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The Finite Element Method in Charged Particle Optics

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...

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Bibliographic Details
Main Author: Khursheed, Anjam
Format: eBook
Language:English
Published: New York, NY Springer US 1999, 1999
Edition:1st ed. 1999
Series:The Springer International Series in Engineering and Computer Science
Subjects:
Laser
Nuclear Physics
Computer Science / Mathematics
Discrete Mathematics In Computer Science
Electrical And Electronic Engineering
Electrical Engineering
Lasers
Discrete Mathematics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
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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