Particle-in-cell Monte Carlo Collision Research Articles

Wide-range characteristics of beam perveance and saddle point potential of LIPS-200 ion thruster

Both the long-life and multi-mode versions of LIPS-200 ion thruster are under investigation in LIP (Lanzhou Institute of Physics). To confirm the feasible ranges of the beam current and accel (abbreviation for accelaration) grid potential to apply to the thruster, the wide-range beam perveance (the state of beam focus) and saddle point potential (the lowest potential along beamlet centerline) characteristics of LIPS-200 are studied with a test-verified PIC-MCC (Particle in Cell-Monte Carlo Collisions) model. These characteristics are investigated with both the initial and the eroded states of the accel grid aperture diameter. The results show that the feasible ranges of these parameters with respect to perveance/crossover (overfocused) limit extend as the operating time accumulates, while the feasible range of accel grid potential narrows due to a reduced EBSF (electron backstreaming failure) margin. The feasible ranges determined by the initial condition are: (i) the beam current up to 0.981 A, and (ii) the accel grid potential up to −85 V. A 23% enlargement of the aperture diameter would bring up to 48 V of EBSF margin loss.

Electron power absorption in capacitively coupled neon–oxygen plasmas: a comparison of experimental and computational results

Phase resolved optical emission spectroscopy (PROES) measurements combined with 1d3v particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations are used to study the electron power absorption and excitation/ionization dynamics in capacitively coupled plasmas (CCPs) in mixtures of neon and oxygen gases. The study is performed for a geometrically symmetric CCP reactor with a gap length of 2.5 cm at a driving frequency of 10 MHz and a peak-to-peak voltage of 350 V. The pressure of the gas mixture is varied between 15 Pa and 500 Pa, while the neon/oxygen concentration is tuned between 10% and 90%. For all discharge conditions, the spatio-temporal distributions of the electron-impact excitation rate from the Ne ground state into the Ne 2p53p0 state measured by PROES and obtained from PIC/MCC simulations show good qualitative agreement. Based on the emission/excitation patterns, multiple operation regimes are identified. Localized bright emission features at the bulk boundaries, caused by local maxima in the electronegativity are found at high pressures and high O2 concentrations. The relative contributions of the ambipolar and the Ohmic electron power absorption are found to vary strongly with the discharge parameters: the Ohmic power absorption is enhanced by both the high collisionality at high pressures and the high electronegativity at low pressures. In the wide parameter regime covered in this study, the PROES measurements are found to accurately represent the ionization dynamics, i.e. the discharge operation mode. This work represents also a successful experimental validation of the discharge model developed for neon–oxygen CCPs.

Application of positive pulse to extract ions from HiPIMS ionization region

High power impulse magnetron sputtering (HiPIMS) is a promising physical vapor deposition technique with one of the main drawbacks being its relatively low deposition rate. In this article, a method was propose by using a positive ions extraction pulse (Uextract) which would be immediately applied to the sputtering target after the HiPIMS negative pulse to extract out the ions from the ionization region near the HiPIMS target. The Particle-In-Cell/Monte Carlo Collision (PIC-MCC) simulation, experiments, and theoretical study were conducted to investigate the ions extraction process. It is demonstrated that the higher potential moved from the target area to the substrate direction and the peak ion density was driven to the substrate direction, after applying the positive ions extraction pulse to the target. The measured ion-energy distribution function (IEDF) characteristics verified that the ions extraction method works. The experimental results indicated that the Ti + ion flux dramatically increased when the Uextract was over 50 V. Good agreement between the experimental and simulation results was obtained, validating the simulation conclusion. Finally, the microscopic mechanism of ions extraction is proposed.

High-precision modeling of dynamic etching in high-power magnetron sputtering

Etching of the cathodes in magnetron sputtering determines the plasma discharge properties and deposition efficiency. In high-power and high-ionization discharges, etching becomes more complicated, resulting in inaccurate results if the conventional models are still used. This work aims at establishing an accurate dynamic model for high-power and high-ionization discharges by combining the cellular automata (CA) method and particle-in-cell/Monte Carlo collision (PIC/MCC) method, in which all the interactions pertaining to the etching morphology, plasma density, electric field, and magnetic field are considered. In high-power discharges such as continuous high-power magnetron sputtering (C-HPMS), strong self-sputtering and intense gas rarefaction stemming from the high temperature in the vicinity of the target influence the etching behavior. Compared to the experimental results, the morphology simulated by the dynamic etching model shows an error of only 0.8% in C-HPMS, which is much less than that obtained by the traditional test-electron Monte Carlo (MC) method (10.1%) and static PIC/MCC method (4.0%). The dynamic etching model provides more accurate results to aid the development and industrial application of HPMS.

The Limitation Analysis of Two Dimensional Magnetic Field Configuration in Annular Ion Thruster

In this paper, the limitations of two-dimensional magnetic field configuration for an annular ion thruster are analyzed theoretically and numerically. The two-dimensional magnetic field, which is commonly used in traditional ion thrusters, has been proved to be a very effective way for the confinement of primary electrons and ions. Hence, the confinement characteristics of primary electrons and ions in an annular ion thruster with the two-dimensional magnetic field configuration are first analyzed theoretically. Then, according to the analysis, a two-dimensional magnetic field for an annular ion thruster is designed. On this basis, the limitations of the two-dimensional magnetic field configuration are analyzed and discussed by a three-dimensional (3D) Particle-in-cell Monte Carlo collision (PIC-MCC) model. The results show that if the collision process is not considered, a uniform distribution of primary electrons can be achieved theoretically. However, when considering the collision process, the atom forms a significant impedance to the circumferential motion of primary electrons, thus greatly increasing the loss rate of primary electrons. Finally, it is found that, since primary electrons are not guided and constrained in the circumferential direction under the two-dimensional magnetic field, the discharge uniformity cannot be improved only by increasing the magnetic field intensity.

Simulation and modeling of radio-frequency atmospheric pressure plasmas in the non-neutral regime

Radio-frequency-driven atmospheric pressure plasma jets (RF APPJs) play an essential role in many technological applications. This work studies the characteristics of these discharges in the so-called non-neutral regime where the conventional structure of a quasi-neutral bulk and an electron depleted sheath does not develop, and the electrons are instead organized in a drift-soliton-like structure that never reaches quasi-neutrality. A hybrid particle-in-cell/Monte Carlo collisions (PIC/MCC) simulation is set up, which combines a fully kinetic electron model via the PIC/MCC algorithm with a drift-diffusion model for the ions. In addition, an analytical model for the electron dynamics is formulated. The formation of the soliton-like structure and the connection between the soliton and the electron dynamics are investigated. The location of the electron group follows a drift equation, while the spatial shape can be described by Poisson–Boltzmann equilibrium in a co-moving frame. A stability analysis is conducted using the Lyapunov method and a linear stability analysis. A comparison of the numerical simulation with the analytical models yields a good agreement.

Qualification of uniform large area multidipolar ECR hydrogen plasma

The design and characterization of a multi-dipolar microwave electron cyclotron resonance (ECR) hydrogen plasma reactor are presented. In this configuration, 16 ECR sources are disposed uniformly along the azimuthal direction at a constant distance from the center of a cylindrical reactor. Several plasma diagnostics have been used to determine key parameters such as neutral species temperature; electron density and temperature; and H+, H2+, and H3+ ion energy distributions. The experimental characterization is supported by electromagnetic and magnetostatic field simulations as well as Particle In-Cell Monte Carlo Collisions simulations to analyze the observed ion energy distribution functions. Especially, we show that both electron density and temperature are spatially uniform, i.e., 1011 cm−3 and 3 eV, respectively. This plasma enables generating ion flux and energy in the ranges 1019–1022 ions m−2 s−1 and few keVs, respectively. The H2+ ion distribution function shows two populations which were attributed to surface effects. These features make this reactor particularly suitable for studying hydrogen plasma surface interaction under controlled conditions.

On the breakdown process of capacitively coupled plasma in carbon tetrafluoride

Capacitively coupled plasma (CCP) in CF4 has been widely used in the semiconductor industry. However, its breakdown process at low pressure has rarely been studied. In this paper, we study the whole CCP breakdown process in CF4 using the 1D implicit particle-in-cell/Monte Carlo collision (PIC/MCC) method. The detailed evolution of the plasma parameters is given, and both the particle balance and power evolution are discussed. The electron density initially grows exponentially, driven by the penetrating electric field. Both the ionization in the discharge gap and the boundary interaction are significant for electron avalanches. The formation of a sheath maximizes the ionization rate and the heating power, which thoroughly changes the field structure. In the post-breakdown phase, the growing negative ion density shrink the sheaths and changes the heating mode from the α mode to the drift-ambipolar mode. The particle generation rate and heating power show a growth trend after a brief decline. The growth of the recombination rate slowly balances the gain and loss of ions, which finally stabilizes the discharge.

Numerical Simulation Of A Bi-directional Plasma Thruster For Space Debris Removal

A spacecraft during mission typically switches from chemical propulsion to electric propulsion once it lifts out of the Earth's gravity as the thrust requirement to drive it reduces substantially. Consequently, electric propulsion technology is commonly used for deep space mission, satellite orbit keeping and orbit correction. In the last few decades, the amount of man-made space junk (space debris) has increased enormously and has become a potential danger for space stations, space shuttles and other live satellites. A bi-directional plasma thruster, mounted on a satellite, can be used to remove space debris during satellite operation (Takahashi et al., Sci. Rep., vol. 8, 2018, p. 14417). A directed ion beam ejected from a plasma thruster imparts a net force on space debris to decelerate and facilitates manoeuvring and re-entry of space debris into the Earth's atmosphere where it can burn out. We present a detailed 1D3V PIC-MCC (particle in cell-Monte Carlo collision) simulation of a bi- directional plasma thruster. To this end, a PIC-MCC solver which resolves thruster axial direction and all three velocity dimensions is used to study a magnetic nozzle plasma thruster with both ends open (bi-directional plasma thruster). We show that such a bi-directional plasma thruster can be used to accelerate–decelerate a live satellite and also to remove space debris by altering the magnetic field spatial profile in the plasma expansion region. A detailed study is presented.

Effects of surplus heat and space charges on dynamic evolution of nanosecond repetitively pulsed discharges

Effects of the surplus heat and space charges on the evolution of discharge dynamics and the discharge regime transition were investigated by a co-simulation platform consisting of a zero-dimensional (0D) plasma kinetics model and a two-dimensional (2D) Particle-In-Cell/Monte Carlo-Collision (PIC/MCC) model under repetitive nanosecond pulses. The results from the 0D plasma kinetics model show that the evolution could be defined as three stages: (a) initial cloud, (b) corona enhancement, and (c) quasi-stable spark. Surplus heat plays a key role in the transition from corona to spark. However, the evolution behavior under the corona enhancement stage cannot be explained by surplus heat alone. Detailed results from the 2D PIC/MCC model show that considering the effects of space charges, the transition from corona to spark tends to be hindered in the nanosecond repetitively pulsed discharges. A feedback mechanism for discharge evolution considering surplus heat and space charges is proposed in this paper, which provides a qualitative criterion for determining the evolutionary direction of corona discharge under repetitive nanosecond pulses.

Ion-focused propagation of a relativistic electron beam in the self-generated plasma in atmosphere

It is known that ion-focused regime (IFR) can effectively suppress expansion of a relativistic electron beam (REB). Using the particle-in-cell Monte Carlo collision (PIC-MCC) method, we numerically investigate the propagation of an REB in neutral gas. The results demonstrate that the beam body is charge neutralization and a stable IFR can be established. As a result, the beam transverse dimensions and longitudinal velocities keep close to the initial parameters. We also calculate the charge and current neutralization factors of the REB. Combined with envelope equations, we obtain the variations of beam envelopes, which agree well with the PIC simulations. However, both the energy loss and instabilities of the REB may lead to a low transport efficiency during long-range propagation. It is proved that decreasing the initial pulse length of the REB can avoid the influence of electron avalanche. Using parts of REB pulses to build a long-distance IFR in advance can improve the beam quality of subsequent pulses. Further, a long-distance IFR may contribute to the implementation of long-range propagation of the REB in space environment.

Multi-diagnostic experimental validation of 1d3v PIC/MCC simulations of low pressure capacitive RF plasmas operated in argon

The particle-in-cell/Monte Carlo collisions (PIC/MCC) simulation approach has become a standard and well-established tool in studies of capacitively coupled radio frequency (RF) plasmas. While code-to-code benchmarks have been performed in some cases, systematic experimental validations of such simulations are rare. In this work, a multi-diagnostic experimental validation of 1d3v electrostatic PIC/MCC simulation results is performed in argon gas at pressures ranging from 1 Pa to 100 Pa and at RF (13.56 MHz) voltage amplitudes between 150 V and 350 V using a custom built geometrically symmetric reference reactor. The gas temperature, the electron density, the spatio-temporal electron impact excitation dynamics, and the ion flux-energy distribution at the grounded electrode are measured. In the simulations, the gas temperature and the electrode surface coefficients for secondary electron emission and electron reflection are input parameters. Experimentally, the gas temperature is found to increase significantly beyond room temperature as a function of pressure, whereas constant values for the gas temperature are typically assumed in simulations. The computational results are found to be sensitive to the gas temperature and to the choice of surface coefficients, especially at low pressures, at which non-local kinetic effects are prominent. By adjusting these input parameters to specific values, a good quantitative agreement between all measured and computationally obtained plasma parameters is achieved. If the gas temperature is known, surface coefficients for different electrode materials can be determined in this way by computationally assisted diagnostics. The results show, that PIC/MCC simulations can describe experiments correctly, if appropriate values for the gas temperature and surface coefficients are used. Otherwise significant deviations can occur.

Behavior of Electrons in the Bullet in the Ar/O₂ Plasma Jet in Changing Oxygen Concentration and the Applied Voltage

This work presents a systematic numerical investigation on the behaviors of electrons in the bullet in the Ar/O2 plasma jet in changing oxygen concentration and the applied voltage, based on a needle-plate discharge configuration and a 1-D particle-in-cell Monte-Carlo collision (PIC-MCC) method. The increase in oxygen concentration allows more electrons to be scattered toward the target, i.e., more electrons to most probably interact with the target, and induces a dramatic increase of reactive oxygen species (ROS), but leads to the decrease of the bullet velocity and average electron energy. In addition, there is a weak correlation between the electron density and ROS generation. When increasing the applied voltage, the electrons scattered toward the target decrease, however, the majority of these electrons, above 70%, are of energy higher than the threshold inducing a dissociative electron attachment (DEA) to water molecule, and meanwhile, there is an evident increase of high-energy electrons being able to excite water molecules. Also, there is a strong correlation between the electron density and ROS generation. The present results are also compared with those in the Ar/H2O plasma jets, indicating qualitative and quantitative differences.

Numerical investigation of plasma behavior in a micro DC ion thruster using the particle-in-cell/Monte Carlo collision (PIC/MCC) method

Micro direct current (DC) ion thruster has advantages of small volume, light weight and significantly improved specific impulse performance compared to conventional chemical propulsion systems, thus having a wide application prospect in the tasks of cube-satellites and micro satellite networking systems. In this paper, a two-dimensional axisymmetric particle-in-cell/Monte Carlo collision model for the discharge chamber is developed for a micro DC ion thruster, which adopt the real configuration of original MiXI thruster with ring-cusp magnetic field. This model takes the thermal electron emission including the Schottky effect, various collision processes and the uneven background gas density distribution in the cathode-anode gap into account. The transient discharge process and the influence of operating conditions on the discharge process in the ionization chamber are presented for the first time so as to provide a detailed understanding of transport characteristics of plasma associated with the DC discharge process. Our calculated properties are compared with literature experimental data under similar conditions and qualitative and quantitative agreements are reached. The leak widths for charged species are obtained and closely related to charge separation. The simulations indicate that low neutral flow rate may lead to a discharge instability accompanied with oscillation of plasma quantities. These results lay a foundation for further optimization of thruster discharge chamber design in the future.

2D Particle-in-cell simulations of charged particle dynamics in geometrically asymmetric low pressure capacitive RF plasmas

Understanding the spatio-temporal dynamics of charged particles in low pressure radio frequency capacitively coupled plasmas (CCP) is the basis for knowledge based process development in these plasma sources. Due to the importance of kinetic non-local effects the particle in cell/Monte Carlo collision (PIC/MCC) simulation became the primary modeling approach. However, due to computational limitations most previous PIC/MCC simulations were restricted to spatial resolution in one dimension. Additionally, most previous studies were based on oversimplified treatments of plasma-surface interactions. Overcoming these problems could clearly lead to a more realistic description of the physics of these plasma sources. In this work, the effects of the reactor geometry in combination with realistic heavy particle and electron induced secondary electron emission coefficients (SEEC) on the charged particle dynamics are revealed by GPU based 2D3V PIC/MCC simulations of argon discharges operated at 0.5 Pa and at a high voltage amplitude of 1000 V. The geometrical reactor asymmetry as well as the SEECs are found to affect the power absorption dynamics and distribution functions of electrons and ions strongly by determining the sheath voltages and widths adjacent to powered and grounded surface elements as well as via the self-excitation of the plasma series resonance. It is noticed that secondary electrons play important roles even at low pressures. Electron induced secondary electrons (δ-electrons) are found to cause up to half of the total ionization, while heavy particle induced secondary electrons (γ-electrons) do not cause much ionization directly, but induce most of the δ-electron emission from boundary surfaces. The fundamental insights obtained into the 2D-space resolved charged particle dynamics are used to understand the formation of energy distribution functions of electrons and ions for different reactor geometries and surface conditions.

Micro atmospheric pressure plasma jets excited in He/O2 by voltage waveform tailoring: a study based on a numerical hybrid model and experiments

A hybrid simulation code is developed to treat electrons fully kinetically by the particle-in-cell/Monte Carlo collision (PIC/MCC) algorithm, while ions and neutral species are handled by a fluid model, including a time slicing technique to reduce the computational expenses caused by the responses of various species on different time scales. The code is used to investigate a capacitively coupled COST reference micro atmospheric pressure helium plasma jet with 0.1% oxygen admixture excited by a valley-type tailored voltage waveform with a fixed peak-to-peak voltage of 400 V, and a fundamental frequency of 13.56 MHz. The computational results are compared to experiments based on several sophisticated diagnostics, showing good agreement in the electron impact helium excitation rate, the helium metastable density, and the atomic oxygen density. The spatio-temporal electron heating dynamics, are found to be asymmetrical due to the specific shape of the driving voltage waveform. Tailoring the voltage waveform is shown to enable to control the electron energy probability function (EEPF) in distinct spatio-temporal regions of interest. As a consequence, the generation of reactive neutral species can be enhanced by increasing the number of consecutive harmonics. Based on a simplified two dimensional neutral transport model in the hybrid code, it is demonstrated that the transport between the electrodes, as well as the gas flow have different effects on various neutral species distributions due to the relevant chemical reaction rates for the generation and destruction of species.

Electrical breakdown in dual-frequency capacitively coupled plasma: a collective simulation

Most plasma sources have to undergo a breakdown process, during which, energy is injected, and particles are ionized. However, we still know little about this fast evolution process. In this work, a one-dimensional direct implicit particle-in-cell/Monte-Carlo collision (PIC/MCC) program is used to study the breakdown process of a capacitively coupled plasma (CCP) driven by dual radio frequencies. The results show that the breakdown process can be divided into three phases: the pre-breakdown, transition, and post-breakdown phases. In the pre-breakdown phase, the plasma density and heating power grow exponentially. The electric field can penetrate the whole discharge region without any shielding, resulting in a higher-than-average electron energy. Secondary electron emission is critical to grow the electron numbers under these discharge conditions. During the transition phase, the formation of sheaths maximizes the electron generation rate and heating power. The formation of sheaths also causes a drastic change in the electrical characteristics of CCP devices. In the post-breakdown phase, the plasma parameters gradually evolve until a steady state is reached. The decreasing rate of generation and the increasing rate of particle loss gradually equalize. The trends of the power gain and plasma loss are similar to the curves for the particle generation and loss rates, and a dynamic equilibrium is finally reached in the last steady state.

The effect of a negative direct-current voltage on striated structures and electrical parameters in a capacitively coupled rf discharge in CF4

The effects of a negative direct-current (dc) voltage on the striated structures and the electrical parameters have been studied by multi-fold experimental diagnostics and particle-in-cell/Monte Carlo collision (PIC/MCC) simulations in a dc superposed rf (radio-frequency, 8 MHz) capacitive discharge in CF4. The electron density, the spatio-temporal distribution of electron-impact excitation rate and the electrical parameters measured by a hairpin probe, phase resolved optical emission spectroscopy and a voltage and a current probe are compared with the corresponding simulation results. With the increase of the magnitude of the dc voltage, , all the experimental observations are well reproduced and analyzed by the simulations. It was found that the plasma bulk is compressed and the electron density decreases slightly at low , while the plasma bulk broadens at high when the ionization at the edge of the completely expanded sheath adjacent to the powered electrode is significantly enhanced due to the secondary electron emission (SEE). By increasing , the region of the strong ionization/excitation shrinks towards the edge of the collapsing sheath adjacent to the grounded electrode. And the ionization inside the bulk region is significantly suppressed during the collapsing phase of the sheath adjacent to the powered electrode. This is mainly attributed to the fact that the dc component of the bulk electric field and the spatial gradient of the electron density are simultaneously enhanced during the transition from the ‘striation’ mode to ‘striation-γ’ hybrid mode when increasing . Besides, we found that increasing can somewhat suppress the rf power deposition at low , and enhance the rf power deposition at high . The magnitude of the dc current exhibits a complex dependence on , due to nonlinear change of the dc resistance of the plasma.

PIC-MCC Investigation on the Influences of Gas Medium and Flashover on the Multipacting Cathode Operation

In this article, the influences of outgassing and flashover on the performance of a novel multipacting cathode are numerically investigated by using particle in cell-Monte Carlo collision (PIC-MCC) method, including the conditions of weak, medium, and strong outgassing. The numerical results demonstrate that under the condition of weak outgassing (0.1 Torr), multipacting is hardly influenced by gas ionization. Multipacting dominates the entire physical process. Due to the further improved output current by additional electrons generated from ionization, the weak outgassing can help cathode performance enhancement. Under the condition of medium outgassing (1 Torr), gas ionization first boosts multipacting developing and then tends to suppress multipacting process. During the initial stage, multipacting dominates the entire physical process. When multipacting tends to saturate, gas ionization will dominate the whole physical process. The rapidly increased output current will finally decrease gap voltage and induce the diode breakdown. Under the condition of strong outgassing (1 atm), multipacting is suppressed by gas ionization from beginning to end. Gas ionization dominates the whole physical process all the time. The strong effect of ionization collision will finally induce streamer discharge and diode breakdown.

Particle-in-cell Monte Carlo-collision modeling of non-ideal effects in wave-heated dense microplasmas

A computational model for non-ideal plasma effects during the time evolution of a second-stage laser-heated discharge at high pressures is presented. The model extends a classical one-dimensional particle-in-cell Monte Carlo-collision (PIC-MCC) approach coupled with Maxwell's equations for the laser-heating process of a xenon plasma at 300 K temperature and 10–100 bar pressure. Plasma non-ideality resulting from Coulomb coupling at high plasma densities is manifested as a depression in the effective ionization potential of atoms and enhanced collision cross sections. These non-ideal effects are represented using the Ecker–Kröll model in the context of the PIC-MCC approach. We find that full ionization of the plasma is obtained on the picosecond timescale, starting from the skin layer and quickly expanding throughout the domain through an anomalous extension of the skin depth. More critically, we show that the inclusion of the non-ideal plasma effects results in more rapid ionization compared to an ideal plasma, especially at higher pressures. The ionization delay reduction is of the order of a fraction of a picosecond, corresponding to a 16% decrease at 100 bar. As the amplitude of the wave field is lowered, the ionization rate is lowered, making the plasma non-ideality effects more prominent.