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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Electromagnetic effects in high-frequency large-area capacitive discharges: A review

In traditional capacitively coupled plasmas, the discharge can be described by an electrostatic model, in which the Poisson equation is employed to determine the electrostatic electric field. However, current plasma reactors are much larger and driven at a much higher frequency. If the excitation wavelength λ in the plasma becomes comparable to the electrode radius, and the plasma skin depth δ becomes comparable to the electrode spacing, the electromagnetic (EM) effects will become significant and compromise the plasma uniformity. In this regime, capacitive discharges have to be described by an EM model, i.e., the full set of Maxwell's equations should be solved to address the EM effects. This paper gives an overview of the theory, simulation and experiments that have recently been carried out to understand these effects, which cause major uniformity problems in plasma processing for microelectronics and flat panel display industries. Furthermore, some methods for improving the plasma uniformity are also described and compared.

42 ENGINEERING↗
NASA NTRS1991

Simulations of curved turbulent boundary layers

The objective of this work is to develop a space-time accurate numerical method for the solution of incompressible Navier-Stokes equations in generalized coordinates. The resulting code is to be used for direct and large-eddy simulation of turbulence in complex geometries. In a previous paper, the system of Navier-Stokes equations in general curvilinear coordinates was solved by a second-order accurate finite-difference scheme. Satisfactory results were obtained for several flows in two and three dimensions. The system of Navier-Stokes for the fluxes are given in Orlandi (1989). The main deficiency of the numerical scheme was the large CPU time required for the solution of the Poisson equation for the 'pressure' field. The point SOR relaxation, in conjunction with a multigrid scheme, was used for the Poisson equation. In some cases, particularly with very fine grids, it was impossible to obtain a divergent-free flow. A preliminary attempt is made to compute the spatially evolving flow of Swearingen & Blackwelder. To reduce the streamwise distance, the inflow was at a distance x = 60 cm from the leading edge.

Orlandi, Paolo↗
NASA NTRS1998

Higher-Order Compact Schemes for Numerical Simulation of Incompressible Flows

A higher order accurate numerical procedure has been developed for solving incompressible Navier-Stokes equations for 2D or 3D fluid flow problems. It is based on low-storage Runge-Kutta schemes for temporal discretization and fourth and sixth order compact finite-difference schemes for spatial discretization. The particular difficulty of satisfying the divergence-free velocity field required in incompressible fluid flow is resolved by solving a Poisson equation for pressure. It is demonstrated that for consistent global accuracy, it is necessary to employ the same order of accuracy in the discretization of the Poisson equation. Special care is also required to achieve the formal temporal accuracy of the Runge-Kutta schemes. The accuracy of the present procedure is demonstrated by application to several pertinent benchmark problems.

Wilson, Robert V.↗
DOE OSTI2018

Alternating Anderson–Richardson method: An efficient alternative to preconditioned Krylov methods for large, sparse linear systems

Here, we present the Alternating Anderson–Richardson (AAR) method: an efficient and scalable alternative to preconditioned Krylov solvers for the solution of large, sparse linear systems on high performance computing platforms. Specifically, we generalize the recently proposed Alternating Anderson–Jacobi (AAJ) method (Pratapa et al., 2016) to include preconditioning, discuss efficient parallel implementation, and provide serial MATLAB and parallel C/C++ implementations. In serial applications to nonsymmetric systems, we find that AAR is comparably robust to GMRES, using the same preconditioning, while often outperforming it in time to solution; and find AAR to be more robust than Bi-CGSTAB for the problems considered. In parallel applications to the Helmholtz and Poisson equations, we find that AAR shows superior strong and weak scaling to GMRES, Bi-CGSTAB, and Conjugate Gradient (CG) methods, using the same preconditioning, with consistently shorter times to solution at larger processor counts. Finally, in massively parallel applications to the Poisson equation, on up to 110,592 processors, we find that AAR shows superior strong and weak scaling to CG, with shorter minimum time to solution. We thus find that AAR offers a robust and efficient alternative to current state-of-the-art solvers, with increasing advantages as the number of processors grows.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Development of a fractional-step method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems

A fractional step method is developed for solving the time-dependent three-dimensional incompressible Navier-Stokes equations in generalized coordinate systems. The primitive variable formulation uses the pressure, defined at the center of the computational cell, and the volume fluxes across the faces of the cells as the dependent variables, instead of the Cartesian components of the velocity. This choice is equivalent to using the contravariant velocity components in a staggered grid multiplied by the volume of the computational cell. The governing equations are discretized by finite volumes using a staggered mesh system. The solution of the continuity equation is decoupled from the momentum equations by a fractional step method which enforces mass conservation by solving a Poisson equation. This procedure, combined with the consistent approximations of the geometric quantities, is done to satisfy the discretized mass conservation equation to machine accuracy, as well as to gain the favorable convergence properties of the Poisson solver. The momentum equations are solved by an approximate factorization method, and a novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two- and three-dimensional laminar test cases are computed and compared with other numerical and experimental results to validate the solution method. Good agreement is obtained in all cases.

Rosenfeld, Moshe↗
DOE OSTI2015

Low-pressure hydrogen discharge maintenance in a large-size plasma source with localized high radio-frequency power deposition

The development of the two-dimensional fluid-plasma model of a low-pressure hydrogen discharge, presented in the study, is regarding description of the plasma maintenance in a discharge vessel with the configuration of the SPIDER source. The SPIDER source, planned for the neutral-beam-injection plasma-heating system of ITER, is with localized high RF power deposition to its eight drivers (cylindrical-coil inductive discharges) and a large-area second chamber, common for all the drivers. The continuity equations for the charged particles (electrons and the three types of positive ions) and for the neutral species (atoms and molecules), their momentum equations, the energy balance equations for electrons, atoms and molecules and the Poisson equations are involved in the discharge description. In addition to the local processes in the plasma volume, the surface processes of particle reflection and conversion on the walls as well as for a heat exchange with the walls are included in the model. The analysis of the results stresses on the role of the fluxes (particle and energy fluxes) in the formation of the discharge structure. The conclusion is that the discharge behavior is completely obeyed to non-locality. The latter is displayed by: (i) maximum values of plasma parameters (charged particle densities and temperatures of the neutral species) outside the region of the RF power deposition, (ii) shifted maxima of the electron density and temperature, of the plasma potential and of the electron production, (iii) an electron flux, with a vortex structure, strongly exceeding the total ion flux which gives evidence of a discharge regime of non-ambipolarity and (iv) a spatial distribution of the densities of the neutral species resulting from their fluxes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Validating corrosion models: A comparison of governing equations

Experimental validation of Finite Element Method (FEM) models varying electrochemical governing equations, inclusion of chemical reactions, and time on the resultant damage profile for two galvanic couples is explored. Two anode materials (Magnesium AZ31 and Carbon Steel) in contact with a cathode (Stainless Steel 304 L) were modeled in/exposed to NaCl (1 and 0.1 M respectively for the anode materials) for up to one week. The physics approach, inclusion of chemical reactions, and the boundary conditions required to accurately represent the damage profile in FEM models depended on the galvanic couple materials and, ultimately, the corrosion rate. For high rates of corrosion (i.e., magnesium anode), the Nernst-Planck equation with Electroneutrality was sufficient to describe the damage, while, for low rates of corrosion (i.e., carbon steel anode), the Laplace equation was sufficient. In all cases, the most complete governing equation (Nernst-Planck-Poisson Equation) was not necessary to accurately describe the damage. Precipitation reactions in solution also played a critical role in the predicted damage profile, especially for high corrosion rate systems. Finally, for short time periods (< 6 h), the choice of governing equations does not significantly influence damage profile results. Overall, the choice of physics to reduce error in simulations relies on the boundary conditions, geometry, conductivity of the solution, electrochemical potential differences, and time of exposure. The above results are discussed with regard to accuracy and computational savings.

Carbon steel↗
DOE OSTI2014

Analytical solution of the Poisson-Nernst-Planck equations for an electrochemical system close to electroneutrality

Single charge densities and the potential are used to describe models of electrochemical systems. These quantities can be calculated by solving a system of time dependent nonlinear coupled partial differential equations, the Poisson-Nernst-Planck equations. Assuming small deviations from the electroneutral equilibrium, the linearized and decoupled equations are solved for a radial symmetric geometry, which represents the interface between a cell and a sensor device. The densities and the potential are expressed by Fourier-Bessels series. The system considered has a ratio between the Debye-length and its geometric dimension on the order of 10{sup −4} so the Fourier-Bessel series can be approximated by elementary functions. The time development of the system is characterized by two time constants, τ{sub c} and τ{sub g}. The constant τ{sub c} describes the approach to the stationary state of the total charge and the potential. τ{sub c} is several orders of magnitude smaller than the geometry-dependent constant τ{sub g}, which is on the order of 10 ms characterizing the transition to the stationary state of the single ion densities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Generalizing Similarity Laws for Radio-Frequency Discharge Plasmas across Nonlinear Transition Regimes

We generalize similarity theory based on the scaling and solution invariance of the Boltzmann equation, coupled with the Poisson equation, and demonstrate similarity laws for radio-frequency (rf) discharge plasmas across three nonlinear transitional regimes, namely, the alpha-gamma mode transition, the stochastic-Ohmic-heating mode transition, and the bounce-resonance-heating mode transition. Fundamental plasma parameters, e.g., the electron power absorption, under similar discharge conditions are examined via fully kinetic particle-in-cell simulations, and electron-kinetic invariance is exemplified in similar rf discharge plasmas. The results unambiguously confirm the applicability of similarity laws for rf plasmas in extended operating regimes, and strengthen the foundations and framework of similarity physics with universality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1992

GRAPEVINE: Grids about anything by Poisson's equation in a visually interactive networking environment

A proven 3-D multiple-block elliptic grid generator, designed to run in 'batch mode' on a supercomputer, is improved by the creation of a modern graphical user interface (GUI) running on a workstation. The two parts are connected in real time by a network. The resultant system offers a significant speedup in the process of preparing and formatting input data and the ability to watch the grid solution converge by replotting the grid at each iteration step. The result is a reduction in user time and CPU time required to generate the grid and an enhanced understanding of the elliptic solution process. This software system, called GRAPEVINE, is described, and certain observations are made concerning the creation of such software.

Sorenson, Reese L.↗
NASA NTRS1995

A Navier-Stokes boundary element solver

Using global interpolation functions (GIF's) boundary element solutions are obtained for two-dimensional laminar flows. Two schemes are proposed for handling the convective terms. The first treats convection as a forcing function, and converts the flow equations to pseudo-Poisson equations. In the second scheme, some convective effect is incorporated into the fundamental solution used in constructing the pertinent integral equations. The lid-driven cavity flow is selected as the benchmark problem.

Reddy, D. R.↗
DOE OSTI2016

Low-frequency surface waves on semi-bounded magnetized quantum plasma

The propagation of low-frequency electrostatic surface waves on the interface between a vacuum and an electron-ion quantum plasma is studied in the direction perpendicular to an external static magnetic field which is parallel to the interface. A new dispersion equation is derived by employing both the quantum magnetohydrodynamic and Poisson equations. It is shown that the dispersion equations for forward and backward-going surface waves are different from each other.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Stationary Solutions of the Vlasov Equations for a High-Temperature Two-Component Plasma

We consider the first mixed problem for the Vlasov–Poisson equations in infinite cylinder. This problem describes evolution of the distribution density for ions and electrons in a high-temperature plasma in the presence of an outer magnetic field. We construct stationary solutions of the Vlasov–Poisson system of equations with the trivial potential of the self-consistent electric field describing a two-component plasma in an infinite cylinder such that their supports are located at a distance from the boundary of the domain.

97 MATHEMATICS AND COMPUTING↗