Two-dimensional Fluid Simulation Research Articles

Computations of intermittent transport in scrape-off layer plasmas.

Two-dimensional fluid simulations of interchange turbulence for geometry and parameters relevant for the scrape-off layer of magnetized plasmas are presented. The computations, which have distinct plasma production and loss regions, reveal bursty ejection of particles and heat from the bulk plasma in the form of blobs. These structures propagate far into the scrape-off layer where they are dissipated due to transport along open magnetic field lines. From single-point recordings it is shown that the blobs have asymmetric conditional wave forms and lead to positively skewed and flattened probability distribution functions. The radial propagation velocity may reach one-tenth of the sound speed. These results are in excellent agreement with recent experimental measurements.

Density Spectrum in the Diffuse Interstellar Medium and Solar Wind

Inertial range turbulence properties are investigated for nearly incompressible density fluctuations using two-dimensional nonlinear fluid simulations. We find that density fluctuations behave as a passive scalar and do not satisfy the pseudosound approximation. As a result, the density fluctuations follow a Kolmogorov-like spectrum, and this is a possible explanation for the observed diffuse interstellar and solar wind density fluctuation spectrum.

Anisotropic Turbulence in Two‐dimensional Electron Magnetohydrodynamics

Spectral anisotropy within decaying incompressible electron magnetohydrodynamics turbulence is investigated by two-dimensional fluid simulations. An initially isotropic turbulent spectrum exhibits anisotropy in the spectral cascade because of the presence of a self-consistent large-scale or an externally imposed magnetic field. Our simulations show that the anisotropy scales linearly with the strength of the ambient magnetic field. The linear scaling of the anisotropic spectral cascades appears to be rather generic as turbulent excitation scales larger than kde 1, the collisionless electron inertial or skin depth length scale (de), follow a similar trend.

Theoretical analysis of the influence of external biasing on long range turbulent transport in the scrape-off layer

Two-dimensional fluid simulations of scrape-off layer (SOL) turbulence with non-constrained energy content (flux driven) are characterized by profile relaxation and strong outward bursts of density. The ballistic propagation extends well beyond the e-folding length of the SOL with a Mach number of M⊥ ∼ 0.04. Turbulence stabilization is achieved by biasing part of the limiter surface. The critical radial extent to achieve this stabilization is derived. This effect governs the size of the biased ring required to insulate the wall from long range bursts of matter. The same characteristic scale also governs the critical size of Langmuir probe tips. For probe tips in excess of this size, the flux tube to the probe is found to be decoupled from the background plasma.

The characteristics of large area processing plasmas

In order to improve production efficiency, large-diameter wafer substrates (300-mm diameter) and large-area glass substrates (from 400 cm/sup 2/ to 1 m/sup 2/) have been adopted recently. As a result, the development of large and high-density plasma source has become essential. To investigate the discharge phenomenon in the chamber that consists of embedded antenna coil in the rectangular system (1020 /spl times/830 /spl times/437 mm), we have developed a two-dimensional fluid simulation model. In order to check our model, the results from our simulation have been compared with available experimental data. The comparison is generally in a good agreement with experiments. Depending on the current direction and powered method, the distribution of plasma parameters has many differences. In our simulation with a chamber larger than is usually used in other experiments, we examine three effects: the distance between antenna coils, structure in the chamber, and the depth of the chamber. The parameters, which affect nonuniformity, electron temperature, and others, can be explained in a manner similar to the inductively coupled plasma source with a cylindrical chamber. Our simulation results confirm that the embedded antenna coil system with a suitable environment can be extended by many antenna coils as a large-area plasma source.

Mechanism of growth reduction of the deceleration-phase ablative Rayleigh-Taylor instability.

The deceleration-phase (dp) ablative Rayleigh-Taylor instability (RTI) of igniting and nonigniting inertial fusion capsules is studied by high-resolution two-dimensional Lagrangian fluid simulations. It is found that growth reduction of the dp-RTI with respect to classical RTI results from the advection of perturbed fluid elements outside a thin unstable fluid layer. Within this layer, at fixed Lagrangian position, perturbations grow approximately classically.

Coherent structures and their stability in ion temperature gradient turbulence

Periodic arrays of large scale coherent vortices and their stability have been investigated, within the framework of /spl eta//sub i/ turbulence, using two-dimensional fluid simulation in slab geometry. These vortices, in combination with viscosity damping of small scales, contribute to the formation of a steady state in a system with linearly unstable modes. The steady state comprises of a few vortex convective turn over times and seems to be fairly robust. It has been recognized that a vortex chain, consisting of positive and negative vorticities, continues to move stably in the poloidal direction (along periodic direction). On the other hand, an initial isolated monopole vortex is unstable and leads to a long-lived stable dipolar structure after a few vortex turnover periods. A variety of simple collisional interaction processes among these coherent vortices have also been explored numerically.

Neutral uniformity and transport mechanisms for plasma etching

Dissociated neutral (radical) uniformity on the wafer has been studied in a high-density large area plasma reactor. Radial profiles of radicals on the wafer are measured by scanning optical probe and by spatially resolved actinometry and are also estimated by a simple analytic model and two-dimensional (2D) commercial fluid simulation code. Center-peaked radial profiles of radical species are observed experimentally and are also predicted by simple calculation and by simulation code. The radial radical density profiles are compared with the radial profiles of etching rate of blanket photoresist films on 200 mm wafers etched by oxygen plasmas. Radial profiles of etch rate and atomic oxygen radical densities are compared and discussed along with other parameters such as the profiles of ion density, ion energy, and wafer temperature with various chuck bias voltages. At low chuck bias voltage the etch rate uniformity is correlated with radical uniformity. As the chuck bias voltage increases, the etch rate profile begins to follow the ion density profile.

Efficiency improvement of high-pressure microplasma by an electron beam

Efficiency has been a paramount issue for the past few years in high pressure microplasma devices such as Plasma Display Panels (PDP). In order to achieve a better efficiency, a novel method based upon electron beam emission has been investigated by a two-dimensional (2-D) fluid simulation. The injection of electron beam inside the PDP cell gives rise to substantially large density of excited Xe species (Xe*), while reducing ionized xenon (Xe/sup +/) and electron densities. This, in turn, enhances the efficiency, luminance, and reduces power consumption. The primary reason for generating more Xe* species could be attributed to the formation of low electric field region inside the PDP cell, which consequently improves its operational efficiency. The validity of 2-D fluid simulation results is ensured through a qualitative comparison between the one-dimensional fluid and the kinetic results.

Origins of Atom-Centered Local Density Enhancements in Compressible Supercritical Fluids

We used molecular dynamics simulation of a neat two-dimensional Lennard-Jones fluid to examine how the distribution of local densities found around an atom varies as the critical point is approached. Through this analysis, we discovered that mean local density enhancements arise as a necessary and direct consequence of the long-range density inhomogeneities present in such fluids, thereby establishing a relationship between the local and long-length-scale phenomena. Additionally, we uncovered a second, “potential-induced” mechanism which generates mean local density enhancements at low bulk densities. The competition between these two mechanisms of local density enhancement formation enables us to explain why these enhancements are not maximized at the critical density, as well as to explain how the location of this maximum will depend on intrinsic experimental parameters such as the size of the local region and the strength of the solute−solvent potential interaction.

Two-dimensional fluid simulation of plasma reactors for the immobilization of krypton

Direct current glow discharge plasma sources are being developed as reactors for immobilization of radioactive krypton gas recovered from the off-gas stream of a nuclear fuel reprocessing plant. In order to design these reactors, two-dimensional simulations have been performed using a fluid model coupled with Poisson's equation. Nonlinear governing equations were expressed by a fully implicit scheme and the equations were solved using the Newton–Krylov method. We investigated algorithm performance of two methods from the Krylov projection techniques, namely the Bi-CGSTAB method and the transpose-free quasi-minimal residual (TFQMR) method. The results showed that the Bi-CGSTAB method converged considerably faster than the TFQMR method. Direct current glow discharge plasmas in three types of krypton immobilization apparatus were simulated to study the differences in electrode geometry. Simulation results agreed qualitatively with measurements of electron density.

Two-Dimensional Fluid Simulation and Langmuir Probe Measurement of a Planar Inductively Coupled Oxygen Plasma

A two-dimensional (2D) self-consistent axisymmetric fluid simulation of an inductively coupled discharge of electronegative oxygen plasma with a one-turn antenna placed on the top of the dielectric roof is presented. The model equations include continuity equations, the Poisson equation, and an electron energy balance equation. For a planar inductive discharge, the electric field component Eθ (r, z) is calculated, assuming axisymmetric geometry. Considering a deep penetration of the induced rf field, the power deposition profile is formulated and used as the electron heating term in the electron energy balance equation. The 2D distributions of charged particle densities, electric potential, electron temperature, and ionization rate are calculated and compared with experiments. The effect of neutral gas pressure on plasma characteristics is investigated. As a result, for a relatively low pressure (5 mTorr) case, the ionization rate and charged particle densities are uniform in the radial direction, and for a medium pressure (20 mTorr) case, the ionization rate and the negative ion density are sharply maximized in the axial and radial directions. The results of the simulation agree reasonably well with the results of the spatially averaged global model and experimental results.

Two-dimensional plasma reactor simulation with self-consistent coupling of gas flow with plasma transport

A two-dimensional (2-D) fluid simulation applicable to high density plasma reactors was developed which couples gas flow with plasma transport in a self-consistent manner. Modified boundary conditions were used at the reactor walls to accommodate transport at low pressures. A modular approach circumvented the disparity in time scales and a quasi-neutral plasma assumption overcame the disparity in length scales. This approach allowed for a simulation tool that can execute rapidly on a desktop computer, and is, therefore, suitable for Technology Computer-Aided Design (TCAD). Simulation results for an electron cyclotron resonance (ECR) plasma system showed good agreement with experimental data on electron density and temperature as a function of plasma power and pressure. Also, the gas pressure drop in the reactor was predicted correctly by the simulation. Further simulation studies showed the effect of power and pressure on ion flux uniformity on a wafer substrate.

A two-dimensional simulation of electron cyclotron resonance plasma and comparison with experimental data

A two-dimensional fluid simulation of argon plasma in an electron cyclotron resonance source was performed and an experiment was conducted to compare the theoretical prediction and experimental measurements. Conservation equations for mass, momentum and energy in a multicomponent system were solved based on the finite element method in order to compute the fluid velocity field, pressure field, neutral species densities, charged species densities, and electron temperature. By using a Langmuir probe, the variations of electron temperature and electron density along chamber axis were measured for pressures in the range 0.4–7 mTorr. Simulation results agreed favorably with experimental data.

Observation of implosion dynamics by line emissions from direct-drive fusion capsules

Line emissions from Ar-doped fusion capsules were observed to investigate influence of drive uniformity on implosion behavior. To manipulate the drive non-uniformity, in particular of the mode number 6, the laser focus position was set in two representative cases. A fusion capsule was directly irradiated with 12 beams of partially-coherent green light. Imploded core plasmas were diagnosed by observing spatial distribution and time history of the Ar line emissions. Clear differences were obtained between the two irradiation cases despite the calculated irradiation uniformities for the two cases being identical. The experimental result was compared with two-dimensional fluid simulations post-processed with an X-ray spectrum analysis code. Drive uniformity and associated perturbation growth at the pusher-fuel boundary are discussed as a plausible reason for the observed differences.

Two-dimensional breakdown characteristics of PDP cells for varying geometry

Equipotential and electron-density contours for various cell geometries from two-dimensional fluid simulation are presented during a single pulse for plasma display panel cells for varying geometry without a dielectric layer. One of the code validations is provided by the Paschen breakdown for a large parallel-plate case.

Design of absolute equation of state measurements in optically thick materials by laser-driven shock waves

Some aspects of the design of a target for the absolute measurement of Equation-of-State data at pressure of tens of Mbar, in optically thick materials are discussed. In the proposed experiment, a shock wave is generated in a laser-irradiated sample, and the shock velocity and the material velocity behind the shock are simultaneously measured by the optical and X-ray diagnostics. Accurate measurements require the generation of a steady, planar shock, and the detection of the motion of a shocked fluid interface by transverse radiography. One- and two-dimensional numerical fluid simulations have been performed to optimize beam and target design, in order to fulfil such requirements.

Comparative study of silane radical composition in continuous and pulsed electron cyclotron resonance discharges

Comparative experiments are performed between continuous and pulsed electron cyclotron resonance discharges for the deposition of poly-Si films. The measured selectivity of over in the pulsed discharges is larger than in the continuous discharges by more than a factor of four. As a consequence, deposited poly-Si films in the pulsed discharge contain fewer hydrogenated bonds than in the continuous discharges. Two-dimensional fluid simulation is also performed to obtain spatial and temporal evolution of plasmas and radical species. It is confirmed that the simulation results are in qualitative agreement with the experimental results.

Modeling and Simulation of a Large-Area Plasma Source

A variant of transformer-coupled plasma, suitable for processing a large-area flat panel with good uniformity, is examined using various models and simulations. Using two-dimensional and one-dimensional fluid simulations, we present the detailed profiles of the plasma density, potential, electron temperature, electric field structure, and ion current density at the substrate. The average values compare reasonably well with those of a global (volume-averaged) model.

Simulation of Plasma Production and Chemical Reaction in an Oxide Deposition Apparatus Using Electron Cyclotron Resonance Plasma

A two-dimensional fluid simulation code is developed which can predict plasma properties and chemical species transport in gas phase in a realistic configuration of a production-line apparatus. The code is applied to an electron cyclotron resonance plasma reactor for oxide deposition on 20-cm wafers. The predicted density in Ar plasma is in good agreement with the experimental result. Two-dimensional distributions of radical densities in plasmas with gas mixtures of Ar/O2/SiH4 and Ar/O2/SiF4 are obtained, which are in accordance with the measured deposition rates of SiO2 and SiOxFy, respectively.