Overview

This multidisciplinary book is intended to serve as a reference for postgraduate students and researchers working in the fields of charged particle optics or other finite-element-related applications. It is also suitable for use as a graduate text. For the non-specialist in charged particle optics, the opening chapters provide an introduction to the kinds of field problems that occur in charged particle beam systems. A comprehensive approach to the subject is taken. The finite element method is placed within a wider framework than strictly charged particle optics. Concepts developed in fluid flow and structural analysis, not hitherto used in charged particle optics, are presented. Benchmark test results provide a way of comparing the finite element method to other field-solving methods. The text also reports on some high-order interpolation techniques and mesh generation methods that will be of interest to other finite element researchers. Additional coverage includes: field theory and field solutions for charged particle optics; aspects of the finite difference method related to the finite element method; finite element theory and procedure, including detailed formulation of local and global matrices; higher-order elements, which can be an effective way of improving finite element accuracy; the finite element method in three dimensions; ways to formulate scalar and vector problems for magnetic fields; and significant reduction of truncation errors using higher-order elements and extrapolation methods.

Full Product Details

Author:   Anjam Khursheed
Publisher:   Springer
Imprint:   Springer
Edition:   1999 ed.
Volume:   519
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.290kg
ISBN:  

9780792386117

ISBN 10:   0792386116
Pages:   274
Publication Date:   30 September 1999
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
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Table of Contents

1. Field Theory.- 1. Electrostatics.- 2. Magnetostatics.- 2. Field Solutions for Charged Particle Optics.- 1. The Equations of motion.- 2. The Paraxial Equation of Motion.- 3. On-axis Lens Aberrations.- 4. Electrostatic and Magnetic Deflection Fields.- 3. The Finite Difference Method.- 1. Local finite 5pt difference equations.- 2. The Matrix Equation.- 3. Truncation errors.- 4. Asymmetric stars.- 5. Material Interfaces.- 6. The nine pointed star in rectilinear coordinates.- 7. Axisymmetric cylindrical coordinates.- 4. Finite Element Concepts.- 1. Finite Elements in one dimension.- 2. The Variational method in two dimensions.- 3. First-order shape functions.- 4. The Galerkin Method.- 5. Nodal equations and Matrix Assembly.- 6. Axisymmetric Cylindrical Coordinates.- 7. Edge elements.- 5. High-Order Elements.- 1. Triangle elements.- 2. Quadrilateral elements.- 3. The Serendipity family of elements.- 6. Elements in Three Dimensions.- 1. Element shape functions.- 2. Generating tetrahedral elements to fit curved boundary surfaces.- 7. FEM formulation in Magnetostatics.- 1. Magnetic vector potential.- 2. The magnetic scalar potential in three dimensions.- 3. Saturation Effects.- 8. Electric Lenses.- 1. Accuracy issues.- 2. Direct ray tracing using off-axis mesh node potentials.- 9. Magnetic Lenses.- 1. Accuracy issues.- 2. Magnetic axial field continuity tests.- 3. Magnetic field computations in three dimensions.- 10. Deflection Fields.- 1. Finite element formulation.- 2. Accuracy tests.- 11. Mesh Related Issues.- 1. Structured vs unstructured.- 2. The Boundary-fitted coordinate method.- 3. Mesh refinement for electron gun simulation.- 4. High-order interpolation.- 5. Flux line refinement for three dimensional electrostatic problems.- 6. Accuracy tests.- Appendix 1: Element Integration formulas.- 1. Gaussian Quadrature.- 2. Triangle elements.- Appendix 2: Second-order 9 node rectangle element pictorial stars.- Appendix 3: Green’s Integration formulas.- Appendix 4: Near-axis analytical solution for the solenoid test example.- Appendix 5: Deflection fields for a conical saddle yoke in free space.

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