SEARCH · Engineering Papers

Results for “mesh compression”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22

All sources NASA NTRS DOE OSTI

DOE OSTI2016

Simulating Fragmentation and Fluid-Induced Fracture in Disordered Media Using Random Finite-Element Meshes

Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. In this paper, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipated during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Finally, applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2000

Lubrication System Failure Baseline Testing on an Aerospace Quality Gear Mesh

Aerospace drive systems are required to survive a loss-of-lubrication test for qualification. In many cases emergency lubrication systems need to be designed and utilized to permit the drive system to pass this difficult requirement. The weight of emergency systems can adversely affect the mission capabilities of the aircraft. The possibility to reduce the emergency system weight through the use of mist lubrication will be described. Mist lubrication involves the delivery of a minute amount of an organic liquid as a vapor or fine mist in flowing compressed air to rubbing surfaces. At the rubbing surface, the vapor or mist reacts to form a solid lubricating film. The aim of this study was to establish a baseline for gear behavior under oil depleted conditions. A reactive vapor-mist lubrication method is described and proposed as a candidate emergency lubrication system.

Handschuh, Robert F.↗

DOE OSTI2017

Canopus: A Paradigm Shift Towards Elastic Extreme-Scale Data Analytics on HPC

Scientific simulations on high performance computing (HPC) platforms generate large quantities of data. To bridge the widening gap between compute and I/O, and enable data to be more efficiently stored and analyzed, simulation outputs need to be refactored, reduced, and appropriately mapped to storage tiers. However, a systematic solution to support these steps has been lacking on the current HPC software ecosystem. To that end, this paper develops Canopus, a progressive JPEGlike data management scheme for storing and analyzing big scientific data. It co-designs the data decimation, compression and data storage, taking the hardware characteristics of each storage tier into considerations. With reasonably low overhead, our approach refactors simulation data into a much smaller, reduced-accuracy base dataset, and a series of deltas that is used to augment the accuracy if needed. The base dataset and deltas are compressed and written to multiple storage tiers. Data saved on different tiers can then be selectively retrieved to restore the level of accuracy that satisfies data analytics. Thus, Canopus provides a paradigm shift towards elastic data analytics and enables end users to make trade-offs between analysis speed and accuracy on-the-fly. We evaluate the impact of Canopus on unstructured triangular meshes, a pervasive data model used by scientific modeling and simulations. In particular, we demonstrate the progressive data exploration of Canopus using the “blob detection” use case on the fusion simulation data.

Lu, Tao↗

DOE OSTI2015

Simulation of Internal Combustion Engines with High-Performance Computing Tools

Traditional Lagrangian spray modeling approaches for internal combustion engines are highly griddependent due to insufficient resolution in the near nozzle region. This is primarily because of inherent restrictions of volume fraction with the Lagrangian assumption together with high computational costs associated with small grid sizes. A state-of-the-art grid-convergent spray modeling approach was developed and implemented by Senecal et al. (ASME-ICEF2012-92043) in the CONVERGE software. The key features of the methodology include Adaptive Mesh Refinement (AMR), advanced liquid-gas momentum coupling, and improved distribution of the liquid phase, which enables use of cell sizes smaller than the nozzle diameter. This modeling approach was rigorously validated against nonevaporating, evaporating, and reacting data from the literature. The current numerical study focusses on further demonstration of the grid-convergent modeling approach for simulating a single-cylinder Cat® compression ignition engine. The simulated injector is characterized with a nominal nozzle exit diameter of 259 μm. Simulations using various minimum grid sizes (ranging from 125 μm to 1000 μm) are compared for engine performance and emissions parameters of interest such as pressure, heat release rate, ignition delay, NOx, HC, and soot emissions. The peak cell-count for the highest resolution simulation was on the order of 34 million. These computationally expensive simulations were facilitated at a high-performance computing facility at Argonne National Laboratory. METIS load-balancing algorithm was developed and implemented in Converge code for the simulations. Scaling studies were also performed. The validity of previously recommended grid settings (ASME-ICEF2012-92043) for accuracy/runtime trade-off is further assessed. Efficacy of a simplified combustion model is also compared against a detailed chemical kinetics based combustion model.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS2013

High-Pressure Lightweight Thrusters

Returning samples of Martian soil and rock to Earth is of great interest to scientists. There were numerous studies to evaluate Mars Sample Return (MSR) mission architectures, technology needs, development plans, and requirements. The largest propulsion risk element of the MSR mission is the Mars Ascent Vehicle (MAV). Along with the baseline solid-propellant vehicle, liquid propellants have been considered. Similar requirements apply to other lander ascent engines and reaction control systems. The performance of current state-ofthe- art liquid propellant engines can be significantly improved by increasing both combustion temperature and pressure. Pump-fed propulsion is suggested for a single-stage bipropellant MAV. Achieving a 90-percent stage propellant fraction is thought to be possible on a 100-kg scale, including sufficient thrust for lifting off Mars. To increase the performance of storable bipropellant rocket engines, a high-pressure, lightweight combustion chamber was designed. Iridium liner electrodeposition was investigated on complex-shaped thrust chamber mandrels. Dense, uniform iridium liners were produced on chamber and cylindrical mandrels. Carbon/carbon composite (C/C) structures were braided over iridium-lined mandrels and densified by chemical vapor infiltration. Niobium deposition was evaluated for forming a metallic attachment flange on the carbon/ carbon structure. The new thrust chamber was designed to exceed state-of-the-art performance, and was manufactured with an 83-percent weight savings. High-performance C/Cs possess a unique set of properties that make them desirable materials for high-temperature structures used in rocket propulsion components, hypersonic vehicles, and aircraft brakes. In particular, more attention is focused on 3D braided C/Cs due to their mesh-work structure. Research on the properties of C/Cs has shown that the strength of composites is strongly affected by the fiber-matrix interfacial bonding, and that weakening interface realizes pseudo-plastic behavior with significant increase in the tensile strength. The investigation of high-temperature strength of C/Cs under high-rate heating (critical for thrust chambers) shows that tensile and compression strength increases from 70 MPa at room temperature to 110 MPa at 1,773 K, and up to 125 MPa at 2,473 K. Despite these unique properties, the use of C/Cs is limited by its high oxidation rate at elevated temperatures. Lining carbon/carbon chambers with a thin layer of iridium or iridium and rhenium is an innovative way to use proven refractory metals and provide the oxidation barrier necessary to enable the use of carbon/ carbon composites. Due to the lower density of C/Cs as compared to SiC/SiC composites, an iridium liner can be added to the C/C structure and still be below the overall thruster weight. Weight calculations show that C/C, C/C with 50 microns of Ir, and C/C with 100 microns of Ir are of less weight than alternative materials for the same construction.

Holmes, Richard↗

DOE OSTI2019

Numerical Analysis of Detonability Assessment in a Natural Gas-Air Fueled Rotating Detonation Engine

Rotating Detonation Engines (RDE) offer an alternative combustion strategy to replace conventional constant pressure combustion with a process that could produce a pressure gain without the use of a mechanical compressor. Recent numerical and experimental publications that consider air as the oxidizer have primarily focused on the ability of these annular combustors to sustain a stable continuous detonation wave when fueled by hydrogen. However, for this to be a viable consideration for the land-based power generation it is necessary to explore the ability to detonate natural gas and air within the confines of the annular geometry of an RDE. Previous studies on confined detonations have expressed the importance of permitting detonation cells to fully form within the combustor in order to achieve stability. This poses a challenge for natural gas–air fueled processes as their detonation cell size can be quite large even at moderate pressures. Despite the practical importance, only a few studies are available on natural gas detonations for air-breathing RDE applications. Moreover, the extreme thermodynamic condition (high temperature inside the combustor) allows limited accessibility inside the combustor for detailed experimental instrumentations, providing mostly single-point data. Recent experimental studies at the National Energy Technology Laboratory (NETL) have reported detonation failure at higher methane concentration in an air-breathing RDE fueled by natural gas-hydrogen fuel blends. This encourages to perform a detailed numerical investigation on the wave characteristics of detonation in a natural gas-air fueled RDE to understand the various aspects of instability associated with the natural gas-air detonation.This study is a numerical consideration of a methane-air fueled RDE with varying operating conditions to ascertain the ability to achieve a stable, continuous detonation wave. The simulations have been performed in a 2D unwrapped RDE geometry using the open-source CFD library “OpenFOAM” employing an unsteady pressure-based compressible reactive flow solver with a <em>k</em>–<em>ε</em> turbulence model in a structured rectangular grid system. Both reduced and detailed chemical kinetic models have been used to assess the effect of the chemistry on the detonation wave characteristics and the underlying flow features. A systematic grid sensitivity study has been conducted with various grid sizes to quantify the weakly stable overdriven detonation on a coarse mesh and oscillating features at fine mesh resolutions.The main focus of the current study is to investigate the effects of operating injection pressure on detonation wave characteristics of an air-breathing Rotating Detonation Engine (RDE) fueled with natural gas-hydrogen fuel blends. Wave speeds, peak pressures and temperatures, and dominant frequencies have been computed from the time histories. The flow structures were then visualized using 2D contours of temperature and species concentration.

Saha, Pankaj↗

DOE OSTI2023

Shock state distributions in porous tantalum and characterization with multipoint velocimetry

Heterogenous materials under shock compression can be expected to reach different shock states throughout the material according to local differences in microstructure and the history of wave propagation. Here, in this work, a compact, multiple-beam focusing optic assembly is used with high-speed velocimetry to interrogate the shock response of porous tantalum films prepared through thermal-spray deposition. The distribution of particle velocities across a shocked interface is compared to results obtained using a set of defocused interferometric beams that sampled the shock response over larger areas. The two methods produced velocity distributions along the shock plateau with the same mean, while a larger variance was measured with narrower beams. The finding was replicated using three-dimensional, mesoscopically resolved hydrodynamics simulations of solid tantalum with a pore structure mimicking statistical attributes of the material and accounting for radial divergence of the beams, with agreement across several impact velocities. Accounting for pore morphology in the simulations was found to be necessary for replicating the rise time of the shock plateau. The validated simulations were then used to show that while the average velocity along the shock plateau could be determined accurately with only a few interferometric beams, accurately determining the width of the velocity distribution, which here was approximately Gaussian, required a beam dimension much smaller than the spatial correlation lengthscale of the velocity field, here by a factor of ∼30×, with implications for the study of other porous materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1986

Transonic airfoil calculations including wind tunnel wall-interference effects

The results of Reynolds-averaged time-dependent inviscid and turbulent compressible Navier-Stokes computations using the implicit finite-difference approach of Steger (1978), modified by incorporating a pressure boundary condition, (PBC) to account for wall interference are compared with experimental data on a NACA 64A010 airfoil (Johnson and Bachalo, 1980) in graphs and briefly characterized. The computational approach is the same as that used by King and Johnson (1980), but a 137 x 50 mesh is used instead of a 97 x 35 mesh, and special care is taken in resolving the nose, shock, and trailing-edge regions. Imposition of PBC is shown to improve significantly the accuracy of the computations for the flowfield on the upper surface of the airfoil, shifting the shock forward to its experimentally measured position in the case of turbulent flow. The failure of the method, even with PBC, to match the experimental shock location in the case of a flow with a separation bubble is attributed to inadequacies in the algebraic turbulence model employed (Baldwin and Lomax, 1978).

King, L. S.↗

DOE OSTI2016

Finite element model for brittle fracture and fragmentation

A new computational model for brittle fracture and fragmentation has been developed based on finite element analysis of non-linear elasticity equations. The proposed model propagates the cracks by splitting the mesh nodes alongside the most over-strained edges based on the principal direction of strain tensor. To prevent elements from overlapping and folding under large deformations, robust geometrical constraints using the method of Lagrange multipliers have been incorporated. In conclusion, the model has been applied to 2D simulations of the formation and propagation of cracks in brittle materials, and the fracture and fragmentation of stretched and compressed materials.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Computational Fluid Dynamics Simulation of Gasoline Compression Ignition

Gasoline compression ignition (GCI) is a low temperature combustion (LTC) concept that has been gaining increasing interest over the recent years owing to its potential to achieve diesel-like thermal efficiencies with significantly reduced engine-out nitrogen oxides (NOx) and soot emissions compared to diesel engines. In this work, closed-cycle computational fluid dynamics (CFD) simulations are performed of this combustion mode using a sector mesh in an effort to understand effects of model settings on simulation results. One goal of this work is to provide recommendations for grid resolution, combustion model, chemical kinetic mechanism, and turbulence model to accurately capture experimental combustion characteristics. Grid resolutions ranging from 0.7 mm to 0.1 mm minimum cell sizes were evaluated in conjunction with both Reynolds averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) based turbulence models. Solution of chemical kinetics using the multi-zone approach is evaluated against the detailed approach of solving chemistry in every cell. The relatively small primary reference fuel (PRF) mechanism (48 species) used in this study is also evaluated against a larger 312-species gasoline mechanism. Based on these studies the following model settings are chosen keeping in mind both accuracy and computation costs – 0.175 mm minimum cell size grid, RANS turbulence model, 48-species PRF mechanism, and multi-zone chemistry solution with bin limits of 5 K in temperature and 0.05 in equivalence ratio. With these settings, the performance of the CFD model is evaluated against experimental results corresponding to a low load start of injection (SOI) timing sweep. The model is then exercised to investigate the effect of SOI on combustion phasing with constant intake valve closing (IVC) conditions and fueling over a range of SOI timings to isolate the impact of SOI on charge preparation and ignition. Simulation results indicate that there is an optimum SOI timing, in this case -30?aTDC (after top dead center), which results in the most stable combustion. Advancing injection with respect to this point leads to significant fuel mass burning in the colder squish region, leading to retarded phasing and ultimately misfire for SOI timings earlier than -42?aTDC. On the other hand, retarding injection beyond this optimum timing results in reduced residence time available for gasoline ignition kinetics, and also leads to retarded phasing, with misfire at SOI timings later than -15?aTDC.

Energy conversion↗

DOE OSTI2026

SAVY-4000 Finite-Element Drop Test Analysis

PFE Auxiliary Systems conducted drop testing on SAVY-4000 containers to evaluate structural response under 12-foot drop conditions. In support of that effort, a finite-element modeling capability was developed to simulate drop response across multiple container sizes and impact orientations. The purpose of this work was to provide a consistent analysis framework that could support interpretation of testing, compare response trends across multiple configurations, and generate quantities of interest for later comparison with experimental data. More broadly, the analysis and testing were intended to assess whether the containers continued to perform their primary function after a 12-foot drop, namely maintaining structural integrity and containment of the contents. The modeling approach combined an implicit preload analysis with an explicit drop simulation so that each drop event began from a mechanically realistic assembled condition, including compression of the silicone O-ring. Separate models were developed for 2-quart, 5-quart, 12-quart, and 10-gallon containers. The results were evaluated in terms of strain-gauge response, collar-lid gap behavior, and accumulated plastic strain. In addition, parametric studies were performed on the 2-quart container to assess sensitivity to O-ring stiffness, friction, canister thickness, geometry tolerance, and mesh density. The simulations showed that predicted drop responses depended strongly on both container size and drop orientation. Gap metrics identified cases in which the predicted collar-lid opening exceeded the nominal O-ring cross-section threshold, while plastic strain metrics identified localized regions of elevated permanent deformation. Parametric studies showed that the predicted response was especially sensitive to the assumed O-ring stiffness and contact friction, while the geometry tolerance study produced smaller changes in the cases examined. The main value of this work was that it established a repeatable modeling and simulation workflow to support drop-test implementation, evaluate effects of future configuration changes, and understand modeling assumptions that most influenced predicted response. At the current stage, the results were viewed as preliminary model predictions rather than validated predictions. The next step would be to compare drop-test data to the model so that predictive values of the workflow could be refined and used with greater confidence to assess whether the containers maintained structural integrity and containment of the contents after a 12-foot drop.

42 ENGINEERING↗

DOE OSTI2026

Design and demonstration of a direct air capture system with moisture-driven CO 2 delivery into aqueous medium

Two direct air capture (DAC) systems were designed and demonstrated to passively capture CO 2 from ambient air and use moisture to release the CO2 into an alkaline medium. A bench-scale system delivering ∼1 g CO 2 d –1 was demonstrated in a laminar flow hood, and a small pilot-scale system that could deliver ∼100 g CO 2 d –1 was operated outdoors in a 4.2 m 2 raceway pond. Novel elongated mesh-tube packets containing anion-exchange resin (AER) beads were found to reduce drying and CO 2 loading time 4.3-fold compared to larger mesh bags. Technoeconomic analysis (TEA) estimates the cost of capturing CO 2 into an alkaline solution, suitable for cultivating photosynthetic microorganisms, to be $\$229$ per tonne for a practical scenario based on current results and $\$72$ per tonne for an aspirational scenario considering improvements to sorbent capacity, hydrophobicity, and sorbent lifetime. TEA further estimates an additional $\$110$ per tonne to extract CO 2 from solution, purify it, and compress it to 15 MPa, suitable for sequestration. Furthermore, moisture-driven processes have the potential to use up to 87% less energy than thermal and/or vacuum swing DAC by using energy from water evaporation.

09 BIOMASS FUELS↗

DOE OSTI2022

Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames

Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.

42 ENGINEERING↗

NASA NTRS1999

On Multi-Dimensional Unstructured Mesh Adaption

Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

Wood, William A.↗

NASA NTRS1975

On the calculation of supersonic, separating, and reattaching flows

A method is developed for solving the laminar and turbulent compressible boundary-layer equations for separating and reattaching flows. Results of this method are compared with experimental data for two laminar and three turbulent boundary-layer, shock-wave interactions. Several Navier-Stokes solutions were obtained for each of the laminar boundary-layer, shock-wave interactions considered. Comparison of these solutions indicates a first-order sensitivity in C sub f to the computational mesh selected in both the viscous and inviscid portions of the flow.

Murphy, J. D.↗

NASA NTRS1980

CAS2D: FORTRAN program for nonrotating blade-to-blade, steady, potential transonic cascade flows

An exact, full-potential-equation (FPE) model for the steady, irrotational, homentropic and homoenergetic flow of a compressible, homocompositional, inviscid fluid through two dimensional planar cascades of airfoils was derived, together with its appropriate boundary conditions. A computer program, CAS2D, was developed that numerically solves an artificially time-dependent form of the actual FPE. The governing equation was discretized by using type-dependent, rotated finite differencing and the finite area technique. The flow field was discretized by providing a boundary-fitted, nonuniform computational mesh. The mesh was generated by using a sequence of conforming mapping, nonorthogonal coordinate stretching, and local, isoparametric, bilinear mapping functions. The discretized form of the FPE was solved iteratively by using successive line overrelaxation. The possible isentropic shocks were correctly captured by adding explicitly an artificial viscosity in a conservative form. In addition, a three-level consecutive, mesh refinement feature makes CAS2D a reliable and fast algorithm for the analysis of transonic, two dimensional cascade flows.

Dulikravich, D. S.↗

NASA NTRS2012

Unresolved Problems by Shock Capturing: Taming the Overheating Problem

The overheating problem, first observed by von Neumann [1] and later studied extensively by Noh [2] using both Eulerian and Lagrangian formulations, remains to be one of the unsolved problems by shock capturing. It is historically well known to occur when a flow is under compression, such as when a shock wave hits and reflects from a wall or when two streams collides with each other. The overheating phenomenon is also found numerically in a smooth flow undergoing rarefaction created by two streams receding from each other. This is in contrary to one s intuition expecting a decrease in internal energy. The excessive amount in the temperature increase does not reduce by refining the mesh size or increasing the order of accuracy. This study finds that the overheating in the receding flow correlates with the entropy generation. By requiring entropy preservation, the overheating is eliminated and the solution is grid convergent. The shock-capturing scheme, as being practiced today, gives rise to the entropy generation, which in turn causes the overheating. This assertion stands up to the convergence test.

Liou, Meng-Sing↗

DOE OSTI2015

Electron beam simulation from gun to collector: Towards a complete solution

An electron-beam simulation technique for high-resolution complete EBIS/T modelling is presented. The technique was benchmarked on the high compression HEC{sup 2} test-stand with an electron beam current, current density and energy of 10 A, 10 kA/cm{sup 2} and 49.2 keV, and on the immersed electron beam at REXEBIS for electron beam characteristics of 0.4 A, 200 A/cm{sup 2} and 4.5 keV. In both Brillouin-like and immersed beams the electron-beam radius varies from several millimeters at the gun, through some hundreds of micrometers in the ionization region to a few centimeters at the collector over a total length of several meters. We report on our approach for finding optimal meshing parameters, based on the local beam properties such as magnetic field-strength, electron energy and beam radius. This approach combined with dividing the problem domain into sub-domains, and subsequent splicing of the local solutions allowed us to simulate the beam propagation in EBISes from the gun to the collector using a conventional PC in about 24–36 h. Brillouin-like electron beams propagated through the complete EBIS were used to analyze the beam behavior within the collector region. We checked whether elastically reflected paraxial electrons from a Brillouin-like beam will escape from the collector region and add to the loss current. We have also studied the power deposition profiles as function of applied potentials using two electrode geometries for a Brillouin-like beam including the effects of backscattered electrons.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗