The Finite Element Method in Charged Particle Optics

By: Anjam Khursheed

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Hardcover | 30 September 1999

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292 Pages

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23.39 x 15.6 x 1.75

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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, the opening chapters provide an introduction to the kinds of field problems that occur in charged particle beam systems.
A new and 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 book 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.

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Published: 11th February 2013

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Preface
Acknowledgements
Field Theory	p. 1
Electrostatics	p. 1
Magnetostatics	p. 11
Field Solutions for Charged Particle Optics	p. 25
The Equations of motion	p. 25
The Paraxial Equation of Motion	p. 29
On-axis Lens Aberrations	p. 32
Electrostatic and Magnetic Deflection Fields	p. 37
The Finite Difference Method	p. 45
Local finite 5pt difference equations	p. 46
The Matrix Equation	p. 47
Truncation errors	p. 49
Asymmetric stars	p. 50
Material Interfaces	p. 53
The nine pointed star in rectilinear coordinates	p. 55
Axisymmetric cylindrical coordinates	p. 56
Finite Element Concepts	p. 61
Finite Elements in one dimension	p. 62
The Variational method in two dimensions	p. 70
First-order shape functions	p. 75
The Galerkin Method	p. 84
Nodal equations and Matrix Assembly	p. 87
Axisymmetric Cylindrical Coordinates	p. 92
Edge elements	p. 96
High-Order Elements	p. 99
Triangle elements	p. 99
Quadrilateral elements	p. 105
The Serendipity family of elements	p. 106
Elements in three Dimensions	p. 111
Element shape functions	p. 112
Generating tetrahedral elements to fit curved boundary surfaces	p. 114
FEM formulation in Magnetostatics	p. 125
Magnetic vector potential	p. 125
The magnetic scalar potential in three dimensions	p. 131
Saturation Effects	p. 135
Electric Lenses	p. 141
Accuracy issues	p. 141
Direct ray tracing using off-axis mesh node potentials	p. 154
Magnetic Lenses	p. 161
Accuracy issues	p. 162
Magnetic axial field continuity tests	p. 176
Magnetic field computations in three dimensions	p. 187
Deflection Fields	p. 191
Finite element formulation	p. 191
Accuracy tests	p. 195
Mesh Related Issues	p. 209
Structured vs unstructured	p. 209
The Boundary-fitted coordinate method	p. 217
Mesh refinement for electron gun simulation	p. 224
High-order interpolation	p. 230
Flux line refinement for three dimensional electrostatic problems	p. 238
Accuracy tests	p. 239
Element Integration formulas	p. 257
Second-order 9 node rectangle element pictorial stars	p. 259
Green's Integration formulas	p. 265
Near-axis analytical solution for the solenoid test example	p. 267
Deflection fields for a conical saddle yoke in free space	p. 269
Index	p. 273
Table of Contents provided by Blackwell. All Rights Reserved.

The Finite Element Method in Charged Particle Optics

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