Two-dimensional Fluid Simulation Research Articles

The role of fast electrons in diffuse discharge formation: Monte Carlo simulation

In this paper, we report on results from a computational investigation of nanosecond pulsed discharges in air of negative polarity using a two-dimensional fluid and fluid-Monte Carlo simulations. The computational parameters and conditions are taken from an experiment. The discharge is initiated near the cathode having a small radius of curvature and propagates towards the flat anode. The simulations are done in atmospheric pressure air with a nanosecond pulse of 120 kV amplitude in a 12 mm gap with a sharp cathode. The essential difference between discharges initiated by low- and high-energy beams of electrons originating in the vicinity of the cathode was observed. The beam of electrons with the initial energy of 20 keV was shown to result in a diffuse discharge, while the 20 eV beam had a negligible influence on the discharge evolution. By analyzing the experimental and computational results, we conclude that a diffuse discharge is formed due to fast electrons without any assumptions on the critical role of the runaway electrons. More study is required to explore the intermediate range of energies and investigate the transition to the diffuse mode of the discharge.

Two-dimensional fluid simulation on transient behavior and plasma uniformity in pulsed RF CCP sustained in SiH4 /N2/O2

Improving plasma uniformity during plasma processing in the microelectronics industry is of critical importance to the quality of etching or deposition. Compared to continuous wave (CW) plasmas, pulsed plasmas have drawn much attention with the introduction of additional pulse parameters, which would be helpful to improve the plasma properties. In this paper, a two-dimensional fluid model is developed to investigate a pulsed radio-frequency capacitively coupled plasma (CCP) sustained in SiH4/N2/O2 mixture at fixed operating conditions of 70V rf power, 300 mTorr (40 Pa) gas pressure and an SiH4/N2/O2 gas ratio of 2.5/92.5/5. First, we study the temporal dynamics of densities of the electron, positive ion and negative ion, at different positions in the pulsed CCP. Under the operation conditions, charged particles, instead of neutral particles, may basically respond to the applied modulated power. The electron density in the bulk could approach a quasi-steady value by the end of the activeglow. However, the achievement of a quasi-steady state of plasma like that in the CW condition not only depends on enough activeglow time of the pulse discharge but also relies on the observed position in the discharge. In addition, we investigate the impact of pulse parameters on plasma characteristics, showing that the radial inhomogeneity of plasma caused by the edge effect can be effectively suppressed by controlling the duty cycle (DC) rather than the pulse repetition frequency (PRF). Improvement of the plasma uniformity in pulsed discharge is due to the competition between the edge effects during the activeglow and diffusion of charged species during the afterglow. Moreover, the electron density undergoes a local minimum value in the temporal profile before it rises sharply beyond that of CW discharge, since production of electrons is less than loss by the spatial movement at the very beginning of one pulse. Also, there appears to be a peak value of ion bombardment energy at the beginning of power, which may damage the wafer in actual industrial processes. At a certain DC, this peak may be flattened to a certain degree by adjusting the PRF.

Fluid versus global model approach for the modeling of active species production by streamer discharge

In this paper, we seek to validate the zero-dimensional (global) model approach for the modeling of the plasma composition in high pressure reactive streamer discharges. We focus on streamers typical of dielectric barrier discharge that are widely used, for instance, for plasma-assisted reforming of greenhouse gases. However, our conclusions can be extended to the streamers used in plasma-assisted ignition/combustion and other related systems. First, we perform two-dimensional fluid simulations for streamers with positive and negative trigger voltages and analyze the difference between the breakdown mechanisms of these two modes. Second, we use the time evolution of the electron heating term obtained from the fluid simulations as the input parameter of the global model and compare the plasma component content predicted by this model with the results of the fluid model. We obtain a very good agreement between fluid and global models for all species generated in plasma. However, we conclude that streamers initiated by the positive and negative trigger voltage cannot be considered as symmetrical which is usually done in global models of barrier discharge reactors.

Numerical analysis of the effect of electrode spacing on deposition rate profiles in a capacitively coupled plasma reactor

The effect of reactor dimension on deposition rate profiles is analyzed with a two-dimensional (2D) fluid simulation of a capacitively coupled plasma (CCP) reactor to deposit a hydrogenated silicon nitride (SiNxHy) film with a SiH4/NH3/N2/He gas mixture. We focus on the complex function of electrode spacing to reveal the physical relation between reactor geometry and deposition rate profiles. The simulation demonstrates that the localization of electron density is concentrated close to the powered electrode periphery for electrode spacing of 9 mm. However, the plasma distribution becomes bulk dominated with electrode spacing of 15 mm by relaxing the localization. As a result, the increase in the electrode spacing creates a more uniform electron power density profile, and the deposition rate profile of SiNxHy film changes from convex to concave in a radial direction. The change in the deposition rate profile is validated through comparison with the experimental observation, which agrees well with the simulation results with errors of less than 5%. The deposition rate profile with electrode spacing of 9 mm is very sensitive to the non-uniform gas density condition applied to the showerhead inlet. However, the deposition rate profile with electrode spacing of 15 mm is not sensitive to the inlet gas profile because of the increasing residence time. The increase of the electrode spacing promotes molecule–molecule gas phase reactions and consequently weakens the effect of the inlet boundary condition.

Extended dielectric relaxation scheme for fluid transport simulations of high density plasma discharges

In order to overcome limitations on the simulation time step for fluid transport simulations of high density plasma discharges, the dielectric relaxation scheme (DRS) was developed. By imitating a realistic and physical shielding process of electric field perturbation, DRS overcomes the dielectric limitation on simulation time step. However, the electric field was obtained by assuming the drift-diffusion approximation for both the electrons and ions. Although the drift-diffusion expressions are good approximations, the inertial term cannot be neglected in the ion momentum equation for low pressure. Therefore, in this work, we developed the extended dielectric relaxation scheme (EDRS) by introducing an effective electric field. Similar to DRS, EDRS is limited to quasi-neutral plasma with zero current, i.e. EDRS is applicable when the local ambipolarity is satisfied. In order to validate EDRS, two-dimensional fluid simulations for inductively coupled plasma discharges were performed. The simulation results are then compared with experimental measurements by using a Langmuir probe.

Control of the Nano-Particle Weight Ratio in Stainless Steel Micro and Nano Powders by Radio Frequency Plasma Treatment

This study describes how to make stainless steel hybrid micro-nano-powders (a mixture of micro-powder and nano-powder) using an in situ one-step process via radio frequency (RF) thermal plasma treatment. Nano-particles attached to micro-powders were successfully prepared by RF thermal plasma treatment of stainless steel powder with an average size of 35 μm. The ratio of nano-powders is estimated with a two-dimensional fluid simulation that calculates the temperature profile influencing the rate of surface evaporation. The simulation is conducted to determine the variation of the input power and the distance from the plasma torch to the feeding nozzle. It was demonstrated experimentally that the nano-powder ratio in the micro-nano-powder mixture can be controlled by adjusting the feeding rate, plasma power, feeding position and quenching effect during plasma treatment. The ratio of nano-particles in the micro-nano-powder mixture was controlled in a range from 0.1 (wt. %) to 30.7 (wt. %).

2D fluid simulation of capacitively coupled plasma with cylindrical electrode for roll-to-roll processing

RF glow discharges are widely used in deposition, etching and surface treatments for semiconductor materials. Especially, roll-to-roll processing is necessary for flexible display or thin film solar cell modules. For a roll-to-roll thin film deposition processing, it is necessary to use cylindrical grounded electrode. The effects of electrode shapes on the plasma properties of capacitively coupled rf argon discharge at 13.56 MHz are investigated using self-consistent two-dimensional fluid simulation. The simulation model includes blocking capacitor and external circuit effects. Comprehensive analysis has been made in terms of time-varying current–voltage characteristic, spatial distributions of plasma density and ion current density on the substrate. The effects of applied voltage (Vf=200∼800[V]) and gas pressure (p=0.5 ∼ 2 Torr) on the plasma properties are also investigated. We found that flat electrode has a little bit higher impedance than that of cylindrical ground electrode. However the difference between the two configurations is less than 5% therefore we may conclude that the shape of grounded electrode does not significantly affect current–voltage characteristics of the discharge system. For roll-to-roll reactor version, displacement current come from dielectric layer between electrodes reaches more than 75% of total displacement current. Large displacement current results in degradation of power factor and matching circuit efficiency. For the cylindrical electrode, increasing electrode gap length along lateral direction makes that the location of peak electron density moves toward center of the reactor. The effect of the cylindrical electrode on the plasma spatial structure is reflected in the ion current density at substrate (dielectric layer) on grounded electrode. At low voltage and low power condition, about 90% of input power is consumed for electron heating. The efficiency decreases with increasing power and decreasing pressure as a consequence of increasing power to drive ion current. Electron heating efficiency decreased with pressure. The increase of pressure mainly reduces the diffusive component of the loss rate for both charged and neutral species.

Fast magnetic reconnection due to anisotropic electron pressure

A new regime of fast magnetic reconnection with an out-of-plane (guide) magnetic field is reported in which the key role is played by an electron pressure anisotropy described by the Chew-Goldberger-Low gyrotropic equations of state in the generalized Ohm's law, which even dominates the Hall term. A description of the physical cause of this behavior is provided and two-dimensional fluid simulations are used to confirm the results. The electron pressure anisotropy causes the out-of-plane magnetic field to develop a quadrupole structure of opposite polarity to the Hall magnetic field and gives rise to dispersive waves. In addition to being important for understanding what causes reconnection to be fast, this mechanism should dominate in plasmas with low plasma beta and a high in-plane plasma beta with electron temperature comparable to or larger than ion temperature, so it could be relevant in the solar wind and some tokamaks.

An immersed boundary-lattice Boltzmann flux solver and its applications to fluid–structure interaction problems

An immersed boundary-lattice Boltzmann flux solver (IB–LBFS) for the simulation of two-dimensional fluid–structure interaction (FSI) problems is presented in this paper. The IB–LBFS applies the fractional-step method to split the overall solution process into the predictor step and the corrector step. In the predictor step, the intermediate flow field is predicted by applying the LBFS (lattice Boltzmann flux solver) without considering the presence of immersed object. The LBFS applies the finite volume method to solve N–S (Navier–Stokes) equations for the flow variables at cell centers. At each cell interface, the LBFS evaluates its viscous and inviscid fluxes simultaneously through local reconstruction of the LBE (lattice Boltzmann equation) solutions. In the corrector step, the intermediate flow field is corrected by the implicit boundary condition-enforced immersed boundary method (IBM) so that the no-slip boundary conditions can be accurately satisfied. The IB–LBFS effectively combines the advantages of the LBFS in solving the flow field and the flexibility of the IBM in dealing with boundary conditions. Consequently, the IB–LBFS presents a much simpler and more effective approach for simulating complex FSI problems on non-uniform grids. Several test cases, including flows past one and two cylinders with prescribed motions, are firstly simulated to examine the accuracy of present solver. After that, two strongly coupled fluid–structure interaction problems, i.e., particle sedimentations and vortex-induced vibrations of a circular cylinder are investigated. Good agreements between the present results and those in literature verify the capability and flexibility of IB–LBFS for simulating FSI problems.

2-D simulation of dual frequency capacitively coupled helium plasma, using COMSOL multiphysics

A two-dimensional (2D) self-consistent fluid simulation of dual frequency capacitively coupled radio discharges of helium plasma is presented. The model solves the continuity equations for charged species and the electron energy balance equation, coupled with Poisson's equation by finite element method, using COMSOL Multiphysics software. In this study, the low frequency (LF) is set to 13.56 MHz with low frequency voltage of 250 V and the high frequency (HF) is set to 54.24 MHz with high frequency voltage of 100 V. The simulations yield the two-dimensional profiles of plasma components as well as the charge densities, electric field, electron temperature and ionization rate between symmetric parallel plate electrodes. The effects of low and high frequency sources parameters such as frequency values and applied voltage amplitude on the discharge characteristics are investigated. It is shown that the increase of the HF frequency causes a moderate increase of electron temperature and plasma density, whereas, the increase of the LF potential produced an increase in the plasma potential, the voltage of the sheath and the ion energy.

Analysis on Nonspherical Oscillation of Microbubble with Two-Dimensional Numerical Fluid Simulation

Recently, ultrasound contrast imaging has been improved greatly, because its application of an approach for therapy is urgently required for area of the heart and abdominal. Sonoporation is also one of the applications using microbubbles that attracts attention in the world. There have been so many studies for understanding the mechanism of sonoporation and improving efficiency of ultrasound contrast agents. Nonspherical oscillation is at a stage before the breakup process of microbubbles. Therefore, consideration of a microbubble's nonspherical oscillation is absolutely imperative for its future development. Thus in this thesis, the author regarded microbubbles as two dimensional air-liquid two-phase flow and calculated their dynamics by using Computational Fluid Dynamics (CFD). Numerical calculation of a microbubble's oscillation and deformation was also carried out, for an air bubble and for a shell-coated bubble in ultrasound field. As a result, it was confirmed that the CFD method developed in this study can be useful for analyzing an insonified microbubble showing nonspherical oscillation.

Two-dimensional numerical study of a period-two dielectric-barrier discharge in atmospheric argon

A two-dimensional fluid simulation is performed on an atmospheric dielectric barrier discharge (DBD) in pure argon to explore the formation mechanism and spatiotemporal evolution of period-two DBD at atmospheric pressure. The results show that the formation of the period-two discharge is directly correlated to the spatial distribution of electron density. It is found that when under certain conditions, a local high electron density region occurs before a new discharge is ignited, and the discharge current varies in magnitude depending on whereabouts of the local high electron density region. When the local high electron density region appears near the momentary anode, it barely affects the discharge current. In contrast, when the high electron density region appears in the vicinity of the cathode, it reduces the discharge current greatly, since it restrains the growth of the electric field. The local high electron density region disappears completely before the two voltage cycles end, and thus the discharge exhibits the appearance of period-two state. The radial current and electron density distributions at different times indicate that different discharge events within one oscillation period of period-two discharge possess different radial behaviors. The causes for these radial behaviors are further analyzed and discussed in this paper.

The effect of electrode tilt angle on the characteristics of coplanar dielectric barrier discharges with Xe-Ne mixtures

The results of a two-dimensional fluid simulation of a plasma display panel (PDP) cell show that the discharge characteristics of a coplanar dielectric barrier discharge can be controlled by the electrode tilt angle rather than by the gas mixture ratio or gap distance. The change in the tilt angle results in a significant change in the wall charge distribution and the discharge duration for each pulse. Therefore, the breakdown voltage, plasma density, light brightness, and luminous efficacy can be controlled by the tilt angle. A concave electrode structure allows large wall charge accumulation near the outer edge of two coplanar electrodes, and it results in a long-duration discharge, high luminance, and high luminous efficacy. On the other hand, a convex electrode structure allows high wall charge accumulation near the gap between two coplanar electrodes, and it results in a short-duration discharge with a decreased breakdown voltage.

Modelling of dielectric barrier discharge plasma actuators with thick electrodes

We have developed a new two-dimensional fluid simulation to model the plasma dynamics in surface dielectric barrier discharges operating in air. Single-barrier (one electrode insulated) and double-barrier (both electrodes insulated) discharges have been observed to generate a force in the nearby air, making them potentially useful as aerodynamic actuators. Many previous simulations of such discharges have modelled the electrodes as thin strips. We instead consider plasma actuators including cylindrical electrodes of various sizes. In single-barrier actuators, the size of the exposed electrode qualitatively affects the discharge dynamics, particularly with a negative-going applied voltage. For both geometries, the simulations predict the formation of plasma structures similar to those imaged in previous experiments. Experimentally observed increases in forces for actuators with smaller high-voltage electrodes were only reproduced for the single-barrier geometry. Due to limitations of computational power, voltage rates of change for all simulations were higher than those used in experiments.

The super X divertor (SXD) and a compact fusion neutron source (CFNS)

A new magnetic geometry, the super X divertor (SXD), is invented to solve severe heat exhaust problems in high power density fusion plasmas. SXD divertor plates are moved to the largest major radii inside the TF coils, increasing the wetted area by 2–3 and the line length by 2–5. Two-dimensional fluid simulations with SOLPS (Schneider et al 2006 SOLPS 2-D edge calculation code Contrib. Plasma Phys. 46) show a several-fold decrease in divertor heat flux and plasma temperature at the plate. A small high power density tokamak using SXD is proposed, for either (1) useful fusion applications using conservative physics, such as a component test facility (CTF) or fission–fusion hybrid, or (2) to develop more advanced physics modes for a pure fusion reactor in an integrated fusion environment.

The effects of permittivity and thickness of dielectric layers on micro dielectric barrier discharges

The discharge characteristics of a plasma display panel (PDP) cell are investigated by two-dimensional fluid simulation and experiment in order to analyze the effects of permittivity and thickness of dielectric layers. Four-inch test panels having the same cell size as a 50-inch FHD (full high definition) resolution were fabricated to measure static margin, luminance, power consumption, and luminous efficacy. As the dielectric permittivity decreases and the dielectric thickness increases, firing voltage increases, but luminous efficacy increases due to the decreases of power consumption. It was observed that the luminous efficacy increases by 30% in the case of relative permittivity ε r = 7 and dielectric thickness d = 25 µm compared with the case of ε r = 12 and d = 35 µm.

Transport scaling in interchange-driven toroidal plasmas

Two-dimensional fluid simulations of a simple magnetized torus are presented, in which the vertical and toroidal components of the magnetic field create helicoidal field lines that terminate on the upper and lower walls of the plasma chamber. The simulations self-consistently evolve the full radial profiles of the electric potential, density, and electron temperature in the presence of three competing effects: the cross-field turbulent transport driven by the interchange instability, parallel losses to the upper and lower walls, and the input of particles and heat by external plasma sources. Considering parameter regimes in which equilibrium E×B shear flow effects are weak, we study the dependence of the plasma profiles—in particular the pressure profile scale length—on the parameters of the system. Analytical scalings are obtained that show remarkable agreement with the simulations.

Enhancement of Optical Emission by Floating Electrodes in a Planar Microdischarge Cell

As the volume of a discharge cell is downsized, its optical emission intensity generally decreases owing to the increase in the loss of charged particles on the surfaces. To improve the emission intensity, in this paper, a new planar cell structure with floating electrodes inside a microdischarge cell is proposed in a dielectric barrier discharge (DBD) scheme. The spatiotemporal behavior was observed using an intensified charge-coupled device (ICCD) camera, and a twofold higher intensity enhancement all over the cell, especially around the floating electrodes, was obtained at most as compared with that of a simple structure without the floating electrodes. For the analysis of the discharge phenomena, a two-dimensional fluid simulation was performed, and the calculated results were in close agreement with those of the experimental data. Thus, the mechanism of the enhancement was attributed to the concentrated electric field around the floating electrodes owing to the electric charge accumulated during the preceding half-cycle of the discharge.

Study on target structure for direct–indirect hybrid implosion mode in heavy ion inertial fusion

The key issues in heavy ion beam (HIB) inertial confinement fusion (ICF) include particle accelerator, physics of intense beam, beam final transport, target-plasma hydrodynamics, etc. In this paper, we focus on fuel implosion. In order to realize an effective implosion, beam illumination non-uniformity on a fuel target must be suppressed less than a few percent. In this study a direct–indirect hybrid implosion mode is discussed in heavy ion beam inertial confinement fusion (HIF) in order to release sufficient fusion energy in a robust manner. In the direct–indirect hybrid mode target, a low-density foam layer is inserted, and the radiation energy is confined in the foam layer. In the foam layer, the radiation transport is expected to smoothen the HIB illumination non-uniformity in the lateral direction. In this paper, we study the influences of the foam thickness and the inner radiation-shield Al density on implosion uniformity. Two-dimensional fluid simulations demonstrate that the hybrid target contributes to the HIB non-uniformity smoothing and releases a sufficient fusion energy output in HIF.

Microdischarge propagation and expansion in a surface dielectric barrier discharge

We have recorded light emission from a surface dielectric barrier discharge with one exposed and one insulated electrode using an intensified digital camera. The discharge was operated in atmospheric pressure air. When the voltage to the exposed electrode is increasing, streamers form and propagate away from the exposed electrode in tens of nanoseconds. When the voltage is decreasing, more diffuse microdischarges form in a few nanoseconds. The qualitative behaviors of the plasma agree well with two-dimensional fluid simulations. Expansion in the average length of microdischarges as the applied voltage changes in both half-cycles of the waveform is also observed.