Chapter |
Section |
Title |
Page |
| | Preface | xi |
1 | | A Review Of Basic Electrostatics | 1 |
| 1.1 | Charge, Force And The Electric Field | 1 |
| 1.2 | Electric Flux Density And Gauss' Law | 5 |
| 1.3 | Conductors | 7 |
| 1.4 | Potential, Gradient And Capacitance | 10 |
| 1.5 | Energy In The Electric Field | 16 |
| 1.6 | Summations | 17 |
| 1.7 | Poisson's and Laplace's Equations | 18 |
| 1.8 | Dielectric Interfaces | 20 |
| 1.9 | The Case For Approximate Numerical Analysis | 27 |
| | Problems | 29 |
| | - - - - - - - - - - | |
2 | | The Uses Of Electrostatics | 33 |
| 2.1 | Basic Circuit Theory | 33 |
| 2.2 | Radio Frequency Transmission Lines | 41 |
| 2.3 | Vacuum Tubes and Cathode Ray Tubes | 44 |
| 2.4 | Field Emission And The Scanning Electron Microscope | 47 |
| 2.5 | Electrostatic Force Devices | 48 |
| 2.6 | Gas Discharges And Lighting Devices | 49 |
| | Problems | 50 |
| | - - - - - - - - - - | |
3 | | Introduction To The Method Of Moments Technique
For Electrostatics | 51 |
| 3.1 | Fundamental Equations | 51 |
| 3.2 | A Working Equation Set | 55 |
| 3.3 | The Single Point Approximation For Off-Diagonal Terms | 56 |
| 3.4 | Exact Solutions For Diagonal And In-Plane Terms | 57 |
| 3.5 | Approximating Li,j | 61 |
| | Problems | 64 |
| | - - - - - - - - - - | |
4 | | Examples Using The Method Of Moments | 67 |
| 4.1 | A First Modeling Program | 67 |
| 4.2 | Input Data File Preparation For The First Modeling Program | 68 |
| 4.3 | Processing The Input Data | 71 |
| 4.4 | Generating The Li,j Array | 73 |
| 4.5 | Solving The System And Examining Some Results | 73 |
| 4.6 | Limits Of Resolution | 76 |
| 4.7 | Voltages And Fields | 78 |
| 4.8 | Varying The Geometry | 82 |
| | Problems | 87 |
| | - - - - - - - - - - | |
5 | | Symmetries, Images And Dielectrics | 89 |
| 5.1 | Symmetries | 89 |
| 5.2 | Images | 90 |
| 5.3 | Multiple Images And The Symmetric Stripline | 95 |
| 5.4 | Dielectric Interfaces | 102 |
| 5.5 | Two-Dimensional Cross Sections Of Three-Dimensional Structures | 108 |
| 5.6 | Charge Profiles And Current Bunching | 113 |
| 5.7 | Cylinder Between Two Planes | 116 |
| | Problems | 121 |
| | - - - - - - - - - - | |
6 | | Triangles | 123 |
| 6.1 | Introduction To Triangular Cells | 123 |
| 6.2 | Right Triangles | 124 |
| 6.3 | Calculating Li,i (Self) Coefficients | 125 |
| 6.4 | Calculating Li,j | 127 |
| 6.5 | Basic Meshing And Data Formats For Triangular Cell
MOM Programs | 127 |
| 6.6 | Using Matlab To Generate Triangular Meshings | 135 |
| 6.7 | Calculting Voltages | 139 |
| 6.8 | Calculating The Electric Field | 141 |
| 6.9 | Three-Dimensional Structures | 143 |
| 6.10 | Charge Profiles | 152 |
| | Problems | 156 |
| | - - - - - - - - - - | |
7 | | Summary And Overview | 159 |
| 7.1 | Where We Were, Where We Are Going | 159 |
| | - - - - - - - - - - | |
8 | | The Finite Difference Method | 163 |
| 8.1 | Introduction And A Simple Example | 163 |
| 8.2 | Setting Up And Solving A Basic Problem | 165 |
| 8.3 | The Gauss-Seidel (Relaxation) Solution Technique | 172 |
| 8.4 | Charge, Gauss' Law, Resolution | 175 |
| 8.5 | Voltages And Fields | 177 |
| 8.6 | Stored Energy And Capacitance | 178 |
| | Problems | 178 |
| | - - - - - - - - - - | |
9 | | Refining The Finite Difference Method | 183 |
| 9.1 | Refined Grids | 183 |
| 9.2 | Arbitrary Conductor Shapes | 189 |
| 9.3 | Mixed Dielectric Regions And A New Derivation Of The
Finite Difference Equation | 195 |
| 9.4 | Example: Structure With A Dielectric Interface | 112 |
| 9.5 | AxiSymmetric Cylindrical Coordinates | 196 |
| 9.6 | Symmetry Boundardy Conditions | 205 |
| 9.7 | Duality, Upper And Lower Bounds To Solutions For
Transmission Lines | 207 |
| 9.8 | Extrapolation | 214 |
| 9.9 | Three-Dimensional Grids | 217 |
| | Problems | 223 |
| | - - - - - - - - - - | |
10 | | Multielectrode Systems | 227 |
| 10.1 | Multielectrode Structures | 227 |
| 10.2 | Utilizing Superposition | 229 |
| 10.3 | Utilitizing Symmetry | 230 |
| 10.4 | Circuital Relations And A Caveat | 230 |
| 10.5 | Floating Electrodes | 232 |
| | Problems | 234 |
| | - - - - - - - - - - | |
11 | | Probabilistic Potential Theory | 237 |
| 11.1 | Random Walks And The Diffusion Equation | 237 |
| 11.2 | Potential At A Point From Random Walks | 239 |
| 11.3 | Diffusion | 246 |
| 11.4 | Variable Step Size Random Walks | 249 |
| 11.5 | Three-Dimensional Structures | 260 |
| | Problems | 216 |
| | - - - - - - - - - - | |
12 | | The Finite Element Method | 261 |
| 12.1 | Introduction | 265 |
| 12.2 | Solving Laplace's Equation By Minimizing
Stored Energy | 266 |
| 12.3 | A Simple One Dimensional Example | 267 |
| 12.4 | A Very Simple Finite Element Approximation | 271 |
| 12.5 | Arbitrary Number Of Lines Approximation | 274 |
| 12.6 | Mixed Dielectrics | 278 |
| 12.7 | A Quadratic Approximation | 279 |
| 12.8 | A Simple Two-Dimensional FEM Program | 282 |
| | Problems | 287 |
| | - - - - - - - - - - | |
13 | | Triangles And Two-Dimensional Unstructured
Grids | 289 |
| 13.1 | Introduction | 289 |
| 13.2 | Aside: The Area Of A Triangle | 290 |
| 13.3 | The Coefficient Matrix | 291 |
| 13.4 | A Simple Example | 293 |
| 13.5 | A Two-Dimensional Triangular Mesh Program | 296 |
| | Problems | 300 |
| | - - - - - - - - - - | |
14 | | A Zoning System And Some Examples | 303 |
| 14.1 | General Introduction | 303 |
| 14.2 | Introduction To gmsh | 304 |
| 14.3 | Translating The gmsh File | 308 |
| 14.4 | Running The FEM Analysis | 319 |
| 14.5 | More gmsh Features And Examining The Electric Field | 320 |
| 14.6 | Multiple Electrodes | 324 |
| | Problems | 327 |
| | - - - - - - - - - - | |
15 | | Some FEM Topics | 329 |
| 15.1 | Symmetries | 329 |
| 15.2 | A Symmetry Example, Including A Two-Sided
Capacitance Estimate | 330 |
| 15.3 | Axisymmetric Structures | 337 |
| 15.4 | The Graded Potetial Boundary Condition | 348 |
| 15.5 | Unbounded Regions | 352 |
| 15.6 | Dielectric Material | 364 |
| | - - - - - - - - - - | |
| | Problems | 371 |
16 | | FEM In Three-Dimensions | 375 |
| 16.1 | Creating Three-Dimensional Meshes | 375 |
| 16.2 | The FEM Coefficient Matrix In Three Dimensions | 384 |
| 16.3 | Parsing The gmsh Files And Setting The Boundary
Conditions | 386 |
| 16.4 | Open Boundaries And Cylinders In Space | 392 |
| | - - - - - - - - - - | |
| | Problems | 396 |
17 | | Electrostatic Forces | 401 |
| 17.1 | Introduction | 401 |
| 17.2 | Electron Beam Acceleration And Control | 402 |
| 17.3 | The Electrostatic Relay | 410 |
| 17.4 | Electrets And Piezoelectricity: An Overview | 416 |
| 17.5 | Points On A Sphere | 417 |
| | Problems | 421 |
| | - - - - - - - - - - | |
| | Appendix: Interfacing With Other Languages | 425 |
| | - - - - - - - - - - | |
| | Index | 430 |
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