Advances in Imaging and Electron Physics (eBook)

Front Cover 1
Advances in Imaging and Electron Physics 4
Copyright page 5
Contents 6
Preface 10
Foreword 12
Some Basic Notation 14
Future Contributions 16
Chapter 1: Integral Equations Method in Electrostatics 20
1.1. Statement of the Problem 21
1.2. Boundary Surface Approximation 25
1.3. Surface Charge Density Approximation 27
1.4. Interface Boundary Conditions for Dielectric Materials 31
1.5. Reducing the Integral Equations to the Finite-Dimensional Linear Equations System 33
1.6. Accuracy Benchmarks for Numerical Solution of 3D Electrostatic Problems 35
1.7. More Complicated Examples of 3D Field Simulation 39
1.8. Planar and Axial Symmetries 41
1.9. Calculation of Potential and its Derivatives Near the Boundary 45
1.10. Acceleration of Field Calculation: Finite-Difference Meshes and Calculation Domain Decomposition 48
1.11. Microscopic and Averaged Fields of Periodic Structures 51
Chapter 2: Surface Charge Singularities Near Irregular Surface Points 58
2.1. Two-Faced Conductive Wedge in Vacuum 59
2.2. Two-Faced Conductive Wedge in the Presence of Dielectrics 61
2.3. The Transfer Matrix Method 62
2.4. The Case of Pure Dielectric Vertex 65
2.5. Upper Bounds for the Singularity Index in the 2D Case 69
2.6. Variational Approach to the Spectral Problem 72
2.7. Three-Dimensional Corners 74
2.8. Variational Method in the Case of Dielectrics 77
2.9. Reduction to the 2D Case 78
2.10. On-Rib Singularities Near Three-Dimensional Corner 79
2.11. The Cases Allowing Separation of Variables 81
2.12. Numerical Solution of the Beltrami-Laplace Spectral Problem 83
2.13. Cubical and Prism Corners 86
Chapter 3: Geometry Perturbations 88
3.1. Integral Variational Equations and Conjugate Integral Equation for the Green Function 90
3.2. 3D Perturbations in Axisymmetric Systems 97
3.3. Examples of 3D Perturbations in Axisymmetric Systems 103
3.4. 3D Perturbations in Planar Systems 112
3.5. Locally Strong 3D Perturbations in Axisymmetric Systems 119
3.6. 3D Fringe Fields in Planar Systems 122
Chapter 4: Some Aspects of Magnetic Field Simulation 130
4.1. Vector and Scalar Potential Approaches 131
4.2. Direct Integration Over the Current Contours 133
4.3. Current Contours in the Presence of Materials with Constant Permeability 135
4.4. Variational Principle in 3D, Planar, and Axisymmetric Cases 136
4.5. Finite Element Modeling of Magnetic Systems with Saturable Materials 140
4.6. Second-Order FEM and Curvilinear Elements 148
4.7. Magnetic Superelements 149
4.8. The Boundary Element Approach in Magnetostatics 152
4.9. Hybrid Computational Methods 157
Chapter 5: Aberration Approach and the Tau-Variation Technique 164
5.1. Some Instructive Facts of the History of Aberration Theory 165
5.2. The Essence of the Tau-Variation Technique 169
5.3. The Tau-Variation Equations in Tensor Form 174
5.4. Arrival Time Variations and Contact Transformation 177
5.5. Jump Condition for Aberration Coefficients 181
5.6. Multiple Principal Trajectories Approach 183
5.7. Tolerance Analysis Using the Aberration Theory 185
5.8. Tracking Technique 188
5.9. Charged Particle Scattering 191
Chapter 6: Space Charge in Charged Particle Bunches 196
6.1. Self-Consistent Simulation of Thermionic Electron Guns 197
6.2. Cold-Cathode Approximation: Semi-Analytical Approach 206
6.3. Coulomb Field in Short Bunches: The Technique of Tree-Type Preordering 213
6.4. Exclusion of the External Field in Space Charge Problems 223
6.5. Some Examples of Ion Beam Simulation 225
Chapter 7: General Properties of Emission-Imaging Systems 230
7.1. Charged Particle Density Transformations and Electron Image 231
7.2. Spatiotemporal Spread Function: Isoplanatism Condition 241
7.3. Modulation and Phase Transfer Functions: Spatial and Temporal Resolution 247
Chapter 8: Static and Time-Analyzing Image Tubes With Axial Symmetry 260
8.1. Spatial Aberrations of the Electron Image Formed by Electrostatic Systems 264
8.2. Temporal Aberrations in Streak Image Tubes 274
8.3. High-Frequency Asymptotics of MTF and PTF in Image Tubes 277
8.4. Examples of the Spread Functions, MTF and PTF in Image Tubes 284
8.5. The Boundary-Layer Effect in Cathode Lenses and Electron Mirrors 289
Chapter 9: Spatial and Temporal Focusing of Photoelectron Bunches in Time-Dependent Electric Fields 298
9.1. Two Different Jobs that Ultrashort Electron Bunches Can Do 299
9.2. The Master Equation of First-Order Temporal Focusing 301
9.3. Moving Potential well as a Simple Example of Temporal Focusing 306
9.4. Thin Temporal Lens Approximation 307
9.5. Second-Order Aberrations and Quantum-Mechanical Limitations 310
9.6. Approximate Estimation of the Space Charge Effects Contribution 311
9.7. Simulation of a Photoelectron Gun with Time-Dependent Electric Field and Some Experimental Results 313
Appendices 324
Appendix 1: Some Gauss Quadrature Formulas 324
Appendix 2: Numerical Integration of the Green Functions with Coulomb Singularities in the Conincidence Limit 330
References 352
Contents of Volumes 151–154 360
Index 362