Carlo Collision Simulations Research Articles

Impact of overvoltage on the mode transition of the spark gap switch: from edge breakdown to stochastic breakdown

Abstract Spark gap switch (SGS) is a fundamental but critical component for large-scale pulsed power devices, whose reliable operation is significantly affected by the breakdown characteristics of SGS. It is observed experimentally that, with the increase of overvoltage, the bridging position of the spark channel transits from edge to stochastic center. In this work, the influence of overvoltage on the breakdown process of a parallel-plate SGS with low geometric distortion of static electric field (<13%) between an atmospheric-pressure air gap of 5 mm is investigated by particle-in-cell/Monte Carlo collision simulation. It is found that, under a low overvoltage (ratio of applied voltage U a to static breakdown voltage U 0, U a/U 0 = 1.5), the streamers at the edge first bridge the gap before that in the central region, due to the field enhancement induced by the electrode curvature. Under higher overvoltage (U a/U 0 = 3), the synchronicity between streamers initiating from the center and those from the edge is greatly improved during the inception stage. After the streamers pass the middle of the gap, the field enhancement at the streamer front is more intensified and promotes the generation of fast electrons. These fast electrons rapidly magnify the difference among the propagating streamers by providing abundant seed electrons ahead of the discharge channel, which leads to the randomness of the bridging position. The results in this work demonstrate the relationship between overvoltage and streamer dynamics, which is beneficial for the performance improvement of SGS.

On the in-situ determination of the effective secondary electron emission coefficient in low pressure capacitively coupled radio frequency discharges based on the electrical asymmetry effect

Abstract We present a method for the in-situ determination of the effective secondary electron emission coefficient (SEEC, γ) in a capacitively coupled plasma (CCP) source based on the γ-dependence of the DC self-bias voltage that develops over the plasma due to the Electrical Asymmetry Effect (EAE). The EAE is established via the simultaneous application of two consecutive radio-frequency harmonics (with a varied phase angle) for the excitation of the discharge. Following the measurement of the DC self-bias voltage experimentally, Particle-in-Cell/Monte Carlo Collision (PIC/MCC) simulations coupled with a diffusion-reaction-radiation (DRR) code to compute the argon atomic excited level dynamics are conducted with a sequence of SEEC values. The actual γ for the given discharge operating conditions is found by searching for the best match between the experimental and computed values of the DC self-bias voltage. The γ ≈ 0.07 values obtained this way are in agreement with typical literature data for the working gas of argon and the electrode material of stainless steel in the CCP source. The method can be applied for a wider range of conditions, as well as for different electrode materials and gases to reveal the effective SEEC for various physical settings and discharge operating conditions.

Stochastic weighted particle control for electrostatic particle-in-cell Monte Carlo collision simulations in an axisymmetric coordinate system

The non-uniform grids in the axisymmetric coordinate system pose a significant challenge for electrostatic particle-in-cell/Monte Carlo collision (PIC/MCC) simulations because they require numerous macroparticles to manage numerical heating around the mid-axis. To address this, we have developed a stochastic weighted particle control method that selectively samples small-weight particles, effectively controlling the particle number without inducing numerical heating. This method is based on a rejection-acceptance probability merging scheme, which is easy to implement and has a low time complexity. We have also made essential modifications, including a corrected density deposition scheme, an energy conservation scheme, and the introduction of target weights. By applying this particle control method, the number of macroparticles in the simulation can be reduced by more than one order of magnitude, significantly reducing the required computing time and storage. Furthermore, appropriately setting target weights also enables enhanced resolution of dilute regions with an acceptable increase in computational cost.

Spontaneous asymmetry effect induced by uniform magnetic fields in capacitively coupled plasmas under perfectly symmetric conditions

Abstract Introducing asymmetry in capacitively coupled plasmas (CCPs) is a common strategy for achieving independent control of ion mean energy and flux. Our 1d3v particle-in-cell/Monte Carlo collision simulations reveal that a uniform magnetic field within a specific range can induce spatial asymmetry in low-pressure CCPs, even under perfectly symmetric conditions. This asymmetry, characterized by a shift in the plasma density distribution and significant differences in electron kinetics between the two sides of the plasma, leads to strong ionization and most electron losses on the low-density side, while the high-density side experiences weak ionization and minimal electron losses. The underlying mechanism triggering this spontaneous asymmetry is the differential influence of the magnetic field on low-energy (local) and high-energy (relatively nonlocal) electrons. Under conditions of low pressure and an appropriate magnetic field, this disparity in electron kinetic behavior leads to a spontaneous amplification of the asymmetry induced by random fluctuations until a steady state is reached, culminating in a spontaneous asymmetric effect.

Kinetic investigation of discharge performance for Xe, Kr, and Ar in a miniature ion thruster using a fast converging PIC-MCC-DSMC model

Abstract The present work develops a full particle-based model that couples the particle-in-cell plus Monte Carlo collision (PIC-MCC) simulation for plasma dynamics and the direct simulation Monte Carlo (DSMC) method for neutral dynamics in a synergistic iterative manner. This new model overcomes the slow convergence issue in the conventional direct coupling approach caused by the disparity of the time scales between the plasma and neutral dynamics. This model is applied to simulate the behavior of xenon (Xe) and its potential alternatives, krypton (Kr) and argon (Ar), in the discharge chamber of a miniature direct current (DC) ion thruster. The results show that a stable discharge is difficult to achieve for Kr and Ar under the operating conditions optimal for Xe. While increasing the discharge voltage can effectively improve the stability of discharge for Kr and Ar, other common strategies such as changing the magnetic field strength, propellant flow rate, and cathode current are not successful. The propellant utilization efficiency and discharge efficiency are affected by both discharge voltage and propellant flow rate. A maximum utilization efficiency and an optimal discharge efficiency are observed for all three propellants, with the values decreasing in the order of Xe, Kr, and Ar. Moreover, the discharge voltage corresponding to the optimal efficiency is inversely proportional to the square root of the propellant mass, indicating that the ion diffusional loss to the wall, rather than the ionization energy, is the dominant factor affecting the discharge performance for alternative propellants in a miniature DC thruster.

A discharge plasma regulation method with spike current for electrical discharge machining

Improving material removal rate (MRR) has been one of the most important issues in electrical discharge machining (EDM). A major factor which hinders the improvement of MRR in EDM is the relatively low expulsion ratio of molten material. During a discharge process, a large portion of molten material cannot be expelled sufficiently from the molten pool but re-solidifies, ultimately resulting in a low machining efficiency. In this study, aiming at enhancing the expulsion ratio of molten material in EDM, a discharge plasma regulation method with a spike current is proposed. A novel discharge pulse shape, with a spike current aligned at pulse turn-off stage, is adopted. The transient behaviors of the discharge plasma when a spike current engaged are captured using a high-speed camera, and the morphologies of the corresponding discharge craters are also analyzed. A particle-in-cell with Monte Carlo collision simulation method is used to analyze the changes in particle state inside the plasma. It is found that the spike current applied at the stage when the plasma contracts to a smaller diameter is more conducive to facilitating molten material expulsion. The results of consecutive-pulse machining experiments verify that the proposed discharge plasma regulation method can increase MRR by at least 25.89 % for stainless steel.

The detachment-induced mode in electronegative capacitively coupled radio-frequency plasmas

Insights into the spatio-temporally resolved electron power absorption dynamics in capacitively coupled radio-frequency plasmas are essential for understanding the fundamentals of their operation and as a basis for knowledge-based plasma process development. Similar to the γ-mode, an ionization maximum is observed at the sheath edge around the time of maximum sheath voltage in electronegative oxygen discharges at a pressure of 300 Pa. Based on Particle-in-Cell/Monte Carlo Collisions (PIC/MCC) simulations, we demonstrate that this maximum is not only caused by secondary electrons emitted at the electrode and collisionally multiplied inside the sheath. In fact, it also occurs in the complete absence of secondary electrons in the simulation, and is caused by the generation of O− ions by electron attachment close to the electrode during the local sheath collapse. These negative ions are accelerated towards the plasma bulk by the sheath electric field during sheath expansion. By electron detachment from these negative ions, electrons are generated inside the sheath and are accelerated towards the plasma bulk by the instantaneous sheath electric field—similarly to secondary electrons. Ionization is also observed in the plasma bulk and caused by electrons generated by detachment and accelerated by the high drift-and ambipolar electric fields. This detachment-induced electron power absorption is found to have significant effects on the discharge in the presence and absence of secondary electron emission. Its fundamentals are understood based on an analysis of the spatio-temporal electron and O− power absorption dynamics as well as the trajectory of selected O− ions close to the electrode.

Kinetic simulations of capacitively coupled plasmas driven by tailored voltage waveforms with multi-frequency matching

Impedance matching is crucial for optimizing plasma generation and reducing power reflection in capacitively coupled plasmas (CCP). Designing these matchings is challenging due to the varying and typically unknown impedance of the plasma, especially in the presence of multiple driving frequencies. Here, a computational design method for impedance matching networks (IMNs) for CCPs is proposed and applied to discharges driven by tailored voltage waveforms (TVW). This method is based on a self-consistent combination of particle in cell/Monte Carlo collision simulations of the plasma with Kirchhoff’s equations to describe the external electrical circuit. Two Foster second-form networks with the same structure are used to constitute an L-type matching network, and the matching capability is optimized by iteratively updating the values of variable capacitors inside the IMN. The results show that the plasma density and the power absorbed by the plasma continuously increase in the frame of this iterative process of adjusting the matching parameters until an excellent impedance matching capability is finally achieved. Impedance matching is found to affect the DC self-bias voltage, whose absolute value is maximized when the best matching is achieved. Additionally, a change in the quality of the impedance matching is found to cause an electron heating mode transition. Poor impedance matching results in a heating mode where electron power absorption in the plasma bulk by drift electric fields plays an important role, while good matching results in the classical α-mode operation, where electron power absorption by ambipolar electric fields at the sheath edges dominates. The method proposed in this work is expected to be of great significance in promoting TVW plasma sources from theory to industrial application, since it allows designing the required complex multi-frequency IMNs.

Self-consistent calculation of the optical emission spectrum of an argon capacitively coupled plasma based on the coupling of particle simulation with a collisional-radiative model

We report the development of a computational framework for the calculation of the optical emission spectrum of a low-pressure argon capacitively coupled plasma (CCP), which is based on the coupling of a particle-in-cell/Monte Carlo collision simulation code with a diffusion-reaction-radiation code for Ar I excited levels. In this framework, the particle simulation provides the rates of the direct and stepwise electron-impact excitation and electron-impact de-excitation for 30 excited levels, as well as the rates of electron-impact direct and stepwise ionization. These rates are used in the solutions of the diffusion equations of the excited species in the second code, along with the radiative rates for a high number of Ar-I transitions. The calculations also consider pooling ionization, quenching reactions, and radial diffusion losses. The electron energy distribution function and the population densities of the 30 excited atomic levels are computed self-consistently. The calculations then provide the emission intensities that reproduce reasonably well the experimentally measured optical emission spectrum of a symmetric CCP source operated at 13.56 MHz with 300 V peak-to-peak voltage, in the 2–100 Pa pressure range. The accuracy of the approach appears to be limited by the one-dimensional nature of the model, the treatment of the radiation trapping through the use of escape factors, and the effects of radiative cascades from higher excited levels not taken into account in the model.

Investigation of sheath structure in surface flashover induced by high-power microwave

Flashover is a major limiting factor for the transmission and miniaturization of high-power microwave (HPM) devices. We conducted a study to investigate the developmental process of surface flashover on HPM dielectric windows through particle-in-cell-Monte Carlo collision simulations. A one-dimensional spatial distribution and three-dimensional velocity distribution model is established, encompassing the entire process of surface flashover, which includes electrode field emission, single-surface multipactor, outgassing, and gas breakdown. The nonuniform mesh generation method is employed to enhance the simulation accuracy. The growth rates of electron and ion densities increase as gas pressure rises. Additionally, the discharge transitions gradually from multipactor to gas ionization dominance. Notably, a space-charge-limited (SCL)-like sheath occasionally forms during an rf cycle near the surface under intermediate background pressure (∼0.05 Torr). The SCL-like sheath cannot exist stably. Instead, it periodically disappears and appears as the rf electric field changes. The underlying physics are explained by the variations of the rf electric field, which lead to the variations in the surface charge density, thereby affecting the normal electric field. The normal electric field interacts with the spatial distribution of charged particles, ultimately leading to the formation of the SCL-like sheath. This work may facilitate a comprehensive understanding of the developmental processes of surface flashover.

Ultrafast oscillation in a field emission-driven miniaturized gaseous diode

We report an ultrafast oscillation (up to ∼104 GHz) in the early stage of field emission-driven microdischarges. Spatiotemporal behaviors of electron density, space charge density, and electric field, exhibiting high-frequency oscillations, are demonstrated based on first-principle particle-in-cell/Monte Carlo collision simulations. Intermittent electron emission fluxes are identified from the electron phase space distributions whereas the ions are rather non-oscillatory in the transient timescale. The mechanisms of oscillation with growing amplitude are found to be related to the rapid modification of the field emission current affected by the space charge electric field, which is also accompanied by the fast response of the electron transport and ionization in a dynamic double-layer sheath. Further, a transport equation for emission current is solved to estimate the oscillation frequency, which agrees well with the simulation results. This study provides a more precise understanding of the formation of the field emission-driven microdischarge, which informs the design and optimization of miniaturized gaseous electronic devices.

Electron power absorption in CF4 capacitively coupled RF plasmas operated in the striation mode

The electron power absorption mechanisms in electronegative capacitively coupled plasmas in CF4 are investigated using particle-in-cell/Monte Carlo collisions simulations at a pressure of p= 60 Pa, a driving frequency of f= 13.56 MHz for voltage amplitudes in the interval of ϕ0= 100 − 300 V, where pronounced self-organized density variations, i.e. striations, develop. The calculations are based on the Boltzmann term analysis, a computational diagnostic method capable of providing a complete spatio-temporal description of electron power absorption. The discharge undergoes an electron power absorption mode transition from the drift-ambipolar- to the striation-mode at φ 0 = 180 V. Although Ohmic power absorption is found to be the dominant electron power absorption mechanism in the parameter range considered, the electron power absorption mode transition can be inferred from the behaviour of the spatio-temporally averaged ambipolar power absorption as a function of the voltage amplitude. Furthermore, it is shown, that as a consequence of the presence of striations, the temporal modulation of the electron density leads to a temporal modulation of the ambipolar electric field, which is responsible for the striated structures of various physical quantities related to electrons, such as the electron temperature and the ionization source function.

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.

Effects of magnetic field gradient on capacitively coupled plasma driven by tailored voltage waveforms

This study utilized one-dimensional implicit particle-in-cell/Monte Carlo collision simulations to investigate the impact of different harmonic numbers and magnetic field strengths on capacitive-coupled argon plasma. Under the conditions of a pressure of 50 mTorr and a voltage of 100 V, simulations were conducted for magnetic field strengths of 0 and 100 G, magnetic field gradients of 10–40, 10–60, 10–80, 10–100, and 100–10 G, as well as discharge scenarios with harmonic numbers ranging from 1 to 5. Through in-depth analysis of the results, it was observed that the combined effect of positive magnetic field gradients and harmonic numbers can significantly enhance plasma density and self-bias properties to a greater extent. As the magnetic field gradient increases, the combined effect also increases, while an increase in harmonic numbers weakens the combined effect. Furthermore, this combined effect expands the range of control over ion bombardment energy. This provides a new research direction for improving control over ion energy and ion flux in capacitive-coupled plasmas.

Particle-in-cell/Monte Carlo collision simulation on gap breakdown characteristics of under the conditions of hot-electrode and high-temperature gas medium in low-voltage circuit breaker chamber

The gas composition inside the low-voltage circuit breaker (LVCB) chamber and the residual plasma in the post-arc stage affect the breakdown process, which in turn affects the breaking capacity of LVCBs. In this paper, the back-arc breakdown and post-arc re-breakdown phenomena occurring inside the LVCB chamber are categorized as the breakdown in the case of high-temperature gas gap of hot electrodes, for which a particle-in-cell/Monte Carlo collision simulation model has been established, which takes into account the effects of high-temperature gas components, cathode electron thermal emission, electron collision ionization, and other effects, and simulation studies have been conducted. The simulation results show that the gap breakdown is mainly caused by the high-temperature hot free background gas and the cathode thermal electron emission. A plasma sheath layer is formed at the cathode during the breakdown process, and the electric field strength in the sheath layer is higher than that in other regions. With the development of the streamer to the cathode, the thickness of the sheath layer becomes narrower and the electric field strength increases, and finally, a discharge plasma channel is formed in the gap.

A neural-network-based model of radio-frequency hollow cathode discharge characterized using particle-in-cell/Monte Carlo collision simulation

An understanding of the plasma dynamics of radio-frequency (RF) hollow cathode discharges (HCDs) at low to moderate pressures is important due to their wide range of applications. A HCD consists of a hollow cylindrical cavity in the RF-powered cathode separated from a grounded electrode by a dielectric. In RF HCDs, RF sheath heating can play a significant role in plasma production in addition to secondary electrons. In this study, a single hollow cathode hole is modeled using the particle-in-cell/Monte Carlo collision (PIC-MCC) technique at low pressure, where kinetic effects are important. Characterization of a single hollow cathode using PIC-MCC simulation is, however, computationally expensive. For improved computational efficiency, a neural network modeling framework has been developed using the temporal variations of applied RF voltages as input and the electrode current as output. A space-filling design for computational experiments is used, where the variables include the RF voltage at the fundamental frequency, RF voltage at the second harmonic, and their phase difference. The predictions of the electrode current using the trained neural network model compare well with the results of the PIC/MCC simulations, but at a significantly lower computational cost. The neural network model predicts the current very well inside the training domain, and reasonably well even outside the training domain considered in this study.

Plasma sheath tailoring by a magnetic field for three-dimensional plasma etching

Three-dimensional (3D) etching of materials by plasmas is an ultimate challenge in microstructuring applications. A method is proposed to reach a controllable 3D structure by using masks in front of the surface in a plasma etch reactor in combination with local magnetic fields to steer the incident ions in the plasma sheath region toward the surface to reach 3D directionality during etching and deposition. This effect has the potential to be controlled by modifying the magnetic field and/or plasma properties to adjust the relationship between sheath thickness and mask feature size. However, because the guiding length scale is the plasma sheath thickness, which for typical plasma densities is at least tens of micrometers or larger, controlled directional etching and deposition target the field of microstructuring, e.g., of solids for sensors, optics, or microfluidics. In this proof-of-concept study, it is shown that E→×B→ drifts tailor the local sheath expansion, thereby controlling the plasma density distribution and the transport when the plasma penetrates the mask during an RF cycle. This modified local plasma creates a 3D etch profile. This is shown experimentally as well as using 2d3v particle-in-cell/Monte Carlo collisions simulation.

Frequency-dependent electron power absorption mode transitions in capacitively coupled argon-oxygen plasmas

Phase Resolved Optical Emission Spectroscopy (PROES) measurements combined with 1d3v Particle-in-Cell/Monte Carlo Collisions simulations are performed to investigate the excitation dynamics in low-pressure capacitively coupled plasmas (CCPs) in argon-oxygen mixtures. The system used for this study is a geometrically symmetric CCP reactor operated in a 70% Ar-30% O2 mixture at 120 Pa, applying a peak-to-peak voltage of 350 V, with a wide range of driving RF frequencies (2 MHz ⩽f⩽ 15 MHz). The measured and calculated spatio-temporal distributions of the electron impact excitation rates from the Ar ground state to the Ar 2p1 level show good qualitative agreement. The distributions show significant frequency dependence, which is generally considered to be predictive of transitions in the dominant discharge operating mode. Three frequency ranges can be distinguished, showing distinctly different excitation characteristics: (i) in the low frequency range ( f⩽ 3 MHz), excitation is strong at the sheaths and weak in the bulk region; (ii) at intermediate frequencies (3.5 MHz ⩽f⩽ 5 MHz), the excitation rate in the bulk region is enhanced and shows striation formation; (iii) above 6 MHz, excitation in the bulk gradually decreases with increasing frequency. Boltzmann term analysis was performed to quantify the frequency-dependent contributions of the Ohmic and ambipolar terms to the electron power absorption.

An experimental and computational study on the ignition process of a pulse modulated dual-RF capacitively coupled plasma operated at various low-frequency voltage amplitudes

The ignition process of a pulse modulated capacitively coupled argon discharge driven simultaneously by two radio frequency voltages [12.5 MHz (high frequency) and 2.5 MHz (low frequency, LF)] is investigated by multifold experimental diagnostics and particle in cell / Monte Carlo collision simulations. In particular, (i) the effects of the LF voltage amplitude measured at the end of the pulse-on period, VL,end , on the spatiotemporal distribution of the electron impact excitation rate determined by phase resolved optical emission spectroscopy, and (ii) the electrical parameters acquired by analyzing the measured waveforms of the plasma current and voltage, are studied. Computed electrical parameters and spatio-temporal excitation maps show a good qualitative agreement with the experimental results. Especially, various breakdown mechanisms are found at different VL,end . At low values of VL,end , the ‘RF-avalanche’ mode (volume process) dominates the electron multiplication process. By increasing VL,end , the ionization caused by the volume electrons is suppressed and the electron loss at the electrodes is enhanced, leading to a delayed ignition. At higher values of VL,end , the avalanche ionization is significantly enhanced by ion-induced secondary electron emission at the electrodes, so that the ignition is significantly advanced.

Particle-in-cell-Monte Carlo collision simulation study on breakdown characteristics on gas side of high-power microwave dielectric window

Gas breakdown is one of the key factors restricting the increase of power capacity around the outer surface of highpower microwave dielectric window. It is of great significance to conduct corresponding simulation studies. Compared with the fluid model, the particle-in-cell-Monte Carlo collision model has two advantages: firstly, the influence of numerical dispersion and instability problems is insignificant; secondly, it can accurately describe microphysical processes. Therefore, the breakdown characteristics on gas side of dielectric window are simulated by the particle-in-cell-Monte Carlo collision model. The two-in-one macro-particle merging method is introduced into the model, which greatly reduces the number of macro-particles tracked, so that the whole breakdown process can be simulated and analyzed. The results show that the spatial and temporal evolution of breakdown under the variable macro-particle weight is in good agreement with that under the constant macro-particle weight. This suggests that the two-in-one macro-particle merging method is applicable under the simulation conditions of interest in this paper, i.e., when the ratio of the effective electric field of microwaves to the pressure is between 1:76×103 and 1:41×10<sup>4</sup> V/(m·Torr). Since the yield of secondary electron emission is much less than 1, gas ionization is the dominant mechanism of breakdown on gas side of dielectric window. Electron ionization and diffusion lead to a significant increase in the density and thickness of the plasma over time. The peak of electron density does not appear at the dielectric surface, but at a position 100-150 <i>μ</i>m away from the dielectric surface. This is because a large number of electrons are deposited on the dielectric surface, and the accompanying self-organized normal electric field drives the electrons away from the dielectric surface. Since the background gas pressure of interest in this paper is higher than the critical pressure corresponding to the maximum ionization rate (about 10 Torr), the ionization rate decreases monotonically with increasing pressure and leads to a slower development of breakdown. The accuracy of the particle-in-cell-Monte Carlo collision model is confirmed by comparing the simulated values of breakdown time with experimental data. This work provides an important theoretical basis for understanding and controlling the breakdown on gas side of dielectric window. The following figure (a) shows that the mean electron energy under the variable macro-particle weight agrees well with that under the constant macro-particle weight at 100 Torr. The following figure (b) shows that using the particle-in-cell-Monte Carlo collision model with a two-in-one macro-particle merging method allows the breakdown process to be considered when the plasma density increases by a factor of 108.