Electron sheaths are commonly found near Langmuir probes collecting the electron saturation current. The common assumption is that the probe collects the random flux of electrons incident on the sheath, which tacitly implies that there is no electron presheath and that the flux collected is due to a velocity space truncation of the electron velocity distribution function (EVDF). This work provides a dedicated theory of electron sheaths, which suggests that they are not so simple. Motivated by EVDFs observed in particle-in-cell (PIC) simulations, a 1D model for the electron sheath and presheath is developed. In the model, under low temperature plasma conditions (Te 蠑 Ti), an electron pressure gradient accelerates electrons in the presheath to a flow velocity that exceeds the electron thermal speed at the sheath edge. This pressure gradient generates large flow velocities compared to what would be generated by ballistic motion in response to the electric field. It is found that in many situations, under common plasma conditions, the electron presheath extends much further into the plasma than an analogous ion presheath. PIC simulations reveal that the ion density in the electron presheath is determined by a flow around the electron sheath and that this flow is due to 2D aspects of the sheath geometry. Simulations also indicate the presence of ion acoustic instabilities excited by the differential flow between electrons and ions in the presheath, which result in sheath edge fluctuations. The 1D model and time averaged PIC simulations are compared and it is shown that the model provides a good description of the electron sheath and presheath.
The goal of this report is to document the current status of Aleph with regards to electron collisions under an electric field. Aleph and the community-accepted BOLSIG+ code are both used to compute reactions rates for a set of 25 electron-nitrogen interactions. A reasonable comparison is found (see below) providing evidence that Aleph is successfully simulating or implementing: (1) Particle-particle collision cross-sections via DSMC methodology, (2) Energy balance for simple particle interactions, and (3) Electron energy distribution function (EEDF) evolution
This document describes the form and use of three supplemental capabilities added to Goma during 1998 -- augmenting conditions, automatic continuation and linear stability analysis. Augmenting conditions allow the addition of constraints and auxiliary conditions which describe the relationship between unknowns, boundary conditions, material properties and post-processing extracted quantities. Automatic continuation refers to a family of algorithms (zeroth and first order here, single and multi-parameter) that allow tracking steady-state solution paths as material parameters or boundary conditions are varied. The stability analysis capability in Goma uses the method of small disturbances and superposition of normal modes to test the stability of a steady- state flow, i.e., it determines if the disturbance grows or decays in time.
Goma 6.0 is a finite element program which excels in analyses of multiphysical processes, particularly those involving the major branches of mechanics (viz. fluid/solid mechanics, energy transport and chemical species transport). Goma is based on a full-Newton-coupled algorithm which allows for simultaneous solution of the governing principles, making the code ideally suited for problems involving closely coupled bulk mechanics and interfacial phenomena. Example applications include, but are not limited to, coating and polymer processing flows, super-alloy processing, welding/soldering, electrochemical processes, and solid-network or solution film drying. This document serves as a user's guide and reference.
We present an error estimation method for immersed interface solutions of elliptic boundary value problems. As opposed to an asymptotic rate that indicates how the errors in the numerical method converge to zero, we seek a posteriori estimates of the errors, and their spatial distribution, for a given solution. Our estimate is based upon the classical idea of defect corrections, which requires the application of a higher-order discretization operator to a solution achieved with a lower-order discretization. Our model problem will be an elliptic boundary value problem in which the coefficients are discontinuous across an internal boundary.
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
