2D Fluid Model Research Articles

Numerical investigation of trichel pulse of negative corona discharge in N2–O2 mixture

Trichel pulse of negative corona discharge in atmospheric air is investigated numerically using a 2D fluid model. The model consists of a hyperbolic cathode tip and a plane anode, and considers 11 kinds of particles and the most important interactions among them. The spatio-temporal evolution of charged species and the electric field are evaluated during the pulse process. During the pulse rising edge, the positive ions accumulate ahead of the tip forming the temporal cathode sheath, significantly enhancing the local field. In the pulse decay edge, the temporal sheath collapses and the discharge falls back to a low-current mode. In the pulse interval, the discharge does not cease but sustains weakly until the next pulse. The location of the temporal sheath is independent of the averaged value during the Trichel pulse regime and also the same with that in a normal glow regime, which determines a nearly constant pulse rising time at given configurations. However, a smaller tip radius will lead to their decrease. The effect of negative ions on the pulse process is studied by adjusting the attachment rates. It indicates that the negative ions are actually not necessary in the Trichel pulse process, but will influence the pulse waveform significantly.

Effect of driving frequency on electron heating in capacitively coupled RF argon glow discharges at low pressure**Project supported by the National Natural Science Foundation of China (Grant No. 51172101).

A one-dimensional (1D) fluid model on capacitively coupled radio frequency (RF) argon glow discharge between parallel-plates electrodes at low pressure is established to test the effect of the driving frequency on electron heating. The model is solved numerically by a finite difference method. The numerical results show that the discharge process may be divided into three stages: the growing rapidly stage, the growing slowly stage, and the steady stage. In the steady stage, the maximal electron density increases as the driving frequency increases. The results show that the discharge region has three parts: the powered electrode sheath region, the bulk plasma region and the grounded electrode sheath region. In the growing rapidly stage (at 18 μs), the results of the cycle-averaged electric field, electron temperature, electron density, and electric potentials for the driving frequencies of 3.39, 6.78, 13.56, and 27.12 MHz are compared, respectively. Furthermore, the results of cycle-averaged electron pressure cooling, electron ohmic heating, electron heating, and electron energy loss for the driving frequencies of 3.39, 6.78, 13.56, and 27.12 MHz are discussed, respectively. It is also found that the effect of the cycle-averaged electron pressure cooling on the electrons is to “cool” the electrons; the effect of the electron ohmic heating on the electrons is always to “heat” the electrons; the effect of the cycle-averaged electron ohmic heating on the electrons is stronger than the effect of the cycle-averaged electron pressure cooling on the electrons in the discharge region except in the regions near the electrodes. Therefore, the effect of the cycle-averaged electron heating on the electrons is to “heat” the electrons in the discharge region except in the regions near the electrodes. However, in the regions near the electrodes, the effect of the cycle-averaged electron heating on the electron is to “cool” the electrons. Finally, the space distributions of the electron pressure cooling the electron ohmic heating and the electron heating at 1/4T, 2/4T, 3/4T, and 4/4T in one RF-cycle are presented and compared.

Numerical study on characteristics of radio-frequency discharge at atmospheric pressure in argon with small admixtures of oxygen

In this paper, a 1D fluid model is developed to study the characteristics of a discharge in argon with small admixtures of oxygen at atmospheric pressure. This model consists of a series of equations, including continuity equations for electrons, positive ions, negative ions and neutral particles, the energy equation, and the Poisson equation for electric potential. Special attention has been paid to the electron energy dissipation and the mechanisms of electron heating, while the admixture of oxygen is in the range of 0.1%–0.6%. It is found that when the oxygen-to-argon ratio grows, the discharge is obviously divided into three stages: electron growth, electron reduction and the electron remaining unchanged. Furthermore, the cycle-averaged electric field, electron temperature, electron Ohmic heating, electron collisionless heating, electron energy dissipation and the net electron production are also studied in detail, and when the oxygen-to-argon ratio is relatively larger (R = 0.6%), double value peaks of electron Ohmic heating appear in the sheath. According to the results of the numerical simulation, various oxygen-to-argon ratios result in different amounts of electron energy dissipation and electron heating.

Abstract A16: Using 3D tumor simulations to determine optimal therapeutic conditions for the cold atmospheric plasma device

Abstract It has been shown that cold atmospheric plasma (CAP) can selectively treat cancer cells while leaving healthy cells relatively unharmed through both in vitro and in vivo experiments. This plasma contains reactive oxygen and nitrogen species at room temperatures, which drives the selective ability of the plasma jet to cancer cells. The translation of this therapeutic into surgical application is being limited by knowledge of its mechanism and poorly-defined standards for optimal treatments. Previous research seeks to answer these questions, including studying the tunable effect of the jet and how external parameters affect treatment outcome. Time-dependent ROS generation rates near the tissue surface provided by plasma jet are studies in 2D fluid model simulation. A specific set of balance equations for chemical species for two types of mixtures He/air and Ar/air are developed. We study additional oxygen portions effect on the ROS production. These simulations will be used to provide boundary conditions for the CAP-tumor interactions. Two types of parameters have been defined in this study that have an affect on the outcome of CAP tumor therapy [1]: (1) CAP-specific parameters and (2) tumor-specific parameters. CAP-specific parameters include the number and type of species produced, the duration of treatment and size of the treatment area. Tumor-specific parameters include the cellular response to plasma, the growth-rate of the tumor and overall tumor geometry. A 3D tumor simulation was created that can model the effect of the CAP therapy on a hemispherical tumor, using agent-based simulation techniques. Both CAP-specific and tumor-specific parameters where varied in treatment simulations to define a set of standards for optima treatment outcomes. When varying CAP-specific parameters, it was determined that the concentration of plasma species used and the percentage of the tumor surface area treated has the greatest affect on tumor treatment outcome. Likewise, the location/angle of treatment seemed to have an affect on treatment outcome with respect to the geometry of the tumor. For tumor-specific parameters, the growth rate of the tumor seemed to not have an affect on the treatment outcome, while cellular chemical reactions that increased internal ROS of the cell decreased the treatment time. Likewise, cellular chemical reactions that decreased ROS of the cell increased the treatment time. Using computational simulations, a set of standards for optimal treatment conditions that describe both the tumor-specific and CAP-specific parameters has been elucidated. This work was partially supported by National Science Foundation, grant 1465061.

Experimental and Theoretical Optimization of Radio Frequency Hollow Cathode Discharge

In this paper, the electron density in radio frequency (RF) hollow cathode discharge (HCD) is investigated in experiments and in simulation based on two-dimensional (2D) fluid model. The role of hole diameter on plasma density in RF HCD have been explored at various gas pressures. It is found that the optimal hole size for maximum plasma density decreases along with the increase of gas pressure, which is confirmed by simulated results. The simulations reveal that the high plasma density is owing to the hollow cathode effect in the hollow cathode. It is obtained that the optimal hole diameter in RF HCD is approximately sum of twice thickness of plasma sheath and triple the electron-neutral mean free path.

Negative ion research at the Culham Centre for Fusion Energy (CCFE)

A summary of negative ion development work being presently undertaken at the Culham Centre for Fusion Energy is given. The small negative ion facility has an RF driven volume ion source with beam extraction at energies up to 30 keV. The extracted beam of H− ions has an associated co-extracted electron beam with an electron to ion ratio of <1 over the whole range of operating parameters. In order to understand this performance spectroscopic investigations have been undertaken using the Balmer series line to determine the electron temperature. In addition a 1D fluid model of an RF driven ion source is also under development. This model is based on a successful model for both arc discharge positive and negative ion sources. Additional system studies of neutral beam injection systems for future fusion machines beyond ITER are being carried out. This is required to understand the limits of various neutralisation and energy recovery systems in order to maximise overall electrical efficiency.

Electron heating and particle fluxes in dual frequency atmospheric-pressure helium capacitive discharge

In this letter, a 1D fluid model has been used to study the electron heating and particle transport in dual frequency atmospheric-pressure helium capacitive discharge with a high-frequency (HF) voltage of 10 MHz and a low-frequency (LF) voltage of 1 MHz. The electric field is decoupled to three components: the HF, the LF and the direct current (DC) ones, and they have much different effects on the plasmas. The eletrons in plasma bulk are mainly heated by the HF electric field, while in plasma sheath they are heated and cooled by the LF and DC electric fields, respectively. With a fixed total input power, the increase of LF power leads to great enhancement of the electrode fluxes of electrons and ions, especially for the energetic electrons of Te > 2 eV, because more power is dissipated in the vicinity of electrodes and the inelastic collision is more pronounced. Therefore, the particle transport on the treated sample can be greatly enhanced without additional gas heating in dual frequency plasmas, which meets the application requirements more compared to the single frequency plasmas.

Linear and Nonlinear Viscoelastic Arterial Wall Models: Application on Animals.

This work deals with the viscoelasticity of the arterial wall and its influence on the pulse waves. We describe the viscoelasticity by a nonlinear Kelvin-Voigt model in which the coefficients are fitted using experimental time series of pressure and radius measured on a sheep's arterial network. We obtained a good agreement between the results of the nonlinear Kelvin-Voigt model and the experimental measurements. We found that the viscoelastic relaxation time-defined by the ratio between the viscoelastic coefficient and the Young's modulus-is nearly constant throughout the network. Therefore, as it is well known that smaller arteries are stiffer, the viscoelastic coefficient rises when approaching the peripheral sites to compensate the rise of the Young's modulus, resulting in a higher damping effect. We incorporated the fitted viscoelastic coefficients in a nonlinear 1D fluid model to compute the pulse waves in the network. The damping effect of viscoelasticity on the high-frequency waves is clear especially at the peripheral sites.

Sub-nanosecond time resolved light emission study for diffuse discharges in air under steep high voltage pulses

Pin-to-plane discharges in centimetre air gaps and standard conditions of pressure and temperature are generated under very high positive nanosecond scale voltage pulses. The experimental study is based on recordings of sub-nanosecond time resolved and Abel-processed light emission profiles and their complete correlation to electrical current waveforms. The effects of the voltage pulse features (amplitude between 20 and 90 kV, rise time between 2 and 5.2 ns, and time rate between 4 and 40 kV · ns−1) and the electrode configuration (gap distance between 10 and 30 mm, pin radius between 10 and 200 µm, copper, molybdenum or tungsten pin material) are described. A three time period development can be found: a glow-like structure with monotonic light profiles during the first 1.5 ns whose size depends on time voltage rate, a shell-like structure with bimodal profiles whose duration and extension in space depends on rise time, and either diffuse or multi-channel regime for the connection to the cathode plane according to gap distance. The transition of the light from monotonic to bimodal patterns reveals the relative effects and dynamics of streamer space charge and external laplacian field. A classical 2D-fluid model for streamer propagation has been used and adapted for very high and steep voltage pulses. It shows the formation of a strong space charge (streamer) very close to the pin, but also a continuity of emission between the pin and the streamer, and electric fields higher than the critical ionization field (28 kV · cm−1 in air) almost in the whole gap and very early in the discharge propagation.

Investigations of argon and neon abnormal glow discharges in the presence of metastable atom density with fluid model

In this manuscript an investigation of a DC argon and neon abnormal glow discharges with metastable atom density is presented. The values of pressure lie between 133.32 and 330 Pa, and the voltage ranges from 250 to 400 V in the case of argon gas. In the case of neon gas, the pressure has a value of 399.92 Pa (3 Torr) and the voltage ranges from 300 to 500 V. In this framework, an analysis of abnormal glow discharge characteristics is carried out in the case of input data taken from the Boltzmann equation in the multi-term approximation, and in the case of input data obtained from BOLISG+ code. With these differences of input data in the same gas, the output results are different; it appears in the cathodic region. The spatio-temporal distributions of electron and ion densities, the potential and electric field, the mean electron energy and the metastable atom density are shown. A 1D fluid model is used to solve self-consistently the first three moments of the Boltzmann’s equation coupled with the Poisson’s equation. The role of the presence of metastable atom density in the fluid model is clearly because of the domination of ionization processes by both stepwise and penning ionizations. Our results are validated with those obtained by both recent paper and experimental results.

Simulation of subnanosecond streamers in atmospheric-pressure air: Effects of polarity of applied voltage pulse

Results of simulation of subnanosecond streamer propagation in corona gap configuration, obtained in the framework of 2D fluid model, are presented. Effects related with the polarity of a voltage pulse applied to the stressed electrode are discussed. It is argued that these effects (dependence of the discharge current and propagation velocity on the polarity of applied voltage) observed in experiments can be attributed to the difference in initial (preceding the streamer formation) distributions of charged species inside the gap. This difference can be caused by preionization (at negative polarity) of the gas inside the discharge gap by runaway electrons. Calculated streamers have large widths (up to 1 cm) and move with velocities in the range of 109–1010 cm s−1, similar to experimental data.

Influence of surface emission processes on a fast-pulsed dielectric barrier discharge in air at atmospheric pressure

This paper presents simulations of an atmospheric pressure air discharge in a point-to-plane geometry with a dielectric layer parallel to the cathode plane. Experimentally, a discharge reignition in the air gap below the dielectrics has been observed. With a 2D fluid model, it is shown that due to the fast rise of the high voltage applied and the sharp point used, a first positive spherical discharge forms around the point. Then this discharge propagates axially and impacts the dielectrics. As the first discharge starts spreading on the upper dielectric surface, in the second air gap with a low preionization density of , the 2D fluid model predicts a rapid reignition of a positive discharge. As in experiments, the discharge reignition is much slower, a discussion on physical processes to be considered in the model to increase the reignition delay is presented. The limit case with no initial seed charges in the second air gap has been studied. First, we have calculated the time to release an electron from the cathode surface by thermionic and field emission processes for a work function eV and an amplification factor . Then a 3D Monte Carlo model has been used to follow the dynamics of formation of an avalanche starting from a single electron emitted at the cathode. Due to the high electric field in the second air gap, we have shown that in a few nanoseconds, a Gaussian cloud of seed charges is formed at a small distance from the cathode plane. This Gaussian cloud has been used as the initial condition of the 2D fluid model in the second air gap. In this case, the propagation of a double headed discharge in the second air gap has been observed and the reignition delay is in rather good agreement with experiments.

Numerical study of breakdown pattern induced by an intense microwave under nitrogen and argon gases

Filamentary plasma induced by microwave beam irradiation was reproduced in nitrogen and argon by combining fluid or particle plasma models with electromagnetic wave propagation. Transport coefficients used in the fluid model are estimated from particle simulation to maintain consistency of the breakdown structure between the fluid and particle models. A discrete structure was obtained using the one-dimensional (1D) fluid model, because a standing wave is generated in front of the plasma when the incident microwave beam is reflected by the overcritical plasma, which agrees with the breakdown structure obtained using the 1D particle model. A 2D plasma filament was also reproduced using the fluid model in nitrogen and argon. Reflection of the incident microwave in argon becomes stronger than that in nitrogen because of the denser argon plasma. Change in filament shape is induced in argon because the electric field is deformed at the plasma tip owing to stronger wave reflection from the neighboring filament. The propagation speed of the plasma front becomes larger in argon breakdown because of the larger ionization frequency and the larger diffusion coefficient.

Electrical Characteristics of an Argon Glow Discharge in the Presence of Metastable Atom Density

The paper deals with numerical modelling studies of DC glow discharge in argon with metastable atom density. The values of pressure is between 133.32 Pa and 330 Pa, and voltage ranges from 250 to 400 V in the case of input data taken from the Boltzmann equation in multi term approximation. In the frameworks, an analysis of glow discharge characteristics is carried out in the case of input data obtained from BOLISG+ code. As conclusion of these different input data in the same gas the output results are different and they appear in the cathode region. The spatio-temporal distributions of electron and ion densities, the potential and electric field, the mean electron energy and the metastable atom density are shown. A 1D fluid model is used to solve self-consistently the first three moments of the Boltzmann equation coupled with the Poisson's equation. The results are validated with those obtained by recent papers.

Two-dimensional, three-fluid modeling of capillary plasma discharges in electrothermal mass accelerators

Electrothermal (ET) plasma launchers have a wide array of applications as mass acceleration devices. An ET plasma launcher utilizes an ET plasma discharge to accelerate a projectile. ET plasma discharges are arc-driven capillary discharges that ablate liner materials and form partially ionized plasmas. ET plasma discharges are generated by driving current pulses through a capillary source. Current pulses typically have peak currents on the order of tens of kA with pulse lengths on the order of hundreds of μs. These types of plasma discharges have been explored for their application to military ballistics, electric thrusters, and nuclear fusion power. ET plasma discharges have been studied using 0D, 1D, and semi-2D fluid models. In this work, a three-fluid, fully two-dimensional model of ET plasma discharges is presented. First approximations used in the newly developed model and code are discussed and simulation results are compared with experiment. Simulation results indicate the development of back flow inside ET plasma discharges due to collisional drag forces between individual plasma species. This back flow is observed for simulations of ET plasma discharges receiving current pulses with peak currents of 10, 20, 30, and 40 kA. Simulation results also reveal the development of fluid perturbations near the breech of the plasma source. These perturbations cause variations in the plasma electrical conductivity and ultimately cause changes in the local ablation rate of the source liner. At higher current pulses, these perturbations are more localized in the region of the source closest to the breech. This effect causes a decrease in the ablated mass in this region relative to the region of the source experiencing the highest ablation.

Microwave harmonic generation and nonlinearity in microplasmas

Nonlinearities in microplasmas excited by microwaves are described both experimentally and through a 2D fluid model. A split-ring resonator generates a microplasma in a 150 μm discharge gap at 1 GHz. Nonlinearity generates both radiated and conducted harmonics which are measured from 0.2–760 Torr (Ar) for power levels between 0.5 and 3 W. Asymmetric electrode configurations produce the highest 3rd harmonic power (>10 mW) at an optimal pressure of the order of 0.3 Torr. The microplasma is also demonstrated as a mixer. The experimental results are explained with the aid of a fluid model of the microplasma. The model shows that the smaller electrode in an asymmetric device is forced to attain a large microwave potential that strongly modulates the sheath thickness and the local electron energy. The voltage-dependent sheath width gives rises to a nonlinear sheath capacitance as well as short pulses of hot electron flux to the electrode. The modeled 3rd harmonic current is converted to an extractable harmonic power by a microwave circuit model. Using this technique the modeled and measured harmonic production of the microplasma are found to compare favorably.

2D fluid model analysis for the effect of 3D gas flow on a capacitively coupled plasma deposition reactor

The wide applicability of capacitively coupled plasma (CCP) deposition has increased the interest in developing comprehensive numerical models, but CCP imposes a tremendous computational cost when conducting a transient analysis in a three-dimensional (3D) model which reflects the real geometry of reactors. In particular, the detailed flow features of reactive gases induced by 3D geometric effects need to be considered for the precise calculation of radical distribution of reactive species. Thus, an alternative inclusive method for the numerical simulation of CCP deposition is proposed to simulate a two-dimensional (2D) CCP model based on the 3D gas flow results by simulating flow, temperature, and species fields in a 3D space at first without calculating the plasma chemistry. A numerical study of a cylindrical showerhead-electrode CCP reactor was conducted for particular cases of SiH4/NH3/N2/He gas mixture to deposit a hydrogenated silicon nitride (SiNxHy) film. The proposed methodology produces numerical results for a 300 mm wafer deposition reactor which agree very well with the deposition rate profile measured experimentally along the wafer radius.

Numerical simulations of superlattice patterns in dielectric barrier discharges at atmospheric pressure

This paper presents the numerical investigation on superlattice patterns in atmospheric pressure glow discharges in dielectric barrier discharges by using a self-consistent 2D fluid model. It is found that the superlattice pattern is an interleaving of two filamentary sub-patterns with alternate spatial and temporal characteristics. The competition between the volume ionization and the memory effects of both surface charges and space charges is expected to the formation mechanism of this superlattice pattern.

Numerical Study of HBr/He Discharges in Capacitive Coupled Plasma Reactor

Br-based plasmas potentially provide selective etching of Si. The characteristics of homogenous discharge in mixed gases of HBr and He are investigated numerically based on a self-consistent 2D fluid model. The model takes into account the primary processes like excitation and ionization. The reactions of radicals with radicals, neutrals with neutrals and radicals and neutrals are taken into account in HBr/He discharge and therefore can adequately represent discharge plasma. Based on simulation results of the self-consistent 2D fluid model, the dominant species for Si etching in HBr/He plasma discharge are Br, Br+, H and HBr+. The impact of frequency, voltage, electrode gap, and gas mixture ratio on the densities of these important species in HBr/He has been explored. Simulation results indicate that elevating high frequency electrode’s frequency and voltage, enhances etching species densities. Increasing the electrode gap, the densities of all plasma species decrease and vice versa. The addition of He to HBr plasma decreases Br and HBr+ densities while increases Br+ density. Densities of active species for Si etching and subsequently chemical etching versus physical sputtering in HBr/He plasma can be controlled by tuning input parameters and the desired etching can be achieved.

Two-dimensional simulation of spatiotemporal generation of dielectric barrier columnar discharges in atmospheric helium

A two-dimensional (2D) fluid model is presented to investigate the spatiotemporal generation and dynamic mechanics of dielectric barrier columnar discharges in atmospheric helium. The model was examined with discharge currents measured in experiments and images taken by an intensified charge couple device camera. Based on the model, a columnar discharge was simulated for several cycles after being ignited. The discharge could be regarded as an initial unstable stage for the first three and a half cycles, then a steady state for the following cycles. In the initial stage, the discharge evolves from a uniform pattern into a columnar one. The calculated equipotential lines, 2D radial electric field, and electron density distributions at the edge of uniform discharges show the radial electric field accounts for the shrinking discharge area and the formation of discharge columns in the end. The columnar glow discharges and the Townsend discharges beyond the columns could coexist in the initial stage, and a Townsend discharge might develop into a new glow column in the next half-cycle. The radial electric field surrounding a glow discharge column has an inhibiting effect on the ionization in the peripheral area.