O2 concentration conditions, but the result was opposite because the new NOx was produced in TM-DBD when O2 concentration was increasing. In addition, results of particle-in-cell with Monte Carlo collisions (PIC-MCC) simulation manifested that the largest and the average electron energy were 12.09 eV and 3.35 eV in TM-DBD reactor, respectively, while they were 5.25 eV and 2.96 eV in CC-DBD reactor, respectively. CC-DBD electrode structures are preferable for better NO abatement and no new NOx under oxygen-containing condition.

Influence of pulse front steepness on vacuum flashover characteristics

Studying flashover characteristics in vacuum environment is extremely significant for designing reliable insulation structures. The waveform of applied voltage excitations greatly affects the flashover process. In this study, the influence of nanosecond pulse front steepness on flashover process in vacuum is investigated. Firstly, flashover experiments with nanosecond pulses are conducted. Nanosecond pulses with different front steepness are generated and used to trigger flashovers on sample surface. The relationship between pulse front steepness and flashover voltage is studied. Meanwhile, a particle-in-cell with Monte Carlo collision (PIC-MCC) two-dimensional self-sustaining discharge model based on secondary electron emission avalanche (SEEA) scheme is established. The distribution of charged particles, electric field and their evolution during flashover process are presented. Furthermore, pulses with various rising steepness are applied to the model. The multiplication and propagation of charged particles in different pulse waveform conditions are studied. In all conditions, two stages during flashover process can be obviously distinguished based on charged particle number evolution which divides the overall flashover delay time into two parts. By analyzing the voltage development in these two time slots, the quasi-linear relationship between pulse front steepness and flashover voltage in nanosecond pulse flashover in vacuum is explained.

Control of Dual Frequency Capacitively Coupled Plasma via blocking capacitor and phase angle

This work investigates the effects of a blocking capacitor C B and a phase angle θ on Dual Frequency Capacitively Coupled Plasma (DF-CCP). This investigation is conducted by a Particle-In-Cell with Monte Carlo Collision (PIC-MCC) model. The simulation results are corroborated by a semi-analytical model. Our simulations show that the couple of parameters ( C B , θ ) allows the control of the DC self bias, η , as well as the potential drop within the sheaths that form in front of the powered and grounded electrodes. We show, also, that it is possible to use the parameters couple ( C B , θ ) such that to control the potential drop within the sheath in front of the powered electrode, ϕ sp , independently of the potential drop within sheath in front of the grounded electrode, ϕ sg , and vice versa. This latter ability allows us to control, quasi independently, the ion energy distribution bombarding each electrode.

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.

Operating modes of field emission assisted microplasmas in the microwave regime

The operating modes of microwave microplasma devices integrated with field emitting cathodes are studied using one-dimensional particle-in-cell with Monte Carlo collision (PIC-MCC) simulations. The PIC-MCC simulations predict operation in two modes—an α-mode characterized by a positive differential resistance with negligible influence of boundary processes and a γ-mode with significant field-induced electron emission. PIC-MCC results are presented for two representative 0.5 GHz argon microplasmas operating in the α and γ modes. The field emission-induced transition to γ-mode modifies the electron number density profiles in the sheath apart from leading to a higher contribution of conduction current in the sheath. The interpretation of electrical characteristics using time history of voltage and current demonstrates that the microplasma device impedance decreases as a result of the thinner sheath. It is also shown that the presence of field emitting cathodes leads to lower power requirements (about 64% of the case presented without field emission) to achieve a given plasma density.

A Comparison of Continuum and Kinetic Simulations of Moderate pd Microplasmas Integrated With High Secondary Yield Cathodes

The computational techniques commonly used for low‐temperature plasma simulations are compared in the context of modeling microplasmas driven by cathodes with high secondary electron emission coefficient. Simulations of 100 µm argon microplasmas operating at pressures of 100 Torr and secondary electron emission coefficient of 0.1 are performed using particle‐in‐cell with Monte Carlo collisions (PIC‐MCC), and fluid model using the full‐momentum equations for both electrons and ions. Results obtained for plasma density, potential, electric field, and electron temperature using continuum simulations are compared with the PIC‐MCC simulations as benchmark. The comparison demonstrates significant discrepancies and a need to calibrate continuum simulation parameters based on kinetic simulations.

Theory and analysis of operating modes in microplasmas assisted by field emitting cathodes

Motivated by the recent interest in the development of novel diamond-based cathodes, we study microplasmas assisted by field emitting cathodes with large field enhancement factors using a simplified model and comparisons with particle-in-cell with Monte Carlo collision (PIC-MCC) simulations and experiments. The model used to determine current-voltage characteristics assumes a linearly varying electric field in the sheath and predicts transition from an abnormal glow to arc mode at moderate current densities in a 1 mm argon gap. The influence of an external circuit is also considered to show the dependence of current as a function of the applied voltage, including potential drop across external resistors. PIC-MCC simulations confirm the validity of the model and also show the significant non-equilibrium nature of these low-temperature microplasmas with electron temperatures ∼1 eV and ion temperatures ∼0.07 eV in the quasi-neutral region. The model is also used to explain experimental data reported for a 1 mm argon gap at a pressure of 2 Torr using three different diamond-based cathodes with superior field emitting properties. The comparison shows that operating conditions in the experiments may not result in significant field emission and the differences observed in current-voltage characteristics can be attributed to small differences in the secondary electron emission coefficient of the three cathodes. However, the model and simulations clearly indicate that field emission using novel cathodes with high field enhancement factors can be used to enhance microplasmas by significantly decreasing the power requirements to achieve a given plasma number density even in gaps at which field emission is traditionally not considered to be a dominant mechanism.

Particle Methods for Nonequilibrium Hypersonic and Plasma Flows

Kinetic modelling of nonequilibrium flows is described as it applies to hypersonic phenomenology. A Monte Carlo method is described for the study of species separation on shock wave fronts; a Particle in Cell with Monte Carlo Collisions (PIC/MCC) technique is described for the simulation of dust in plasma flows; modelling of nonequilibrium radiation in shock heated gases; implementation of slip models for the description of separation zones occurring in shock- boudary layer interactions.

Three-dimensional particle-in-cell with Monte Carlo collision simulation of the electron energy distribution function in the multi-cusp ion source for proton therapy

For optimization and accurate prediction of the amount of proton production in the multi-cusp ion source, analysis of the electron energy distribution function (EEDF) is necessary. A three dimensional particle-in-cell with Monte Carlo collision (PIC-MCC) code based on the CHIPIC software platform are developed. The code is applied to the multi-cusp proton source. The results show that there are two energy distributions in the discharge chamber, and a spatial non-uniformity of electron density due to the B⃗×∇B drift of the top permanent magnets is observed.

P3M simulations of dusty plasmas

In this paper a review of the work on particle simulations of dusty plasmas using a three-dimensional Particle–Particle Particle–Mesh (P3M) code is presented. The code is applied to study the charging process of micrometre size dust grains confined in low temperature plasmas. This code gives a full-scale self-consistent kinetic description of both the background plasma and the charging of the dust particle. Particles (electrons and ions) are treated kinetically (Particle-in-Cell with Monte Carlo Collisions (PIC-MCC)), which allows us to self-consistently resolve the electrostatic sheath in front of the material wall. In order to accurately resolve the plasma particles' motion close to the dust grain, the PIC technique is supplemented with molecular dynamics (MD), employing the Coulomb potential for the interaction with the dust grain. The plasma particle trajectories are accurately followed in the close vicinity of the dust grain and by this finite-size effects for dust grains are included. Dust grain charging due to absorption of plasma particles and ion drag forces arising from momentum transfer of flowing ions to dust grains are studied.

Particle-In-Cell Modelling of a Neutral Beam Source for Material Processing in Nanoscale Structures Fabrication

Neutral beam processing has evolved into one of the most promising methods for overcoming plasma process induced damage. Surface treatment by neutrals avoids problems with surface charging effects, frequently encountered when using common ion treatment, especially for low k-materials. In this paper, the influence of various parameters on the neutralization of ion beams in Ar-CF4 mixture based on a Particle in Cell with Monte Carlo collisions (PIC/MCC) simulation is studied. The efficiency of neutralization has been treated by considering both surface neutralization of ions and collisions of ions in the gas.