Monte Carlo Collision Simulation 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.

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 simulation of a cylindrical plasma mass separator based on Penning discharge with thermionic cathodes

This work is devoted to the modeling of a Penning discharge with a hot cathode, which is used to create a background plasma with a radial electric field in a plasma mass separator. We used a 2D3V electrostatic particle-in-cell plus Monte Carlo Collision (PIC/MCC) simulation model with a gyrokinetic approximation for magnetized electrons and a geometrical scaling scheme. The proposed model predicts the development of a rotating spoke structure, leading to fluctuations in the electric potential. The fluctuation amplitude and the averaged radial profile of the potential are in qualitative agreement with experiment. On the example of a model flow of silver and lead ions, we have shown that potential fluctuations can impair separation, leading to a partial overlap of ion deposition spots on a substrate. Each of the separated fractions contain about 11% impurities.

On the importance of excited state species in low pressure capacitively coupled plasma argon discharges

In the past three decades, first principles-based fully kinetic particle-in-cell Monte Carlo collision (PIC/MCC) simulations have been proven to be an important tool for the understanding of the physics of low pressure capacitive discharges. However, there is a long-standing issue that the plasma density determined by PIC/MCC simulations shows quantitative deviations from experimental measurements, even in argon discharges, indicating that certain physics may be missing in previous modeling of the low pressure radio frequency (rf) driven capacitive discharges. In this work, we report that the energetic electron-induced secondary electron emission (SEE) and excited state atoms play an important role in low pressure rf capacitive argon plasma discharges. The ion-induced secondary electrons are accelerated by the high sheath field to strike the opposite electrode and produce a considerable number of secondary electrons that lead to additional ionizing impacts and further increase of the plasma density. Importantly, the presence of excited state species even further enhances the plasma density via excited state neutral and resonant state photon-induced SEE on the electrode surface. The PIC/MCC simulation results show good agreement with the recent experimental measurements in the low pressure range (1–10 Pa) that is commonly used for etching in the semiconductor industry. At the highest pressure (20 Pa) and driving voltage amplitudes 250 and 350 V explored here, the plasma densities from PIC/MCC simulations considering excited state neutrals and resonant photon-induced SEE are quantitatively higher than observed in the experiments, requiring further investigation on high pressure discharges.

Studies on plasma transport processes in the cathode sheath of atmospheric direct-current arc discharge with particle-in-cell and Monte Carlo collision simulation

A voltage-driven cathode sheath model in an atmospheric-pressure argon arc discharge is developed in the framework of an implicit particle-in-cell Monte Carlo collision (PIC–MCC) method. Plasma transport processes are solved numerically in one dimension without any local-equilibrium hypotheses, in particular, without explicitly dividing sheath and a quasi-neutral plasma region. The right boundary of the computational domain located at the pre-sheath is determined first by observing the variation in typical parameters. A comparison of results is given with different positions of the right boundary to study the plasma transport processes in the cathode sheath. Number densities, spatially averaged energies, electric field and potential, collision frequency, heating rate of electrons, as well as the spatially averaged electron energy probability function inside the sheath, are predicted self-consistently based on this newly developed kinetic model. It is shown that both excitation collisions and ionization collisions occur inside the sheath, and collision frequency of the former is larger than the latter. The collision frequency of charge exchange is higher than that of elastic collision for ions. In addition, the effects of different electron emission processes are described. It is indicated that the thermionic emission on the hot cathode surface is not the only significant emission mechanism to sustain the arc discharges.

Control of ion flux-energy distribution at dielectric wafer surfaces by low frequency tailored voltage waveforms in capacitively coupled plasmas

Capacitively coupled plasmas are routinely used in an increasing number of technological applications, where a precise control of the flux and energy distribution of ions impacting boundary surfaces is required. In the presence of dielectric wafers and targets the accumulation of charges on these surfaces can significantly alter the time evolution of the sheath electric field that is accountable for ion acceleration from the plasma bulk to the surfaces and, thus, lead to parasitic distortions of process relevant ion flux-energy distributions. We apply particle in cell with Monte Carlo collisions simulations to provide insights into the operation, ion acceleration mechanisms, and the formation of such distributions at dielectric wafers for discharges in argon gas. The discharges are driven by a combination of a single high frequency (HF) (27.1 MHz) voltage signal and a low frequency (LF) (100 kHz) customized pulsed voltage waveform. The LF waveform includes a base square signal to realize narrow and controllable high energy peaks of the ion distribution, and steady-slope ramp voltage components. We discuss the distorting effect of dielectric surface charging on the ion flux-energy distribution and provide details about how the voltage ramps can restore its narrow peaked shape. The dependence of the surface charging properties on the LF pulse duty cycle and amplitude, as well as the HF voltage amplitude is revealed. The radial homogeneity of the ion flux is found to be maintained within % around the mean value for all quantities investigated. The radial electric field developing at the edge of the dielectric wafer with finite width has only a small influence on the overall homogeneity of the plasma across the whole surface, its effect remains localized to the outermost few mm of the wafer.

Effects of macroparticle weighting in axisymmetric particle-in-cell Monte Carlo collision simulations

In this paper, the effects of macroparticle (MP) weighting on the plasma discharge, particularly near the centerline, are investigated using a two-dimensional axisymmetric particle-in-cell Monte Carlo collision (PIC/MCC) model. A variable MP weight according to the radial position of the MPs is employed to maintain sufficient number of MPs near the centerline of the plasma source. The plasma density obtained from the PIC/MCC simulations for low-pressure (25–100 mTorr) capacitively coupled plasmas is found to be artificially large when the MP weight near the centerline is not well resolved, demonstrating the need for particle convergence studies for axisymmetric PIC/MCC simulations.

Guiding effect of runaway electrons in atmospheric pressure nanosecond pulsed discharge: mode transition from diffuse discharge to streamer

In this study, the role of runaway electrons (RAEs) during the pulsed breakdown in the atmosphere is investigated. Nanosecond pulsed discharge (NPD) is driven by high-voltage pulses between blade-to-plate electrodes (with the blade as the cathode). RAEs with an energy higher than 10 keV are selected by a titanium foil with a thickness of 1 μm and detected by a beam collector with a front of about 50 ps. The temporal-spatial evolution of the electric field over the NPD period is measured using electric field induced second harmonic method adopting a picosecond pulsed laser. It is verified that the current amplitude of RAEs decreases drastically with the voltage amplitude V p and the peak electric field at the front of the ionization wave formed during the breakdown of NPD plays a key role in maintaining the runaway state of electrons. With single-shot discharge imaging, it is observed that the discharge is initially in a diffuse mode near the cathode, while it branches and transits into streamers, which can be either synchronously propagating multi streamers (with a high V p) or certain dominant streamers (with a low V p). Using particle-in-cell Monte-Carlo collision simulation, a similar mode transition of diffuse to streamer is observed with RAEs emitted from the cathode and it is illustrated that the flux of RAEs controls the pre-ionization degree and further dictates branching and non-uniformity of discharge, which qualitatively explains the experimental observation. It is proposed that an enhanced RAEs emission would produce a large volume diffuse discharge at atmospheric pressure.

Particle Simulation of Positive Streamer Discharges on Surface of DC Transmission Conductors With Coating Materials

Streamer discharges occurring on bare and coated conductors are investigated, respectively, by means of 2-D particle-in-cell (PIC)/Monte Carlo collision simulations. The evolutions of streamer discharges and the involved electric fields, electron densities, and propagation velocities have been demonstrated. The electron energy probability functions (EEPFs) reveal the nonequilibrium properties of streamer plasmas. Moreover, the effects of relative permittivity, the thickness of coating layers, and the presence of protrusions upon the formation of streamer discharges have been studied. It is shown that streamer discharges can be inhibited effectively by the application of coating materials, which have the largest effect on the initial stage of the discharge. The electron density, electric field strength, and propagation velocity of the streamers can be reduced significantly. The results provide insights into fundamental physics governing the streamer discharge and may find promising applications in the protection of direct current transmission lines.

A plasma loss to sidewall model for 1D PIC/MCC simulation for plasma transport estimation

A plasma loss to sidewall model is used for one-dimensional (1D) particle-in-cell (PIC) with Monte Carlo collision (MCC) simulation to calculate plasma transport through a transverse magnetic field in a negative ion source chamber. The presented 1D model includes plasma radial loss treatment when calculating the plasma transport in the axial direction. It does not cost computation effort as much as a 2D or 3D model and can be used to estimate the plasma transport process quickly. The conventional 1D kinetic model calculates particle motion only in the ‘x’-direction. The sidewall loss in the ‘y’ ‘z’ direction is not included, leading to unusual plasma distribution. Especially when applying a transverse magnetic field, the motion and loss of electrons along the magnetic field line to the sidewall are ignored. Thus electrons are completely constrained by the magnetic field, resulting in abnormal plasma density accumulation. The sidewall loss estimation method uses Bohm velocity calculated from plasma parameters as radial loss velocity to obtain the plasma flux to the sidewall. And the sidewall loss rate can be obtained from the flux combined with chamber geometry. This method is integrated into a self-developed 1D PIC–MCC program to examine its effect. Several verification cases are performed separately for the PIC, MCC, and the sidewall loss treatment module, and the results exhibit good reliability. Simulations are then carried out to study plasma transport across the magnetic field under similar conditions to actual experiments. Simulation results agree with the experiment, which indicates that the 1D sidewall loss model is useful when dealing with plasma transport in the source chamber.

Effect of photoionisation on initial discharge in air under nanosecond pulse voltage

AbstractEffects of photoionisation on the development and electron runaway of the initial discharge in atmospheric air under nanosecond pulse voltage were studied via two‐dimensional particle‐in‐cell/Monte Carlo collision simulations. It was found that photoionisation has little effect at the beginning of the initial discharge. However, as the discharge channel gradually develops towards the anode, photoionisation shows greater impacts on the morphology of discharge but has little influence on the velocity of discharge development. Photoionisation does not appear to have a decisive effect on the growth trend of the highest energy of runaway electrons, but it does affect the change rate of the highest energy and overall distribution of electron energy, resulting in a higher proportion of energetic electrons. The difference in the distributions of the electron energy between the two cases, with and without considering photoionisation, can be attributed to the impact of photoionisation on the discharge morphology, which in turn distorted the electric field. The spatial density distributions of the electrons produced by photoionisation further explained the differences. The authors’ results explicitly demonstrate the influence of photoionisation on the development and the electron runaway of the initial discharge under nanosecond pulse voltage, which provides more comprehensive knowledge for the atmospheric air gap nanosecond pulse discharge physics.

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.

Influence of temporal variations in plasma conditions on the electric potential near self-organized dust chains

Self-organization of dust grains into stable filamentary dust structures (or “chains”) largely depends on dynamic interactions between individual charged dust grains and complex electric potential arising from the distribution of charges within a local plasma environment. Recent studies have shown that the positive column of the gas discharge plasma in the Plasmakristall-4 (PK-4) experiment at the International Space Station supports the presence of fast-moving ionization waves, which lead to variations of plasma parameters by up to an order of magnitude from the average background values. The highly variable environment resulting from ionization waves may have interesting implications for the dynamics and self-organization of dust particles, particularly concerning the formation and stability of dust chains. Here, we investigate the electric potential surrounding dust chains in the PK-4 experiment by employing a molecular dynamics model of the dust and ions with boundary conditions supplied by a particle-in-cell with Monte Carlo collision simulation of the ionization waves. The model is used to examine the effects of the plasma conditions within different regions of the ionization wave and compare the resulting dust structure to that obtained by employing the time-averaged plasma conditions. The comparison between simulated dust chains and experimental data from the PK-4 experiment shows that the time-averaged plasma conditions do not accurately reproduce observed results for dust behavior, indicating that more careful treatment of plasma conditions in the presence of ionization waves is required. It is further shown that commonly used analytic forms of the electric potential do not accurately describe the electric potential near charged dust grains under these plasma conditions.

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.

Benchmarked and upgraded particle-in-cell simulations of a capacitive argon discharge at intermediate pressure: the role of metastable atoms

The capacitive argon discharge operated in the intermediate pressure regime is studied by performing one-dimensional particle-in-cell Monte Carlo collision simulations. First, the basic object-oriented plasma device code (oopd1-v1) is strictly benchmarked against the well-established xpdp1 code over a wide range of pressure (0.05–15 Torr) and varying blocking capacitor of the external circuit (5–105 nF), and excellent agreement is obtained. The oopd1-v1 is upgraded to oopd1-v2 and oopd1-v3, by adding excited atoms modeled as time- and space-evolving fluid species. The metastable Arm, the radiative Arr, and the Ar(4p) manifold, and their roles in discharge equilibrium are explored. It is found that the presence of the metastable Arm enhances the plasma density by a factor of 3 at 1.6 Torr and even higher at pressures up to 5 Torr. At low pressure (0.05 Torr), electron impact ionization from the ground state atom dominates the ionization over the whole discharge region, while metastable pooling and step-wise ionization has small contribution. The proportion of metastable pooling ionization and step-wise ionization increases with increasing pressure and becomes the dominant ionization source at 5–15 Torr.

Direct evidence of gradient drift instability being the origin of a rotating spoke in a crossed field plasma

A plasma rotating spoke in a crossed field discharge is studied using 2D radial-azimuthal fully kinetic particle-in-cell Monte Carlo collision simulations. The kinetic model reveals the whole perturbation spectrum of the gradient drift instability in the linear stage: Simon–Hoh, lower hybrid, and ion sound modes, providing direct evidence of the spoke of gradient drift instability nature. The two-fluid dispersion relation of gradient drift instability was utilized to analyze the linear development of instabilities in the simulations. The charge separation effect was incorporated in the fluid linear theory and a super-resolution signal processing method (multiple signal classification) was applied to obtain the numerical frequency spectrum. The simulated spectrum and growth rate show excellent agreement with the theoretical dispersion relation (real frequency and imaginary frequency) in the investigated cases. The most linearly unstable mode was found to be the lower hybrid instability and the mode transition into the m = 1 macroscopic rotating structure after saturation of the linear phase is accompanied by an inverse energy cascade. In the nonlinear stage, pronounced spoke phenomena can occur when the heating of E θ × B electron flow channeled in the spoke front passage suffices to provide enhanced ionization.

Restructuring of rotating spokes in response to changes in the radial electric field and the neutral pressure of a cylindrical magnetron plasma

Nonlinear plasma structures in the partially magnetized E×B plasma of a cylindrical magnetron are investigated using 2D3V particle-in-cell Monte Carlo collision simulations. In the early phase of the discharge, plasma gradients and radial electric fields excite a lower hybrid type instability that forms long wavelength rotating density spokes. As the discharge grows in density by ionization and the cathode gets shielded by the formation of an ion sheath, radial electric fields diminish in the quasineutral region of the discharge. This induces a transition of the spokes into short-scale spoke-on-spoke modes. The short wavelength structures can be reversed back into a long spiral spoke by lowering the neutral pressure, which revives the radial electric fields via a turbulent plasma expansion. Plasma phenomena connected to the rotating spoke include the anomalous radial transport and loss of electrons through the spoke, azimuthal dragging of ions by the spoke’s field, plasma temperature modulations by the spoke structure, and formation of electron vortices around equipotential islands, in some cases with opposing rotations to the underlying E×B drift. Electron scattering from non-ionizing collisions with neutrals also has a minor influence on the instability.

Electron power absorption in radio frequency driven capacitively coupled chlorine discharge

Particle-in-cell Monte Carlo collision simulations and Boltzmann term analysis are applied to study the origination and properties of the electric field and the electron power absorption within the electronegative core of a capacitively coupled discharge in chlorine as the pressure is varied from 1 to 50 Pa. The capacitively coupled chlorine discharge exhibits high electronegativity and high electric field develops within the electronegative core. It is found that the electron power absorption increases and the ion power absorption decreases as the pressure is increased. At 1 Pa the electron power absorption is due to both the pressure and ohmic terms. At the higher pressures >10 Pa the ohmic term dominates and all the other contributions to the electron power absorption become negligible. Therefore, the discharge becomes increasingly ohmic with increased pressure and eventually behaves as a resistive load.

The formation mechanism of nonuniformity from 2D nonlocal particle-dynamics in capacitive RF discharges

Kinetic effects and nonlinear characteristics caused by multi-dimensional effects in capacitively coupled plasma (CCP) devices are reported using particle-in-cell (PIC) Monte-Carlo collision simulations. Many PIC simulations so far are limited to one-dimensional (1D) dynamics due to computational load, and the nonuniformity occurring in a direction parallel to the electrode cannot be reflected consequently. A two-dimensional (2D) PIC–MCC simulation based on a graphics processing unit is utilized to observe the variations in the spatial distribution that cannot be dealt with by 1D simulations. This simulation considers the pressure regime of the nonlocal electron kinetics. Contrary to the expectation that motions in the vertical direction to the electrode in a CCP dominate most of the particle dynamics, it was observed that electron heating in the horizontal direction around the electrode edge plays an important role. Accordingly, the change in the spatial distribution between the center of the CCP equipment and the peripheral region of the electrode edge has been analyzed by phase-resolved electron flux and power deposition to understand the principle of the formation of spatial nonuniformity.

Effects of electron spatial inertia and magnetic field gradient on transport across magnetic filter

This work investigates, via particle-in-cell with Monte Carlo collision simulations, electron transport across magnetic filter (MF) in obstructed-drift plasma sources. The studied source consists of three stages, namely: the ionization stage where power is coupled to the plasma, the magnetic filter stage where the magnetic field strength is maximal and impedes electron transport, and the diffusion stage where most of the charged particles come from the first stage. The plasma source is schematized by a square whose walls (sides) are dielectric, except for the wall at the exhaust plane which is metallic and simulates a biased screen grid. As expected, our results show that as the plasma passes through the MF, electron density and temperature decrease. The electron flux and fluid velocity spatial distributions present an S-shaped path through which these plasma properties are significant. These high flux and fluid velocity are due to the superimposition of E×B and diamagnetic drifts that are enhanced by the walls. Moreover, at the entrance and exhaust of this S-shaped path, i.e., in the vicinity of the walls, the magnitude of the spatial inertia is significant in comparison to acceleration induced by an electric field and pressure gradient. The analytical analysis of this inertia shows that its magnitude and direction are mainly controlled by the gradients of the electric field, pressure force, electron density, and magnetic field strength. Therefore, the control of the spatial inertia, and thus, of electron flux across the magnetic filter, can be achieved by controlling the spatial distribution of the magnetic field strength.