The Finite Element Method in Charged Particle Optics / Edition 1

by Anjam Khursheed

Overview

In the span of only a few decades, the finite element method has become an important numerical technique for solving problems in the subject of charged particle optics. The situation has now developed up to the point where finite element simulation software is sold commercially and routinely used in industry. The introduction of the finite element method in charged particle optics came by way of a PHD thesis written by Eric Munro at the University of Cambridge, England, in 1971 [1], shortly after the first papers appeared on its use to solve Electrical Engineering problems in the late sixties. Although many papers on the use of the finite element method in charged particle optics have been published since Munro's pioneering work, its development in this area has not as yet appeared in any textbook. This fact must be understood within a broader context. The first textbook on the finite element method in Electrical Engineering was published in 1983 [2]. At present, there are only a handful of other books that describe it in relation to Electrical Engineering topics [3], let alone charged particle optics. This is but a tiny fraction of the books dedicated to the finite element method in other subjects such as Civil Engineering. The motivation to write this book comes from the need to redress this imbalance. There is also another important reason for writing this book.

Product Details

ISBN-13:	9780792386117
Publisher:	Springer US
Publication date:	09/30/1999
Series:	The Springer International Series in Engineering and Computer Science , #519
Edition description:	1999
Pages:	274
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

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.