High Power Microwave Sources and Technologies Using Metamaterials

JOHN LUGINSLAND, PHD, is a Senior Scientist at Confluent Sciences, LLC and an Adjunct Professor at Michigan State University. Previously, he worked at AFOSR serving as the Plasma Physics and Lasers and Optics Program Officer, as well as various technical leadership roles. Additionally, he worked for SAIC and NumerEx, as well as the Directed Energy Directorate of the Air Force Research Laboratory (AFRL). He is a Fellow of the IEEE and AFRL. JASON A. MARSHALL, PHD, is The Associate Superintendent, Plasma Physics Division, Naval Research Laboratory. Prior to this he was a Principal Scientist with the Air Force Office of Scientific Research responsible for management and execution of the Air Force basic research investments in Plasma and Electro-energetic Physics. ARJE NACHMAN, PHD, is the Program Officer for Electromagnetics at AFOSR. He has worked at AFOSR since 1985. Before that he was on the mathematics faculty of Texas A&M and Old Dominion University, and a Senior Scientist at Southwest Research Institute (SwRI). EDL SCHAMILOGLU, PHD, is a Distinguished Professor of Electrical and Computer Engineering at the University of New Mexico, where he also serves as Associate Dean for Research and Innovation in the School of Engineering, and Special Assistant to the Provost for Laboratory Relations. He is a Fellow of the IEEE and the American Physical Society.

• Editor Biographies xiList of Contributors xiiiForeword xviiPreface xix1 Introduction and Overview of the Book 1Rebecca Seviour1.1 Introduction 11.2 Electromagnetic Materials 21.3 Effective-Media Theory 41.4 History of Effective Materials 41.4.1 Artificial Dielectrics 41.4.2 Artificial Magnetic Media 51.5 Double Negative Media 71.5.1 DNG Realization 91.6 Backward Wave Propagation 91.7 Dispersion 101.8 Parameter Retrieval 121.9 Loss 131.10 Summary 14References 142 Multitransmission Line Model for Slow Wave Structures Interacting with Electron Beams and Multimode Synchronization 17Ahmed F. Abdelshafy, Mohamed A.K. Othman, Alexander Figotin, and Filippo Capolino2.1 Introduction 172.2 Transmission Lines: A Preview 182.2.1 Multiple Transmission Line Model 182.3 Modeling of Waveguide Propagation Using the Equivalent Transmission Line Model 202.3.1 Propagation in Uniform Waveguides 212.3.2 Propagation in Periodic Waveguides 222.3.3 Floquet’s Theorem 242.4 Pierce Theory and the Importance of Transmission Line Model 252.5 Generalized Pierce Model for Multimodal Slow Wave Structures 282.5.1 Multitransmission Line Formulation Without Electron Beam: “Cold SWS” 282.5.2 Multitransmission Line Interacting with an Electron Beam: “Hot SWS” 302.6 Periodic Slow-Wave Structure and Transfer Matrix Method 322.7 Multiple Degenerate Modes Synchronized with the Electron Beam 342.7.1 Multimode Degeneracy Condition 342.7.2 Degenerate Band Edge (DBE) 342.7.3 Super Synchronization 352.7.4 Complex Dispersion Characteristics of a Periodic MTL Interacting with an Electron Beam 382.8 Giant Amplification Associated to Multimode Synchronization 392.9 Low Starting Electron Beam Current in Multimode Synchronization-Based Oscillators 422.10 SWS Made by Dual Nonidentical Coupled Transmission Lines Inside a Waveguide 462.10.1 Dispersion Engineering Using Dual Nonidentical Pair of TLs 472.10.2 BWO Design Using Butterfly Structure 492.11 Three-Eigenmode Super Synchronization: Applications in Amplifiers 502.12 Summary 53References 543 Generalized Pierce Model from the Lagrangian 57Alexander Figotin and Guillermo Reyes3.1 Introduction 573.2 Main Results 593.2.1 Lagrangian Structure of the Standard Pierce Model 593.2.2 Multiple Transmission Lines 603.2.3 The Amplification Mechanism and Negative Potential Energy 603.2.4 Beam Instability and Degenerate Beam Lagrangian 613.2.5 Full Characterization of the Existence of an Amplifying Regime 613.2.6 Energy Conservation and Fluxes 623.2.7 Negative Potential Energy and General Gain Media 623.3 Pierce’s Model 633.4 Lagrangian Formulation of Pierce’s Model 653.4.1 The Lagrangian 653.4.2 Generalization to Multiple Transmission Lines 673.5 Hamiltonian Structure of the MTLB System 683.5.1 Hamiltonian Forms for Quadratic Lagrangian Densities 683.5.2 The MTLB System 703.6 The Beam as a Source of Amplification: The Role of Instability 713.6.1 Space Charge Wave Dynamics: Eigenmodes and Stability Issues 713.7 Amplification for the Homogeneous Case 743.7.1 Asymptotic Behavior of the Amplification Factor as ξ → 0 and as ξ → ∞ 773.8 Energy Conservation and Transfer 773.8.1 Energy Exchange Between Subsystems 783.9 The Pierce Model Revisited 803.10 Mathematical Subjects 823.10.1 Energy Conservation via Noether’s Theorem 823.10.2 Energy Exchange Between Subsystems 833.11 Summary 84References 844 Dispersion Engineering for Slow-Wave Structure Design 87Ushe Chipengo, Niru K. Nahar, John L. Volakis, Alan D. R. Phelps, and Adrian W. Cross4.1 Introduction 874.2 Metamaterial Complementary Split Ring Resonator-Based Slow-Wave Structure 884.2.1 Complementary Split Ring Resonator Plate-Loaded Metamaterial Waveguide: Design 894.2.2 Complementary Split Ring Resonator Plate-Loaded Metamaterial Waveguide: Fabrication and Cold Test 924.3 Broadside Coupled Split Ring Resonator-Based Metamaterial Slow-Wave Structure 944.3.1 Broadside-Coupled Split Ring-Loaded Metamaterial Waveguide: Design 944.3.2 Broadside-Coupled Split Ring-Loaded Metamaterial Waveguide: Fabrication and Cold Test 974.4 Iris Ring-Loaded Waveguide Slow-Wave Structure with a Degenerate Band Edge 974.4.1 Iris Loaded-DBE Slow-Wave Structure: Design 1004.4.2 Iris-Loaded DBE Slow-Wave Structure: Fabrication and Cold Test 1024.5 Two-Dimensional Periodic Surface Lattice-Based Slow-Wave Structure 1024.5.1 Two-Dimensional Periodic Surface Lattice Slow-Wave Structure: Design 1044.5.2 Two-Dimensional Periodic Surface Lattice Slow-Wave Structure: Fabrication and Cold Test 1064.6 Curved Ring-Bar Slow-Wave Structure for High-Power Traveling Wave Tube Amplifiers 1074.6.1 Curved Ring-Bar Slow-Wave Structure: Design 1084.6.2 Curved Ring-Bar Slow-Wave Structure: Fabrication and Cold Testing 1124.7 A Corrugated Cylindrical Slow-Wave Structure with Cavity Recessions and Metallic Ring Insertions 1144.7.1 Design of a Corrugated Cylindrical Slow-Wave Structure with Cavity Recessions and Metallic Ring Insertions 1164.7.2 Fabrication and Cold testing of a Homogeneous, Corrugated Cylindrical Slow-Wave Structure with Cavity Recessions and Metallic Ring Insertions 1194.7.3 Inhomogeneous SWS design based on the Corrugated Cylindrical SWS with Cavity Recessions and Metallic Ring Insertions: Fabrication and Cold Testing 1214.8 Summary 123References 1235 Perturbation Analysis of Maxwell’s Equations 127Robert Lipton, Anthony Polizzi, and Lokendra Thakur5.1 Introduction 1275.2 Gain from Floating Interaction Structures 1295.2.1 Anisotropic Effective Properties and the Dispersion Relation 1305.2.2 A Pierce-Like Approach to Dispersion 1335.3 Gain from Grounded Interaction Structures 1335.3.1 Model Description 1345.3.2 Physics of Waveguides and Maxwell’s Equations 1345.3.3 Perturbation Series for Leading Order Dispersive Behavior 1375.3.4 Leading Order Theory of Gain for Hybrid Space Charge Modes for a Corrugated SWS with Beam 1385.3.4.1 Hybrid Modes in Beam 1405.3.4.2 Impedance Condition 1415.3.4.3 Cold Structure 1415.3.4.4 Pierce Theory 1425.4 Electrodynamics Inside a Finite-Length TWT: Transmission Line Model 1425.4.1 Solution of the Transmission Line Approximation 1455.4.2 Discussion of Results 1455.5 Corrugated Oscillators 1485.5.1 Oscillator Geometry 1485.5.2 Solutions of Maxwell’s Equations in the Oscillator 1495.5.3 Perturbation Expansions 1515.5.4 Leading Order Theory: The Subwavelength Limit of the Asymptotic Expansions 1515.5.5 Dispersion Relation for δω 1525.6 Summary 154References 1546 Similarity of the Properties of Conventional Periodic Structures with Metamaterial Slow Wave Structures 157Sabahattin Yurt, Edl Schamiloglu, Robert Lipton, Anthony Polizzi, and Lokendra Thakur6.1 Introduction 1576.2 Motivation 1576.3 Observations 1596.3.1 Appearance of Negative Dispersion for Low-Order Waves 1596.3.2 Evolution of Wave Dispersion in Uniform Periodic Systems with Increasing Corrugation Depth 1606.3.2.1 SWS with Sinusoidal Corrugations 1616.3.2.2 SWS with Rectangular Corrugations 1646.4 Analysis of Metamaterial Surfaces from Perfectly Conducting Subwavelength Corrugations 1686.4.1 Approach 1696.4.2 Model Description 1696.4.2.1 Physics of Waveguides and Maxwell’s Equations 1706.4.2.2 Two-Scale Asymptotic Expansions 1726.4.2.3 Leading Order Theory: The Subwavelength Limit of the Asymptotic Expansions 1726.4.2.4 Nonlocal Surface Impedance Formulation for Time Harmonic Fields 1736.4.2.5 Effective Surface Impedance for Hybrid Modes in Circular Waveguides 1746.4.3 Metamaterials and Corrugations as Microresonators 1756.4.4 Controlling Negative Dispersion and Power Flow with Corrugation Depth 1776.4.5 Summary 182References 1827 Group Theory Approach for Designing MTM Structures for High-Power Microwave Devices 185Hamide Seidfaraji, Christos Christodoulou, and Edl Schamiloglu7.1 Group Theory Background 1857.1.1 Symmetry Elements 1867.1.2 Symmetry Point Group 1877.1.3 Character Table 1877.2 MTM Analysis Using Group Theory 1887.2.1 Split Ring Resonator Behavior Analysis Using Group Theory 1897.2.1.1 Principles of Group Theory 1897.2.1.2 Basis Current in SSRs 1917.3 Inverse Problem-Solving Using Group Theory 1947.4 Designing an Ideal MTM 1957.5 Proposed New Structure Using Group Theory 1957.6 Design of Isotropic Negative Index Material 1977.7 Multibeam Backward Wave Oscillator Design using MTM and Group Theory 1997.7.1 Introduction and Motivation 1997.7.2 Metamaterial Design 2007.7.3 Theory of Electron Beam Interaction with Metamaterial Waveguide 2037.7.4 Hot Test Particle-in-Cell Simulations 2047.8 Particle-in-Cell Simulations 2047.9 Efficiency 2077.10 Summary 208References 2098 Time-Domain Behavior of the Evolution of Electromagnetic Fields in Metamaterial Structures 211Mark Gilmore, Tyler Wynkoop, and Mohamed Aziz Hmaidi8.1 Introduction 2118.2 Experimental Observations 2128.2.1 Bandstop Filter (BSF) System 2158.2.2 Bandpass Filter (BPF) System 2178.3 Numerical Simulations 2248.3.1 Bandstop System (BSF) 2258.3.2 Bandpass Filter System (BPF) 2268.3.3 Experiment-Model Comparison 2278.4 Attempts at a Linear Circuit Model 229References 2309 Metamaterial Survivability in the High-Power Microwave Environment 233Rebecca Seviour9.1 Introduction 2339.2 Split Ring Resonator Loss 2349.3 CSRR Loss 2379.4 Artificial Material Loss 2399.5 Disorder 2419.6 Summary 242References 24410 Experimental Hot Test of Beam/Wave Interactions with Metamaterial Slow Wave Structures 245Michael A. Shapiro, Jason S. Hummelt, Xueying Lu, and Richard J. Temkin10.1 First-Stage Experiment at MIT 24610.1.1 Metamaterial Structure 24610.1.2 Experimental Results 24710.1.3 Summary of First-Stage Experiments 25110.2 Second-Stage Experiment at MIT 25110.3 Metamaterial Structure with Reverse Symmetry 25210.4 Experimental Results on High-Power Generation 25510.5 Frequency Measurement in Hot Test 25710.6 Steering Coil Control 26210.7 University of New Mexico/University of California Irvine Collaboration on a High Power Metamaterial Cherenkov Oscillator 26410.8 Summary 264References 26511 Conclusions and Future Directions 267John Luginsland, Jason A. Marshall, Arje Nachman, and Edl SchamilogluReferences 268Index 271