Electromagnetic Pulse Simulations Using Finite-Difference Time-Domain Method

Shahid Ahmed, PhD, is a Senior Application Engineer at ANSYS, Inc. He has taught undergrad and graduate-level courses in physics, electrical, and electronics engineering. His research included experiments as well as computational modeling and simulations. He has published forty scholarly papers on various aspects of electromagnetics in peer-reviewed journals and conferences.

• Acknowledgments xiiiPreface xv1 Electromagnetic Pulse 11.1 Sources of EMP 11.2 EMP Coupling and its Effects 31.3 EMP Simulators 31.4 Review of Earlier Work 51.5 Overview of this Book 101.6 Summary 122 Time and Frequency Domain Analysis 132.1 Introduction 132.2 Nuclear Electromagnetic Pulse 142.2.1 Differences of Two Exponentials Times in a Unit Step Function 142.2.1.1 Time-Domain 152.2.1.2 Frequency-Domain 152.2.2 Reciprocal of the Sum of Two Exponentials 172.2.2.1 Time-Domain Characteristics 182.2.2.2 Frequency-Domain 192.3 Summary 223 Simulations Using FDTD Method 233.1 Introduction 233.2 Need for FDTD Analysis of an EMP Simulator 243.2.1 Choice of Method for Self-consistent Analysis 253.3 Maxwell’s Equations and the Yee Algorithm 253.4 FDTD Implementation 273.5 Numerical Issues 293.6 Summary 314 Electromagnetic Pulse in Free Space and Material Media 324.1 Introduction 324.2 Input Waveform 324.2.1 MATLAB® Script for Visualization: Listing #1 334.2.2 Execution of MATLAB/OCTAVE Code 354.3 One-dimension Approach 364.3.1 Free Space 364.3.1.1 MATLAB Code Listing #1: EM Wave Propagation in Free-space 384.3.2 Data Recording and Visualization 414.3.2.1 MATLAB Script for Visualization: Listing #2 414.3.3 Dielectric Medium 434.3.3.1 Lossless Dielectric Medium 444.3.3.2 MATLAB Code Listing #2: EM Wave in Air and Lossless-dielectric Medium 454.3.3.3 Lossy Dielectric Medium 494.3.3.4 MATLAB Code Listing #3: EM Wave in Air and Lossy-dielectric Medium 514.3.3.5 MATLAB Code Listing #4: Analytical Approach for Wave in Lossy Medium 554.3.4 Perfect Electric Conductor (PEC) 564.3.4.1 MATLAB Code Listing #5: EM Wave in Air-PEC Half-space 574.4 Summary 61Exercises 615 Simulation of Capacitor Bank 635.1 Introduction 635.2 Details of Model 645.2.1 Description of Geometry 645.2.2 Method of Charging 655.2.3 Method for Calculating FDTD Charge and Capacitance 665.2.4 FDTD Model of Closing Switch 685.2.5 Discharging a Charged Capacitor 695.3 Results and Discussion 705.3.1 Charge Deposition on Plates 705.3.2 Stabilization of Charge Density Distribution 715.3.3 Determination of Characteristic Discharge Time 725.4 Cross-check of FDTD Results Using Method-of-Moments 735.4.1 Check of Capacitance 745.4.2 Edge Effects on Charge Density Distribution 755.4.3 Check of Charge Density Distribution 765.5 Effect of Boundary Condition 785.6 Summary 80Exercises 816 Bounded Wave Simulator for Electromagnetic Pulses 836.1 Introduction 836.1.1 Organization of This Chapter 836.2 Geometry and Computational Model 856.2.1 Idealizations 856.2.2 Geometry 866.2.3 FDTD Model 876.3 Validation of TEM Structure Geometry 886.3.1 Analytical Check 886.3.2 Numerical Check 886.4 FDTD Model of Closing Switch 916.5 Choice of Distance to Domain Boundary 936.6 Electric Field within TEM Structure 936.6.1 Effect of Switch Closure Time 946.6.2 Pulse Fidelity 956.7 Flow of Current through Simulator Plates 966.8 Prepulse 966.9 Effect of Test Object 996.10 Validation Checks for FDTD Analysis 1016.11 Summary 102Exercises 1037 Electromagnetic Modes Inside Bounded Wave Simulators 1047.1 Introduction 1047.1.1 Choice of Method for Modal Analysis 1047.1.2 Organization of This Chapter 1057.2 Details of Model 1057.2.1 FDTD Model 1057.2.2 Qualitative Discussion of Mode Structure 1067.2.3 Application of SVD for Modal Analysis 1087.2.4 Validation of SVD Results 1097.2.5 Sample Calculation 1097.3 Modal Analysis of Simulator Without Test Object 1117.4 Modal Analysis of Simulator With Test Object 1197.4.1 Qualitative Analysis 1207.4.2 Quantitative Analysis Using SVD of Ex Data 1227.4.3 Quantitative Analysis Using SVD of Ez Data 1277.5 Physical Interpretation for Electric Field Increase 1317.6 Summary 135Exercises 1368 Parametric Study of Radiation Leakage from a Bounded-Wave Simulator 1388.1 Introduction 1388.2 Details of Computational Model 1398.3 Sensitivity to Length of Parallel-plate Extension 1408.4 Sensitivity to Angle Between Tapered Plates 1418.5 Effect of Type of Termination 1438.6 Sensitivity to Closure Time of Switch 1478.7 Effect of Test Object 1508.8 Physical Interpretation 1508.9 Summary 153Exercises 1549 Modal Perspective of Radiation Leakage from a Bounded-Wave Simulator 1559.1 Introduction 1559.2 Calculation Procedure 1569.3 Effect of Angle of Inclination Between Tapered Plates 1569.3.1 Correlation Study 1579.3.2 Physical Interpretation 1599.3.3 Variation of Leakage with Plate Angle 1619.4 Effect of Pulse Compression 1629.4.1 Effect on Radiation Leakage 1629.4.2 Explanation in Terms of Mode Structure 1639.5 Summary 165Exercises 16710 Spatial Mode Filter for Reducing Radiation Leakage 16810.1 Introduction 16810.2 Suppression of Higher Order Modes 16810.2.1 Optimal Value of Longitudinal Resistance 17010.2.2 Optimal Length of Suppressor Inside Test Volume 17310.2.3 Mode Structure with Suppressor in Presence of Test Object 17410.3 Summary 176Exercises 17711 EMP Interaction with Biological Tissues 17811.1 Introduction 17811.2 Model Description 17911.3 Results and Discussion 18111.3.1 Pulse Evolution in the TEM Cell 18111.3.2 Interaction of EMP with Human Body 18211.4 Summary 186Exercises 18612 FDTD Computer Program 18712.1 Introduction 18712.2 Computer Code Details 18712.3 Sample Output 24612.4 Summary 325References 326Index 331