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The Finite Element Method in Charged Particle Optics / by Anjam Khursheed.

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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,...

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Bibliographic Details
Online Access: Full Text (via Springer)
Main Author: Khursheed, Anjam
Format: eBook
Language:English
Published: Boston, MA : Springer US, 1999.
Series:International series in engineering and computer science ; 519.
Subjects:
Engineering.
Computational complexity.
Nuclear physics.
Computer engineering.
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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