High Power Microwave Sources and Technologies Using Metamaterials
Description
A stand-alone follow-up to the highly successful High Power Microwave Sources and Technologies, the new High Power Microwave Sources and Technologies Using Metamaterials, demonstrates how metamaterials have impacted the field of high-power microwave sources and the new directions revealed by the latest research. It's written by a distinguished team of researchers in the area who explore a new paradigm within which to consider the interaction of microwaves with material media.
Providing contributions from multiple institutions that discuss theoretical concepts as well as experimental results in slow wave structure design, this edited volume also discusses how traditional periodic structures used since the 1940s and 1950s can have properties that, until recently, were attributed to double negative metamaterial structures.
The book also includes:
* A thorough introduction to high power microwave oscillators and amplifiers, as well as how metamaterials can be introduced as slow wave structures and other components
* Comprehensive explorations of theoretical concepts in dispersion engineering for slow wave structure design, including multi-transmission line models and particle-in-cell code virtual prototyping models
* Practical discussions of experimental measurements in dispersion engineering for slow wave structure design
* In-depth examinations of passive and active components, as well as the temporal evolution of electromagnetic fields
High Power Microwave Sources and Technologies Using Metamaterials is a perfect resource for graduate students and researchers in the areas of nuclear and plasma sciences, microwaves, and antennas.
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Persons
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.
Content
Editor Biographies xi
List of Contributors xiii
Foreword xvii
Preface xix
1 Introduction and Overview of the Book 1
Rebecca Seviour
1.1 Introduction 1
1.2 Electromagnetic Materials 2
1.3 Effective-Media Theory 4
1.4 History of Effective Materials 4
1.4.1 Artificial Dielectrics 4
1.4.2 Artificial Magnetic Media 5
1.5 Double Negative Media 7
1.5.1 DNG Realization 9
1.6 Backward Wave Propagation 9
1.7 Dispersion 10
1.8 Parameter Retrieval 12
1.9 Loss 13
1.10 Summary 14
References 14
2 Multitransmission Line Model for Slow Wave Structures Interacting with Electron Beams and Multimode Synchronization 17
Ahmed F. Abdelshafy, Mohamed A.K. Othman, Alexander Figotin, and Filippo Capolino
2.1 Introduction 17
2.2 Transmission Lines: A Preview 18
2.2.1 Multiple Transmission Line Model 18
2.3 Modeling of Waveguide Propagation Using the Equivalent Transmission Line Model 20
2.3.1 Propagation in Uniform Waveguides 21
2.3.2 Propagation in Periodic Waveguides 22
2.3.3 Floquet's Theorem 24
2.4 Pierce Theory and the Importance of Transmission Line Model 25
2.5 Generalized Pierce Model for Multimodal Slow Wave Structures 28
2.5.1 Multitransmission Line Formulation Without Electron Beam: "Cold SWS" 28
2.5.2 Multitransmission Line Interacting with an Electron Beam: "Hot SWS" 30
2.6 Periodic Slow-Wave Structure and Transfer Matrix Method 32
2.7 Multiple Degenerate Modes Synchronized with the Electron Beam 34
2.7.1 Multimode Degeneracy Condition 34
2.7.2 Degenerate Band Edge (DBE) 34
2.7.3 Super Synchronization 35
2.7.4 Complex Dispersion Characteristics of a Periodic MTL Interacting with an Electron Beam 38
2.8 Giant Amplification Associated to Multimode Synchronization 39
2.9 Low Starting Electron Beam Current in Multimode Synchronization-Based Oscillators 42
2.10 SWS Made by Dual Nonidentical Coupled Transmission Lines Inside a Waveguide 46
2.10.1 Dispersion Engineering Using Dual Nonidentical Pair of TLs 47
2.10.2 BWO Design Using Butterfly Structure 49
2.11 Three-Eigenmode Super Synchronization: Applications in Amplifiers 50
2.12 Summary 53
References 54
3 Generalized Pierce Model from the Lagrangian 57
Alexander Figotin and Guillermo Reyes
3.1 Introduction 57
3.2 Main Results 59
3.2.1 Lagrangian Structure of the Standard Pierce Model 59
3.2.2 Multiple Transmission Lines 60
3.2.3 The Amplification Mechanism and Negative Potential Energy 60
3.2.4 Beam Instability and Degenerate Beam Lagrangian 61
3.2.5 Full Characterization of the Existence of an Amplifying Regime 61
3.2.6 Energy Conservation and Fluxes 62
3.2.7 Negative Potential Energy and General Gain Media 62
3.3 Pierce's Model 63
3.4 Lagrangian Formulation of Pierce's Model 65
3.4.1 The Lagrangian 65
3.4.2 Generalization to Multiple Transmission Lines 67
3.5 Hamiltonian Structure of the MTLB System 68
3.5.1 Hamiltonian Forms for Quadratic Lagrangian Densities 68
3.5.2 The MTLB System 70
3.6 The Beam as a Source of Amplification: The Role of Instability 71
3.6.1 Space Charge Wave Dynamics: Eigenmodes and Stability Issues 71
3.7 Amplification for the Homogeneous Case 74
3.7.1 Asymptotic Behavior of the Amplification Factor as ¿ ¿ 0 and as ¿ ¿ 8 77
3.8 Energy Conservation and Transfer 77
3.8.1 Energy Exchange Between Subsystems 78
3.9 The Pierce Model Revisited 80
3.10 Mathematical Subjects 82
3.10.1 Energy Conservation via Noether's Theorem 82
3.10.2 Energy Exchange Between Subsystems 83
3.11 Summary 84
References 84
4 Dispersion Engineering for Slow-Wave Structure Design 87
Ushe Chipengo, Niru K. Nahar, John L. Volakis, Alan D. R. Phelps, and Adrian W. Cross
4.1 Introduction 87
4.2 Metamaterial Complementary Split Ring Resonator-Based Slow-Wave Structure 88
4.2.1 Complementary Split Ring Resonator Plate-Loaded Metamaterial Waveguide: Design 89
4.2.2 Complementary Split Ring Resonator Plate-Loaded Metamaterial Waveguide: Fabrication and Cold Test 92
4.3 Broadside Coupled Split Ring Resonator-Based Metamaterial Slow-Wave Structure 94
4.3.1 Broadside-Coupled Split Ring-Loaded Metamaterial Waveguide: Design 94
4.3.2 Broadside-Coupled Split Ring-Loaded Metamaterial Waveguide: Fabrication and Cold Test 97
4.4 Iris Ring-Loaded Waveguide Slow-Wave Structure with a Degenerate Band Edge 97
4.4.1 Iris Loaded-DBE Slow-Wave Structure: Design 100
4.4.2 Iris-Loaded DBE Slow-Wave Structure: Fabrication and Cold Test 102
4.5 Two-Dimensional Periodic Surface Lattice-Based Slow-Wave Structure 102
4.5.1 Two-Dimensional Periodic Surface Lattice Slow-Wave Structure: Design 104
4.5.2 Two-Dimensional Periodic Surface Lattice Slow-Wave Structure: Fabrication and Cold Test 106
4.6 Curved Ring-Bar Slow-Wave Structure for High-Power Traveling Wave Tube Amplifiers 107
4.6.1 Curved Ring-Bar Slow-Wave Structure: Design 108
4.6.2 Curved Ring-Bar Slow-Wave Structure: Fabrication and Cold Testing 112
4.7 A Corrugated Cylindrical Slow-Wave Structure with Cavity Recessions and Metallic Ring Insertions 114
4.7.1 Design of a Corrugated Cylindrical Slow-Wave Structure with Cavity Recessions and Metallic Ring Insertions 116
4.7.2 Fabrication and Cold testing of a Homogeneous, Corrugated Cylindrical Slow-Wave Structure with Cavity Recessions and Metallic Ring Insertions 119
4.7.3 Inhomogeneous SWS design based on the Corrugated Cylindrical SWS with Cavity Recessions and Metallic Ring Insertions: Fabrication and Cold Testing 121
4.8 Summary 123
References 123
5 Perturbation Analysis of Maxwell's Equations 127
Robert Lipton, Anthony Polizzi, and Lokendra Thakur
5.1 Introduction 127
5.2 Gain from Floating Interaction Structures 129
5.2.1 Anisotropic Effective Properties and the Dispersion Relation 130
5.2.2 A Pierce-Like Approach to Dispersion 133
5.3 Gain from Grounded Interaction Structures 133
5.3.1 Model Description 134
5.3.2 Physics of Waveguides and Maxwell's Equations 134
5.3.3 Perturbation Series for Leading Order Dispersive Behavior 137
5.3.4 Leading Order Theory of Gain for Hybrid Space Charge Modes for a Corrugated SWS with Beam 138
5.3.4.1 Hybrid Modes in Beam 140
5.3.4.2 Impedance Condition 141
5.3.4.3 Cold Structure 141
5.3.4.4 Pierce Theory 142
5.4 Electrodynamics Inside a Finite-Length TWT: Transmission Line Model 142
5.4.1 Solution of the Transmission Line Approximation 145
5.4.2 Discussion of Results 145
5.5 Corrugated Oscillators 148
5.5.1 Oscillator Geometry 148
5.5.2 Solutions of Maxwell's Equations in the Oscillator 149
5.5.3 Perturbation Expansions 151
5.5.4 Leading Order Theory: The Subwavelength Limit of the Asymptotic Expansions 151
5.5.5 Dispersion Relation for d¿ 152
5.6 Summary 154
References 154
6 Similarity of the Properties of Conventional Periodic Structures with Metamaterial Slow Wave Structures 157
Sabahattin Yurt, Edl Schamiloglu, Robert Lipton, Anthony Polizzi, and Lokendra Thakur
6.1 Introduction 157
6.2 Motivation 157
6.3 Observations 159
6.3.1 Appearance of Negative Dispersion for Low-Order Waves 159
6.3.2 Evolution of Wave Dispersion in Uniform Periodic Systems with Increasing Corrugation Depth 160
6.3.2.1 SWS with Sinusoidal Corrugations 161
6.3.2.2 SWS with Rectangular Corrugations 164
6.4 Analysis of Metamaterial Surfaces from Perfectly Conducting Subwavelength Corrugations 168
6.4.1 Approach 169
6.4.2 Model Description 169
6.4.2.1 Physics of Waveguides and Maxwell's Equations 170
6.4.2.2 Two-Scale Asymptotic Expansions 172
6.4.2.3 Leading Order Theory: The Subwavelength Limit of the Asymptotic Expansions 172
6.4.2.4 Nonlocal Surface Impedance Formulation for Time Harmonic Fields 173
6.4.2.5 Effective Surface Impedance for Hybrid Modes in Circular Waveguides 174
6.4.3 Metamaterials and Corrugations as Microresonators 175
6.4.4 Controlling Negative Dispersion and Power Flow with Corrugation Depth 177
6.4.5 Summary 182
References 182
7 Group Theory Approach for Designing MTM Structures for High-Power Microwave Devices 185
Hamide Seidfaraji, Christos Christodoulou, and Edl Schamiloglu
7.1 Group Theory Background 185
7.1.1 Symmetry Elements 186
7.1.2 Symmetry Point Group 187
7.1.3 Character Table 187
7.2 MTM Analysis Using Group Theory 188
7.2.1 Split Ring Resonator Behavior Analysis Using Group Theory 189
7.2.1.1 Principles of Group Theory 189
7.2.1.2 Basis Current in SSRs 191
7.3 Inverse Problem-Solving Using Group Theory 194
7.4 Designing an Ideal MTM 195
7.5 Proposed New Structure Using Group Theory 195
7.6 Design of Isotropic Negative Index Material 197
7.7 Multibeam Backward Wave Oscillator Design using MTM and Group Theory 199
7.7.1 Introduction and Motivation 199
7.7.2 Metamaterial Design 200
7.7.3 Theory of Electron Beam Interaction with Metamaterial Waveguide 203
7.7.4 Hot Test Particle-in-Cell Simulations 204
7.8 Particle-in-Cell Simulations 204
7.9 Efficiency 207
7.10 Summary 208
References 209
8 Time-Domain Behavior of the Evolution of Electromagnetic Fields in Metamaterial Structures 211
Mark Gilmore, Tyler Wynkoop, and Mohamed Aziz Hmaidi
8.1 Introduction 211
8.2 Experimental Observations 212
8.2.1 Bandstop Filter (BSF) System 215
8.2.2 Bandpass Filter (BPF) System 217
8.3 Numerical Simulations 224
8.3.1 Bandstop System (BSF) 225
8.3.2 Bandpass Filter System (BPF) 226
8.3.3 Experiment-Model Comparison 227
8.4 Attempts at a Linear Circuit Model 229
References 230
9 Metamaterial Survivability in the High-Power Microwave Environment 233
Rebecca Seviour
9.1 Introduction 233
9.2 Split Ring Resonator Loss 234
9.3 CSRR Loss 237
9.4 Artificial Material Loss 239
9.5 Disorder 241
9.6 Summary 242
References 244
10 Experimental Hot Test of Beam/Wave Interactions with Metamaterial Slow Wave Structures 245
Michael A. Shapiro, Jason S. Hummelt, Xueying Lu, and Richard J. Temkin
10.1 First-Stage Experiment at MIT 246
10.1.1 Metamaterial Structure 246
10.1.2 Experimental Results 247
10.1.3 Summary of First-Stage Experiments 251
10.2 Second-Stage Experiment at MIT 251
10.3 Metamaterial Structure with Reverse Symmetry 252
10.4 Experimental Results on High-Power Generation 255
10.5 Frequency Measurement in Hot Test 257
10.6 Steering Coil Control 262
10.7 University of New Mexico/University of California Irvine Collaboration on a High Power Metamaterial Cherenkov Oscillator 264
10.8 Summary 264
References 265
11 Conclusions and Future Directions 267
John Luginsland, Jason A. Marshall, Arje Nachman, and Edl Schamiloglu
References 268
Index 271
1
Introduction and Overview of the Book
Rebecca Seviour
University of Huddersfield, School of Computing and Engineering, Queensgate, Huddersfield HD1 3DH, UK
1.1 Introduction
High-power microwaves (HPMs), or directed energy RF, is an evolution of vacuum electron devices (VEDs) that seeks to generate the highest peak power levels in the frequency range of 100 s MHz through 100 GHz (and even higher frequencies) in short pulses (10-100 s ns in duration) that can be repetitively pulsed [1,2]. They came onto the scene in the late 1960s following the advent of pulsed power drivers that not only provided high-energy electron beams (in the order of a MeV and higher), but concomitantly provided high currents as well (1-10's kA) [3]. Similar to VEDs, the electron beam is the power source from which the microwaves grow. Unlike VEDs, HPM sources have much less-stringent vacuum and material requirements since their applications tend to be limited in scope with short mission times.
The state-of-the-art in the practice of HPM sources has been led by intense beam-driven oscillators whose output scale as , where is the peak output microwave power and is the operating frequency [2,4]. This is the Figure-of-Merit (FOM) for HPM oscillators. The equivalent FOM for HPM amplifiers is where is the bandwidth (BW). Until recently, conventional wisdom suggested that for emerging defense applications, the highest power on target (highest intensity field) was of greatest utility. However, recent advances in the understanding of the interaction of intense microwave fields with components and circuits argue that a tailored waveform synthesized at low power and amplified to very high power, might provide even superior capabilities. This is termed waveform diversity. Consider a comparison of the state-of-the-art oscillator and amplifier in terms of the FOM: (i) the ITER/DIII-D's plasma-heating gyrotron oscillator at 110 GHz, 1 MW (10 s pulse), 1.1 MHz BW, has a FOM W- and essentially no BW. (ii) Haystack radar's gyrotron amplifier at 94 GHz, 55 kW output power (5.5 kW average), 1600 MHz BW yields a FOM W-. Thus, there is a 2 order-of-magnitude opportunity to advance the FOM in high-power amplifiers with considerable BW.
Interest in metamaterials (MTMs) grew rapidly following the publication of Pendry [5] and its practical implementation by Smith afterwards [6]. As discussed in this chapter, the history of MTMs dates back to the nineteenth century with numerous contributors, many of whom have only recently been rediscovered. This history has been reviewed in several books [7,8] and continues to be unraveled.
While numerous books have been written on the EM properties of MTMs, all of the applications that have been described in these books to-date are at low-power levels. In this book, we bring together advances that have been made in studying MTMs as slow-wave structures (SWSs) for active electron beam-driven HPM devices. We discuss structures that satisfy Wasler's definition of a MTM (see Section 1.2), and we also describe periodic SWSs with degenerate band edges (DBEs) that do not satisfy this definition, yet do offer novel engineered dispersion relations that are relevant to our overall goal-seeking to discover novel beam/wave interactions that can be exploited for new HPM amplifiers.
1.2 Electromagnetic Materials
In many VEDs, the particle wave interaction is mediated in part via a material, where the functionality of the material manipulates the electromagnetic (EM) wave in a controlled fashion. The creativity of engineers to construct new devices is largely limited by the EM properties of available materials and the ability to precision engineer geometries from these materials. Of course, we are not restricted to naturally occurring materials; for decades, RF engineers have used materials synthesized at the molecular level with peculiar RF properties, such as Polytetraflufoethylene (TeflonT) and . These molecular synthesized materials can be used in VEDs to modify the behavior of an EM wave in a useful manner. In a simplistic form, this behavior between wave and material is described via the constitutive relations:
(1.1)Here the permittivity () and the permeability () are the complex averaged EM response functions of the molecules that make up the material due to the interaction with the electric and magnetic components of an incident wave. The molecules in the material respond to the incident EM wave by forming dipoles, and these individual responses are averaged over all molecules in a volume to yield the permittivity and permeability. This averaging process discussed further in Section 1.3 even holds for gases as the number of molecules is still large enough that the parameters and accurately describe the interaction of an EM wave well into ultraviolet frequencies.
As and are the primary parameters that define a materials response to an EM wave it is useful to categorize materials based on the real components of these two parameters, as shown in Figure 1.1. Materials in the upper right quadrant of Figure 1.1 are often termed Double Positive Media (DPM), common dielectric materials, such as Polytetraflufoethylene, . The upper-left and lower-right quadrants of Figure 1.1 are the single negative media, such as plasmas or metals with a negative permittivity and negative permeability materials such as "wet" ice crystals. Unlike the DPM these single-negative media only allow evanescent wave transport. The lower-left quadrant of Figure 1.1 represents a special case of materials where both permittivity and permeability are simultaneously negative. These Double Negative materials (DNGs) like their double-positive counterparts support wave propagation though the media. The key difference between the DNG quadrant and the other three is that single-negative and double-positive media all occur naturally, whereas we are yet to find a naturally occurring DNG media.
Figure 1.1 Broad categorization of materials based on the real components of the permittivity and permeability.
Although presenting fantastic opportunities, molecular synthesized materials are limited in the range of RF properties they can produce due to the nature of the EM interaction with the molecules of the material. An interaction where the light-mass negatively charged electrons surrounding the relatively large-mass positively charged nucleus of the atoms move in response to an EM wave forming a dipole. This response is fixed by both the fundamental properties (charge, mass) and the chemical bonds formed in the material, limiting the available parameter range and these materials can access. These limitations have led scientists and engineers to create a range of artificial composite structures with periodic subwavelength functional inclusions. Although these inclusions are many orders of magnitude larger than the molecules of the constitutive materials, they are still much smaller that the EM wavelength of interest. In this case, to an incident EM wave, these inclusions respond no differently than giant molecules with a very large polarizability. This enables the interactions between wave and the collective structures to be described in terms of the "homogenized" abstracted bulk material parameters permittivity and permeability. Treating the collective periodic structures in this homogenized manner is called an "effective" medium or material. This approach in theory allows the engineer to fabricate artificial effective materials with specific engineered EM properties, most notable of which is the creation of the above DNG materials. There are of course restrictions on achievable physical material properties that are impossible to engineer, such as the creation of media where waves propagate with group velocities greater than the speed of light in vacuum.
Around 20 years ago, the word "MTM" entered the lexicon to refer to certain types of effective media. Even though a large number of peer-reviewed papers using the word "MTM" have been published an agreed definition of what a MTM is remains elusive. The origin of the word "meta" from the Greek "beyond" implies in some sense that "metamaterials" are a form of material beyond conventional materials. Sources suggest the term "MTM" was first coined by Rodger Walser in 1999 [9], who defined a MTM as; ".macroscopic composites having man-made, three-dimensional, periodic cellular architecture designed to produce an optimized combination, not available in nature, of two or more responses to specific excitation." Whereas the Metamorphose Network defines a metamaterial as ".an arrangement of artificial structural elements, designed to achieve advantageous and unusual electromagnetic properties" [10].
This later definition although encompassing the...
